WHAT IS LIFE? by ERWIN SCHRODINGER

WHAT IS LIFE?

ERWIN SCHRODINGER

First published 1944

What is life? The Physical Aspect of the Living

Cell.

Based on lectures delivered under the auspices of

the Dublin Institute for Advanced Studies at

Trinity College, Dublin, in February 1943.

To the memory of My Parents

Preface

A scientist is supposed to have a complete and

thorough I of knowledge, at first hand, of some

subjects and, therefore, is usually expected not to

write on any topic of which he is not a life,

master. This is regarded as a matter of noblesse

oblige. For the present purpose I beg to renounce

the noblesse, if any, and to be the freed of the

ensuing obligation. My excuse is as follows: We

have inherited from our forefathers the keen

longing for unified, all-embracing knowledge.

The very name given to the highest institutions

of learning reminds us, that from antiquity to and

throughout many centuries the universal aspect

has been the only one to be given full credit. But

the spread, both in and width and depth, of the

multifarious branches of knowledge by during

the last hundred odd years has confronted us

with a queer dilemma. We feel clearly that we

are only now beginning to acquire reliable

material for welding together the sum total of all

that is known into a whole; but, on the other

hand, it has become next to impossible for a

single mind fully to command more than a small

specialized portion of it. I can see no other

escape from this dilemma (lest our true who aim

be lost for ever) than that some of us should

venture to embark on a synthesis of facts and

theories, albeit with second-hand and incomplete

knowledge of some of them -and at the risk of

making fools of ourselves. So much for my

apology. The difficulties of language are not

negligible. One’s native speech is a closely fitting

garment, and one never feels quite at ease when

it is not immediately available and has to be

replaced by another. My thanks are due to Dr

Inkster (Trinity College, Dublin), to Dr Padraig

Browne (St Patrick’s College, Maynooth) and,

last but not least, to Mr S. C. Roberts. They were

put to great trouble to fit the new garment on me

and to even greater trouble by my occasional

reluctance to give up some ‘original’ fashion of

my own. Should some of it have survived the

mitigating tendency of my friends, it is to be put

at my door, not at theirs. The head-lines of the

numerous sections were originally intended to be

marginal summaries, and the text of every

chapter should be read in continuo. E.S.

Dublin September 1944

Homo liber nulla de re minus quam de morte

cogitat; et ejus sapientia non mortis sed vitae

meditatio est. SPINOZA’S Ethics, Pt IV, Prop.

67

(There is nothing over which a free man ponders

less than death; his wisdom is, to meditate not on

death but on life.)

CHAPTER 1

The Classical Physicist’s Approach to the Subject

This little book arose from a course of public

lectures, delivered by a theoretical physicist to an

audience of about four hundred which did not

substantially dwindle, though warned at the

outset that the subject-matter was a difficult one

and that the lectures could not be termed popular,

even though the physicist’s most dreaded

weapon, mathematical deduction, would hardly

be utilized. The reason for this was not that the

subject was simple enough to be explained

without mathematics, but rather that it was much

too involved to be fully accessible to

mathematics. Another feature which at least

induced a semblance of popularity was the

lecturer’s intention to make clear the fundamental

idea, which hovers between biology and physics,

to both the physicist and the biologist. For

actually, in spite of the variety of topics

involved, the whole enterprise is intended to

convey one idea only -one small comment on a

large and important question. In order not to lose

our way, it may be useful to outline the plan very

briefly in advance. The large and important and

very much discussed question is: How can the

events in space and time which take place

within the spatial boundary of a living organism

be accounted for by physics and chemistry? The

preliminary answer which this little book will

endeavor to expound and establish can be

summarized as follows: The obvious inability of

present-day physics and chemistry to account for

such events is no reason at all for doubting that

they can be accounted for by those sciences.

STATISTICAL PHYSICS. THE

FUNDAMENTAL W DIFFERENCE IN

STRUCTURE

That would be a very trivial remark if it were

meant only to stimulate the hope of achieving in

---

the future what has not been achieved in the past.

But the meaning is very much more positive, viz.

that the inability, up to the present moment, is

amply accounted for. Today, thanks to the

ingenious work of biologists, mainly of

geneticists, during the last thirty or forty years,

enough is known about the actual material

structure of organisms and about their

functioning to state that, and to tell precisely

why present-day physics and chemistry could not

possibly account for what happens in space and

time within a living organism. The arrangements

of the atoms in the most vital parts of an

organism and the interplay of these arrangements

differ in a fundamental way from all those

arrangements of atoms which physicists and

chemists have hitherto made the object of their

experimental and theoretical research. Yet the

difference which I have just termed fundamental

is of such a kind that it might easily appear slight

to anyone except a physicist who is thoroughly

imbued with the knowledge that the laws of

physics and chemistry are statistical throughout.

For it is in relation to the statistical point of view

that the structure of the vital parts of living

organisms differs so entirely from that of any

piece of matter that we physicists and chemists

have ever handled physically in our laboratories

or mentally at our writing desks. It is well-nigh

unthinkable that the laws and regularities thus

discovered should happen to apply immediately

to the behaviour of systems which do not exhibit

the structure on which those laws and regularities

are based. The non-physicist cannot be expected

even to grasp let alone to appreciate the

relevance of the difference in ‘statistical

structure’ stated in terms so abstract as I have

just used. To give the statement life and colour,

let me anticipate what will be explained in much

more detail later, namely, that the most essential

part of a living cell-the chromosome fibre may

suitably be called an aperiodic crystal. In physics

we have dealt hitherto only with periodic

crystals. To a humble physicist’s mind, these are

very interesting and complicated objects; they

constitute one of the most fascinating

and complex material structures by which

inanimate nature puzzles his wits. Yet, compared

with the aperiodic crystal, they are rather plain

and dull. The difference in structure is of the

same kind as that between an ordinary wallpaper

in which the same pattern is repeated again and

again in regular periodicity and a masterpiece of

embroidery, say a Raphael tapestry, which shows

no dull repetition, but an elaborate, coherent,

meaningful design traced by the great master. In

calling the periodic crystal one of the most

complex objects of his research, I had in mind

the physicist proper. Organic chemistry, indeed,

in investigating more and more complicated

molecules, has come very much nearer to that

‘aperiodic crystal’ which, in my opinion, is the

material carrier of life. And therefore it is small

wonder that the organic chemist has already

made large and important contributions to the

problem of life, whereas the physicist has made

next to none.

THE NAIVE PHYSICIST’S APPROACH TO

THE SUBJECT

After having thus indicated very briefly the

general idea -or rather the ultimate scope -of our

investigation, let me describe the line of attack. I

propose to develop first what you might call ‘a

naive physicist’s ideas about organisms’, that is,

the ideas which might arise in the mind of a

physicist who, after having learnt his physics

and, more especially, the statistical foundation of

his science, begins to think about organisms and

about the way they behave and function and who

comes to ask himself conscientiously whether

he, from what he has learnt, from the point of

view of his comparatively simple and clear and

humble science, can make any relevant

contributions to the question. It will turn out that

he can. The next step must be to f compare his

theoretical anticipations with the biological facts.

It will then turn out that -though on the whole his

ideas seem quite sensible -they need to be

appreciably amended. In this way we shall

gradually approach the correct view -or, to put it

more modestly, the one that I propose as the

correct one. Even if I should be right in this, I do

not know whether my way of approach is really

the best and simplest. But, in short, it was mine.

The ‘naive physicist’ was myself. And I could not

find any better or clearer way towards the goal

than my own crooked one.

WHY ARE THE ATOMS SO SMALL?

A good method of developing ‘the naive

physicist’s ideas’ is to start from the odd, almost

ludicrous, question: Why are atoms so small? To

begin with, they are very small indeed. Every

little piece of matter handled in everyday life

contains an enormous number of them. Many

examples have been devised to bring this fact

home to an audience, none of them more

impressive than the one used by Lord Kelvin:

Suppose that you could mark the molecules in a

glass of water; then pour the contents of the glass

into the ocean and stir the latter thoroughly so as

---

to distribute the marked molecules uniformly

throughout the seven seas; if then you took a

glass of water anywhere out of the ocean, you

would find in it about a hundred of your marked

molecules. The actual sizes of atoms lie between

about 1/5000 and 1/2000 the wave-length of

yellow light. The comparison is significant,

because the wave-length roughly indicates the

dimensions of the smallest grain still

recognizable in the microscope. Thus it will be

seen that such a grain still contains thousands of

millions of atoms. Now, why are atoms so

small? Clearly, the question is an evasion. For it

is not really aimed at the size of the atoms. It is

concerned with the size of organisms, more

particularly with the size of our own corporeal

selves. Indeed, the atom is small, when referred

to our civic unit of length, say the yard or the

metre. In atomic physics one is accustomed to

use the so-called Angstrom (abbr. A), which is

the 10lOth part of a metre, or in decimal notation

0.0000000001 metre. Atomic diameters range

between 1 and 2A. Now those civic units (in

relation to which the atoms are so small) are

closely related to the size of our bodies. There is

a story tracing the yard back to the humour of an

English king whom his councillors asked what

unit to adopt -and he stretched out his arm

sideways and said: ‘Take the distance from the

middle of my chest to my fingertips, that will do

all right.’ True or not, the story is significant for

our purpose. The king would naturally I indicate

a length comparable with that of his own body,

knowing that anything else would be very

inconvenient. With all his predilection for the

Angstrom unit, the physicist prefers to be told

that his new suit will require six and a half yards

of tweed -rather than sixty-five thousand

millions of Angstroms of tweed. It thus being

settled that our question really aims at the ratio

of two lengths -that of our body and that of the

atom – with an incontestable priority of

independent existence on the side of the atom,

the question truly reads: Why must our bodies be

so large compared with the atom? I can imagine

that many a keen student of physics or chemistry

may have deplored the fact that everyone of our

sense organs, forming a more or less substantial

part of our body and hence (in view of the

magnitude of the said ratio) being itself

composed of innumerable atoms, is much too

coarse to be affected by the impact of a single

atom. We cannot see or feel or hear the single

atoms. Our hypotheses with regard to them differ

widely from the immediate findings of our gross

sense organs and cannot be put to the test of

direct inspection. Must that be so? Is there an

intrinsic reason for it? Can we trace back this

state of affairs to some kind of first principle, in

order to ascertain and to understand why nothing

else is compatible with the very laws of

Nature? Now this, for once, is a problem which

the physicist is able to clear up completely. The

answer to all the queries is in the affirmative.

THE WORKING OF AN ORGANISM

REQUIRES EXACT PHYSICAL LAWS

If it were not so, if we were organisms so

sensitive that a single atom, or even a few atoms,

could make a perceptible impression on our

senses -Heavens, what would life be like! To

stress one point: an organism of that kind would

most certainly not be capable of developing the

kind of orderly thought which, after passing

through a long sequence of earlier stages,

ultimately results in forming, among many other

ideas, the idea of an atom. Even though we select

this one point, the following considerations

would essentially apply also to the functioning of

organs other than the brain and the sensorial

system. Nevertheless, the one and only thing of

paramount interest to us in ourselves is, that we

feel and think and perceive. To the physiological

process which is responsible for thought and

sense all the others play an auxiliary part, at least

from the human point of view, if not from that of

purely objective biology. Moreover, it will

greatly facilitate our task to choose for

investigation the process which is closely

accompanied by subjective events, even though

we are ignorant of the true nature of this close

parallelism. Indeed, in my view, it lies outside

the range of natural science and very probably of

human understanding altogether. We are thus

faced with the following question: Why should

an organ like our brain, with the sensorial system

attached to it, of necessity consist of an

enormous number of atoms, in order that its

physically changing state should be in close and

intimate correspondence with a highly developed

thought? On what grounds is the latter task of the

said organ incompatible with being, as a whole

or in some of its peripheral parts which interact

directly with the environment, a mechanism

sufficiently refined and sensitive to respond to

and register the impact of a single atom from

outside? The reason for this is, that what we call

thought (1) is itself an orderly thing, and (2) can

only be applied to material, i.e. to perceptions or

experiences, which have a certain degree of

orderliness. This has two consequences. First, a

physical organization, to be in close

---

correspondence with thought (as my brain is

with my thought) must be a very well-ordered

organization, and that means that the events that

happen within it must obey strict physical laws,

at least to a very high degree of accuracy.

Secondly, the physical impressions made upon

that physically well-organized system by other

bodies from outside, obviously correspond to the

perception and experience of the corresponding

thought, forming its material, as I have called it.

Therefore, the physical interactions between our

system and others must, as a rule, themselves

possess a certain degree of physical orderliness,

that is to say, they too must obey strict physical

laws to a certain degree of accuracy.

PHYSICAL LAWS REST ON ATOMIC

STATISTICS AND ARE THEREFORE ONLY

APPROXIMATE

And why could all this not be fulfilled in the case

of an organism composed of a moderate number

of atoms only and sensitive already to the impact

of one or a few atoms only? Because we know

all atoms to perform all the time a completely

disorderly heat motion, which, so to speak,

opposes itself to their orderly behaviour and does

not allow the events that happen between a small

number of atoms to enrol themselves according

to any recognizable laws. Only in the co-

operation of an enormously large number of

atoms do statistical laws begin to operate and

control the behaviour of these assemblies with an

accuracy increasing as the number of atoms

involved increases. It is in that way that the

events acquire truly orderly features. All the

physical and chemical laws that are known to

play an important part in the life of organisms

are of this statistical kind; any other kind of

lawfulness and orderliness that one might think

of is being perpetually disturbed and made

inoperative by the unceasing heat motion of the

atoms.

THEIR PRECISION IS BASED ON THE

LARGE OF NUMBER OF ATOMS

INTERVENING

FIRST EXAMPLE (PARAMAGNETISM)

Let me try to illustrate this by a few examples,

picked somewhat at random out of thousands,

and possibly not just the best ones to appeal to a

reader who is learning for the first time about

this condition of things -a condition which in

modern physics and chemistry is as fundamental

as, say, the fact that organisms are composed of

cells is in biology, or as Newton’s Law in

astronomy, or even as the series of integers, 1, 2,

3, 4, 5, …in mathematics. An entire newcomer

should not expect to obtain from the following

few pages a full understanding and appreciation

of the subject, which is associated with the

illustrious names of Ludwig Boltzmann and

Willard Gibbs and treated in textbooks under the

name of ‘statistical thermodynamics’. If you fill

an oblong quartz tube with oxygen gas and put it

into a magnetic field, you find that the gas is

magnetized. The magnetization is due to the fact

that the oxygen molecules are little magnets and

tend to orientate themselves parallel to the field,

like a compass needle. But you must not think

that they actually all turn parallel. For if you

double the field, you get double the

magnetization in your oxygen body, and that

proportionality goes on to extremely high field

strengths, the magnetization increasing at the rate

of the field you apply. This is a particularly clear

example of a purely statistical law. The

orientation the field tends to produce is

continually counteracted by the heat motion,

which works for random orientation. The effect

of this striving is, actually, only a small

preference for acute over obtuse angles between

the dipole axes and the field. Though the single

atoms change their orientation incessantly, they

produce on the average (owing to their enormous

number) a constant small preponderance of

orientation in the direction of the field and

proportional to it. This ingenious explanation is

due to the French physicist P. Langevin. It can

be checked in the following way. If the observed

weak magnetization is really the outcome of rival

tendencies, namely, the magnetic field, which

aims at combing all the molecules parallel, and

the heat motion, which makes for random

orientation, then it ought to be possible to

increase the magnetization by weakening the

heat motion, that is to say, by lowering the

temperature, instead of reinforcing the field. That

is confirmed by experiment, which gives the

magnetization inversely proportional to the

absolute temperature, in quantitative agreement

with theory (Curie’s law). Modern equipment

even enables us, by lowering the temperature, to

reduce the heat motion to such insignificance

that the orientating tendency of the magnetic

field can assert itself, if not completely, at least

sufficiently to produce a substantial fraction of

‘complete magnetization’. In this case we no

longer expect that double the field strength will

double the magnetization, but that the latter will

increase less and less with increasing field,

approaching what is called ‘saturation’. This

expectation too is quantitatively confirmed by

---

experiment. Notice that this behaviour entirely

depends on the large numbers of molecules

which co-operate in producing the observable

magnetization. Otherwise, the latter would not be

an constant at all, but would, by fluctuating quite

irregularly of from one second to the next, bear

witness to the vicissitudes of pe the contest

between heat motion and field.

SECOND EXAMPLE (BROWNIAN

MOVEMENT, DIFFUSION)

If you fill the lower part of a closed glass vessel

with fog, pt consisting of minute droplets, you

will find that the upper or boundary of the fog

gradually sinks, with a well-defined velocity,

determined by the viscosity of the air and the

size and the specific gravity of the droplets. But

if you look at one of the droplets under the

microscope you find that it does not permanently

sink with constant velocity, but performs a very

irregular movement, the so-called Brownian

movement, which corresponds to a regular

sinking only on the average. Now these droplets

are not atoms, but they are sufficiently small and

light to be not entirely insusceptible to the

impact of one single molecule of those which

hammer their surface in perpetual impacts. They

are thus knocked about and can only on the

average follow the influence of gravity. This

example shows what funny and disorderly

experience we should have if our senses were

susceptible to the impact of a few molecules

only. There are bacteria and other organisms so

small that they are strongly affected by this

phenomenon. Their movements are determined

by the thermic whims of the surrounding

medium; they have no choice. If they had some

locomotion of their own they might nevertheless

succeed in on getting from one place to another –

but with some difficulty, since the heat motion

tosses them like a small boat in a rough sea. A

phenomenon very much akin to Brownian

movement is that of diffusion. Imagine a vessel

filled with a fluid, say water, with a small

amount of some coloured substance dissolved in

it, say potassium permanganate, not in uniform

concentration, but rather as in Fig. 4, where the

dots indicate the molecules of the dissolved

substance (permanganate) and the concentration

diminishes from left to right. If you leave this

system alone a very slow process of ‘diffusion’

sets in, the at permanganate spreading in the

direction from left to right, that is, from the

places of higher concentration towards the places

of lower concentration, until it is equally

distributed of through the water. The remarkable

thing about this rather simple and apparently not

particularly interesting process is that it is in no

way due, as one might think, to any tendency or

force driving the permanganate molecules away

from the crowded region to the less crowded one,

like the population of a country spreading to

those parts where there is more elbow-room.

Nothing of the sort happens with our

permanganate molecules. Every one of them

behaves quite independently of all the others,

which it very seldom meets. Everyone of them,

whether in a crowded region or in an empty one,

suffers the same fate of being continually

knocked about by the impacts of the water

molecules and thereby gradually moving on in

an unpredictable direction -sometimes towards

the higher, sometimes towards the lower,

concentrations, sometimes obliquely. The kind

of motion it performs has often been compared

with that of a blindfolded person on a large

surface imbued with a certain desire of ‘walking’,

but without any preference for any particular

direction, and so changing his line

continuously. That this random walk of the

permanganate molecules, the same for all of

them, should yet produce a regular flow towards

the smaller concentration and ultimately make

for uniformity of distribution, is at first sight

perplexing -but only at first sight. If you

contemplate in Fig. 4 thin slices of

approximately constant concentration, the

permanganate molecules which in a given

moment are contained in a particular slice will,

by their random walk, it is true, be carried with

equal probability to the right or to the left. But

precisely in consequence of this, a plane

separating two neighbouring slices will be

crossed by more molecules coming from the left

than in the opposite direction, simply because to

the left there are more molecules engaged in

random walk than there are to the right. And as

long as that is so the balance will show up as a

regular flow from left to right, until a uniform

distribution is reached. When these

considerations are translated into mathematical

language the exact law of diffusion is reached in

the form of a partial differential equation

§p/§t= DV2P

which I shall not trouble the reader by

explaining, though its meaning in ordinary

language is again simple enough. The reason for

mentioning the stern ‘mathematically exact’ law

here, is to emphasize that its physical exactitude

must nevertheless be challenged in every

---

particular application. Being based on pure

chance, its validity is only approximate. If it is,

as a rule, a very good approximation, that is only

due to the enormous number of molecules that

co-operate in the phenomenon. The smaller their

number, the larger the quite haphazard deviations

we must expect and they can be observed under

favourable circumstances.

THIRD EXAMPLE (LIMITS OF ACCURACY

OF MEASURING)

The last example we shall give is closely akin to

the second c one, but has a particular interest. A

light body, suspended by a long thin fibre in

equilibrium orientation, is often used by

physicists to measure weak forces which deflect

it from that position of equilibrium, electric,

magnetic or gravitational forces being applied so

as to twist it around the vertical axis. (The light

body must, of course, be chosen appropriately

for ! the particular purpose.) The continued effort

to improve the accuracy of this very commonly

used device of a ‘torsional balance’, has

encountered a curious limit, most interesting in

itself. In choosing lighter and lighter bodies and

thinner and longer fibres -to make the balance

susceptible to weaker and weaker forces -the

limit was reached when the suspended body

became noticeably susceptible to the impacts of

the heat motion of the surrounding molecules

and began to perform an incessant, irregular

‘dance’ about its equilibrium position, much like

the trembling of the droplet in the second

example. Though this behaviour sets no absolute

limit to the accuracy of measurements obtained

with the balance, it sets a practical one. The

uncontrollable effect of the heat motion

competes with the effect of the force to be

measured and makes the ;t’ law single deflection

observed insignificant. You have to multiply

never- observations, in order to eliminate the

effect of the Brownian Being movement of your

instrument. This example is, I think, particularly

illuminating in our present investigation. For our

to the organs of sense, after all, are a kind of

instrument. We can see in the how useless they

would be if they became too sensitive.

THE \/n RULE

So much for examples, for the present. I will

merely add that there is not one law of physics or

chemistry, of those that are relevant within an

organism or in its interactions with its

environment, that I might not choose as an

example. The second detailed explanation might

be more complicated, but the salient point would

always be the same and thus the description

would become monotonous. But I should like to

add one very important quantitative statement

concerning the degree of inaccuracy to be

expected in any physical law, the so-called \/n

law. I will first illustrate it by a simple example

and then generalize it. If I tell you that a certain

gas under certain conditions of pressure and

temperature has a certain density, and if I

expressed this by saying that within a certain

volume (of a size relevant for some experiment)

there are under these conditions just n molecules

of the gas, then you might be sure that if you

could test my statement in a particular moment

of time, you would find it inaccurate, the

departure being of the order of \/n. Hence if the

number n = 100, you would find a departure of

about 10, thus relative error = 10%. But n = 1

million, you would be likely to find a departure

of about 1,000, thus relative error = 1\10%. Now,

roughly speaking, this statistical law is quite

general. The laws of physics and physical

chemistry are inaccurate within a probable

relative error of the order of 1/ \/Vn, where n is

the number of molecules that co-operate to bring

about that law -to produce its validity within

such regions of space or time (or both) that

matter, for some considerations or for some

particular experiment. You see from this again

that an organism must have a comparatively

gross structure in order to enjoy the benefit of

fairly accurate laws, both for its internal life and

for its , interplay with the external world. For

otherwise the number of co-operating particles

would be too small, the ‘law’ too inaccurate. The

particularly exigent demand is the square root.

For though a.million is a reasonably large

number, an accuracy of Just 1in 1,000 is not

overwhelmingly good, If a thing claims the

dignity of being a ‘Law of Nature.

CHAPTER 2

The Hereditary Mechanism

THE CLASSICAL PHYSICIST’S

EXPECTATION, FAR FROM BEING

TRIVIAL, IS WRONG

Thus we have come to the conclusion that an

organism and all the biologically relevant

processes that it experiences must have an

extremely ‘many-atomic’ structure and must be

safeguarded against haphazard, ‘single-atomic’

events attaining too great importance. That, the

‘naive physicist’ tells us, is essential, so that the

organism may, so to speak, have sufficiently

accurate physical laws on which to draw for

---

setting up its marvellously regular and well-

ordered working. How do these conclusions,

reached, biologically speaking, a priori (that is,

from the purely physical point of view), fit

in with actual biological facts? At first sight one

is inclined to think that the conclusions are little

more than trivial. A biologist of, say, thirty years

ago might have said that, although it was quite

suitable for a popular lecturer to emphasize the

importance, in the organism as elsewhere, of

statistical physics, the point was, in fact, rather a

familiar truism. For, naturally, not only the body

of an adult individual of any higher species, but

every single cell composing it contains a

‘cosmical’ number of single atoms of every kind.

And every particular physiological process that

we observe, either within the cell or in its

interaction with the cell environment, appears -or

appeared thirty years ago -to involve such

enormous numbers of single atoms and single

atomic processes that all the relevant laws of

physics and physical chemistry would be

safeguarded even under the very exacting

demands of statistical physics in respect of large

numbers; this demand illustrated just now by the

\/n rule. Today, we know that this opinion would

have been a mistake. As we shall presently see,

incredibly small groups of atoms, much too

small to display exact statistical laws, do play a

dominating role in the very orderly and lawful

events within a living organism. They have

control of the observable large-scale features

which the organism acquires in the course of its

development, they determine important

characteristics of its functioning; and in all this

very sharp and very strict me biological laws are

displayed. I must begin with giving a brief

summary of the situation in biology, more

especially in genetics -in other words, I have to

summarize the present state of knowledge in a

subject of which I am not a master. This cannot

be helped and I apologize, particularly to any

biologist, for the dilettante character of my

summary. On the other hand, I beg leave to put

the prevailing ideas before you more or less

dogmatically. A poor theoretical physicist could

not be expected to produce anything like a

competent survey of the experimental evidence,

which consists of a large number of long and

beautifully interwoven series of breeding

experiments of truly unprecedented ingenuity on

the one hand and of direct observations of the

living cell, conducted with all the refinement of

modern microscopy, on the other.

THE HEREDITARY CODE-SCRIPT

(CHROMOSOMES)

Let me use the word ‘pattern’ of an organism in

the sense in be which the biologist calls it ‘the

four-dimensional pattern’, meaning not only the

structure and functioning of that organism in the

adult, or in any other particular stage, but the

whole of its ontogenetic development from the

fertilized egg the cell to the stage of maturity,

when the organism begins to reproduce itself.

Now, this whole four-dimensional pattern is

known to be determined by the structure of that

one cell, the fertilized egg. Moreover, we know

that it is essentially determined by the structure

of only a small part of that cell, its large nucleus.

This nucleus, in the ordinary ‘resting state’ of the

cell, usually appears as a network of chromatine,

distributed over the cell. But in the vitally

important processes of cell division (mitosis and

meiosis, see below) it is seen to consist of a set

of particles, usually fibre-shaped or rod-like,

called the chromosomes, which number 8 or 12

or, in man, 48. But I ought really to have written

these illustrative numbers as 2 X 4, 2 X 6, …, 2 X

24, …, and I ought to have spoken of two sets, in

order to use the expression in the customary

strict meaning of the biologist. For though the

single chromosomes are sometimes clearly

distinguished and individualized by shape and

size, the two sets are almost entirely alike. As we

have shall see in a moment, one set comes from

the mother (egg cell), one from the father

(fertilizing spermatozoon). It is these

chromosomes, or probably only an axial skeleton

fibre of what we actually see under the

microscope as the chromosome, that contain in

some kind of code-script the entire pattern of the

individual’s future development and of its

functioning in the mature state. Every complete

set of chromosomes contains the full code; so

there are, as a rule, two copies of the latter in the

fertilized egg cell, which forms the earliest stage

of the future individual. In calling the structure

of the chromosome fibres a code-script we mean

that the all-penetrating mind, once conceived by

Laplace, to which every causal connection lay

immediately open, could tell from their structure

whether the egg would develop, under suitable

conditions, into a black cock or into a speckled

hen, into a fly or a maize plant, a rhododendron,

a beetle, a mouse or a woman. To which we may

add, that the appearances of the egg cells are

very often remarkably similar; and even when

they are not, as in the case of the comparatively

gigantic eggs of birds and reptiles, the difference

is not been so much the relevant structures as in

---

the nutritive material which in these cases is

added for obvious reasons. But the term

code-script is, of course, too narrow. The

chromosome structures are at the same time

instrumental in bringing about the development

they foreshadow. They are law-code and

executive power -or, to use another simile, they

are architect’s plan and builder’s craft -in one.

GROWTH OF THE BODY BY CELL

DIVISION (MITOSIS)

How do the chromosomes behave in

ontogenesis? The growth of an organism is

effected by consecutive cell met divisions. Such

a cell division is called mitosis. It is, in the life of

a cell, not such a very frequent event as one

might expect, considering the enormous number

of cells of which our body is composed. In the

beginning the growth is rapid. The egg divides

into two ‘daughter cells’ which, at the next step,

will produce a generation of four, then of 8, 16,

32, 64, …, etc. The frequency of division will not

remain exactly the same in all parts of the

growing body, and that will break the regularity

of these numbers. But from their rapid increase

we infer by an easy computation that on the

average as few as 50 or 60 successive divisions

suffice to produce the number of cells in a grown

man -or, say, ten times the number, taking into

account the exchange of cells during lifetime.

Thus, a body cell of mine is, on the average, only

the 50th or 60th ‘descendant’ of the egg that was

I.

IN MITOSIS EVERY CHROMOSOME IS

DUPLICATED

How do the chromosomes behave on mitosis?

They duplicate -both sets, both copies of the

code, duplicate. The process has been intensively

studied under the microscope and is of

paramount interest, but much too involved to

describe here in detail. The salient point is that

each of the two ‘daughter cells’ gets a dowry of

two further complete sets of chromosomes

exactly similar to those of the parent cell. So all

the body cells are exactly alike as regards their

chromosome treasure. However little we

understand the device we cannot but think that it

must be in some way very relevant to the

functioning of the organism, that every single

cell, even a less important one, should be in

possession of a complete (double) copy of the

code-script. Some time ago we were told in the

newspapers that in his African campaign General

Montgomery made a point of having every

single soldier of his army meticulously informed

of all his designs. If that is true (as it conceivably

might be, considering the high intelligence and

reliability of his troops) it provides an excellent

analogy to our case, in which the corresponding

fact certainly is literally true. The most

surprising fact is the doubleness of the

chromosome set, maintained throughout the

mitotic divisions. That it is the outstanding

feature of the genetic mechanism is most

strikingly revealed by the one and only departure

from the rule, which we have now to discuss.

REDUCTIVE DIVISION (MEIOSIS) AND

FERTILIZATION (SYNGAMY)

Very soon after the development of the

individual has set in, a group of cells is reserved

for producing at a later stage the so-called

gametes, the sperm cells or egg cells, as the case

may be, needed for the reproduction of the

individual in maturity. ‘Reserved’ means that

they do not serve other purposes in the meantime

and suffer many fewer mitotic divisions. The

exceptional or reductive division (called meiosis)

is the one by which eventually, on maturity, the

gametes posed to are produced from these

reserved cells, as a rule only a short time before

syngamy is to take place. In meiosis the double

chromosome set of the parent cell simply

separates into two single sets, one of which goes

to each of the two daughter cells, the gametes. In

other words, the mitotic doubling of the number

of chromosomes does not take place in meiosis,

the number remains constant and thus every

gamete receives only half -that is, only one

complete copy of the code, not two, e.g. in man

only 24:, not 2 X 24: = 4:8. Cells with only one

chromosome set are called haploid (from Greek

απλοϖχ, single). Thus the gametes are haploid,

the ordinary body cells diploid (from Greek

Οπλϖχ, double). Individuals with three, four,

…or generally speaking with many chromosome

sets in all their body cells occur occasionally; the

latter are then called triploid, tetraploid, …,

polyploid. In the act of syngamy the male gamete

(spermatozoon) and the female gamete (egg),

both haploid cells, coalesce to form the fertilized

egg cell, which is thus diploid. One of its

chromosome sets comes from the mother, one

from the father.

HAPLOID INDIVIDUALS

One other point needs rectification. Though not

indispensable for our purpose it is of real

interest, since it shows that actually a fairly

complete code-script of the ‘pattern’ is contained

in every single set of chromosomes. There are

---

instances of meiosis not being followed shortly

after by fertilization, the haploid cell (the

‘gamete’) under- going meanwhile numerous

mitotic cell divisions, which result in building up

a complete haploid individual. This is the case in

the male bee, the drone, which is produced

parthenogenetically, that is, from non-fertilized

and therefore haploid eggs of the queen. The

drone has no father! All its body cells are

haploid. If you please, you may call it a grossly

exaggerated spermatozoon; and actually, as

everybody knows, to function as such happens to

be its one and only task in life. However, that is

perhaps a ludicrous point of view. For the case is

not two quite unique. There are families of plants

in which the haploid gamete which is produced

by meiosis and is called a spore in the such cases

falls to the ground and, like a seed, develops into

a the true haploid plant comparable in size with

the diploid. Fig. 5 is a rough sketch of a moss,

well known in our forests. The leafy lower part is

the haploid plant, called the gametophyte,

because at its upper end it develops sex organs

and gametes, which by mutual fertilization

produce in the ordinary way the diploid plant,

the bare stem with the capsule at the top. This is

called the sporophyte, because it produces, by

meiosis, the spores in the capsule at the top.

When the capsule opens, the spores fall to the

ground and develop into a leafy stem, etc. The

course of events is appropriately called

alternation of generations. You may, if you

choose, look upon the ordinary case, man and the

animals, in the same way. But the ‘gametophyte’

is then as a rule a very short-lived, unicellular

generation, spermatozoon or egg cell as the case

may be. Our body corresponds to the sporophyte.

Our ‘spores’ are the reserved cells from which, by

meiosis, the unicellular generation springs.

THE OUTSTANDING RELEVANCE OF

THE REDUCTIVE DIVISION

The important, the really fateful event in the

process of reproduction of the individual is not

fertilization but meiosis. One set of

chromosomes is from the father, one from the

mother. Neither chance nor destiny can interfere

with that. Every man owes just half of his

inheritance to his mother, half of it to his father.

That one or the other strain seems often to

prevail is due to other reasons which we shall

come to later. (Sex itself is, of course, the

simplest instance of such prevalence.). But when

you trace the origin of your inheritance back to

your grandparents, the case is different. Let me

fix attention on my paternal set of chromosomes,

in particular on one of them, say No.5. It is a

faithful replica either of the No.5 my father

received from his father or of the No.5 he had

received from his mother. The issue was decided

by a 50:50 chance in the meiosis taking place in

my father’s body in November 1886 and

producing the spermatozoon which a few days

later was to be effective in begetting me. Exactly

the same story could be repeated about

chromosomes Nos. 1, 2, 3, …,24 of my paternal

set, and mutatis mutandis about every one of my

maternal chromosomes. Moreover, all the 48

issues are fi entirely independent. Even if it were

known that my paternal it chromosome No.5

came from my grandfather Josef Schrodinger,

the No.7 still stands an equal chance of being

either also from him, or from his wife Marie, nee

Bogner.

CROSSING-OVER. LOCATION OF

PROPERTIES

But pure chance has been given even a wider

range in mixing the grandparental inheritance in

the offspring than would appear from the

preceding description, in which it has been

tacitly assumed, or even explicitly stated, that a

particular chromosome as a whole was either

from the grandfather or back to from the

grandmother; in other words that the single

chromosomes are passed on undivided. In actual

fact they are not, or on one of not always. Before

being separated in the reductive division, No.5

my say the one in the father’s body, any two

‘homologous’ chromosomes come into close

contact with each other, during chance in which

they sometimes exchange entire portions in the

way illustrated in Fig. 6. By this process, called

‘crossing-over’, days later two properties situated

in the respective parts of that chromosome will

be separated in the grandchild, who will follow

the grandfather in one of them, the grandmother

in the other one. The act of crossing-over, being

neither very rare nor very issues are frequent, has

provided us with invaluable information

regarding the location of properties in the

chromosomes. For a full account we should have

to draw on conceptions not introduced before the

next chapter (e.g. heterozygosy, dominance,

etc.); but as that would take us beyond the range

of this little book, let me indicate the salient

point right away. If there were no crossing-over,

two properties for which the same chromosome

is responsible would always be passed on in

mixing together, no descendant receiving one of

them without receiving the other as well; but two

properties, due to different it has been

---

chromosomes, would either stand a 50:50 chance

of being separated or they would invariably be

separated -the latter when they were situated in

homologous chromosomes of the same ancestor,

which could never go together. These rules and

chances are interfered with by crossing-over.

Hence the probability of this event can be

ascertained by registering carefully the

percentage composition of the off-spring in

extended breeding experiments, suitably laid out

for at the purpose. In analysing the statistics, one

accepts the suggestive working hypothesis that

the ‘linkage’ between two properties situated in

the same chromosome, is the less frequently

broken by crossing-over, the nearer they lie to

each other. For then there is less chance of the

point of exchange lying between them, whereas

properties located near the opposite ends of the

chromosomes are separated by every crossing-

over. (Much the same applies to the

recombination of properties located in

homologous chromosomes of the same ancestor.)

In this way one may expect to get from the

‘statistics of linkage’ a sort of ‘map of properties’

within every chromosome. These anticipations

have been fully confirmed. In the cases to which

tests have been thoroughly applied (mainly, but

not only, Drosophila) the tested properties

actually divide into as h many separate groups,

with no linkage from group to group, as there are

different chromosomes (four in Drosophila).

Within every group a linear map of properties

can be drawn up which accounts quantitatively

for the degree of linkage it between any two of

that group, so that there is little doubt h that they

actually are located, and located along a line, as

the rod-like shape of the chromosome suggests.

Of course, the scheme of the hereditary

mechanism, as drawn up here, is still rather

empty and colourless, even slightly naive. For

we have not said what exactly we understand by

a property. It seems neither adequate nor

possible to dissect into discrete ‘properties’ the

pattern of an organism which is essentially a

unity, a ‘whole’. Now, what we actually state in

any particular case is, that a pair of ancestors

were different in a certain well-defined respect

(say, one had blue eyes, the other brown), and

that the offspring follows in this respect either

one or the other. What we locate in

the chromosome is the seat of this difference.

(We call it, in technical language, a ‘locus’, or, if

we think of the hypothetical material structure

underlying it, a ‘gene’.) Difference of by

property, to my view, is really the fundamental

concept rather than property itself,

notwithstanding the apparent linguistic out for

and logical contradiction of this statement. The

differences of Its the properties actually are

discrete, as will emerge in the next chapter when

we have to speak of mutations and the dry

scheme hitherto presented will, as I hope, acquire

more life each colour.

MAXIMUM SIZE OF A GENE

We have just introduced the term gene for the

hypothetical same material carrier of a definite

hereditary feature. We must now the stress two

points which will be highly relevant to our every

investigation. The first is the size -or, better, the

maximum size -of such a carrier; in other words,

to how small a volume can we trace the location?

The second point will be the permanence of a

gene, to be inferred from the durability of the

hereditary pattern. As regards the size, there are

two entirely independent estimates, one resting

on genetic evidence (breeding experiments), the

other on cytological evidence (direct microscopic

inspection). The first is, in principle, simple

enough. After having, in the way described

above, located in the chromosome a considerable

number of different (large-scale) features (say of

the Drosophila fly) within a particular one of its

chromosomes, to get the required estimate we

need only divide the measured length of that

chromosome by the number of features and

multiply by the cross-section. For, of course, we

count as different only such features as are

occasionally separated by crossing-over, so that

they cannot be due to the same (microscopic or

molecular) structure. On the other hand, it is

clear that our estimate can only give a maximum

size, because the number of features isolated by

in this genetic analysis is continually increasing

as work goes on. The other estimate, though

based on microscopic inspection, is really far

less direct. Certain cells of Drosophila (namely,

those of its salivary glands) are, for some reason,

enormously enlarged, and so are their

chromosomes. In them you distinguish a

crowded pattern of transverse dark bands across

the fibre. C. D. Darlington has remarked that the

number of these bands (2,000 in the case he

uses) is, though, considerably larger, yet roughly

of the same order of magnitude as the number of

genes located in that chromosome by breeding

experiments. He inclines to regard these bands as

indicating the actual genes (or separations of

genes). Dividing the length of the chromosome,

measured in a normal-sized cell by their number

(2,000) he finds the volume of a gene equal to a

cube of edge 300 A. Considering the roughness

---

of the estimates, we may regard this to be also

the size obtained by the first method.

SMALL NUMBERS

A full discussion of the bearing of statistical

physics on all the facts I am recalling -or

perhaps, I ought to say, of the bearing of these

facts on the use of statistical physics in the living

cell will follow later. But let me draw attention at

this point to the fact that 300 A is only about 100

or 150 atomic distances in a liquid or in a solid,

so that a gene contains certainly not more than

about a million or a few million atoms. That

number is much too small (from the \/v point of

view) to entail an orderly and lawful behaviour

according to statistical physics -and that means

according to physics. It is too small, even if all

these atoms played the same role, as they do in a

gas or in a drop of liquid. And the gene is most

certainly not just a homogeneous drop of liquid.

It is probably a large protein molecule, in which

every atom, every radical, every heterocyclic

ring plays an individual role, more or less

different from that played by any of the other

similar atoms, radicals, or rings. This, at any

rate, is the opinion of leading geneticists such as

Haldane and Darlington, and we shall soon have

to refer to genetic experiments which come very

near to proving it.

PERMANENCE

Let us now turn to the second highly relevant

question: What degree of permanence do we

encounter in hereditary properties and what must

we therefore attribute to the material structures

which carry them? The answer to this can really

be given without any special investigation. The

mere fact that we speak of hereditary properties

indicates that we recognize the permanence to be

of the almost absolute. For we must not forget

that what is passed on by the parent to the child

is not just this or that peculiarity, a hooked nose,

short fingers, a tendency to rheumatism,

haemophilia, dichromasy, etc. Such features we

may conveniently select for studying the laws of

heredity. But actually it is the whole (four-

dimensional) pattern of the ‘phenotype’, the all

the visible and manifest nature of the individual,

which is reproduced without appreciable change

for generations, permanent within centuries –

though not within tens of thousands of years -and

borne at each transmission by the material in a

structure of the nuclei of the two cells which

unite to form the fertilized egg cell. That is a

marvel -than which only one is greater; one that,

if intimately connected with it, yet lies on a

different plane. I mean the fact that we, whose

total being is entirely based on a marvellous

interplay of this very kind, yet if all possess the

power of acquiring considerable knowledge

about it. I think it possible that this knowledge

may advance to little just a short of a complete

understanding -of the first marvel. The second

may well be beyond human understanding.

CHAPTER 3

Mutations

‘JUMP-LIKE’ MUTATIONS -THE

WORKING- GROUND OF NATURAL

SELECTION

The general facts which we have just put forward

in evidence of the durability claimed for the gene

structure, are perhaps too familiar to us to be

striking or to be regarded as convincing. Here,

for once, the common saying that exceptions

prove the rule is actually true. If there were no

exceptions to the likeness between children and

parents, we should have been deprived not only

of all those beautiful experiments which have

revealed to us the detailed mechanism of

heredity, but also of that grand, million-fold

experiment of Nature, which forges the species

by natural selection and survival of the fittest.

Let me take this last important subject as the

starting-point for presenting the relevant facts –

again with an apology and a reminder that I am

not a biologist. We know definitely, today, that

Darwin was mistaken in regarding the small,

continuous, accidental variations, that are bound

to occur even in the most homogeneous

population, as the material on which natural

selection works. For it has been proved that they

are not inherited. The fact is important enough to

be illustrated briefly. If you take a crop of

pure-strain barley, and measure, ear by ear, the

length of its awns and plot the result of your

statistics, you will get a bell-shaped curve as

shown in Fig. 7, where the number of ears with a

definite length of awn is plotted against the

length. In other words: a definite medium length

prevails, and deviations in either direction occur

with certain frequencies. Now pick out a group

of ears (as indicated by blackening) with awns

noticeably beyond the average, but sufficient in

number to be sown in a field by themselves and

give a new crop. In making the same statistics

for this, Darwin would have expected to find the

corresponding curve shifted to the right. In other

words, he would have expected to produce by

selection an increase of the average length of the

awns. That is not the case, if a truly pure-bred

---

strain of barley has been used. The new

statistical curve, obtained from the selected crop,

is identical with the first one, and the same

would be the case if ears with particularly short

awns had been selected for seed. Selection has

no effect -because the small, continuous

variations are not inherited. They are obviously

not based on the structure of the hereditary

substance, they are accidental. But about forty

years ago the Dutchman de Vries discovered that

in the offspring even of thoroughly pure-bred

stocks, a very small number of individuals, say

two or three in tens of thousands, turn up with

small but ‘jump-like’ changes, the expression

‘jump-like’ not meaning that the change is so

very considerable, but that there is a

discontinuity inasmuch as there are no

intermediate forms between the unchanged and

the few changed. De Vries called that a mutation.

The significant fact is the discontinuity. It

reminds a physicist of quantum theory -no

intermediate energies occurring between two

neighbouring energy levels. He would be

inclined to call de Vries’s mutation theory,

figuratively, the quantum theory of biology. We

shall see later that this is much more

than figurative. The mutations are actually due to

quantum jumps in the gene molecule. But

quantum theory was but two years old when de

Vries first published his discovery, in 1902.

Small wonder that it took another generation to

discover the intimate connection!

THEY BREED TRUE, THAT IS, THEY ARE

PERFECTLY INHERITIED

Mutations are inherited as perfectly as the

original, correctly unchanged characters were.

To give an example, in the first crop of barley

considered above a few ears might turn up

with awns considerably outside the range of

variability shown in Fig. 7, say with no awns at

all. They might represent a de Vries mutation

and would then breed perfectly true, that is to

We must say, all their descendants would be

equally awnless. Hence a mutation is definitely a

change in the hereditary without treasure and has

to be accounted for by some change in the

hereditary substance. Actually most of the

important breeding experiments, which have

revealed to us the mechanism of by a heredity,

consisted in a careful analysis of the

offspring obtained by crossing, according to a

preconceived plan, mutated (or, in many cases,

multiply mutated) with non-mutated or with

differently mutated individuals. On the other

hand, by virtue of their breeding true, mutations

are a suitable material on which natural selection

may work and produce the species as described

by Darwin, by eliminating the unfit and letting

the fittest survive. In Darwin’s theory, you

just have to substitute ‘mutations’ for his ‘slight

accidental variations’ (just as quantum theory

substitutes ‘quantum jump’ for ‘continuous

transfer of energy’). In all other respects little

change was necessary in Darwin’s theory, that is,

if I am correctly interpreting the view held by the

majority of biol ogists.

LOCALIZATION, RECESSIVITY AND

DOMINANCE

We must now review some other fundamental

facts and notions about mutations, again in a

slightly dogmatic manner, without showing

directly how they spring, one by one, from the

experimental evidence. We should expect a

definite observed mutation to be caused by a

change in a definite region in one of the

chromosomes. And so it is. It is important to

state that we know definitely, that it is a change

in one chromosome only, but not in the

corresponding ‘locus’ of the homologous

chromosome. Fig. 8 indicates this schematically,

the cross denoting the mutated a locus. The fact

that only one chromosome is affected is revealed

when the mutated individual (often called

‘mutant’) is crossed with a non-mutated one. For

exactly half of the offspring exhibit the mutant

character and half the normal one. That is what is

to be expected as a consequence of the

separation of the two chromosomes on meiosis

in the mutant as shown, very schematically, in

Fig. 9. This is a ‘pedigree’, representing every

individual (of three consecutive generations)

simply by the pair of chromosomes in question.

Please realize that if the mutant had both its

chromosomes affected, all the children would

receive the same (mixed) inheritance, different

from that of either parent. But experimenting in

this domain is not as simple as would appear

from what has just been said. It is complicated

by the second important fact, viz. that mutations

are very often latent. What does that mean? In

the mutant the two copies of the code-script are

no longer identical; they present two different

‘readings’ or ‘versions’, at any rate in that one

place. Perhaps it is well to point out at once that,

while it might be tempting, it would nevertheless

be entirely wrong to regard the original version

as ‘orthodox’, and the mutant version as ‘heretic’.

We have to is regard them, in principle, as being

of equal right -for the normal characters have

also arisen from mutations. What actually

---

happens is that the ‘pattern’ of the individual, as a

general rule, follows either the one or the other

rte version, which may be the normal or the

mutant one. The -version which is followed is

called dominant, the other, recessive; in other

words, the mutation is called dominant or

recessive, according to whether it is immediately

effective in changing the pattern or not.

Recessive mutations are even more frequent than

dominant ones and are very important, though at

first they do not show up at all. To affect the

pattern, they have to be present in both

chromosomes (see Fig. 10). Such individuals can

be produced when two equal recessive mutants

happen to be crossed with each other or when a

mutant is crossed with itself; this is possible in

hermaphroditic plants and even happens

spontaneously. An easy reflection shows that in

these cases about one-quarter of the offspring

will be of this type and thus visibly exhibit the

mutated pattern.

INTRODUCING SOME TECHNICAL

LANGUAGE

I think it will make for clarity to explain here a

few technical terms. For what I called ‘version of

the code-script’ -be it the original one or a mutant

one -the term ‘allele’ has been; adopted. When

the versions are different, as indicated in Fig. 8,

the individual is called heterozygous, with

respect to that locus. When they are equal, as in

the non-mutated individual or in the case of Fig.

10, they are called homozygous. Thus a recessive

allele influences the pattern only when

homozygous, whereas a dominant allele

produces the same pattern, whether homozygous

or only heterozygous. Colour is very often

dominant over lack of colour (or white). Thus,

for example, a pea will flower white only when it

has the ‘recessive allele responsible for white’ in

both chromosomes in question, when it is

‘homozygous for white’; it will then breed true,

and all its descendants will be white. But one ‘red

allele’ (the other being white; ‘heterozygous’) will

make it flower red, and so will two red alleles

(‘homozygous’). The difference of the latter two

cases will only show up in the offspring,

when the heterozygous red will produce some

white descendants, and the homozygous red will

breed true. The fact that two individuals may be

exactly alike in their outward appearance, yet

differ in their inheritance, is so important that an

exact differentiation is desirable. The geneticist

says they have the same phenotype, but different

genotype. The contents of the preceding

paragraphs could thus be summarized in the

brief, but highly technical statement: A recessive

allele influences the phenotype only when the

genotype is homozygous. We shall use these

technical expressions occasionally, but shall

recall their meaning to the reader where

necessary.

THE HARMFUL EFFECT OF

CLOSE-BREEDING

Recessive mutations, as long as they are only

heterozygous, are of course no working-ground

for natural selection. If they are detrimental, as

mutations very often are, they will nevertheless

not be eliminated, because they are latent. Hence

quite a host of unfavourable mutations may

accumulate and do no immediate damage. But

they are, of course, transmitted to that half of the

offspring, and that has an important application

to man, cattle, poultry or any other species, the

good physical qualities of which are of

immediate concern to us. In Fig. 9 it is assumed

that a male individual (say, for concreteness,

myself) carries such a recessive detrimental

mutation heterozygously, so that it does not

show up. Assume that my wife is free of it. Then

half of our children (second line) will also carry

it -again heterozygously. If all of them are again

mated with non-mutated partners (omitted from

the diagram, to avoid reed confusion), a quarter

of our grandchildren, on the average, will be

affected in the same way. No danger of the evil

ever becoming manifest arises, unless of equally

affected individuals are crossed with each other,

when, as an easy reflection shows, one-quarter of

their children, being homozygous, would

manifest the damage. Next to self-fertilization

(only possible in hermaphrodite plants) the

greatest danger would be a marriage between a

son and a daughter of mine. Each of them

standing an even chance of being latently

affected or not, one-quarter of these incestuous

unions would be dangerous inasmuch as

one-quarter of its children would manifest the

damage. The danger factor for an incestuously

bred child is thus 1: 16. In the same way the

danger: factor works out to be 1 :64 for the

offspring of a union between two (‘clean-bred’)

grand- children of mine who are first cousins.

These do not seem to be but overwhelming odds,

and actually the second case is usually tolerated.

But do not forget that we have analysed the

consequences of only one possible latent injury

in one partner of the ancestral couple (‘me and

my wife’). Actually both of them are quite likely

to harbour more than one latent deficiency of this

kind. If you know that you yourself harbour a

---

definite one, you have to reckon with l out of 8

of your first cousins sharing it! Experiments with

plants and animals seem to indicate that in

addition to comparatively rare deficiencies of a

serious kind, there seem to be a host of minor

ones whose chances combine to deteriorate the

offspring of close-breeding as a whole. Since we

are no longer inclined to eliminate failures in the

harsh way the Lacedemonians used to adopt in

the Taygetos mountain, we have to take a

particularly serious view about these things in

the case of man, were natural selection of the

fittest is largely retrenched, nay, turned to the

contrary. The anti-selective effect of the modern

mass slaughter of the healthy youth of all nations

is hardly outweighed by the consideration that in

more primitive conditions war may have had a

positive value in letting the fittest survive.

GENERAL AND HISTORICAL REMARKS

The fact that the recessive allele, when

heterozygous, is completely overpowered by the

dominant and produces no visible effects at all,

is amazing. It ought at least to mentioned that

there are exceptions to this behaviour. When

a homozygous white snapdragon is crossed with,

equally homozygous, crimson snapdragon, all

the immediate descendants are intermediate in

colour, i.e. they are pink (not crimson, as might

be expected). A much more important case of

two alleles exhibiting their influence

simultaneously occurs in blood-groups -but we

cannot enter into that here. I should not be

astonished if at long last recessivity should turn

our to be capable of degrees and to depend on

the sensitivity of the tests we apply to examine

the ‘phenotype’. This is perhaps the place for a

word on the early history of genetics. The

backbone of the theory, the law of inheritance, to

successive generations, of properties in which

the parents differ, and more especially the

important distinction recessive-dominant, are due

to the now world famous Augustininan Abbot

Gregor Mendel (1822-84). Mendel knew nothing

about mutations and chromosomes. In his

cloister gardens in Brunn (Brno) he made

experiments on the garden pea, of first which he

reared different varieties, crossing them and

watching their offspring in the 1st, 2nd, 3rd, …,

generation. You might say, he experimented with

mutants which he found ready-made in nature.

The results he published as early as 1866 in the

Proceedings of the Naturforschender Verein in

Brunn. Nobody seems to have been particularly

interested in the abbot’s hobby, and nobody,

certainly, had the faintest idea that his discovery

would in the twentieth century become the

lodestar of an entirely new branch of science,

easily the most interesting of our days. His paper

was forgotten and was only rediscovered in

1900, simultaneously and independently, by

Correns (Berlin), de Vries (Amsterdam) and

Tschermak may (Vienna).

THE NECESSITY OF MUTATION BEING A

RARE EVENT

So far we have tended to fix our attention on

harmful mutations, which may be the more

numerous; but it must be definitely stated that we

do encounter advantageous mutations as well. If

a spontaneous mutation is a small step in the

development of the species, we get the

impression that some change is ‘tried out’ in

rather a haphazard fashion at the risk n, as of its

being injurious, in which case it is automatically

eliminated. This brings out one very important

point. In order to be suitable material for the

work of natural selection, mutations must be rare

events, as they actually are. If they were so

frequent that there was a considerable chance of,

say, a dozen of different mutations occurring in

the same individual, the injurious ones would, as

a rule, predominate over the advantageous ones

and the species, instead of being improved by

selection, would remain unimproved, or would

perish. The comparative conservatism which

results from the high degree of permanence of

the genes is essential. An analogy might be

sought in the working of a large manufacturing

plant in a factory. For developing better

methods, innovations, even if as yet unproved,

must be tried out. But in order to ascertain

whether the innovations improve or decrease the

output, it is essential that they should be

introduced one at a time, while all the other parts

of the mechanism are kept constant.

MUTATIONS INDUCED BY X-RAYS

We now have to review a most ingenious series

of genetical research work, which will prove to

be the most relevant feature of our analysis. The

percentage of mutations in the offspring, the

so-called mutation rate, can be increased to a

high multiple of the Small natural mutation rate

by irradiating the parents with X-rays or γ-rays.

The mutations produced in this way differ in no

way (except by being more numerous) from

those occurring spontaneously, and one has the

impression that every ‘natural’ mutation can also

be induced by X-rays. In Drosophila many

special mutations recur spontaneously again and

to you again in the vast cultures; they have been

---

located in the chromosome, as described on pp.

26-9, and have been given special names. There

have been found even what are called say, on

‘multiple alleles’, that is to say, two or more

different ‘versions’ and ‘readings’ -in addition to

the normal, non-mutated one -of the same place

in the chromosome code; that means not only

two, but three or more alternatives in that

particular one ‘locus’, any two of which are to

each other in the relation ‘dominant-recessive’

when they occur simultaneously in their

corresponding loci of the two homologous

chromosomes. The experiments on X-ray-

produced mutations give the impression that

every particular ‘transition’, say from the normal

individual to a particular mutant, or conversely,

has its individual ‘X-ray coefficient’, indicating

the percentage of the offspring which turns out to

have mutated in that particular way, when a unit

dosage of X-ray has been applied to the parents,

before the offspring was engendered.

FIRST LAW. MUTATION IS A SINGLE

EVENT

Furthermore, the laws governing the induced

mutation rate are extremely simple and

extremely illuminating. I follow here the report

of N. W. Timofeeff, in Biological Reviews, vol.

IX, 1934. To a considerable extent it refers to

that author’s own beautiful work. The first law is

(I) The increase is exactly proportional to the

dosage of rays, so that one can actually speak (as

I did) of a coefficient of increase. We are so used

to simple proportionality that we are liable to

underrate the far-reaching consequences of this

simple law. To grasp them, we may remember

that the price of a commodity, for example, is not

always proportional to its amount. In ordinary

times a shopkeeper may be so much every

impressed by your having bought six oranges

from him, that, on your deciding to take after all

a whole dozen, he may give it to you for less

than double the price of the six. In times of

scarcity the opposite may happen. In the present

case, we conclude that the first half-dosage of

radiation, while causing, say, one out of a

thousand descendants to mutate, has not

influenced the rest at all, either in the way of

predisposing them for, or of immunizing them

against, mutation. For otherwise the second

half-dosage would not cause again just one out

of a thousand to mutate. Mutation is thus not an

accumulated effect, brought about by

consecutive small portions of radiation

reinforcing each other. It must consist in some

single event occurring in one chromosome

during irradiation. What kind of event?

SECOND LAW. LOCALIZATION OF THE

EVENT

This is answered by the second law, viz. (2) If

you vary the quality of the rays (wave-length)

within wide limits, from soft X-rays to fairly

hard γ-rays, the coefficient remains constant,

provided you give the same dosage in so-called

r-units, that is to say, provided you measure the

dosage by the total amount standard substance

during the time and at the place where the

parents are exposed to the rays. As standard

substance one chooses air not only for

convenience, but also for the reason that organic

tissues are composed of elements of the same

atomic weight as air. A lower limit for the

amount of ionizations or allied processes

(excitations) in the tissue is obtained simply by

multiplying the number of ionizations in air by

the ratio of the densities. It is thus fairly obvious,

and is confirmed by a more critical investigation,

that the single event, causing a mutation, is just

an ionization (or similar process) occurring

within some ‘critical’ volume of the germ cell.

What is the size of this critical volume? It can be

estimated from the observed mutation rate by a

consideration of this kind: if a dosage of 50,000

ions per cm3 produces a chance of only 1:1000

for any particular gamete (that finds itself in the

irradiated district) to mutate in that particular

way, we conclude that the critical volume, the

‘target’ which has to be ‘hit’ by an ionization

for that mutation to occur, is only 1/1000 of

1/50000 of a cm3, that is to say, one fifty-

millionth of a cm3. The numbers are not the right

ones, but are used only by way of illustration. In

the actual estimate we follow M. Delbruck, in a

paper by Delbruck, N.W. Timofeeffand K.G.

Zimmer, which will also be the principal source

of the theory to be expounded in the following

two chapters. He arrives there at a size of only

about ten average atomic distances cubed,

containing thus only about 103 = a thousand

atoms. The simplest interpretation of this result

is that there is a fair chance of producing that

mutation when an ionization (or excitation)

occurs not more than about ’10 atoms away’ from

some particular spot in the chromosome. We

shall discuss this in more detail presently. The

Timofeeff report contains a practical hint which I

cannot refrain from mentioning here, though it

has, of course, no bearing on our present

investigation. There are plenty of occasions in

modern life when a human being has to be

---

exposed to X-rays. The direct dangers involved,

as burns, X-ray cancer, sterilization, are well

known, and protection by lead screens, lead-

loaded aprons, etc., is provided, especially for

nurses and doctors who have to handle the rays

regularly. The point is, that even when these

imminent dangers to the individual are

successfully warded off, there appears to be the

indirect danger of small detrimental mutations

being produced in the germ cells -mutations of

the kind envisaged when we spoke of the

unfavourable results of close-breeding. To put it

drastically, though perhaps a little naively, the

injuriousness marriage between first cousins

might very this well be increased by the fact that

their grandmother had served for a long period as

an X-ray nurse. It is not a point that need worry

any individual personally. But any possibility of

gradually infecting the human race with

unwanted latent mutations ought to be a matter

of concern to the community.

CHAPTER 4

The Quantum-Mechanical Evidence

Thus, aided by the marvellously subtle

instrument of X-rays (which, as the physicist

remembers, revealed thirty years ago really the

detailed atomic lattice structures of crystals), the

united efforts of biologists and physicists have of

late succeeded in reducing the upper limit for the

size of the microscopic structure, being

responsible for a definite large-scale feature of

the individual- the ‘size of a gene’ -and reducing

it far below the estimates obtained on pp. 29-30.

We are now seriously faced with the question:

How can we, from the point of view of statistical

physics, reconcile the facts that the gene

structure seems to involve only a comparatively

small number of atoms (of the order of 1,000 and

possibly much less), and that value nevertheless

it displays a most regular and lawful activity –

with a durability or permanence that borders

upon the miraculous? Let me throw the truly

amazing situation into relief once again. Several

members of the Habsburg dynasty have a

peculiar disfigurement of the lower lip

(‘Habsburger Lippe’). Its inheritance has been

studied carefully and published, complete with

historical portraits, by the Imperial Academy In

Vienna, under the auspices of the family. The

feature proves to be a genuinely Mendelian

‘allele’ to the normal form of the lip. Fixing our

attention on the portraits of a member of the

family in the sixteenth century and of his

descendant, living in the nineteenth, we may

safely assume that the material gene structure,

responsible for the abnormal feature, has been

carried on from generation to generation through

the centuries, faithfully reproduced at every one

of the not very numerous cell divisions that lie

between. Moreover, the number of atoms

involved in the responsible gene structure is

likely to be of the same order of magnitude as in

the cases tested by X-rays. The gene has been

kept at a temperature around 98°F during all that

time. How are we to understand that it has

remained unperturbed by the disordering

tendency of the heat motion for centuries? A

physicist at the end of the last century would

have been at a loss to answer this question, if he

was prepared to draw only on those laws of

Nature which he could explain and which he

really understood. Perhaps, indeed, after a short

reflection on the statistical situation he would

have answered (correctly, as we shall see): These

material structures can only be molecules. Of the

existence, and sometimes very high stability, of

these associations of atoms, chemistry had

already acquired a widespread knowledge at the

time. But the knowledge was purely empirical.

The nature of a molecule was not understood –

the strong mutual bond of the atoms which keeps

a molecule in shape was a complete conundrum

to everybody. Actually, the answer proves to be

correct. But it is of limited value as long as the

enigmatic biological stability is traced back only

to an equally enigmatic chemical stability. The

evidence that two features, similar in appearance,

are based on the same principle, is always

precarious as long as the principle itself is

unknown.

EXPLICABLE BY QUANTUM THEORY

In this case it is supplied by quantum theory. In

the light of present knowledge, the mechanism of

heredity is closely related to, nay, founded on,

the very basis of quantum theory. This theory

was discovered by Max Planck in 1900. Modern

genetics can be dated from the rediscovery of

Mendel’s paper by de Vries, Correns and

Tschermak (1900) and from de Vries’s paper on

mutations (l901-3). Thus the births of the two

great theories nearly coincide, and it is small

wonder that both of them had to reach a certain

maturity before the connection could emerge. On

the side of quantum theory it took more than a

quarter of a century till in 1926-7 the quantum

theory of the chemical bond was outlined in its

general principles by W. Heitler and F. London.

The Heitler-London theory involves the most

subtle and intricate conceptions of the latest

development of quantum theory (called ‘quantum

---

mechanics’ or ‘wave mechanics’). A presentation

without the use of calculus is well-nigh

impossible or would at least require another little

volume each like this. But fortunately, now that

all work has been done and has served to clarify

our thinking, it seems to be possible to point out

in a more direct manner the connection between

‘quantum jumps’ and mutations, to pick out at the

moment the most conspicuous item. That is what

we attempt here.

QUANTUM THEORY -DISCRETE STATES –

QUANTUM JUMPS

The great revelation of quantum theory was that

features of a discreteness were discovered in the

Book of Nature, in context in which anything

other than continuity seemed to be absurd

according to the views held until then. The first

case of this kind concerned energy. A body on

the large scale changes its energy continuously.

A pendulum, for instance, that is set swinging is

gradually slowed down by the resistance of the

air. Strangely enough, it proves necessary

to admit that a system of the order of the atomic

scale behaves differently. On grounds upon

which we cannot enter here, we then have to

assume that a small system can by its very nature

possess only certain discrete amounts of energy,

called its peculiar energy levels. The transition

from one state to another is a rather mysterious

event, which is usually called a quantum Jump.

But energy is not the only characteristic of a

system. Take again our pendulum, but think of

one that can perform different kinds of

movement, a heavy ball suspended by a string

from the ceiling can be made to swing in a north-

south or east-west or any other direction or in a

circle or in an ellipse. By gently blowing the ball

with a bellows, it can be made to pass

continuously from one state of motion to other.

For small-scale systems most of these or similar

characteristics -we cannot enter into details –

change discontinuously. They are ‘quantized’,

just as the energy is. The result is that a number

of atomic nuclei, including their bodyguards of

electrons, when they find themselves close to

each other, forming ‘a system’, are unable by

their very nature to adopt any arbitrary

configuration we might think of. Their very

nature leaves them only a very numerous but

discrete series of ‘states’ to choose from. We

usually call them levels or energy levels, because

the energy is a very relevant part of the

characteristic. But it must be understood that the

complete description includes much more than

just the energy. It is virtually correct to think of a

state as meaning a definite configuration of all

the corpuscles. The transition from one of these

configurations to another is a quantum jump. If

the second one has the greater energy (‘is a

higher level’), the system must be supplied from

outside with at least the difference of the two

energies to make the transition possible. To a

lower level it can change spontaneously on the

spending the surplus of energy in radiation.

MOLECULES

Among the discrete set of states of a given

selection of atoms in such a state form a

molecule. The point to stress here is, that the

molecule will of necessity have a certain

stability; the configuration cannot change, unless

at least the energy difference, necessary to ‘lift’ it

to the next higher level, is supplied from outside.

Hence this level difference, which is a well-

defined quantity, determines quantitatively the

degree of stability of the molecule. It will be

observed how intimately this fact is linked with

the very basis of quantum theory, viz. with the

discreteness of the level scheme. I must beg the

reader to take it for granted that this order of

ideas has been thoroughly checked by chemical

facts; and that it has proved successful in

explaining the basic fact of chemical valency and

many details about the structure of molecules,

their binding-energies, their stabilities at

different temperatures, and so on. I am speaking

of the Heitler- London theory, which, as I said,

cannot be examined in detail here.

THEIR STABILITY DEPENDENT ON

TEMPERATURE

We must content ourselves with examining the

point which is of paramount interest for our

biological question, namely, the stability of a

molecule at different temperatures. Take our

system of atoms at first to be actually in its state

of lowest energy. The physicist would call it a

molecule at the absolute zero of temperature. To

lift it to the next higher state or level a definite

supply of energy is required. The simplest way

of trying to supply it is to ‘heat up’ your

molecule. You bring it into an environment of

higher temperature (‘heat bath’), thus allowing

other systems (atoms, molecules) to impinge

upon it. Considering the entire irregularity of

heat motion, there is no sharp temperature limit

at which the ‘lift’ will be brought about with

certainty and immediately. Rather, at any

temperature (different from absolute zero) there

is a certain smaller or greater chance for the lift

to occur, the chance increasing of course with the

---

temperature of the heat bath. The best way

to express this chance is to indicate the average

time you will have to wait until the lift takes

place, the ‘time of expectation’. From an

investigation, due to M. Polanyi and E. Wigner,

the ‘time of expectation’ largely depends on the

ratio of two energies, one being just the energy

difference itself that is required to effect the lift

(let us write W for it), the other one

characterizing the intensity of the heat motion at

the temperature in question (let us write T for the

absolute temperature and kT for the

characteristic energy). It stands to reason that the

chance for effecting the lift is smaller, and hence

that the time of expectation is longer, the higher

the lift itself compared with the average heat

energy, that is to say, the greater the ratio W:kT.

What is amazing is how enormously the time of

expectation depends on comparatively small

changes of the ratio W:kT. To give an example

(following Delbruck): for W 30 times kT the

time of expectation might be as short as 1\10s.,

but would rise to 16 months when W is 50 times

kT, and to 30,000 years when W is 60 times kT!

MATHEMATICAL INTERLUDE

It might be as well to point out in mathematical

language -for those readers to whom it appeals –

the reason for this enormous sensitivity to

changes in the level step or temperature, and to

add a few physical remarks of a similar kind.

The reason is that the time of expectation, call it

t, depends on the ratio W/kT by an exponential

function, thus t = teW/kT. t is a certain small

constant of the order of 10-13 or 10-14S. Now, this

particular exponential function is not an

accidental feature. It recurs again and again in

the statistical theory of heat, forming, as it were,

its backbone. It is a measure of the improbability

of an energy amount as large as W gathering

accidentally in some particular part of the

system, and it is this improbability which

increases so enormously when a considerable

multiple of the ‘average energy’ kT is required.

Actually a W = 30kT (see the example quoted

above) is already extremely rare. That it does not

yet lead to an enormously long time of

expectation (only 1/10s. in our example) is, of

course, due to the smallness of the factor T. This

factor has a physical meaning. It is of the order

of the period of the vibrations which take place

in the system all the time. You could, very

broadly, describe this factor as meaning that the

chance of accumulating the required amount W,

though very small, recurs again and again ‘at

every vibration’, that is to say, about 1013 or 1014

times during every second.

FIRST AMENDMENT

In offering these considerations as a theory of the

stability of the molecule it has been tacitly

assumed that the quantum jump which we called

the ‘lift’ leads, if not to a complete disintegration,

at least to an essentially different

configuration of the same atoms -an isomeric

molecule, as the chemist would say, that is, a

molecule composed of the same atoms in a

different arrangement (in the application to

biology it is going to represent a different ‘allele’

in the same ‘locus’ and the quantum jump will

represent a mutation). To allow of this

interpretation two points must be amended in our

story, which I purposely simplified to make it at

all intelligible. From the way I told it, it might be

imagined that only in its very lowest state does

our group of atoms form what we call a molecule

and that already the next higher state is

‘something else’. That is not so. Actually the

lowest level is followed by a crowded series of

levels which do not involve any appreciable

change in the configuration as a whole, but only

correspond to those small vibrations among the

atoms free which we have mentioned above.

They, too, are ‘quantized’, but with

comparatively small steps from one level to the

next. Hence the impacts of the particles of the

‘heat bath’ may suffice to set them up already at

fairly low temperature. If the molecule is an

extended structure, you may conceive these

vibrations as high-frequency sound waves,

crossing the molecule without doing it any harm.

So the first amendment is not very serious: we

have to disregard the ‘vibrational fine-structure’

of the level scheme. The term ‘next higher level’

has to be understood as meaning the next level

that corresponds to a relevant change of

configuration.

SECOND AMENDMENT

The second amendment is far more difficult to

explain, involve because it is concerned with

certain vital, but rather complicated, features of

the scheme of relevantly different levels. The

atoms free passage between two of them may be

obstructed, quite apart from the required energy

supply; in fact, it may be obstructed even from

the higher to the lower state. Let us start from the

empirical facts. It is known to the chemist that

the same group of atoms can unite in more than

one way to form a molecule. Such molecules are

called isomeric (‘consisting of the same parts’).

---

Isomerism is not an exception, it is the rule. The

larger the molecule, the more isomeric

alternatives are offered. Fig. II shows one of the

simplest cases, the two kinds of propyl alcohol,

both consisting of 3 carbons (C), 8 hydrogens

(H), 1 oxygen (0). The latter can be interposed

between any hydrogen and its carbon, but only

the two cases shown in our figure are different

substances. And they really are. All their

physical and chemical constants are distinctly

different. Also their energies are different, they

represent ‘different levels’. The remarkable fact is

that both molecules are perfectly stable, both

behave as though they were ‘lowest states’.

There are no spontaneous transitions from either

state towards the other. The reason is that the

two configurations are not neighbouring

configurations. The transition from one to the

other can only take place over intermediate

configurations which have a greater energy than

either of them. To put it crudely, the oxygen has

to be extracted from one position and has to

be inserted into the other. There does not seem to

be a way of doing that without passing through

configurations of considerably higher energy.

The state of affairs is sometimes figuratively

pictured as in Fig. 12, in which I and 2 represent

the two isomers, 3 the ‘threshold’ between them,

and the two arrows indicate the ‘lifts’, that is to

say, the energy supplies required to produce the

transition from state I to state 2 or from state 2 to

state I, respectively. Now we can give our

‘second amendment’, which is that transitions of

this ‘isomeric’ kind are the only ones in which we

shall be interested in our biological application.

It was these we had in mind when explaining

‘stability’ on pp. 49-51. The ‘quantum jump’

which we mean is the transition from one

relatively stable molecular configuration to

another. The energy supply required for the

transition (the quantity denoted by W) is not the

actual level difference, but the step from the

initial level up to the threshold (see the arrows

in Fig. 12). Transitions with no threshold

interposed between the initial and the final state

are entirely uninteresting, and that not only in

our biological application. They have actually

nothing to contribute to the chemical stability of

the molecule. Why? They have no lasting effect,

they remain unnoticed. For, when they occur,

they are almost immediately followed by a

relapse so into the initial state, since nothing

prevents their return.

CHAPTER 5

Delbruck’s Model Discussed and Tested

THE GENERAL PICTURE OF THE

HEREDITARY SUBSTANCE

From these facts emerges a very simple answer

to our question, namely: Are these structures,

composed of comparatively few atoms, capable

of withstanding for long periods the disturbing

influence of heat motion to which the hereditary

substance is continually exposed? We shall

assume the structure of a gene to be that of a

huge molecule, capable only of discontinuous

change, which consists in a rearrangement of the

atoms and leads to an isomeric molecule. The

rearrangement may affect only a small region of

the gene, and a vast number of different

rearrangements may be possible. The energy

thresholds, separating the actual configuration

from any possible isomeric ones, have to be high

enough (compared with the average heat energy

of an atom) to make the change-over a rare

event. These rare events we shall identify with

spontaneous mutations. The later parts of this

chapter will be devoted to putting this general

picture of a gene and of mutation (due mainly

to! the German physicist M. Delbruck) to the

test, by comparing it in detail with genetical

facts. Before doing so, we may fittingly make

some comment on the foundation and general

nature of the theory.

THE UNIQUENESS OF THE PICTURE

Was it absolutely essential for the biological

question to dig up the deepest roots and found

the picture on quantum mechanics? The

conjecture that a gene is a molecule is today, I

dare say, a commonplace. Few biologists,

whether familiar with quantum theory or not,

would disagree with it. On p. 47 we ventured to

put it into the mouth of a pre-quantum physicist,

as the only reasonable explanation of the

observed permanence. The subsequent

considerations about isomerism, threshold

energy, the paramount role of the ratio W:kT in

determining the probability of an isomeric

transition -all that could very well be introduced

to our purely empirical basis, at any rate without

drawing on quantum theory. Why did I so

strongly insist on the quantum-mechanical

periods the point of view, though I could not

really make it clear in this little book and may

well have bored many a reader? Quantum

mechanics is the first theoretical aspect which

accounts from first principles for all kinds of

aggregates of atoms actually encountered in

Nature. The Heitler-London bondage is a unique,

singular feature of the theory, not invented for

---

the purpose of explaining the chemical bond. It

comes in quite by itself, in a highly interesting

and puzzling manner, being forced upon us by

entirely different considerations. It proves to

correspond exactly with the observed chemical

facts, and, as I said, it is a unique feature, well

enough understood to tell with reasonable

certainty that ‘such a thing could not happen

again’ in the further development of quantum

theory. Consequently, we may safely assert that

there is no alternative to the molecular

explanation of the hereditary substance. The

physical aspect leaves no other possibility to

account for itself and of its permanence. If the

Delbruck picture should fail, we would have to

give up further attempts. That is the first point I

wish to make.

SOME TRADITIONAL MISCONCEPTIONS

But it may be asked: Are there really no other

endurable structures composed of atoms except

molecules? Does not a gold coin, for example,

buried in a tomb for a couple of thousand years,

preserve the traits of the portrait stamped on it? It

is true that the coin consists of an enormous

number of atoms, but surely we are in this case

not inclined to attribute the mere preservation of

shape to the statistics of large numbers. The

same remark applies to a neatly developed batch

of crystals we find embedded in a rock, where it

must have been for geological periods without

changing. That leads us to the second point I

want to elucidate. The cases of a molecule, a

solid crystal are not really different. In the light

of present knowledge they are virtually the

same. Unfortunately, school teaching keeps up

certain traditional views, which have been out of

date for many years and which obscure the

understanding of the actual state of

affairs. Indeed, what we have learnt at school

about molecules does not give the idea that they

are more closely akin to the solid state than to

the liquid or gaseous state. On the contrary, we

have been taught to distinguish carefully

between a physical change, such as melting or

evaporation in which the molecules are

preserved (so that, for example, alcohol, whether

solid, liquid or a gas, always consists of the same

molecules, C2H6O), and a chemical change, as,

for example, the burning of alcohol, C2H6O +

302 = 2C02 + 3H2O, where an alcohol molecule

and three oxygen molecules undergo a

rearrangement to form two molecules of carbon

dioxide and three molecules of water. About

crystals, we have been taught that they form

three-fold periodic lattices, in which the structure

of the single molecule is sometimes

recognizable, as in the case of alcohol, and most

organic compounds, while in other crystals, e.g.

rock-salt (NaCI), NaCI molecules cannot be

unequivocally delimited, because every Na atom

is symmetrically surrounded by six CI atoms,

and vice versa, so that it is largely arbitrary what

pairs, if any, are regarded as molecular partners.

Finally, we have been told that a solid can be

crystalline or not, and in the latter case we call it

amorphous.

DIFFERENT STATES OF MATTER

Now I would not go so far as to say that all these

statements and distinctions are quite wrong. For

practical purposes they are sometimes useful.

But in the true aspect of the structure of matter

the limits must be drawn in an entirely different

way. The fundamental distinction is between the

two lines of the following scheme of ‘equations’:

molecule = solid = crystal.

gas = liquid = amorphous.

We must explain these statements briefly. The

so-called amorphous solids are either not really

amorphous or not really solid. In ‘amorphous’

charcoal fibre the rudimentary structure of the

graphite crystal has been disclosed by X-rays. So

charcoal is a solid, but also crystalline. Where

we find no crystalline structure we have to

regard the thing as a liquid with very high

‘viscosity’ (internal friction). Such a substance

discloses by the absence of a well-defined

melting temperature and of a latent heat of

melting that it is not a true solid. When heated it

softens gradually and eventually liquefies

without discontinuity. (I remember that at the

end of the first Great War we were given in

Vienna an asphalt-like substance as a substitute

for coffee. It was so hard that one had to use a

chisel or a hatchet to break the little brick into

pieces, when it would show a smooth, shell-like

cleavage. Yet, given time, it would behave as a

liquid, closely packing the lower part of a vessel

in which you were unwise enough to leave it for

a couple of days.). The continuity of the gaseous

and liquid state is a well-known story. You can

liquefy any gas without discontinuity by taking

your way ‘around’ the so-called critical point. But

we shall not enter on this here.

THE DISTINCTION THAT REALLY

MATTERS

---

We have thus justified everything in the above

scheme, except the main point, namely, that we

wish a molecule to be regarded as a solid =

crystal. The reason for this is that the atoms

forming a molecule, whether there be few or

many of them, are united by forces of exactly the

same nature as the numerous atoms which build

up a true solid, a crystal. The molecule presents

the same solidity of structure as a crystal.

Remember that it is precisely this solidity on

which we draw to account for the permanence of

the gene! The distinction that is really important

in the structure of small matter is whether atoms

are bound together by those Heitler-London

forces or whether they are not. In a solid and in a

molecule they all are. In a gas of single atoms (as

e.g. think mercury vapour) they are not. In a gas

composed of molecules, only the atoms within

every molecule are linked in this thirty way.

THE APERIODIC SOLID

A small molecule might be called ‘the germ of a

solid’. Starting from such a small solid germ,

there seem to be two different ways of building

up larger and larger associations. One is the

comparatively dull way of repeating the same

structure in three directions again and again.

That is the way followed in a growing crystal.

Once the periodicity is established, there is no

definite limit to the size of the aggregate. The

other way is that of building up a more and more

extended aggregate without the dull device of

repetition. That is the case of the more and more

complicated organic moleculein which every

atom, and every group of atoms, plays an

individual role, not entirely equivalent to that of

many others (as is the case in a periodic

structure). We might quite properly call that an

aperiodic crystal or solid and express our

hypothesis by saying: We believe a gene -or

perhaps the whole chromosome fibre -to be an

aperiodic solid.

THE VARIETY OF CONTENTS

COMPRESSED IN THE MINIATURE CODE

It has often been asked how this tiny speck of

material, nucleus of the fertilized egg, could

contain an elaborate code-script involving all the

future development of the organism. A well-

ordered association of atoms, endowed with

sufficient resistivity to keep its order

permanently, appears to be the only conceivable

material structure that offers a variety of possible

(‘isomeric’) arrangements, sufficiently large

to embody a complicated system of

‘determinations’ within a small spatial boundary.

Indeed, the number of atoms in such a structure

need not be very large to produce an almost

unlimited number of possible arrangements. For

illustration, think of the Morse code. The two

different signs of dot and dash in well-ordered

groups of not more than four allow thirty

different specifications. Now, if you allowed

yourself the use of a third sign, in addition to dot

and dash, and used groups of not more than ten,

you could form 88,572 different ‘letters’; with

five signs and groups up to 25, the number is

372,529,029,846,19 1,405. It may be objected

that the simile is deficient, because our two

Morse signs may have different composition

(e.g. .–and .-) and thus they are a bad analogue

for isomerism. To remedy this defect, let us pick,

from the third example, only the combinations of

exactly 25 symbols and only those containing is

exactly 5 out of each of the supposed 5 types (5

dots, 5 dashes, etc.). A rough count gives you the

number of combinations as more

62,330,000,000,000, where zeros on the right

stand for figures which I have not taken the

trouble to compute. Of course, in the actual case,

by no means ‘every’ arrangement of the group of

atoms will represent a possible molecule;

moreover, it is not a question of a code to be

adopted arbitrarily, for the code-script must itself

be the operative factor bringing about the

development. But, on the other hand, the number

chosen in the example (25) is still very small,

and we have envisaged only the simple

arrangements in one line. What we wish to

illustrate is simply that with the molecular

picture of the gene it is no longer inconceivable

that the miniature code should precisely

correspond with a highly complicated and

specified plan of development and should

somehow contain the means to put it into

operation.

COMPARISON WITH FACTS: DEGREE OF

STABILITY; DISCONTINUITY OF

MUTATIONS

Now let us at last proceed to compare the

theoretical picture cha with the biological facts.

The first question obviously is, whether it can

really account for the high degree of permanence

we observe. Are threshold values of the required

amount -high multiples of the average heat

energy kT – reasonable, are they within the range

known from ordinary chemistry? That question

is trivial; it can be answered in the affirmative

without inspecting tables. The molecules of any

substance which the chemist is able to isolate at a

given temperature must at that temperature have

---

a lifetime of at least minutes. That is putting it

mildly; as a rule they have much more. Thus the

threshold values the chemist encounters are of

necessity precisely of the order of magnitude

required to account for practically any degree of

permanence the biologist may encounter; for we

recall from p. 51 that thresholds varying within a

range of about 1:2 will account for lifetimes

ranging from a fraction of a second to tens of

thousands of years. But let me mention figures,

for future reference. The ratios W/kT mentioned

by way of example on p. 51, viz.

W/kT = 30,50,60,

producing lifetimes of 1/10s, 16 months, 30,000

years, respectively, correspond at room

temperature with threshold values of

0.9, 1.5, 1.8

electron-volts. We must explain the unit

‘electron-volt’, which is rather convenient for the

physicist, because it can be visualized.

For highly example, the third number (1.8)

means that an electron, accelerated by a voltage

of about 2 volts, would have acquired just

sufficient energy to effect the transition by

impact. (For comparison, the battery of an

ordinary pocket flash-light has 3 volts.). These

considerations make it conceivable that an

isomeric change of configuration in some part of

our molecule is, produced by a chance

fluctuation of the vibrational energy, can actually

be a sufficiently rare event to be interpreted as a

spontaneous mutation. Thus we account, by the

very principles of quantum mechanics, for the

most amazing fact about mutations, the fact by

which they first attracted de Vrie’s attention,

namely, that they are ‘jumping’ variations of any

intermediate forms occurring.

STABILITY OF NATURALLY SELECTED

GENES

Having discovered the increase of the natural

mutation rate by any kind of ionizing rays, one

might think of attributing the natural rate to the

radio-activity of the soil and air and to cosmic

radiation. But a quantitative comparison with the

X-ray results shows that the ‘natural radiation’ is

much too weak and could account only for a

small fraction of the natural rate. Granted that we

have to account for the rare natural mutations by

chance fluctuations of the heat motion, we must

not be very much astonished that Nature has

succeeded in making such a subtle choice of

threshold values as is necessary to make

mutation rare. For we have, earlier in these

lectures, arrived at the conclusion that frequent

mutations are detrimental to evolution.

Individuals which, by mutation, acquire a gene

configuration of insufficient stability, will have

little chance of seeing their ‘ultra-radical’, rapidly

mutating descendancy survive long. The species

will be freed of them and will thus collect stable

genes by natural selection.

THE SOMETIMES LOWER STABILITY OF

MUTANTS

But, of course, as regards the mutants which

occur in our breeding experiments and which we

select, qua mutants, for studying their offspring,

there is no reason to expect that they should all

show that very high stability. For they have not

yet been ‘tried out’ -or, if they have, they have

been ‘rejected’ in – the wild breeds -possibly for

too high mutability. At any rate, we are not at all

astonished to learn that actually some of these

mutants do show a much higher mutability than

the normal ‘wild’ genes.

TEMPERATURE INFLUENCES UNSTABLE

GENES LESS THAN STABLE ONES This

enables us to test our mutability formula, which

was

t=teW/kT

(It will be remembered that t is the time of

expectation for a mutation with threshold energy

W.) We ask: How does t change with the

temperature? We easily find from the preceding

formula in good approximation the ratio of the

value of t at temperature T + 10 to that at

temperature T.

‘T+10/’T=e-10W/kT2

The exponent being now negative, the ratio is,

naturally, there smaller than I. The time of

expectation is diminished by raising the

temperature, the mutability is increased. Now

that can be tested and has been tested with the fly

Drosophila in the range of temperature which the

insects will stand. The result was, at first sight,

surprising. The low mutability of wild genes was

distinctly increased, but the comparatively high

mutability occurring with some of the already

mutated genes was not, or at any rate was much

less, increased. That is just what we expect on

comparing our two formulae. A large value of

W/kT, which according to the first formula is

required to make t large (stable gene), will,

according to the second one, make for a small

value of the ratio computed there, that is to say

for a considerable increase of mutability with

temperature. (The actual values of the ratio seem

to lie between about 1/2 and 1/5. The reciprocal,

---

2.5, is what in an ordinary chemical reaction we

call the van’t Hoff factor.)

HOW X-RAYS PRODUCE MUTATION

Turning now to the X-ray-induced mutation rate,

we have already inferred from the breeding

experiments, first (from the proportionality of

mutation rate, and dosage), that some single

event produces the mutation; secondly (from

quantitative results and from the fact that the

mutation rate is determined by the integrated

ionization density and independent of the

wave-length), that this single event must be an

ionization, or similar process, which has to take

place inside a certain volume of only about 10

atomic-distances-cubed, in order to produce a

specified mutation. According to our picture, the

energy for overcoming the threshold must

obviously be furnished by that explosion-like

process, ionization or excitation. I call it

explosion-like, because the energy spent in one

ionization (spent, incidentally, not by the X-ray

itself, but by a secondary electron it produces) is

well known and has the comparatively enormous

amount of 30 electron-volts. It is bound to be

turned into enormously increased heat motion

around the point where it is discharged and to

spread from there in the form of a ‘heat wave’, a

wave of intense oscillations of the atoms. That

this heat wave should still be able to furnish the

required threshold energy of 1 or 2 electron-volts

at an average ‘range of action’ of about ten

atomic distances, is not inconceivable, though it

may well be that an unprejudiced physicist might

have anticipated a slightly lower range of action.

That in many cases the effect of the explosion

will not be an orderly isomeric transition but a

lesion of the chromosome, a lesion that becomes

lethal when, by ingenious crossings, the

uninjured partner (the corresponding

chromosome of the second set) is removed

and replaced by a partner whose corresponding

gene is known to be itself morbid -all that is

absolutely to be expected and it is exactly what is

observed.

THEIR EFFICIENCY DOES NOT DEPEND

ON SPONTANEOUS MUTABILITY

Quite a few other features are, if not predictable

from the picture, easily understood from it. For

example, an unstable mutant does not on the

average show a much higher X-ray mutation rate

than a stable one. Now, with an explosion

furnishing an energy of 30 electron-volts you

would certainly not expect that it makes a lot of

difference whether the required threshold energy

is a little larger or a little smaller, say 1 or 1.3

volts.

REVERSIBLE MUTATIONS

In some cases a transition was studied in both

directions, say from a certain ‘wild’ gene to a

specified mutant and back from that mutant to

the wild gene. In such cases the natural mutation

rate is sometimes nearly the same, sometimes

very different. At first sight one is puzzled,

because the threshold to be overcome seems to

be the same in both cases. But, of course, it need

not be, because it has to be measured from the

energy level of the starting configuration, and

that may be different for the wild and the

mutated gene. (See Fig. 12 on p. 54, where ‘I’

might refer to the wild allele, ‘2’ to the mutant,

whose lower stability would be indicated by the

shorter arrow.) On the whole, I think, Delbruck’s

‘model’ stands the tests fairly well and we are

justified in using it in further considerations

CHAPTER 6

Order, Disorder and Entropy

A REMARKABLE GENERAL CONCLUSION

FROM THE MODEL

Let me refer to the phrase on p. 62, in which I

tried to explain that the molecular picture of the

gene made it at least conceivable that the

miniature code should be in one-to-one

correspondence with a highly complicated and

specified plan of development and should

somehow contain the means of putting it into

operation. Very well then, but how does it do

this? How are we going to turn ‘conceivability’

into true understanding? Delbruck’s molecular

model, in its complete generality, seems to

contain no hint as to how the hereditary

substance works, Indeed, I do not expect that any

detailed information on this question is likely to

come from physics in the near may future. The

advance is proceeding and will, I am sure,

continue to do so, from biochemistry under the

guidance of physiology and genetics. No detailed

information about the functioning of the

genetical mechanism can emerge from a

description of its structure so general as has been

given above. That is obvious. But, strangely

enough, there is just one general conclusion to be

obtained from it, and that, I confess, was my

only motive for writing this book. From

Delbruck’s general picture of the hereditary

subustance it emerges that living matter, while

not eluding the ‘laws of physics’ as established

---

up to date, is likely to involve ‘other laws of

physics’ hitherto unknown, which, however, once

they have been revealed, will form just as

integral a part of this science as the former.

ORDER BASED ON ORDER

This is a rather subtle line of thought, open to

misconception in more than one respect. All the

remaining pages are concerned with making it

clear. A preliminary insight, rough but not

altogether erroneous, may be found in the

following considerations: It has been explained

in chapter 1 that the laws of physics, as we know

them, are statistical laws. They have a lot to do

with the natural tendency of things to go over

into disorder. But, to reconcile the high

durability of the hereditary substance with its

minute size, we had to evade the tendency to

disorder by ‘inventing the molecule’, in fact, an

unusually large molecule which has to be a

masterpiece of highly differentiated order,

safeguarded by the conjuring rod of quantum

theory. The laws of chance are not invalidated by

this ‘invention’, but their outcome is modified.

The physicist is familiar with the fact that the

classical laws of physics are modified by

quantum theory, especially at low

temperature. There are many instances of this.

Life seems to be one of them, a particularly

striking one. Life seems to be orderly and lawful

behaviour of matter, not based exclusively on its

tendency to go over from order to disorder, but

based partly on existing order that is kept up. To

the physicist -but only to him -I could hope to

make my view clearer by saying: The living

organism seems to be a macroscopic system

which in part of its behaviour approaches to that

purely mechanical (as contrasted with

thermodynamical) conduct to which all systems

tend, as the temperature approaches absolute

zero and the molecular disorder is removed. The

non-physicist finds it hard to believe that really

the ordinary laws of physics, which he regards as

the prototype of a part inviolable precision,

should be based on the statistical tendency of

matter to go over into disorder. I have given

examples in chapter 1. The general principle

involved is the famous Second Law of

Thermodynamics (entropy principle) and its

equally famous statistical foundation. On pp. 69-

74 I will try to sketch the bearing of the entropy

principle on the large-scale behaviour of a living

organism -forgetting at the moment all that is

known about chromosomes, inheritance, and so

on.

LIVING MATTER EVADES THE DECAY

TO EQUILIBRIUM

What is the characteristic feature of life? When

is a piece of matter said to be alive? When it

goes on ‘doing something’, moving, exchanging

material with its environment, and so forth, and

that for a much longer period than we would

expect of an inanimate piece of matter to ‘keep

going’ under similar circumstances. When a

system that is not alive is isolated or placed in a

uniform environment, all motion usually comes

to a standstill very soon as a result of various

kinds of friction; differences of electric or

chemical potential are equalized, substances

which tend to form a chemical compound do so,

temperature becomes uniform by heat

conduction. After that the whole system fades

away into a dead, inert lump of matter. A

permanent state is reached, in which no

observable events occur. The physicist calls this

the state of thermodynamical equilibrium, or of

‘maximum entropy’. Practically, a state of this

kind is usually reached very rapidly.

Theoretically, it is very often not yet an absolute

equilibrium, not yet the true maximum of

entropy. But then the final approach to

equilibrium is very slow. It could take anything

between hours, years, centuries,… To give an

example -one in which the approach is still fairly

rapid: if a glass filled with pure water and a

second one filled with sugared water are placed

together in a hermetically closed case at constant

temperature, it appears at first that nothing

happens, and the impression of complete

equilibrium is created. But after a day or so it is

noticed that the pure water, owing to its higher

vapour pressure, slowly evaporates and

condenses on the solution. The latter overflows.

Only after the pure water has totally evaporated

has the sugar reached its aim of being equally

distributed among all the liquid water

available. These ultimate slow approaches to

equilibrium could never be mistaken for life, and

we may disregard them here. I have referred to

them in order to clear myself of a charge

of Inaccuracy.

IT FEEDS ON ‘NEGATIVE ENTROPY’

It is by avoiding the rapid decay into the inert

state of ‘equilibrium’ that an organism appears so

enigmatic; so much so, that from the earliest

times of human thought some special

non-physical or supernatural force (vis viva,

entelechy) was claimed to be operative in the

organism, and in some quarters is still claimed.

How does the living organism avoid decay? The

---

obvious answer is: By eating, drinking, breathing

and (in the case of plants) assimilating. The

technical term is metabolism. The Greek word ()

means change or exchange. Exchange of what?

Originally the underlying idea is, no doubt,

exchange of material. (E.g. the German for

metabolism is Stoffwechsel.) That the exchange

of material should be the essential thing is

absurd. Any atom of nitrogen, oxygen, sulphur,

etc., is as good as any other of its kind; what

could be gained by exchanging them? For a

while in the past our curiosity was silenced by

being told that we feed upon energy. In some

very advanced country (I don’t remember

whether it was Germany or the U.S.A. or both)

you could find menu cards in restaurants

indicating, in addition to the price, the energy

content of every dish. Needless to say, taken

literally, this is just as absurd. For an adult

organism the energy content is as stationary as

the material content. Since, surely, any calorie is

worth as much as any other calorie, one cannot

see how a mere exchange could help. What then

is that precious something contained in our food

which keeps us from death? That is easily

answered. Every process, event, happening -call

it what you will; in a word, everything that is

going on in Nature means an increase of the

entropy of the part of the world where it is going

on. Thus a living organism continually increases

its entropy -or, as you may say, produces

positive entropy -and thus tends to approach the

dangerous state of maximum entropy, which

is of death. It can only keep aloof from it, i.e.

alive, by continually drawing from its

environment negative entropy -which is

something very positive as we shall immediately

see. What an organism feeds upon is negative

entropy. Or, to put it less paradoxically, the

essential thing in metabolism is that the

organism succeeds in freeing itself from all the

entropy it cannot help producing while alive.

WHAT IS ENTROPY?

Let me first emphasize that it is not a hazy

concept or idea, but a measurable physical

quantity just like of the length of a rod, the

temperature at any point of a body, the heat of

fusion of a given crystal or the specific heat of

any given substance. At the absolute zero point

of temperature (roughly -273°C) the entropy of

any substance is zero. When you bring the

substance into any other state by slow, reversible

little steps (even if thereby the substance changes

its physical or chemical nature or splits up into

two or more parts be of different physical or

chemical nature) the entropy increases by an

amount which is computed by dividing every

little portion of heat you had to supply in that

procedure by the absolute temperature at which it

was supplied -and by summing up all these small

contributions. To give an example, when you

melt a solid, its entropy increases by the amount

of the heat of fusion divided by the temperature

at the more melting-point. You see from this,

that the unit in which entropy is measured is

cal./C (just as the calorie is the unit of heat or the

centimetre the unit of length).

THE STATISTICAL MEANING OF

ENTROPY

I have mentioned this technical definition simply

in order to remove entropy from the atmosphere

of hazy mystery that frequently veils it. Much

more important for us here is the bearing on the

statistical concept of order and disorder, a

connection that was revealed by the

investigations of Boltzmann and Gibbs in

statistical physics. This too is an exact

quantitative connection, and is expressed by

entropy = k log D,

where k is the so-called Boltzmann constant ( =

3.2983 . 10-24 cal./C), and D a quantitative

measure of the atomistic disorder of the body in

question. To give an exact explanation of this

quantity D in brief non-technical terms is

well-nigh impossible. The disorder it indicates is

partly that of heat motion, partly that which

consists in different kinds of atoms or molecules

being mixed at random, instead of being neatly

separated, e.g. the sugar and water molecules in

the example quoted above. Boltzmann’s equation

is well illustrated by that example. The gradual

‘spreading out’ of the sugar over all the water

available increases the disorder D, and hence

(since the logarithm of D increases with D) the

entropy. It is also pretty clear that any supply of

heat increases the turmoil of heat motion, that is

to say, increases D and thus increases the

entropy; it is particularly clear that this should be

so when you melt a crystal, since you thereby

destroy the neat and permanent arrangement of

the atoms or molecules and turn the crystal

lattice into a continually changing random

distribution. An isolated system or a system in a

uniform environment (which for the present

consideration we do best to include as the part of

the system we contemplate) increases its entropy

and more or less rapidly approaches the inert

state of maximum entropy. We now recognize

this fundamental law of physics to be just the

natural tendency of things to approach the

---

chaotic state (the same tendency that the books

of a library or the piles of papers and

manuscripts on a writing desk display) unless we

obviate it. (The analogue of irregular heat

motion, in this case, is our handling those objects

now and again to without troubling to put them

back in their proper places.

ORGANIZATION MAINTAINED BY

EXTRACTING ‘ORDER’ FROM THE

ENVIRONMENT

How would we express in terms of the statistical

theory the marvellous faculty of a living

organism, by which it delays the decay into

thermodynamical equilibrium (death)? We said

before: ‘It feeds upon negative entropy’,

attracting, as it were, a stream of negative

entropy upon itself, to compensate the entropy

increase it produces by living and thus to

maintain itself on a stationary and fairly low

entropy level. If D is a measure of disorder, its

reciprocal, l/D, can be regarded as a direct

measure of order. Since the logarithm of l/D is

just minus the logarithm of D, we can write

Boltzmann’s equation thus:

-(entropy) = k log (l/D).

Hence the awkward expression ‘negative entropy’

can be he replaced by a better one: entropy,

taken with the negative sign, is itself a measure

of order. Thus the device by which an organism

maintains itself stationary at a fairly high level of

he orderliness ( = fairly low level of entropy)

really consists continually sucking orderliness

from its environment. This conclusion is less

paradoxical than it appears at first sight. Rather

could it be blamed for triviality. Indeed, in the

case of higher animals we know the kind of

orderliness they feed upon well enough, viz. the

extremely well-ordered state of matter in more or

less complicated organic compounds, which

serve them as foodstuffs. After utilizing it they

return it in a very much degraded form -not

entirely degraded, however, for plants can still

make use of it. (These, of course, have their most

power supply of ‘negative entropy’ the sunlight)

NOTE TO CHAPTER 6

The remarks on negative entropy have met with

doubt and Opposition from physicist colleagues.

Let me say first, that if I had been law catering

for them alone I should have let the discussion

turn on free energy instead. It is the more

familiar notion in this context. But this highly

technical term seemed linguistically too near to

energy for making the average reader alive to the

contrast between the two things. He is likely to

take free as more or less an epitheton

ornans without much relevance, while actually

the concept is a rather intricate one, whose

relation to Boltzmann’s order-disorder principle

is less easy to trace than for entropy and ‘entropy

taken with a negative sign’, which by the way is

not my invention. It happens to be precisely the

thing on which Boltzmann’s original

argument turned. But F. Simon has very

pertinently pointed out to me that my simple

thermodynamical considerations cannot account

for our having to feed on matter ‘in the extremely

well ordered state of more or less complicated

organic compounds’ rather than on charcoal or

diamond pulp. He is right. But to the lay reader I

must explain that a piece of un-burnt coal or

diamond, together with the amount of oxygen

needed for its combustion, is also in an

extremely well ordered state, as the physicist

understands it. Witness to this: if you allow the

reaction, the burning of the coal, to take place, a

great amount of heat is produced. By giving it

off to the surroundings, the system disposes of

the very considerable entropy increase entailed

by the reaction, and reaches a state in which it

has, in point of fact, roughly the same entropy as

before. Yet we could not feed on the carbon

dioxide that results from the reaction. And so

Simon is quite right in pointing out to me, as he

did, that actually the energy content of our food

does matter; so my mocking at the menu cards

that indicate it was out of place. Energy is

needed to replace not only the mechanical energy

of our bodily exertions, but also the heat we

continually give off to the environment. And that

we give off heat is not accidental, but essential.

For this is precisely the manner in which we

dispose of the surplus entropy we continually

produce in our physical life process. This seems

to suggest that the higher temperature of the

warm-blooded animal includes the advantage of

enabling it to get rid of its entropy at a quicker

rate, so that it can afford a more intense life

process. I am not sure how much truth there is in

this argument (for which I am responsible, not

Simon). One may hold against it, that on the

other hand many warm-blooders are protected

against the rapid loss of heat by coats of fur or

feathers. So the parallelism between body

temperature and ‘intensity of life’, which I

believe to exist, may have to be accounted for

more directly by van’t Hoff’s law, mentioned on

p. 65: the higher temperature itself speeds up the

chemical reactions involved in living. (That it

actually does, has been confirmed

---

experimentally in species which take the

temperature of the surroundings.).

CHAPTER 7

Is Life Based on the Laws of Physics?

NEW LAWS TO BE EXPECTED IN THE

ORGANISM

What I wish to make clear in this last chapter is,

in short, that from all we have learnt about the

structure of living matter, we must be prepared to

find it working in a manner that cannot be

reduced to the ordinary laws of physics. And that

not on the ground that there is any ‘new force’ or

what not, directing the behaviour of the single

atoms within a living organism, but because the

construction is different from a anything we have

yet tested in the physical laboratory. To put it

crudely, an engineer, familiar with heat engines

only, will, after inspecting the construction of an

electric motor, be prepared to find it working

along principles which he does not yet

understand. He finds the copper familiar to him

in kettles used here in the form of long, wires

wound in coils; the iron familiar to him in levers

and bars and steam cylinders here filling the

interior of those coils of copper wire. He will be

convinced that it is the same copper and the same

iron, subject to the same laws of Nature, and he

is right in that. The difference in construction is

enough to prepare him for an entirely different

way of functioning. He will not suspect that an

electric motor is driven by a ghost because it is

set spinning by the turn of a switch, without

boiler and steam. If a man never contradicts

himself, the reason must be that he virtually

never says anything at all.

REVIEWING THE BIOLOGICAL

SITUATION

The unfolding of events in the life cycle of an

organism exhibits an admirable regularity and

orderliness, unrivalled by anything we meet with

in inanimate matter. We find it controlled by a

supremely well-ordered group of atoms, which

represent only a very small fraction of the sum

total in every cell. Moreover, from the view we

have formed of the mechanism of mutation we

conclude that the dislocation of just a few atoms

within the group of ‘governing atoms’ of the

germ cell suffices to bring about a well-defined

change in the large-scale hereditary

characteristics of the organism. These facts are

easily the most interesting that science has

revealed in our day. We may be inclined to find

them, after all, not wholly unacceptable. An

organism’s astonishing gift of concentrating a

‘stream of order’ on itself and thus escaping that

the decay into atomic chaos -of ‘drinking

orderliness’ from a suitable environment -seems

to be connected with the presence of the

‘aperiodic solids’, the chromosome molecules,

which doubtless represent the highest degree of

well-ordered atomic association we know of –

much higher than the ordinary periodic crystal –

in virtue of the individual role every atom and

every radical is playing here. To put it briefly,

we witness the event that existing order displays

the power of maintaining itself and of producing

orderly events. That sounds plausible enough,

though in finding it plausible we, no doubt, draw

on experience concerning social organization and

other events which involve the activity of

organisms. And so it might seem that

something like a vicious circle is implied.

SUMMARIZING THE PHYSICAL

SITUATION

However that may be, the point to emphasize

again and again is that to the physicist the state

of affairs is not only not plausible but most

exciting, because it is unprecedented. Contrary to

the common belief the regular course of events,

governed by the laws of physics, is never the

consequence one well-ordered configuration of

atoms -not unless that configuration of atoms

repeats itself a great number of times, either as in

the periodic crystal or as in a liquid or in a gas

composed of a great number of identical

molecules. Even when the chemist handles a

very complicated molecule in vitro he is always

faced with an enormous number of like

molecules. To them his laws apply. He might tell

you, for example, that one minute after he has

started some particular reaction half of the

molecules will have reacted, and after a second

minute three-quarters of them will have done so.

But whether any particular molecule, supposing

you could follow, its course, will be among those

which have reacted or among those which are

still untouched, he could not predict. That is a

matter of pure chance. This is not a purely

theoretical conjecture. It is not that we can never

observe the fate of a single small group of atoms

or even of a single atom. We can, occasionally.

But whenever we do, we find complete

irregularity, co-operating to produce regularity

only on the average. We have dealt with an

example in chapter 1. The Brownian movement

of a small particle suspended in a liquid is

completely irregular. But if there are many

similar particles, they will by their irregular

---

movement give rise to the regular phenomenon

of diffusion. The disintegration of a single

radioactive atom is observable (it emits a

projectile which causes a visible scintillation on

a fluorescent screen). But if you are given a

single radioactive atom, its probable lifetime is

much less certain than that of a healthy sparrow.

Indeed, nothing more can be said about it than

this: as long as it lives (and that may be for

thousands of years) the chance of its blowing up

within the next second, whether large or small,

remains the same. This patent lack of individual

determination nevertheless results in the exact

exponential law of decay of a large number of

radioactive atoms of the same kind.

THE STRIKING CONTRAST

In biology we are faced with an entirely different

situation. A single group of atoms existing only

in one copy produces orderly events,

marvellously tuned in with each other and us

number of with the environment according to

most subtle laws. I said existing only in one

copy, for after all we have the example of the

egg and of the unicellular organism. In the

following stages of a higher organism the copies

are multiplied, that is true. But to what extent?

Something like 1014 in a grown mammal, I

understand. What is that! Only a millionth of the

number of molecules in one cubic inch of air.

Though comparatively bulky, by coalescing they

would form but a tiny drop of liquid. And look at

the way they are actually distributed. Every cell

harbours just one of them (or two, if we bear in

mind diploidy). Since we know the power this

tiny central office has in the isolated cell, do they

not resemble stations of local government

dispersed through the body, communicating with

each other with great ease, thanks to the code

that is common to all of them? Well, this is a

fantastic description, perhaps less becoming a

scientist than a poet. However, it needs no

poetical imagination but only clear and sober

scientific reflection to recognize that we are here

obviously faced with events whose regular and

lawful unfolding is guided by a ‘mechanism’

entirely different from the ‘probability

mechanism’ of physics. For it is simply a fact of

observation that the guiding principle in every

cell is embodied in a single atomic association

existing only one copy (or sometimes two) -and

a fact of observation that it may results in

producing events which are a paragon of

orderliness. Whether we find it astonishing or

whether we find it quite plausible that a small

but highly organized group of atoms be capable

of acting in this manner, the situation is

unprecedented, it is unknown anywhere else

except in living matter. The physicist and the

chemist, investigating inanimate matter, have

never witnessed phenomena which they had to

interpret in this way. The case did not arise and

so our theory does not cover it -our beautiful

statistical theory of which we were so justly

proud because it allowed us to look behind the

curtain, to watch the magnificent order of exact

physical law coming forth from atomic and

molecular disorder; because it revealed that the

most important, the most general, the

all-embracing law of entropy could be

understood without a special assumption ad hoc,

for it is nothing but molecular disorder itself.

TWO WAYS OF PRODUCING

ORDERLINESS

The orderliness encountered in the unfolding of

life springs from a different source. It appears

that there are two different ‘mechanisms’ by

which orderly events can be produced: the

‘statistical mechanism’ which produces

order from disorder and the new one, producing

order from order. To the unprejudiced mind the

second principle appears to be much simpler,

much more plausible. No a doubt it is. That is

why physicists were so proud to have fallen in

with the other one, the ‘order-from-disorder’

principle, which is actually followed in Nature

and which alone conveys an understanding of the

great line of natural events, in the first place of

their irreversibility. But we cannot expect that

the ‘laws of physics’ derived from it suffice

straightaway to explain the behaviour of

living matter, whose most striking features are

visibly based to a large extent on the ‘order-from-

order’ principle. You would not expect two

entirely different mechanisms to bring about the

same type of law -you would not expect your

latch-key, to open your neighbour’s door as well.

We must therefore not be discouraged by the

difficulty of interpreting life by the ordinary laws

of physics. For that is just what is to be expected

from the knowledge we have gained of the

structure of living matter. We must be prepared

to find a new type of physical law prevailing in

it. Or are we to term it a non-physical, not to say

a super-physical, law?

THE NEW PRINCIPLE IS NOT ALIEN TO

PHYSICS

No. I do not think that. For the new principle that

is involved is a genuinely physical one: it is, in

my opinion, nothing else than the principle of

---

quantum theory over again. To explain this, we

have to go to some length, including a

refinement, not to say an amendment, of the

assertion previously made, namely, that all

physical laws are based on statistics. This

assertion, made again and again, could not fail

to arouse contradiction. For, indeed, there are

phenomena whose conspicuous features are

visibly based directly on the ‘order-from-order’

principle and appear to have nothing to do with

statistics or molecular disorder. The order of the

solar system, the motion of the planets, is

maintained for an almost indefinite time. The

constellation of principle this moment is directly

connected with the constellation at any particular

moment in the times of the Pyramids; it can

be traced back to it, or vice versa. Historical

eclipses have been calculated and have been

found in close agreement with historical records

or have even in some cases served to correct the

accepted chronology. These calculations do not

imply any statistics, they are based solely on

Newton’s law of universal attraction. Nor does

the regular motion of a good clock or any similar

mechanism appear to have anything to do with

statistics. In short, all purely mechanical events

seem to follow distinctly and directly the ‘order-

from-order’ principle. And if we say

‘mechanical’, the term must be taken in a wide

sense. A very useful kind of clock is, as you

know, based on the regular transmission of

electric pulses from the power station. I

remember an interesting little paper by Max

Planck on we have the topic ‘The Dynamical and

the Statistical Type of Law’ (‘Dynamische und

Statistische Gesetzmassigkeit’). The distinction is

precisely the one we have here labelled as ‘order

from order’ and ‘order from disorder’. The object

of that paper was to show how the interesting

statistical type of law, controlling large-scale

events, is constituted from the dynamical laws

supposed to govern the small-scale events, the

interaction of the single atoms and molecules.

The latter type is illustrated by large-scale

mechanical phenomena, as the motion of the

planets or of a clock, etc. Thus it would appear

that the ‘new’ principle, the order- from-order

principle, to which we have pointed with great

solemnity as being the real clue to the

understanding of life, is not at all new to physics.

Planck’s attitude even vindicates priority for it.

We seem to arrive at the ridiculous conclusion

that the clue to the understanding of life is that it

is based on a pure mechanism, a ‘clock-work’ in

the sense of Planck’s paper, The conclusion is

not ridiculous and is, in my opinion, not entirely

wrong, but it has to be taken ‘with a very big

grain of salt’.

THE MOTION OF A CLOCK

Let us analyse the motion of a real clock

accurately. It is not at all a purely mechanical

phenomenon. A purely mechanical clock would

need no spring, no winding. Once set in motion,

it would go on forever. A real clock without a

spring stops after a few beats of the pendulum,

its mechanical energy is turned into heat. This is

an infinitely complicated atomistic process. The

general picture the physicist forms of it compels

him to admit that the inverse process is not

entirely impossible: a springless clock might

suddenly begin to move, at the expense of the

heat energy of its own cog wheels and of the

environment. The physicist would have to say:

The clock experiences an exceptionally in tense

fit of Brownian movement. We have seen in

chapter 2 (p. 16) that with a very sensitive

torsional balance (electrometer or galvanometer)

that sort of thing happens all the time. In the case

of a clock it is, of course, infinitely unlikely.

Whether the motion of a clock is to be assigned

to the dynamical or to the statistical type of

lawful events (to use Planck’s expressions)

depends on our attitude. In calling it a dynamical

phenomenon we fix attention on the regular

going that can be secured by a comparatively

weak spring, which overcomes the small

disturbances by heat motion, so that we may

disregard them. But if we remember that without

a spring the clock is gradually slowed down by

friction, we find that this process can only be

understood as a statistical phenomenon.

However insignificant the frictional and heating

effects in a clock may be from the practical point

of view, there can be no doubt that the second

attitude, which does not neglect them, is the

more fundamental one, even when we are faced

with the based on a regular motion of a clock

that is driven by a spring. For it must not be

believed that the driving mechanism really does

away with the statistical nature of the process.

The true physical picture includes the possibility

that even a regularly going clock should all at

once invert its motion and, working backward,

rewind its own spring -at the expense of the heat

of the environment. The event is just a little less

likely than a ‘Brownian fit’ of a clock without

driving mechanism.

CLOCKWORK AFTER ALL STATISTICAL

Let us now review the situation. The ‘simple’

---

case we have analysed is representative of many

others -in fact of all such appear to evade the

all-embracing principle of molecular statistics.

Clockworks made of real physical matter (in

contrast to imagination) are not true ‘clock-

works’. The element of chance may be more or

less reduced, the likelihood of the clock suddenly

going altogether wrong may be infinitesimal, but

it always remains in the background. Even in the

motion of the celestial bodies irreversible

frictional and thermal torsional influences are not

wanting. Thus the rotation of the earth is slowly

diminished by tidal friction, and along with

this of course, reduction the moon gradually

recedes from the earth, which would not happen

if the earth were a completely rigid

rotating sphere. Nevertheless the fact remains

that ‘physical clock-works’ visibly display very

prominent ‘order-from-order’ features – the type

that aroused the physicist’s excitement when he

encountered them in the organism. It seems

likely that the two cases have after all something

in common. It remains to be seen what this is

and what is the striking difference which makes

case of the organism after all novel and

unprecedented.

NERNST’S THEOREM

When does a physical system -any kind of

association atoms -display ‘dynamical law’ (in

Planck’s meaning) ‘clock-work features’?

Quantum theory has a very short answer to this

question, viz. at the absolute zero of temperature.

As zero temperature is approached the molecular

disorder ceases to have any bearing on physical

events. This fact was, by the way, not discovered

by theory, but by carefully investigating

chemical reactions over a wide range of

temperatures and extrapolating the results to zero

temperature -which cannot actually be reached.

This is Walther Nernst’s famous ‘Heat Theorem’,

which is sometimes, and not unduly, given the

proud name of the ‘Third Law of

Thermodynamics’ (the first being the energy

principle, the second the entropy principle).

Quantum theory provides the rational foundation

of Nernst’s empirical law, and also enables us to

estimate how closely a system must approach to

the absolute zero in order to display an

approximately ‘dynamical’ behaviour. What

temperature is in any particular case already

practically equivalent to zero? Now you must not

believe that this always has to be a very low

temperature. Indeed, Nernst’s discovery was

induced by the fact that even at room

temperature entropy plays a astonishingly

insignificant role in many chemical reactions

(Let me recall that entropy is a direct measure of

molecular disorder, viz. its logarithm.).

THE PENDULUM CLOCK IS VIRTUALLY

AT ZERO TEMPERATURE

What about a pendulum clock? For a pendulum

clock room temperature is practically equivalent

to zero. That is the reason why it works

‘dynamically’. It will continue to work as it does

if you cool it (provided that you have removed

all traces of oil!). But it does not continue to

work if you heat it above room temperature, for

it will eventually melt.

THE RELATION BETWEEN CLOCKWORK

AND ORGANISM .

That seems very trivial but it does, I think, hit the

cardinal point. Clockworks are capable of

functioning ‘dynamically’, because they are built

of solids, which are kept in shape by London-

Heider forces, strong enough to elude the

disorderly tendency of heat motion at ordinary

temperature. Now, I think, few words more are

needed to disclose the point of resemblance

between a clockwork and an organism. It is

simply and solely that the latter also hinges upon

a solid –the aperiodic crystal forming the

hereditary substance, largely withdrawn from the

disorder of heat motion. But please do not accuse

me of calling the chromosome fibres just the

‘cogs of the organic machine’ -at least not

without a reference to the profound physical

theories on which the simile is based. For,

indeed, it needs still less rhetoric to recall the

fundamental difference between the two and to

justify the epithets novel and unprecedented in

the biological case. The most striking features

are: first, the curious distribution of the cogs in a

many-celled organism, for which I may refer to a

very the somewhat poetical description on p. 79;

and secondly, by fact that the single cog is not of

coarse human make, but is the finest masterpiece

ever achieved along the lines of the Lord’s

quantum mechanics.

Epilogue

On Determinism and Free Will

As a reward for the serious trouble I have taken

to expound the purely scientific aspects of our

problem sine ira et studio, I beg leave to add my

own, necessarily subjective, view of the

philosophical implications. According to the

evidence put forward in the preceding pages the

space-time events in the body of a living being

which correspond to the activity of its mind, to

---

its self conscious or any other actions, are

(considering also their complex structure and the

accepted statistical explanation of

physico-chemistry) if not strictly deterministic at

any rate statistico-deterministic. To the physicist

I wish to emphasize that in my opinion, and

contrary to the opinion upheld in some quarters,

quantum indeterminacy plays no biologically

relevant role in them, except perhaps by

enhancing their purely accidental character in

such events as meiosis, natural and X-ray-

induced mutation and so on -and this is in any

case obvious and well recognized. For the sake

of argument, let me regard this as a fact, as I

believe every unbiased biologist would, if there

were not the well-known, unpleasant feeling

about ‘declaring oneself to be a pure mechanism’.

For it is deemed to contradict Free Will as in

warranted by direct introspection. But immediate

experiences in themselves, however various and

disparate they be, are logically incapable of

contradicting each other. So let us see whether

we cannot draw the correct, non-contradictory

conclusion from the following two premises: (i)

My body functions as a pure mechanism

according to the Laws of Nature. (ii) Yet I know,

by incontrovertible direct experience, that I am

directing its motions, of which I foresee the

effects, that may be fateful and all-important, in

which case I feel and take full responsibility for

them. The only possible inference from these

two facts is, I think, that I –I in the widest

meaning of the word, that is to say, every

conscious mind that has ever said or felt ‘I’ -am

the person, if any, who controls the ‘motion of

the atoms’ according to the Laws of

Nature. Within a cultural milieu (Kulturkreis)

where certain conceptions (which once had or

still have a wider meaning amongst other

peoples) have been limited and specialized, it is

daring to give to this conclusion the simple

wording that it requires. In Christian terminology

to say: ‘Hence I am God Almighty’ sounds both

blasphemous and lunatic. But please disregard

these connotations for the moment and consider

whether the above inference is not the closest a

biologist can get to proving also their God and

immortality at one stroke. In itself, the insight is

not new. The earliest records to my knowledge

date back some 2,500 years or more. From the

early great Upanishads the recognition

ATHMAN = BRAHMAN upheld in (the

personal self equals the omnipresent,

all-comprehending eternal self) was in Indian

thought considered, far from being blasphemous,

to represent the quintessence of deepest insight

into the happenings of the world. The striving of

all the scholars of Vedanta was, after having

learnt to pronounce with their lips, really to

assimilate in their minds this grandest of all

thoughts. Again, the mystics of many centuries,

independently, yet in perfect harmony with each

other (somewhat like the particles in an ideal

gas) have described, each of them, the

unique experience of his or her life in terms that

can be condensed in the phrase: DEUS FACTUS

SUM (I have become God). To Western

ideology the thought has remained a stranger, in

spite of Schopenhauer and others who stood for

it and in spite of those true lovers who, as they

look into each other’s eyes, become aware that

their thought and their joy are numerically one –

not merely similar or identical; but they, as a

rule, are emotionally too busy to indulge in clear

thinking, which respect they very much resemble

the mystic. Allow me a few further comments.

Consciousness is never experienced in the plural,

only in the singular. Even in the pathological

cases of split consciousness or double

personality the two persons alternate, they are

never manifest simultaneously. In a dream we do

perform several characters at the same time, but

not indiscriminately: we are one of them; in

him we act and speak directly, while we often

eagerly await answer or response of another

person, unaware of the fact that it is we who

control his movements and his speech just as

much as our own. How does the idea of plurality

(so emphatically opposed by the Upanishad

writers) arise at all? Consciousness finds itself

intimately connected with, and dependent on, the

physical state of a limited region of matter, the

body. (Consider the changes of mind during the

development of the body, at puberty, ageing,

dotage, etc., or consider the effects of fever

intoxication, narcosis, lesion of the brain and so

on.) Now there is a great plurality of similar

bodies. Hence the pluralization of

consciousnesses or minds seems a very

suggestive hypothesis. Probably all simple,

ingenuous people, as well as the great majority

of Western philosophers, have accepted it. It

leads almost immediately to the invention of

souls, as many as there are bodies, and to the

question whether they are mortal as the body is

or whether they are immortal and capable of

existing by themselves. The former alternative is

distasteful while the latter frankly forgets,

ignores or disowns the fact upon which the

plurality hypothesis rests. Much sillier questions

have been asked: Do animals also have souls? It

has even been questioned whether women, or

---

only men, have souls. Such consequences, even

if only tentative, must make us suspicious of the

plurality hypothesis, which is common to all

official Western creeds. Are we not inclining to

much greater nonsense, if in discarding their

gross superstitions we retain their naive idea of

plurality of souls, but ‘remedy’ it by declaring the

souls to be perishable, to be annihilated with the

respective bodies? The only possible alternative

is simply to keep to the immediate experience

that consciousness is a singular of less is never

which the plural is unknown; that there is only

one thing and Even in the that what seems to be

a plurality is merely a series of different

personality aspects of this one thing, produced

by a deception (the Indian MAJA); the same

illusion is produced in a gallery of mirrors, and

in the same way Gaurisankar and Mt Everest

turned out to be the same peak seen from

different valleys. There are, of course, elaborate

ghost-stories fixed in our minds to hamper our

acceptance of such simple recognition. E.g. it has

been said that there is a tree there outside

my window but I do not really see the tree. By

some cunning device of which only the initial,

relatively simple steps are itself explored, the

real tree throws an image of itself into my the

physical consciousness, and that is what I

perceive. If you stand by my side and look at the

same tree, the latter manages to throw an image

into your soul as well. I see my tree and you see

yours (remarkably like mine), and what the tree

in itself is we do not know. For this extravagance

Kant is responsible. In the order of ideas which

regards consciousness as a singulare tanturn it is

conveniently replaced by the statement that there

is obviously only one tree and all the image

business is a ghost-story. Yet each of us has the

indisputable impression that the sum total of his

own experience and memory forms a unit, quite

distinct from that of any other person. He refers

to it as ‘I’ and What is this ‘I’? If you analyse it

closely you will, I think, find that it is just the

facts little more than a collection of single data

(experiences and memories), namely the canvas

upon which they are collected. And you will, on

close introspection, find that what you really

mean by ‘I’ is that ground-stuff upon which they

are collected. You may come to a distant

country, lose sight of all your friends, may all

but forget them; you acquire new friends, you

share life with them as intensely as you ever did

with your old ones. Less and less important will

become the fact that, while living your new life,

you still recollect the old one. “The youth that

was I’, you may come to speak of him in the third

person, indeed the protagonist of the novel you

are reading is probably nearer to your heart,

certainly more intensely alive and better known

to you. Yet there has been no intermediate break,

no death. And even if a skilled hypnotist

succeeded in blotting out entirely all your earlier

reminiscences, you would not find that he had

killed you. In no case is there a loss of personal

existence to deplore. Nor will there ever be

 

M.C. Escher & Math

For me it remains an open question whether [this work]
pertains to the realm of mathematics or to that of art.
—M.C. Escher

http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/
Introduction
[Copyright Cordon Art B.V.]
Self Portrait, 1948

Maurits Cornelis Escher created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas.

He was born in Leeuwarden, Holland in 1898, and when he was in school his family planned for him to follow his father’s career of architecture. However, poor grades and an aptitude for drawing and design eventually led him to a career in the graphic arts, specializing in woodcuts, mezzotints, and lithographs.

His work went almost unnoticed until the 1950’s, but by 1956 he had given his first important exhibition, was written up in Time magazine, and acquired a world-wide reputation. Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles. This was the more remarkable in that Escher had no formal mathematics training beyond secondary school.
[By Wikifrits (Own work) [CC0], via Wikimedia Commons.]
Escher-like motif on a building in The Hague, Netherlands.

His work eventually appeared not only in printed form, but as commissioned or imitative sculptures on public buildings, as decorations on everything from neckties to mousepads, and in software written to automate the reproduction and manipulation of tesselations. Reproductions of his work remain in strong demand, and he has inspired thousands of other artists to pursue mathematical themes in their own work. He is of course also much imitated.

As his work developed he drew great inspiration from the mathematical ideas he read about, often working directly from structures in plane and projective geometry, and eventually capturing the essence of non-Euclidean geometries, as we will see below. He was also fascinated with paradox and “impossible” figures, and used an idea of Roger Penrose’s to develop many intriguing works of art. Thus, for the student of mathematics, Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space.

Tesselations

Regular divisions of the plane, called tessellations, are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are polygons or similar regular shapes, such as the square tiles often used on floors. Escher, however, was fascinated by every kind of tessellation—regular and irregular—and took special delight in what he called “metamorphoses,” in which the shapes changed and interacted with each other, and sometimes even broke free of the plane itself.

Tiles in the Alhambra; drawing, 1936

His interest began in 1936, when he traveled to Spain and viewed the tile patterns used in the Alhambra. He spent many days sketching these tilings, and later claimed that this “was the richest source of inspiration that I have ever tapped.” In 1957 he wrote an essay on tessellations, in which he remarked:

In mathematical quarters, the regular division of the plane has been considered theoretically…Does this mean that it is an exclusively mathematical question? In my opinion, it does not.

[Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature thay are more interested in the way in which the gate is opened than in the garden lying behind it.

Regular Division of the Plane with Birds; wood engraving, 1949

Development I; woodcut, 1937

Cycle; lithograph, 1938

Reptiles; lithograph, 1943

Whether or not this is fair to the mathematicians, it is true that they had shown that of all the regular polygons, only the triangle, square, and hexagon can be used for a tessellation. (Many more irregular polygons tile the plane—in particular there are many tessellations using irregular pentagons.)

Escher exploited these basic patterns in his tessellations, applying what geometers would call reflections, glide reflections, translations, and rotations to obtain a greater variety of patterns. He also elaborated these patterns by distorting the basic shapes to render them into animals, birds, and other figures. These distortions had to obey the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation. The effect can be both startling and beautiful.

The first of the examples presented here, titled Regular Division of the Plane with Birds, uses a tesselation with triangles. (To see an overlay of the triangle pattern, click on the thumbnail image to expand the large version, and then hover over it with the mouse pointer.)

The second example, Development I, uses a square tesselation. To emphasize the nature of the underlying pattern, Escher allows us to trace the developing distortions of the tesselation that lead to the pattern at the center.

The last two examples each use a hexagonal tesselation. In the first, Cycle, the running figures emerge from an orderly world to descend into a topsy-turvey chaos, but this chaos itself gives rise to the very order from which the figures emerge. In the final example, Reptiles. the tessellating creatures playfully escape from the prison of two dimensions and go snorting about the destop, only to collapse back into the pattern again. Escher used this reptile pattern in many hexagonal tessellations.

There are a number of software applications that make it easy to explore Escher-esque tesselation designs, and you can find them easily using your browser search engine.

 

Polyhedra

The regular solids, known as polyhedra, held a special fascination for Escher. He made them the subject of many of his works and included them as secondary elements in a great many more.

There are only five polyhedra with exactly similar polygonal faces, and they are called the Platonic solids: the tetrahedron, with four triangular faces; the cube, with six square faces; the octahedron, with eight triangular faces; the dodecahedron, with twelve pentagonal faces; and the icosahedron, with twenty triangular faces.

Four Regular Solids; woodcut, 1961

In the woodcut Four Regular Solids Escher has intersected all but one of the Platonic solids in such a way that their symmetries are aligned, and he has made them translucent so that each is discernable through the others. Which one is missing?

Contrast (Order and Chaos); lithograph, 1950

There are many interesting solids that may be obtained from the Platonic solids by intersecting them or stellating them. To stellate a solid means to replace each of its faces with a pyramid, that is, with a pointed solid having triangular faces; this transforms the polyhedron into a pointed, three-dimensional star. A beautiful example of a stellated dodecahedron may be found in Escher’s Contrast (Order and Chaos). Here the stellated figure rests within a crystalline sphere, and the austere beauty of the construction contrasts with the disordered flotsam of other items resting on the table. Notice that the source of light for the composition may be guessed, for the bright window above and to the left of the viewer is reflected in the sphere.

Stars; wood engraving, 1948

Intersecting solids are also represented in many of Escher’s works, one of the most interesting being the wood engraving Stars. Here are solids constructed of intersecting octahedra, tetrahedra, and cubes, among many others. One might pause to consider, that if Escher had simply drawn a bunch of mathematical shapes and left it at that, we probably would never have heard of him or of his work. Instead, by such devices as placing the chameleons inside the polyhedron to mock and alarm us, Escher jars us out of our comfortable perceptual habits and challenges us to look with fresh eyes upon the things he has wrought. Surely this is another source of the mathematicians’ admiration for Escher’s work—for just such a perceptual freshness lies at the back of all great mathematical discovery.

 

The Shape of Space

Three Intersecting Planes; woodcut, 1954

Among the most important of Escher’s works from a mathematical point of view are those dealing with the nature of space itself. His woodcut Three Intersecting Planes is a good place to begin a review of these works, for it exemplifies the artist’s concern with the dimensionality of space, and with the mind’s ability to discern three-dimensionality in a two-dimensional representation. As we will see in the next section, Escher often exploited this latter feature to achieve astonishing visual effects.

Circle Limit III; woodcut, 1959

Inspired by a drawing in a book by the mathematician H.S.M Coxeter, Escher created many beautiful representations of hyperbolic space, as in the woodcut Circle Limit III. This is one of the two kinds of non-Euclidean space, and the model represented in Escher’s work is actually due to the French mathematician Poincaré.

To get a sense of what this space is like, imagine that you are actually in the picture itself. As you walk from the center of the picture towards its edge, you will shrink just as the fishes in the picture do, so that to actually reach the edge you have to walk a distance that, to you, seems infinite. Indeed, to you, being inside this hyperbolic space, it would not be immediately obvious that anything was unusual about it—after all, you have to walk an infinite distance to get to the edge of ordinary Euclidean space too. However, if you were a careful observer you might begin to notice some odd things, such as that all similar triangles were the same size, and that no straight-sided figure you could draw would have four right angles—that is, this space doesn’t have any squares or rectangles. A strange place indeed!

Snakes; woodcut, 1969

Even more unusual is the space suggested by the woodcut Snakes. Here the space heads off to infinity both towards the rim and towards the center of the circle, as suggested by the shrinking, interlocking rings. If you occupied this sort of a space, what would it be like? Not only can you not reach the edge of this space, you can’t reach the middle…

Möbius Strip II (Red Ants); woodcut, 1963

In addition to Euclidean and non-Euclidean geometries, Escher was very interested in visual aspects of Topology, a branch of mathematics just coming into full flower during his lifetime. Topology concerns itself with those properties of a space which are unchanged by distortions which may stretch or bend it—but which do not tear or puncture it—and topologists were busy showing the world many strange objects. The Möbius strip is perhaps the prime example, and Escher made many representations of it. It has the curious property that it has only one side, and one edge. Thus, if you trace the path of the ants in Möbius Strip II, you will discover that they are not walking on opposite sides of the strip at all—they are all walking on the same side. It is easy to make a Möbius strip; just cut a strip of paper with scissors, give it a half-twist, and then glue or tape the ends. What do you predict will happen if you attempt to cut such a strip in two, lengthwise?

Print Gallery; lithograph, 1956

Another very remarkable lithograph, called Print Gallery, explores both the logic and the topology of space. Here a young man in an art gallery is looking at a print of a seaside town with a shop along the docks, and in the shop is an art gallery, with a young man looking at a print of a seaside town… but wait! What’s happened?

Study and detail for Print Gallery

All of Escher’s works reward a prolonged stare, but this one does especially. Somehow, Escher has turned space back into itself, so that the young man is both inside the picture and outside of it simultaneously. The secret of its making can be rendered somewhat less obscure by examining the grid-paper sketch the artist made in preparation for this lithograph. Note how the scale of the grid grows continuously in a clockwise direction. And note especially what this trick entails: A hole in the middle. A mathematician would call this a singularity, a place where the fabric of the space no longer holds together. There is just no way to knit this bizarre space into a seamless whole, and Escher, rather than try to obscure it in some way, has put his trademark initials smack in the center of it.

The Logic of Space

By the “logic” of space we mean those spatial relations among physical objects which are necessary, and which when violated result in visual paradoxes, sometimes called optical illusions. All artists are concerned with the logic of space, and many have explored its rules quite deliberately. Picasso, for instance.

Cube With Ribbons; lithograph, 1957

Escher understood that the geometry of space determines its logic, and likewise the logic of space often determines its geometry. One of the features of the logic of space which he often applied is the play of light and shadow on concave and convex objects. In the lithograph Cube with Ribbons, the bumps on the bands are our visual clue to how they are intertwined with the cube. However, if we are to believe our eyes, then we cannot believe the ribbons!

Up and Down; lithograph, 1947

Another of Escher’s chief concerns was with perspective. In any perspective drawing, vanishing points are chosen which represent for the eye the “point(s) at inifinity.” It was the study of perspective and points at infinity by Alberti, Desargues, and others during the renaissance that led directly to the modern field of projective geometry.

Study for Up and Down

By introducing unusual vanishing points and forcing elements of a composition to obey them, Escher was able to render scenes in which the “up/down” and “left/right” orientations of its elements shift, depending on how the viewer’s eye takes it in. In his perspective study for High and Low, the artist has placed five vanishing points: top left and right, bottom left and right, and center. The result is that in the bottom half of the composition the viewer is looking up, but in the top half he or she is looking down. To emphasize what he has accomplished, Escher has made the top and bottom halves depictions of the same composition.

Penrose Triangle

A third type of “impossible drawing” relies on the brain’s insistence upon using visual clues to construct a three-dimensional object from a two-dimensional representation, and Escher created many works which address this type of anomaly.

Waterfall; lithograph, 1961

One of the most intriguing is based on an idea of the mathematician Roger Penrose’s—the impossible triangle. In this lithograph, Waterfall, two Penrose triangles have been combined into one impossible figure. One sees immediately one of the reasons the logic of space must preclude such a construction: the waterfall is a closed system, yet it turns the mill wheel continuously, like a perpetual motion machine, violating the law of conservation of energy. (Notice the intersecting cubes and octahedrons on the towers.)

Self-Reference

Our final consideration of Escher’s art involves its relationship to the fields of information science and artificial intelligence. This aspect of his work has been largely overlooked in previous studies, but the case for its importance to these fields was forcefully made by Douglas R. Hofstadter in his 1980 Pulitzer Prize winning book, Gödel, Escher, Bach: An Eternal Golden Braid.

Drawing Hands; lithograph, 1948

A central concept Escher captured is that of self-reference, which many believe lies near the heart of the enigma of consciousness—and the brain’s ability to process information in a way that no computer has yet mimicked successfully.

Fish and Scales; woodcut, 1959

The lithograph Drawing Hands and the woodcut Fish and Scales each captures this idea in a different way. In the former the self-reference is direct and conceptual; the hands draw themselves much the way that consciousness considers and constructs itself, mysteriously, with both self and self-reference inseparable and coequal. In Fish and Scales, on the other hand, the self-reference is more functional; one might rather call it self-resemblence. In this way the woodcut describes not only fish but all organisms, for although we are not built, at least physically, from small copies of ourselves, in an information-theoretic sense we are indeed built in just such a way, for every cell of our bodies carries the complete information describing the entire creature, in the form of DNA.

Three Spheres II; lithograph, 1946

On a deeper level, self-reference is found in the way our worlds of perception reflect and intersect one another. We are each like a character in a book who is reading his or her own story, or like a picture of a mirror reflecting its own landscape. Many of Escher’s works exhibit this theme of intersecting worlds, but we will here consider only one of the exemplars. As is common in Escher’s treatment of this idea, the lithograph Three Spheres II makes use of the reflective properties of a spherical mirror. Here, as Hofstatder noted, “every part of the world seems to contain, and be contained in, every other part….” The spheres relfect one another, the artist, the room in which he works, and the paper upon which he draws the spheres.

And so we end where we began, with a self portrait: the work a reflection of the artist, the artist reflected in his work.

Conclusion

We have here considered only a handful among the hundreds of drawings, lithographs, woodcuts, and mezzotints Escher left to us upon his death in 1972. Much more could be said, and has been said, about the depth, meaning, and importance of his work. The reader is encouraged to explore further the rich legacy of M.C. Escher, and to ponder anew the intersections he has drawn for us among the world of imagination, the world of mathematics, and the world of our waking life.

Google’s Artificial Brain Is Pumping Out Trippy—And Pricey—Art.

http://www.wired.com/2016/02/googles-artificial-intelligence-gets-first-art-show/#slide-3

On Friday evening, inside an old-movie-house-cum-art-gallery at the heart of San Francisco’s Mission district, Google graphics guru Blaise Agüera y Arcas delivered a speech to an audience of about eight hundred geek hipsters.

He spoke alongside a series of images projected onto the wall that once held a movie screen, and at one point, he showed off a nearly 500-year-old double portrait by German Renaissance painter Hans Holbein. The portrait includes a strangely distorted image of a human skull, and as Agüera y Arcas explained, it’s unlikely that Holbein painted this by hand. He almost certainly used mirrors or lenses to project the image of a skull onto a canvas before tracing its outline. “He was using state-of-the-art technologies,” Agüera y Arcas told his audience.

Neural networks are not only driving the Google search engine but spitting out art for which some people will pay serious money.

His point was that we’ve been using technology to create art for centuries—that the present isn’t all that different from the past. It was his way of introducing the gallery’s latest exhibit, in which every work is the product of artificial neural networks—networks of computer hardware and software that approximate the web of neurons in the human brain. Last year, researchers at Google created a new kind of art using neural nets, and this weekend, the tech giant put this machine-generated imagery on display in a two-day exhibit that raised roughly $84,000 for the Gray Area Foundation for the Arts, a San Francisco nonprofit devoted to the confluence of art and tech.

The night was one of those uniquely hip yet wonderfully geeky Silicon Valley scenes. “Look! There’s Clay Bavor, the head of Google’s suddenly enormous virtual reality project.” “There’s TechCrunch’s Josh Constine!” “And there’s MG Siegler, who used to write for TechCrunch but now, um, goes to neural network art shows. Or, at least, I think that’s him.” But it was also a night to reflect on the rapid and unceasing rise of artificial intelligence. Technology has now reached the point where neural networks are not only driving the Google search engine, but spitting out art for which some people will pay serious money.

For Agüera y Arcas, this is just a natural progression—part of the traditional that extends through Han Holbein and back to, well, the first art ever produced. For others, it’s a rather exciting novelty. “This is the first time I’ve seen art that works more like a science project,” said Alexander Lloyd, a regular patron of the Gray Area Foundation, after he spent a few thousand dollars on one piece of neural network art. But Friday’s show was also a reminder that we’re careening towards a new world where machines are more autonomous than they have ever been, where they do even more of the work, where they can transport us to places beyond even our own analog imaginations.

Deep (Learning) Dreams

Today, inside big online services like Google and Facebook and Twitter, neural networks automatically identify photos, recognize commands spoken in smartphones, and translate conversations from one language to another. If you feed enough photos of your uncle to a neural net, it can learn to recognize your uncle. That’s how Facebook identifies faces in all those photos you upload. Now, with an art “generator” it calls DeepDream, Google has turned these neural nets inside out. They’re not recognizing images. They’re creating them.

Google calls this “Inceptionism,” a nod to the 2010 Leonardo DiCaprio movie, Inception, that imagines a technology capable of inserting us into each other’s dreams. But that may not be the best analogy. What this tech is really doing is showing us the dreams of a machine.

What this tech is really doing is showing us the dreams of a machine.

To peer into the brain of DeepDream, you start by feeding it a photo or some other image. The neural net looks for familiar patterns in the image. It enhances those patterns. And then it repeat the process with the same image. “This creates a feedback loop: if a cloud looks a little bit like a bird, the network will make it look more like a bird,” Google said in a blog post when it first unveiled this project. “This in turn will make the network recognize the bird even more strongly on the next pass and so forth, until a highly detailed bird appears, seemingly out of nowhere.”

The result is both fascinating and a little disturbing. If you feed a photo of yourself into the neural net and it finds something that kinda looks like a dog in the lines of your faces, it turns that part of your face into a dog. “It’s almost like the neural net is hallucinating,” says Steven Hansen, who recently worked as an intern at Google’s DeepMind AI lab in London. “It sees dogs everywhere!” Or, if you feed the neural net an image of random noise, it may produce a tree or a tower or a whole city of towers. In that same noise, it might find the faint images of a pig and a snail, creating a rather frightening new creature by combining the two. Think: machines on LSD.

Virtually Art

Created by a Google engineer named Alexander Mordvintsev, this technique began as a way of better understanding the way neural networks behave. Though neural nets are enormously powerful, they’re still a bit of a mystery. We can’t completely grasp what goes on inside this web of hardware and software. Mordvintsev and others are still reaching for this understanding. But in the meantime, another Google engineer, Mike Tyka, seized on the technique as a way of creating art. Tyka works with neural networks at Google, but he’s also a sculptor. He saw the technique as a way of combining his two interests.

Artists like Tyka choose the images that get fed into the neural nets. And they can tune the neural nets to behave in certain ways. They may even re-train them to recognize new patterns, unleashing seemingly limitless possibilities. Some of this artwork looks quite similar, with their spirals and dogs and trees. But many pieces venture in their own directions, across bleaker and more mechanical landscapes.

Four of Tyka’s neural net creations were auctioned off on Friday. Castles in the Sky With Diamonds. Ground Still State of God’s Original Brigade. Carboniferous Fantasy. And The Babylon of the Blue Sun (see above). Across the gallery, the names matched the strange visual splendor of the images. And that’s not surprising. Joshua To, who curated the show, says that many of the titles were also chosen by neural networks, feeding off the images themselves. An NYU grad student named Ross Goodwin used this technique to generate the titles for Tyka’s work.

For Hansen, these auto-generated works aren’t a big leap from what we’ve had before. “I feels like an advanced version of PhotoShop,” he says. But at the very least, DeepDream serves a symbol for a much bigger change. Machines are doing so much more on their own. You see this, most notably, in the Google Search engine, where the rise of neural networks means that humans play less of a role—or, at least, humans are farther removed from the engine’s final decisions. It’s not just following rules that human engineers tell it to follow.

And that gap will only grow, not just in Google’s search engine but across so many other services and technologies. On Friday, at the edges of the gallery, Google invited visitors to strap on its Cardboard virtual reality headsets to venture even deeper into DeepDream. For now, Cardboard stops a little short of a true alternate universe. But the technology is rapidly improving. It’s no stretch to predict that on day, machines will create these virtual worlds largely on their own. Clay Bavor, Google’s head of VR, wasn’t just a guest as the exhibit. He was a sponsor of this weekend’s show and one of driving forces behind it. Joshua To also works on VR at Google. Yes, Hans Holbien used technology to make his art. But this is going somewhere else entirely.

Update: This story has been updated with the latest attendance and auction numbers from Google

Lectures on Aesthetics by G.W.F. Hegel – Part I

Lectures on Aesthetics
by G.W.F. Hegel
Part I
Of the Symbolic Form of Art
I. Of the Symbol in General

The symbol, in the sense which we here give to this term, constitutes, according to its very idea, as well as from the epoch of its appearance in history, the beginning of art. Thus it ought rather to be considered as the precursor of art. It belongs especially to the Orient, and will conduct us, by a multitude of transitions, transformations, and mediations, to the true realisation of the ideal under the classic form. We must then distinguish the symbol, properly speaking, as furnishing the type of all the conceptions or representations of art at this epoch, from that species of symbol which, on its own account, nothing more than a mere unsubstantial, outward form. Where the symbol presents itself under its appropriate and independent form, it exhibits in general the character of sublimnity. The idea, being vague and indeterminate, incapable of a free and measured development, cannot find in the real world any fixed form which perfectly corresponds to it; in default of which correspondence and proportion, it transcends infinitely its external manifestation. Such is the sublime style, which is rather the immeasurable than the true sublime?

We will first explain what should here be understood by the term symbol.

1. It is a sensuous object, which must not be taken in itself such as it presents itself immediately to us, but in more extended and more general sense. There are, then, in the symbol two terms to be distinguished: first, the meaning, and, secondly, the expression. The first is a conception of the mind; the second, a sensuous phenomenon, an image which address itself to the senses.

Thus the symbol is a sign, but it is distinguished from the signs of language in this: that between the image and the idea which it represents, there is a relation which is natural, not arbitrary or conventional. It is thus that the lion is the symbol of courage, the circle of eternity, the triangle of the trinity.

Still, the symbol does not represent the idea perfectly, but only from a single side. The lion is not merely courageous, the fox cunning. Whence it follows that the symbol, having many meanings, is equivocal. This ambiguity ceases only when the two terms are first conceived separately and then in combination; the symbol then gives place to comparison.

Thus conceived, the symbol, with its enigmatical and mysterious character, is peculiarly applicable to a whole epoch of history – to Oriental art and its extraordinary creations. It characterises that order of monuments and emblems by which the peoples of the Orient have sought to express their ideas, but have been able to do so only in an equivocal and obscure fashion. Instead of beauty and regularity, these works of art have a bizarre, grandiose, fantastic aspect.

When we find ourselves in this world of symbolic representations and images of ancient Persia, India, and Egypt, all seems strange to us. We feel that we are groping about in the midst of problems. These images do not entertain us of themselves. The spectacle neither pleases nor satisfies us in itself; we must pass beyond the sensuous form in order to penetrate its the more extended and more profound meaning. In other productions we see at the first glance that they have nothing serious; that, like the stories of children, they are a simple play of the imagination, which is pleased with accidental and particular associations. But these peoples, although in their infancy, demand a meaning and a truer and more substantial basis of ideas. This, indeed, is what we find among the Indians, the Egyptians, etc., although in these enigmatical figures the meaning may be often very difficult to divine. What part must it play amid this poverty and grossness of conceptions? How far, on the contrary, in the incapability of expressing by purer more beautiful forms the depth of religious ideas, is it proper to call in the fantastic and the grotesque to the aid of a representation of which the aspiration is not to remain beneath its object? This is a difficult point to decide.

The classic ideal, it is true, presents the same difficulty. Though the idea seized by the mind may here be lodged in an adequate form, the image, beyond this idea of which it serves as the expression, represents other and foreign ideas. Is it possible to see in these representations and these stories only absurd inventions which shock the religious sense – as the amours of Jupiter, etc.? Such stories being related of superior divinities, is it not very probable that they contain a wider and deeper meaning concealed? Whence two different opinions, the one of which regards mythology as a collection of fables unworthy of the idea of God; which present, it is true, much that is interesting and charming, but which cannot furnish a basis for a more serious interpretation. In the other, on the contrary, they pretend that a more general and more profound meaning resides in these fables. To penetrate beneath the veil with which they envelop their mysterious meanings is the task of those who devote themselves to the philosophic study of myths.

All mythology is then conceived as essentially symbolical. This would be to say that myths, as creations of the human spirit, however bizarre and grotesque they may appear, contain in themselves a meaning for the reason; general thoughts upon the divine nature — in a word, philosophemes.

From this point of view myths and traditions have their origin in the spirit of man, who can easily make a play of the representations of his gods, but seeks and finds in them also a higher interest, whenever he finds himself unable to set forth his ideas in a more suitable manner. Now, this is the true opinion. Thus, when reason finds again these forms in history, it realises the necessity of probing their meaning.

If, then, we penetrate to the source of these myths in order to discover there their concealed truth, yet without losing from view the accidental element which belongs to the imagination and to history, we are able thus to justify the different mythologies. And to justify man in the images and the representations which his spirit has created is a noble enterprise, far preferable to that which consists in particulars more or less insignificant.

Without doubt, priests and poets have never known under an abstract and general form the thoughts which constitute the basis of mythological representations, and it is not by design that they have been enveloped in a symbolical veil. But it does not follow that their representations cannot be symbols and ought not to be considered as such. Those peoples, at the time when they composed their myths, lived in a state altogether poetic; they expressed their most secret and most profound sentiments, not by abstract formulae, but by the imagination.

Thus the mythological fables contain a wholly rational basis, and more or less profound religious ideas.

Nor is it less correct to say that for every true work of art there serves as basis a universal thought which, afterward presented under an abstract form, must give the meaning of the work. The critical spirit, or the understanding, hastens on to the symbol or allegory. Here it separates image from signification, and thus destroys the art-form; to which, indeed, in respect of the symbolic explanation which only brings out the universal as such, no importance attaches.

2. But this mode of extending the symbol to the entire domain of mythology is by no means the method which we are here to pursue. Our aim is not to discover to what point the representations of art have had a symbolic or allegorical meaning.

On the contrary, we have to inquire how far the symbol, properly speaking, extends as a special form of art, while still preserving its appropriate character, and thereby we shall distinguish it in particular from the two other forms, Classic and Romantic.

Now, the symbol, in the special sense which we attach to this term, ceases where free subjectivity (personality), taking the place of vague and indeterminate conceptions, constitutes the basis of representation in art. Such is the character which the Greek gods present us. Greek art represents them as free individuals, independent in themselves; genuine moral persons. Hence we cannot consider them from the symbolic point of view. The acts, for example, of Jupiter, of Apollo, of Minerva, belong only to these divinities themselves; represent only their power and their passions. Should we abstract from these free individualities a general idea and set it up as an explanation, we should abandon and destroy in these figures just that which corresponds to the idea of art. Whence artists have never been satisfied with these symbolic or allegorical explanations applied to works of art and to mythology. If there remains a place for allegory or the symbol, it is in the accessories, in simple attributes, signs — as the eagle by the side of Jupiter, the ox by the side of St. Luke; while the Egyptians saw in the bull Apis a divinity itself.

The difficult point in our investigation is to distinguish whether what are represented as personages in mythology or art possess a real individuality or personality, or whether they contain but the empty semblance of it, and are only mere personifications. This is what constitutes the real problem of the limitation of Symbolic Art.

What interests us here is that we are present at the very origin of art. At the same time we shall observe the progressive advancement of the symbol, the stages by which it proceeds toward genuine art. Whatever may he the narrow line which unites religion and art, we have here to consider the symbol solely from the artistic point of view. We abandon to the history of mythology itself the religious side.

DIVISION. — Many degrees are to be noted in the development of this form of art in the Orient.

But first we must mark its origin. This, which is, blended with that of art in general, can be explained in the following manner:

The sentiment of art like the religious sentiment, like scientific curiosity, is born of wonder; the man who wonders at nothing lives in a state of imbecility and stupidity. This state ceases when his spirit, disengaging itself from matter and from physical necessities, is struck by the phenomena of nature, and seeks their meaning; when he is impressed by in them grand and mysterious, a concealed power which reveals itself.

Then he experiences also the need of representing this internal sentiment of a general and universal power. Particular objects – the elements, the sea, the waves, the mountains — lose their immediate meaning and become for the spirit images of this invisible power.

It is then that art appears. It is born of the necessity of representing this idea by sensuous images, which address themselves at once to the senses and to the mind.

In religions, the idea of an absolute power is at first manifested by the worship of physical objects. The divinity is identified with nature itself; but this gross worship cannot last. Instead of seeing the absolute in real objects, man conceives it as a distinct and universal being; he seizes, though very imperfectly, the relation which unites the invisible principle to the objects of nature; he fashions an image, a symbol destined to represent it. Art is then the interpreter of religious ideas.

Such, in its origin, is art, and with it the Symbolic Form is born.

We will attempt, by a precise division, to trace exactly the circle in which the symbol moves.

That which characterises, in general, Symbolic Art is that it vainly endeavours to find pure conception and a mode of representation which is suitable to them. It is a conflict between matter and form; both imperfect and heterogeneous. Whence the incessant strife between the two elements of art, which seek, uselessly, to place themselves in harmony. The degrees of its development present successive phases or modes of this conflict.

1. At the beginning of art this conflict does not yet exist. The point of departure, at least, is a still undivided unity, in the center of which ferments the discord between the two principles. Here, then, the creations of art, little distinguished from objects of nature, are still, scarcely symbols.

2. The termination of this epoch is the disappearance of the symbol, which takes place by the reflective separation of the two terms, the idea being clearly conceived; the image, on its side, being perceived as distinct from the idea. From their reconciliation (rapprochement) is born the reflective symbol or comparison, the allegory, etc.

The two extreme points being thus fixed, we may now see, in what follows, the intermediary points or degrees. The general division is this:

I. The true symbol is the unconscious, irreflective symbol, the forms of which appear to us in Oriental civilisation.

II. Then follows, as a mixed form, or form of transition, the reflective symbol, of which the basis is comparison, and which marks the close of this epoch.

We have, then, to follow each of these two forms in the successive stages of its development; to mark its steps in the career which it has passed through in the Orient before arriving at the Greek ideal.

Lectures on Aesthetics by G.W.F. Hegel – Part II

Lectures on Aesthetics
by G.W.F. Hegel
Part II
Of the Ideal of Classic Art

I. The Classic Ideal

1. The ideal as free creation of the imagination of the artist.- 2. The new gods of Classic Art.- 3. External character of the representation.
1. The ideal as free creation of the imagination of the artist

1. As the ideal of Classic Art comes to be realised only by the transformation of preceding elements, the first point to develop consists in making manifest that it is truly sprung from the creative activity of the spirit; that it has found its origin in the inmost and most personal thought of the poet and of the artist.

This seems contradicted by the fact that Greek mythology rests upon ancient traditions, and is related to the religious doctrines of the peoples of the Orient. If we admit all these foreign elements — Asiatic, Pelasgic, Dodonian, Indian, Egyptian, Orphic — how can we say that Hesiod and Homer gave to the Greek gods their names and their form? But these two things — tradition and poetic invention — may he very easily be reconciled. (Tradition furnishes the materials, but it does not bring with it the precise idea and the form which each god is to represent. This idea these great poets drew from their genius, and they also discovered the actual forms appropriate to it. Thus were they the creators of the mythology which we admire in Greek art. The Greek gods are for this reason neither poetic invention nor an artificial creation. They have their root in the spirit and the beliefs of the Greek people — in the very foundation of the national religion; these are the absolute forces and powers, whatever is most elevated in the Greek imagination, inspired in the poet by the muse herself.

With this faculty of free creation, the artist, we have already seen, takes a position altogether different from that which he had in the Orient. The Indian poets and sages have, also, for their point of departure the primitive data, consisting of the elements of nature — the sky, animals, the rivers or the abstract conception of Brahma; but their inspiration is the annihilation of personality. Their spirit loses itself in wishing to represent ideas so foreign to their inner nature, while the imagination, in the absence of rule and of measure, incapable of directing itself, allows itself to wander in the midst of conceptions which have neither the character of freedom nor that of beauty. It is like an architect obliged to accommodate himself to an unequal soil, upon which rise old debris, walls half destroyed, hillocks and rocks; forced, besides to subordinate his plans to particular ends. He can erect only irregular structures which must be wholly irrational and fantastic. Such is not the work of a free imagination, creating according to its own inspirations.

In classic Art the artists and poets are also prophets and teachers; but their inspiration is personal.

a. At first that which constitutes the essence of their gods is neither a nature foreign to spirit, nor the conception of a single god who admits of no sensuous representation and remains invisible. They borrow their ideas from the human heart, from human life. Thus man recognises himself in these creations, for what he produces outwardly is the most beautiful manifestation of himself.

b. They are on this account only the more truly poets. They fashion at their will the matter and the idea so as to draw from them figures free and original. All these heterogeneous or foreign elements they cast into the crucible of their imagination; but they do not form therein a bizarre mixture which suggests the cauldron of the magician. Everything that is confused, material, impure, gross, disordered, is consumed in the flame of the their genius. Whence springs a pure and beautiful creation wherein the materials of which it has. been formed are scarcely perceptible. In this respect their task consists in despoiling tradition of everything gross, symbolic, ugly, and deformed, and afterward bringing to light the precise idea which they wish to individualise and to represent under an appropriate form. This form is the human form, and it is not employed here as a simple personification of the acts and accidents of life; it appears as the sole reality which corresponds to the idea. True, the artist also finds his image in the real world; but he must remove whatever of accidental or inappropriate they present before they can express the spiritual element of human nature, which, seized in its essence should represent the everlasting might of the gods. Such is the free, though not arbitrary, manner in which the artist proceeds in the production of his works.

c. As the gods take an active part in human affairs, the task of the poet consists in acknowledging therein their presence and their activity, as well as in signalizing whatever is remarkable in natural events, in human deeds, and in fact in all in which the divine powers appear to be involved. Thus the poet fulfils in part the role of priest, as well as that of prophet. We moderns, with our prosaic reason, explain physical phenomena by universal laws and forces; human actions, by personal wills. The Greek poets, on the contrary, saw, above all these phenomena, their divine author. In representing human acts as divine acts, they showed the diverse aspects under which the gods reveal their power. Thus a great number of these divine manifestations are only human acts, when such or such divinity intervenes. If we open the poems of Homer, we find there scarcely any important event which may not be explained by the will or the direct influence of the gods. Such interpretations belong to the mode of seeing, to the faith born the imagination of the poet. Thus, Homer often expresses them in his own name, and places them only in part in the mouth of his personages, whether priests or heroes. Thus it is at the beginning of the Iliad, he has explained the pestilence by the wrath of Apollo; further on he will cause it to be he predicted by Calchas. It is the same with the recital of the story of the death of Achilles, in the last canto of the Odyssey. The shades of the loves conducted by Hermes to the meadows where blooms the asphodel, there encounter Achilles and other heroes who have battled on the Trojan plain. Agamemnon himself relates to them the death of the young hero: “The Greeks had fought all day; when Jupiter had separated the two armies, they bore the noble body upon vessels and embalmed it, shedding tears. Then they heard coming from above a divine sound, and the Achaians, alarmed, would have rushed to their ships had not an old man, in whom years had ripened experience, arrested them.” He explained to them the phenomenon, by saying: “It is the mother of the hero who comes from the depth of the ocean, with the immortal goddesses of the sea, to receive the body of her son.” At these words fear abandoned the sage Achaians. From that moment, indeed there was no longer anything in it strange to them. Something human, a mother, the sorrowful mother of the hero, came before them; Achilles is her son, she mingles her moans with theirs. Afterward Agamemnon, turning to Achilles, continues to describe the general grief: “About thee gathered the daughters of old ocean, uttering cries of grief. They spread over thee vestments, perfumed with ambrosia. The muses also, the nine sisters, caused to be heard, each in her turn, a beautiful’ song of mourning; and there was not then an Argive there who could restrain his tears, so greatly had the song of the muses melted all hearts.”
2. The new gods of Classic Art

Still, of what nature are the creations which Classic Art produces in following such a method? What are the characteristics of the new gods of Greek art?

a. The most general idea that we should form of them is that of a concentrated individuality, which, freed from the multiplicity of accidents, actions, and particular circumstances of human life, is collected upon itself at the focus of its simple unity. Indeed, what we must first remark is their spiritual and, at the same time, immutable and substantial individuality. Far removed from the world of change and illusion, where want and misery reign, far from the agitation and trouble which attach to the pursuit of human interests, retired within themselves they rest upon their own universality as upon an everlasting foundation where they find their repose and felicity. By this alone the gods appear as imperishable powers, of which the changeless majesty rises above particular existence. Disengaged from all contact with whatever is foreign or external, they manifest themselves uniquely in their immutable and absolute independence.

Yet, above all, these are not simple abstraction — mere spiritual generalities — they are genuine individuals. With this claim each appears as an ideal which possesses in itself reality, life; it has, like spirit, a clearly defined nature, a character. Without character there can be no true individuality. In this respect as we have seen above, the spiritual gods contain, as integrant part of themselves, a definite physical power, with which is established an equally definite moral principle, which assigns to each divinity a limited circle in which his outward activity must be displayed. The attributes, the specific qualities which result therefrom, constitute the distinctive character of each divinity.

Still, in the ideal proper, this definite character must not be limited to the point of exclusive being; it must maintain itself in a just medium, and must return to universality, which is the essence Of the divine nature. Thus each god, in so far as he is at once a particular individuality and a general existence, is also, at the same time, both part and whole. He floats in a just medium between pure generality and simple particularity. This is what gives to the true ideal of classic Art its security and infinite calm, together with a freedom relieved from every obstacle.

b. But, as constituting beauty in Classic Art, the special character of the gods is not purely spiritual; it is disclosed so much the more under an external and corporeal form which addresses itself to the eyes as well as to the spirit. This, we have seen, no longer admits the symbolic element, and should not even pretend to affect the Sublime. Classic beauty causes spiritual individuality to enter into the bosom of sensuous reality. It is born of a harmonious fusion of the outward form with the inward principle which animates. Whence, for this very reason, the physical form, as well as the spiritual principle, must appear enfranchised from all the accidents which belong to outer existence, from all dependence upon nature, from the miseries inseparable from the finite and transitory world. It must be so purified and ennobled that, between the qualities appropriate to the particular character of the god and the general forms of the human body, there shall be manifest a free accord, a perfect harmony. Every mark of weakness and of dependence has disappeared; all arbitrary particularity which could mar it is cancelled or effaced. In its unblemished purity it corresponds to the spiritual principle of which it should be the incarnation.

c. Notwithstanding their particular character the gods preserve also their universal and absolute character. Independence must be revealed, in their representation, under the appearance of calmness and of a changeless serenity. Thus we see, in the figures of the gods that nobility and that elevation which announces in them that, though clothed in a natural and sensuous form, they have nothing in common with the necessities of finite existence. Absolute existence, if it were pure, freed all particularity, would conduct to the sublime but, in the Classic ideal, spirit realises and manifests itself under a sensuous form which is its perfect image, and whatever of sublimnity it has shown to be grounded in its beauty, and as having passed wholly into itself. This is what renders necessary, for the representation of the gods, the classic expression of grandeur and beautiful sublimnity.

In their beauty they appear, then, elevated above their own corporeal existence; but there is manifest a disagreement between the happy grandeur which resides in their spirituality and their beauty, which is external and corporeal. Spirit appears to be entirely absorbed in the sensuous and yet at the same time, aside form this, to be merged in itself alone; it is, as it were, the moving presence of a deathless god in the midst of mortal men.

Thus, although this contradiction does not appear as a manifest opposition, the harmonious totality conceals in its individual unity a principle of destruction which is found there already expressed. This is that sigh of sadness in the midst of grandeur which men full of sagacity have felt in the presence of the images of the ancient gods, notwithstanding their perfect beauty and the charm shed around them. In their calmness and their serenity they cannot permit themselves to indulge in pleasure, in enjoyment nor in what we especially term satisfaction. The eternal calm must not even extend so far as to admit of a smile nor the pleasing contentment with itself. Satisfaction, properly speaking, is the sentiment which is born of the perfect accord of our soul with its present situation. Napoleon, for example, never expressed his satisfaction more profoundly than when he had attained to something with which all the world was dissatisfied; for true satisfaction is nothing else than the inner approbation which the individual gives himself because of his own acts and personal effort. Its last degree is that commonplace feeling (bourgeois sentiment, Philisterempfindung) of contentment which every man can experience. Now, this sentiment and this expression cannot be granted to the immortal gods of Classic Art.

It is this character of universality in the Greek gods which people have intended to indicate by characterising them as cold. Nevertheless, these figures are cold only in relation to the vivacity of modern sentiment; in themselves they have warmth and life. The divine peace which is reflected in the corporeal form comes from the fact that they are separated from the finite; it is born of their indifference to all that is mortal and transitory. It is an adieu without sadness and without effort, but an adieu to the earth and to this perishable world. In these divine existences the greater the degree in which seriousness and freedom are outwardly manifested, the more distinctly are we made to feel the contrast between their grandeur and their corporeal form. These happy divinities deprecate at once both their felicity and their physical existence. We read their lineaments the destiny which weighs upon their heads, and which, in the measure that its power increases (causing this contradiction between moral grandeur and sensuous reality to become more and more pronounced), draws Classic Art onto its ruin.
3. External character of the representation

If we ask what is the outer mode of manifestation suitable to Classic Art, it needs only to repeat what has already been said: In the Classic ideal, properly speaking, the spiritual individuality of the gods is represented, not in situations where they enter into relation one with another, and which might occasion strife and conflicts, but in their eternal repose, in their independence, freed as they are from all aspects of pain and suffering — in a word, in their divine calmness and peace. Their determinate character is not developed so as to excite in them very lively sentiments and violent passions, or to force them to pursue particular interests. Freed from all collision, they are delivered from all embarrassment, exempt from all care. This perfect calm (wherein appears nothing void, cold, inanimate, but which is full of life and sensibility), although unalterable, is to the gods of Classic Art the most appropriate form of representation. If, then, they take part in the attainment of particular ends, the acts in which they engage must not be of a nature to engender collisions. Free from offence on their own part, their felicity must not be troubled by these conflicts. Among the arts it is, therefore, Sculpture which more than the others represents the classic idea with that absolute independence wherein the divine nature preserves its universality united with the particular character. It is, above all, Ancient Sculpture, of a severer taste, which is strongly attached to this ideal side. Later it was allowed to be applied to the representation of situations and characters of a dramatic vitality. Poetry, which causes the gods to act, draws them into strife and conflicts. Otherwise, the calm of the plastic, when it remains in its true domain, is alone capable of expressing the contrast between the greatness of spirit and its finite existence with that seriousness of sadness to which we have already referred.

Lectures on Aesthetics by G.W.F. Hegel – Part III

Lectures on Aesthetics
by G.W.F. Hegel
Part III
Of the Romantic Form of Art
Introduction — of the Romantic in General

1. Principle of inner subjectivity — 2. Of the ideas and forms which constitute the basis of Romantic Art. — 3. Of the special mode of representation.

As in the preceding parts of our investigation, so now in Romantic Art, the form is determined by the inner idea of the content or substance which this art is called upon to represent. We must, therefore, in the next place, attempt to make clear the characteristic principle of the new content which, in this new epoch of the development of human thought is revealed to consciousness as the absolute essence of truth, and which appears in its appropriate form of art.

At the very origin of art there existed the tendency of the imagination to struggle upward out of nature into spirituality. But, as yet, the struggle consisted in nothing more than a yearning of the spirit, and, insofar as this failed to furnish a precise content for art, art could really be of service only in providing external forms for mere natural significations, or impersonal abstractions of the substantial inner principle which constitutes the central point of the world.

In Classic Art, however, we find quite the contrary. Here spirituality, though it is now for the first time able to struggle into conscious existence through the cancellation or setting aside of mere natural significations, it is nevertheless the basis and principle of the content; it is a natural phenomenon inseparable from the corporeal and sensuous. It is an external form. This form however, does not, as in the first epoch, remain indefinite, unpervaded by spirit. On the contrary, the perfection of art is here reached in the very fact that the spiritual completely pervades its outer manifestation, that it idealizes the natural in this beautiful union with it, and rises to the measure of the reality of spirit in its substantial individuality. It is thus that Classic Art constituted the absolutely perfect representation of the ideal, the final completion of the realm of Beauty. There neither is nor can there ever be anything more beautiful.

But there exists something still more elevated than the simply beautiful manifestation of spirit in its immediate sensuous form, even though this form be fashioned by spirit as adequate to itself. For this very union of matter and form, which is thus accomplished in the element of the external, and which thus lifts sensuous reality to an adequate existence, nonetheless contradicts the true conception of spirit which is thus forced out of its reconciliation with the corporeal, back upon itself, and compelled to find its own true reconciliation within itself. The simple, pure totality of the ideal (as found in the Classic) dissolves and falls asunder into the double totality of self-existent subjective substance on the one side, and external manifestation on the other, in order that, through this separation, spirit may arrive at a deeper reconciliation in its own element of the inner or purely spiritual. The very essence of spirit is conformity with itself (self-identity), the oneness of its idea with the realisation of the same. It is, then, only in its own world, the spiritual or inner world of the soul, that spirit can find a reality (Dasein) which corresponds to spirit. It is, thus in consciousness that spirit comes to possess its other, its existence, as spirit, with and in itself, and so for the first time to enjoy its infinitude and its freedom.

Spirit thus rises to itself or attains to self-consciousness, and by this means finds within itself its own objectivity, which it was previously compelled to seek in the outer and sensuous forms of material existence. Henceforth it perceives and knows itself in this its unity with itself; and it is precisely this clear self-consciousness of spirit that constitutes the fundamental principle of Romantic Art. But the necessary consequence is that in this last stage of the development of art the beauty of the Classic ideal, which is beauty under its most perfect form and in its purest essence, can no longer be deemed a finality; for spirit now knows that its true nature is not to brought into a corporeal form. It comprehends that it belongs to its essence to abandon this external reality in order to return upon itself, and expressly posits or assumes outer reality to be an existence incapable of fully representing spirit. But if this new content proposes to render itself beautiful, still it is evident that beauty, in the sense in which we have thus far considered it, remains for this content something inferior and subordinate, and develops into the spiritual beauty of the essentially internal — into the beauty of that spiritual subjectivity or personality which is in itself (i.e., potentially) infinite.

But in order that spirit may thus realise its infinite nature it is so much the more necessary that it should rise above mere natural and finite personality in order to reach the height of the Absolute. In other terms, the human soul must bring itself into actual existence as a person (Subjekt) possessing self consciousness and rational will; and this it accomplishes through becoming itself pervaded with the absolutely substantial. On the other hand, the substantial, the true, must not be understood as located outside of humanity, nor must the anthropomorphism of Greek thought be swept away. Rather the human as actual subjectivity or personality must become the principle, and thus, as we have already seen, anthropomorphism for the first time attains to its ultimate fullness and perfection.

II. From the particular elements which are involved in this fundamental principle we have now in general to develop the circle of objects, as well as the form, whose changed aspect is conditioned by the new content of Romantic Art.

The true content of Romantic thought, then, is absolute internality, the adequate and appropriate form of which is spiritual subjectivity, or conscious personality, as comprehension of its own independence and freedom. Now that which is in itself infinite and wholly universal is absolute negativity of all that is finite and particular. It is the simple unity with self which has destroyed all mutually exclusive objects, all processes of nature, with their circle of genesis, decay, and renewal which, in short, has put an end to all limitation of spiritual existence, and dissolved all particular divinities into itself. In this pantheon all the gods are dethroned. The flame of subjectivity has consumed them. In place of plastic polytheism, art now knows but one God, one Spirit, one absolute independence, which, as absolute knowing and determining, abides in free unity with itself, and no longer falls asunder into those special characters and functions whose sole bond of unity was the constraint of a mysterious necessity. Absolute subjectivity, or personality as such, however, would escape from art and be accessible only to abstract thought, if, in order to be an actual subjectivity commensurate with its idea, it did not pass into external existence, and again collect itself out of this reality into itself. Now, this element of actuality belongs to the Absolute, for the product of the activity of the Absolute as infinite negativity is the Absolute itself, as simple self-unity of knowing, and, therefore, as immediacy. Yet, as regards this immediate existence, which is grounded in the Absolute itself, it does not manifest itself as the one jealous God who dissolves the natural, together with finite human existence, without bringing itself into manifestation as actual divine personality, but the true Absolute reveals itself (schliesst sich auf), and thus presents a phase which art is able to comprehend and represent.

But the external existence (Dasein) of God is not the natural and sensuous, as such, but the sensuous elevated to the supersensuous, to spiritual subjectivity, to personality, which, instead of losing the certainty of itself in its outer manifestation, truly for the first time attains to the present actual certainty of itself through its own reality. God in His truth is, therefore, no mere ideal created by the imagination. Rather, He places Himself in the midst of the finitude and outer accidentality of immediate existence, and yet knows Himself in all this as the divine principle (Subjekt) which in itself remains infinite and creates for itself this infinitude. Since, therefore, actual subject or person is the manifestation of God, art now acquires the higher right of employing the human form, together with the modes and conditions of externality generally, for the expression of the Absolute. Nevertheless, the new problem for art can consist only in this: that in this form the inner shall not be submerged in outer corporeal existence, but shall, on the contrary, return into itself in order to bring into view the spiritual consciousness of God in the individual (Subekt). The various moments or elements brought to light by the totality of this view of the world as totality of the truth itself therefore, now find their manifestation in man. And this, in the sense that neither nature as such — as the sun, the sky, the stars, etc. — gives the content and the form, nor does the circle of the divinities of the Greek world of beauty, nor the heroes, nor external deeds in the province of the morality of the family and of political life, attain to infinite value. Rather it is the actual, individual subject or person who acquires this value, since it is in him alone that the eternal moments or elements of absolute truth, which exist actually only as spirit, are multifariously individualised and at the same time reduced to a consistent and abiding unity.

If now we compare these characteristics of Romantic Art with the task of classic Art in its perfect fulfilment in Greek Sculpture, we see that the plastic forms of the gods do not express the movement and activity of spirit which has gone out of its corporeality into itself, and has become pervaded by internal independent-being (Fursichsein). The changeable and accidental phases of empirical individuality are indeed in those lofty images of the gods, but what is lacking in them is the actuality of self-existent personality, the essential characteristic of which is self-knowledge and independent will.

Externally this defect betrays itself in the fact that in the representations of sculpture the expression of the soul simply as soul — namely, the light of the eye — is wanting. The sublimest works of sculptured art are sightless. Their subtle inner being does not beam forth from them, as a self-knowing in that spiritual concentration of which the eye gives intelligence. The ray of the spirit comes from beyond and meets nothing which gives it a response; it belongs alone to the spectator, who cannot contemplate the forms, so to speak, soul in soul, eye in eye. The god of Romantic Art, on the contrary, makes his appearance as a god who sees, who knows himself, who seizes himself in his own inner personality, and who opens the recesses of his nature to the contemplation of the conscious spirit of man. For infinite negativity, the self return of the spiritual into itself, cancels this outflow into the corporeal. Subjectivity is spiritual light which shines into itself, into its hitherto dark realm; and while natural light can shine upon an object, this spiritual light is itself its own ground and object on which it shines and which it recognises as being one and the same with itself. But since now the absolute inner or spiritual manifests itself, in its actual outer existence, under the human form, and since the human stands in relation to the entire world, there is thus inseparably joined to this manifestation of the Absolute a vast multiplicity of objects belonging not only to the spiritual and subjective world, but to the corporeal and objective, and to which the spirit bears relation as to its own.

The thus constituted actuality of absolute subjectivity can have the following forms of content and of manifestation:

1. Our first point of departure we must take from the Absolute itself, which, as actual spirit, gives itself an outer existence (Dasein), knows itself and is self-active. Here the human form is so represented that it is recognised at once as having the divine within itself. Man appears, not as man in mere human character, in the constraint of passion, in finite aims and achievements, nor as in the mere consciousness of God, but is the self-knowing one and universal God Himself, in whose life and suffering, birth, death, and resurrection, is now made manifest, also, for the finite consciousness, what spirit, what the eternal and infinite, is in truth. This content Romantic Art sets forth in the history of Christ, of His mother, of His disciples, and even in the history of all those in whom the Holy Spirit is actual, in whom the entire divine nature is present. For in so far as it is God, who, though in Himself universal, still appears in human form, this reality is, nevertheless, not limited to particular immediate existence in the form of Christ, but unfolds itself in all humanity in which the Divine Spirit becomes ever present, and in this actuality remains one with itself. The spreading abroad [in humanity] of this self-contemplation, of this independent and self-sufficing existence (In-sich-und-bei-sich-sein) of the spirit, is the peace, the reconciliation of the spirit with itself in its objectivity. It constitutes a divine world — a kingdom of God-in which the Divine, from the center outward, possesses the reconciliation of its reality with its idea, completes itself in this reconciliation, and thus attains to independent existence.

2. But however fully this identification may seem to be grounded in the essence of the Absolute itself, still, as spiritual freedom and infinitude, it is by no means a reconciliation which is immediate and ready at hand, from the center outward, in mundane, natural, and spiritual actuality. On the contrary, it attains to completeness only as the elevation of the spirit out of the finitude of its immediate or unrealised existence to its truth, its realised existence. As a consequence of this, the spirit, in order to secure its totality and freedom, separates itself from itself — that is, establishes the distinction between itself, as, on the one hand, a being belonging in part to the realm of nature, in part to that of spirit, but limited in both; and as, on the other hand, a being which is in itself (i.e., potentially) infinite. But with this separation, again, is closely joined the necessity of escaping out of the estrangement from self — in which the finite and natural, the immediacy of existence, the natural heart, is characterised as the negative, the evil, the base and of entering into the kingdom of truth and contentment by the sole means of subjugating this nugatoriness. Thus, spiritual reconciliation is to be conceived and represented only as an activity, a movement of the spirit — as a process in the course of which there arises a struggle, a conflict; and the pain, the death, the agony of nothingness, the torment of the spirit and of materiality (Leiblichkeit) make their appearance as essential moments or elements. For as, in the next place, God separates or distinguishes (ausscheidet) finite actuality from Himself, so also finite man, who begins with himself as outside the divine kingdom, assumes the task of elevating himself to God, of freeing himself from the finite, of doing away with nugatoriness, and of becoming, through this sacrifice (Ertoedten) of his immediate actuality, that which God, in His appearance as man, has made objective as true actuality. The infinite pain attendant upon this Sacrifice of the individual’s own subjectivity or personality, the suffering and death which were more or less excluded from the representations of Classic Art — or, rather, which appeared there only as natural suffering — attain to the rank of real necessity for the first time in Romantic Art.

It cannot be said that among the Greeks death was comprehended in its essential significance. Neither the natural, as such, nor the immediacy of the spirit in its unity with materiality, appeared to them as anything in itself negative, and to them, therefore, death was only an abstract transition, inspiring neither terror nor fear. It was a cessation with which there were associated no further and immeasurable consequences for the dying. But when personality (Subjektivität) in its spiritual self-centred being comes to be of infinite importance, then the negation which death bears within itself is a negation of this so significant and valuable self, and hence becomes fearful. It is a death of the soul, which thus, as utterly and completely negative, is excluded forever from all happiness, is absolutely miserable, and may find itself given up to eternal damnation. Greek individuality, on the contrary did not ascribe to itself this value considered as spiritual personality and hence ventured to surround death with bright images; for man fears only for that which is to him of great worth. But life has this infinite value for consciousness only when the person, as spiritual and self-conscious, is the sole actuality, and must now, in well grounded fear, conceive himself as rendered (gesetzt) negative through death. On the other hand however, death does not acquire for Classic Art that affirmative signification to which it attains in Romantic Art. That which we call immortality did not attain to the dignity of a serious conception with the Greeks. It is for the later reflection of the subjective consciousness, with Socrates, that immortality for the first time acquires a deeper meaning and satisfies a more advanced requirement. For example Odyssey. XI., v. 482-491), Ulysses in the under world congratulated Achilles as being happier than all others before or after him, because he had formerly been honoured as the gods, and now was a ruler among the dead. Achilles, as we know, railed at this happiness, and answered that Ulysses should not utter a word of consolation respecting the dead. Rather would he be a servant of the fields, and poor himself, serve a poor man for a pittance, than lord it here over all the vanished dead. On the contrary, in Romantic Art death is only an extinction of the natural soul and of the finite personality; an extinction which operates only against what is in itself negative; which cancels the nugatory, and thus not only brings about the deliverance of the spirit from its finitude and state of inner division, but also secures the spiritual reconciliation of the actual person (des Subjekts) with the absolute or ideal Person. For the Greeks, that life alone was affirmative which was united with natural, outer, material existence; and death, therefore, was the mere negation, the dissolution, of immediate actuality. But in the Romantic conception of the world it has the significance of absolute negativity — that is, the negation of the negative; and, therefore, as the rising of the spirit out of its mere naturalness and inadequate finitude, turns out to be just as much affirmative as negative. The pain and death of expiring personality (Subjektivität) is reversed into a return to self; into contentment and happiness; into that reconciled affirmative existence which the Spirit can with difficulty secure only through the destruction of its negative existence, in which, so long as it remains, it is separated from its own truth and vitality. This fundamental characteristic, therefore, not only relates to that form of death which approaches man from the natural side, but it is also a process which the spirit, in order that it may truly live, complete within itself independent of this external negation.

3. The third side of this absolute world of the spirit has its representative in man, in so far as he neither immediately, in himself, brings the absolute and divine, as divine, into manifestation, nor represents the process of elevation to God, and reconciliation with God, but remains within the limits of his own human circle. Here, too, the finite, as such, constitutes the absolute as well from the side of the external affairs of nature and its realm, together with the most restricted phenomena belonging thereto. For the mode of apprehending this content a two fold attitude presents itself. On the one hand, spirit -because it has acquired affirmation with itself — announces itself upon this ground as a self-justified and satisfying element, which it only puts forth (herauskert) this positive character and permits itself in its affirmative satisfaction and internality to reflect itself therefrom. On the other hand, this content is reduced to mere accidentality, which can lay claim to no independent validity. For in it spirit does not find its own true being, and therefore can arrive at unity in no other way than by itself, since for itself it dissolves as finite and negative this finite character of spirit and of nature.

III. We have now, finally, to consider somewhat more at length the significance of the relation of this entire content to the mode of its representation.

1. The material of Romantic Art, at least with reference to the divine, is extremely limited. For, in the first place, as we have already pointed out, nature is deprived of its divine attributes; sea, mountain, and valley, streams, springs, time, and night, as well as the universal process of nature, have all lost their true value with respect to the representation and content of the Absolute. The images of nature are no longer set forth symbolically. They are stripped of the characteristic which rendered their forms and activities appropriate as traits of divinity. For all the great questions concerning the origin of the world — concerning the whence, the whither, the wherefore of created nature and humanity, together with all the symbolic and plastic attempts to solve and to represent these problems have vanished in consequence of the revelation of God in the spirit; and even the gay, thousand-hued earth, with all its classically-figured characters, deeds, and events, is swallowed up in spirit, condensed in the single luminous point of the Absolute and its eternal process of Redemption (Erloessungs-geschichte). The entire content, therefore, is thus concentrated upon the internality of the spirit — upon the perception, the imagination and the soul-which strives after unity with the truth — and seeks and struggles to produce and to retain the divine in the individual (Subjekt). Thus, though the soul is still destined to pass through the world, it no longer pursues merely worldly aims and undertakings. Rather it has for its essential purpose and endeavour the inner struggle of man with himself, and his reconciliation with God, and brings into representation only personality and its conservation, together with appliances for the accomplishment of this end. The heroism which can here make its appearance is by no means a heroism which makes its own law, establishes regulations, creates and transforms conditions, but a heroism of submission, for which everything is settled and determined beforehand, and to which there thenceforth remains only the task of regulating temporal affairs according to it, of applying to the existing world that higher principle which has validity in and for itself, and, finally, of rendering it practically valuable in the affairs of everyday life. But since now this absolute content appears to he concentrated in the spaceless, subjective soul, and thus each and every process comes to he transferred to the inner life of man, the circle of this content is thus again infinitely extended. It develops into so much the more unrestrained manifoldness. For though the objective process (of history) to which we have referred does not itself include the substantial character of the soul, still the individual, as subject, penetrates that process from every side, brings to light every point therein, or presents itself in ever newly developed human inclinations, and is, besides, still able to absorb into itself the whole extent of nature, as mere environment and locality of the spirit, and to assign to it an important purpose. Thus the life (Geschichte) of the soul comes to be infinitely rich, and can adapt itself in the most manifold ways to ever changing circumstances and situations. And if now, for the first time, man steps out of this absolute circle and mingles in worldly affairs, by so much the more immeasurable will be the sphere (Umfang) of interests, aims, and inclinations; as the spirit, in accordance with this principle, has become more profound, and has, therefore, unfolded itself in its development to its infinitely enhanced fullness of inner and outer collisions, distractions. progressive stages of passion, and to the most varied degrees of satisfaction. Though the Absolute is in itself completely universal, still, as it makes itself known in mankind especially, it constitutes the inner content of Romantic Art, and thus, indeed, all humanity, with its entire development, forms the immeasurable and legitimate material of that art.

2. It may be, indeed, that Romantic Art, as art, does not bring this content into prominence, as was done in great measure in the Symbolic, and, above all, in the Classic form of Art, with its ideal gods. As we have already seen, this art is not, as art, the revealed teaching (Belehren) which produces the content of truth directly only in the form of art for the imagination, but the content is already at hand for itself outside the region of art in imagination and sensuous perception. Here, religion, as the universal consciousness of truth in a wholly other sphere (Grade), constitutes the essential point of departure for art. It lies quite outside the external modes of manifestation for the actual consciousness, and makes its appearance in sensuous reality as prosaic events belonging to the present. Since, indeed, the content of revelation to the spirit is the eternal, absolute nature of sprit, which separates itself from the natural as such and debases it, manifestation in the immediate thus holds such rank (Stellung) that this outer, so far as it subsists and has actual-being (Dasein), remains only an incidental world out of which the Absolute takes itself up into the spiritual and inner, and thus for the first time really arrives at the truth. At this stage the outer is looked upon as an indifferent element to which the spirit can no longer give credence, and in which it no longer has an abode. The less worthy the spirit esteems this outer actuality, by so much the less is it possible for the spirit ever to seek its satisfaction therein, or to find itself reconciled through union with the external as with itself.

3. In Romantic Art, therefore, on the side of external manifestation, the mode of actual representation in accordance with this principle does not go essentially beyond specific, ordinary actuality, and in nowise fears to take up into itself this real outer existence (Dasein) in its finite incompleteness and particularity. Here, again, has vanished that ideal beauty which repudiates the external view of temporality and the traces of transitoriness in order to replace its hitherto imperfect development by the blooming beauty of existence. Romantic Art no longer has for its aim this free vitality of actual existence, in its infinite calmness and submergence of the soul in the corporeal, nor even this life, as such, in its most precious significance, but turns its back upon this highest phase beauty. Indeed, it interweaves its inner being with the accidentality of external organisation, and allows unrestricted play room to the marked characteristics of the ugly.

In the Romantic, therefore, we have two worlds. The one is the spiritual realm, which is complete in itself — the soul, which finds its reconciliation within itself, and which now for the first time bends around the otherwise rectilinear repetition of genesis, destruction and renewal, to the true circle, to return-into-self, to the genuine Phoenix-life of the spirit. The other is the realm of the eternal, as such, which, shut out from a unity with the spirit, now becomes a wholly empirical actuality, respecting whose form the soul is unconcerned. In Classic Art, spirit controlled empirical manifestation and pervaded it completely, because it was that form itself in which spirit was to gain its perfect reality. Now, however, the inner or spiritual is indifferent respecting the mode of manifestation of immediate or sensuous world, because immediacy is unworthy of the happiness or the soul in itself. The external and phenomenal is no longer able to express internality; and since, indeed, it is no longer called upon to do this, it thus retains the task of proving that the external or sensuous is an incomplete existence, and must refer back to the spiritual, to intellect, (Gemut), and the sensibility, as to the essential element. But for this very reason Art allows externality to again appear on its own account, and in this respect permits each and every matter to enter unhindered into the representation. Even flowers, trees, and the most ordinary household furniture are admitted, and this, too, in the natural accidentality of mere present existence. This content, however, bears with it at the same time the characteristic that as mere external matter it is insignificant and low; that it only attains its true value when it is pervaded by human interest; and that it must express not merely the inner or subjective, but even internality or subjectivity itself, which, instead of blending or fusing itself with outer or material, appears reconciled only in and with itself. Thus driven to externality, the inner at this point becomes manifestation destitute of externality. It is, as it were, invisible, and comprehended only by itself; a tone, as such without objectivity or form; a wave upon water, a resounding through a world, which in and upon its heterogeneous phenomena can only take up and send back a reflected ray of this independent-being (Isichseins) of the soul.

We may now comprise in a single word this relation between content and form as it appears in the Romantic — for here it is that this relation attains to its complete characterisation. It is this: just because the ever increasing universality and restless working depth of the soul constitute the fundamental principle of the keynote thereof is musical, and, in connection with the particularised content of the imagination lyrical. For Romantic Art is, as it were, the elementary characteristic — a tone which the epic and the drama also strike, and which breathes about the works of the arts of visible representation themselves like a universal, fragrant odour of the soul; for here spirit and soul will speak to spirit and soul through all their images.

DIVISION: We come now to the division necessary to be established for the further and more precisely developing investigation of this third great realm of art. The fundamental idea of the Romantic in its internal unfolding lies in the following three moments or elements:

1. The Religious as such, constitutes the first circle, of which the central point is given in the history of redemption — in the life, death, and resurrection of Christ. Introversion (Umkehr) here assumes importance as the chief characteristic. The spirit assumes an attitude of hostility toward, and overcomes, its own immediacy and finitude, and through thus rendering itself free it attains to its infinity, and absolute independence in its own sphere.

2. Secondly, this independence passes out of the abstract divine of the spirit, and also leaves aside the elevation of finite man to God, and passes into the affairs of the secular world. Here at once it is the individual (Subjekt), as such, that has become affirmative for itself, and has for the substance of its consciousness, as also for the interest of its existence, the virtues of this affirmative individuality, namely, honour, love, fidelity, and valour — that is, the aims and duties which belong to Romantic Knighthood.

3. The content and form of the third division may be summed up, in general, as Formal Independence of Character. If, indeed, personality is so far developed that spiritual independence has come to be its essential interest, then there comes, also, to be a special Content, with which personality identifies itself as with its own, and shares with it the same independence, which, however, can only be of a formal type, since it does not consist in the substantiality of its life, as is the case in the circle of religious truth, properly speaking. But, on the other hand, the form of outer circumstances and situations, and of the development of events, is indeed that of freedom, the result of which is a reckless abandonment to a life of capricious adventures. We thus find the termination of the Romantic, in general, to consist in the accidentality both of the external and of the internal, and with this termination the two elements fall asunder. With this we emerge from the sphere of art altogether. It thus appears that the necessity which urges consciousness on to the attainment of a complete comprehension of the truth demands higher forms that Art is able in anywise to produce.

(The following section is translated by Bosanquet)

1. After the above introductory remarks, it is now time to pass to the study of our object-matter. But we are still in the introduction, and an introduction cannot do more than lay down, for the sake of explanation, the general sketch of the entire course which will be followed by our subsequent scientific considerations. As, however, we have spoken of art as proceeding from the absolute Idea, and have even assigned as its end the sensuous representation of the absolute itself, we shall have to conduct this review in a way to show, at least in general, how the particular divisions of the subject spring from the conception of artistic beauty as the representation of the absolute. Therefore we must attempt to awaken a very general idea of this conception itself.

It has already been said that the content of art is the Idea, and that its form lies in the plastic use of images accessible to sense. These two sides art has to reconcile into a full and united totality. The first attribution which this involves is the requirement that the content, which is to be offered to artistic representation, shall show itself to be in its nature worthy of such representation. Otherwise we only obtain a bad combination, whereby a content that will not submit to plasticity and to external presentation, if forced into that form, and a matter which is in its nature prosaic is expected to find an appropriate mode of manifestation in the form antagonistic to its nature.

The second requirement, which is derivable from this first, demands of the content of art that it should not be anything abstract in itself. This does not mean that it must be concrete as the sensuous is concrete in contrast to everything spiritual and intellectual, these being taken as in themselves simple and abstract. For everything that has genuine truth in the mind as well as in nature is concrete in itself, and has, in spite of its universality, nevertheless, both subjectivity and particularity within it. If we say, e.g., of God that He is simply One, the supreme Being as such, we have only enunciated a lifeless abstraction of the irrational understanding. Such a God, as he himself is not apprehended in his concrete truth, can afford no material for art, least of all for plastic art. Hence the Jews and the Turks have not been able to represent their God, who does not even amount to such an abstraction of the understanding, in the positive way in which Christians have done so. For God in Christianity is conceived in his truth, and therefore as in Himself thoroughly concrete, as a person, as a subject, and more closely determined, as mind or spirit. What He is as spirit unfolds itself to the religious apprehensions as the Trinity of Persons, which at the same time in relation with itself is One. Here is essentiality, universality, and particularity together with their reconciled unity; and it is only such unity that constitutes the concrete. Now, as a content, in order to posses truth at all, it must be of this concrete nature, and art demands the same concreteness, because a mere abstract universal has not in itself the vocation to advance to particularity and noumenal manifestation and to unity with itself therein.

If a true and therefore concrete content is to have corresponding to it a sensuous form and modelling, this sensuous form must, in the third place, be no less emphatically something individual, wholly concrete in itself and one. The character of concreteness as belonging to both elements of art, to the content as to the representation, is precisely the point in which both may coincide and correspond to one another; as, for instance, the natural shape of the human body is such a sensuous concrete as is capable of representing spirit, which is concrete in itself, and of displaying itself in conformity therewith. Therefore we ought to abandon the idea that it is a mere matter of accident that an actual phenomenon of the external world is chosen to furnish a shape thus conformable to truth. Art does not appropriate this form either because it simply finds it existing or because there is no other. The concrete content itself involves the element of external and actual, we may say indeed of sensible manifestation. But in compensation this sensuous concrete, in which a content essentially belonging to mind expresses itself, is in its own nature addressed to the inward being; its external element of shape, whereby the content is made perceptible and imaginable, has the aim of existing purely for the heart and mind. This is the only reason for which content and artistic shape are fashioned in conformity with each other. The mere sensuous concrete, external nature as such, has not this purpose for its exclusive ground of origin. The birds’ variegated plumage shines unseen, end their song dies away unheard, the Cereus (Fackeldistel- “torch thistle”)which blossoms only for a night withers without having been admired in the wilds of southern forests, and these forests, jungles of the most beautiful and luxuriant vegetation, with the most odorous and aromatic perfumes, perish and decay no less unenjoyed. The work of art has not such a naive self-centred being, but is essentially a question, an address to the responsive heart, an appeal to affections and to minds.

Although the artistic bestowal of sensuous form is in this respect not accidental, yet on the other hand it is not the highest mode of apprehending the spiritually concrete. Thought is a higher mode than representation by means of the sensuous concrete. Although in a relative sense abstract, yet it must not be one-sided but concrete thinking, in order to be true and rational. Whether a given content has sensuous artistic representation for its adequate form, or in virtue of its nature essentially demands a higher and more spiritual embodiment, is a distinction that displays itself at once, if, for instance, we compare the Greek gods with God as conceived according to Christian ideas. The Greek god is not abstract but individual, closely akin to the natural human shape; the Christian God is equally a concrete personality, but in the mode of pure spiritual existence, and is to be known as spirit and in spirit. His medium of existence is therefore essentially inward knowledge and not external natural form, by means of which He can only be represented imperfectly, and not in the whole depth of His idea.

But in as much as the task of art is to represent the idea to direct perception in sensuous shape, and not in the form of thought or of pure spirituality as such, and seeing that this work of representation has its value and dignity in the correspondence and the unity of the two sides, i.e., of the Idea and its plastic embodiment, it follows that the level and excellency of art in attaining a realisation adequate to its idea, must depend upon the grade of inwardness and unity with which Idea and Shape display themselves as fused into one.

Thus the higher truth is spiritual being that has attained a shape adequate to the conception of spirit. This is what furnishes the principle of division for the science of art. For before the mind can attain the true notion of its absolute essence, it has to traverse a course of stages whose ground is in this idea itself; and to this evolution of the content with which it supplies itself, there corresponds an evolution, immediately connected therewith, of the plastic forms of art, under the shape of which the mind as artist presents to itself the consciousness of itself.

This evolution within the art spirit has again in its own nature two sides. In the first place the development itself is a spiritual and universal one, in so far as the graduated series of definite conceptions of the world as the definite but comprehensive consciousness of nature, man and God, gives itself artistic shape; and, in the second place, this universal development of art is obliged to provide itself with external existent and sensuous form, and the definite modes of the sensuous art-existence are themselves a totality of necessary distinctions in the realm of art — which are the several arts. It is true, indeed, that the necessary kinds of artistic representation are on the one hand qua spiritual of a very general nature, and not restricted to any one material; while sensuous existence contains manifold varieties of matter. But as this latter, like the mind, has the Idea potentially for its inner soul, it follows from this that particular sensuous materials have a close affinity and secret accord with the spiritual distinctions and types of art presentation.

In its completeness, however, our science divides itself into three principal portions.

First, we obtain a general part. It has for its content and object the universal Idea of artistic beauty — this beauty being conceived as the Ideal — together with the nearer relation of the latter both to nature and to subjective artistic production.

Secondly, there develops itself out of the idea of artistic beauty a particular part, in as far as the essential differences which this idea contains in itself evolve themselves into a scale of particular plastic forms.

In the third place there results a final part, which has for its subject the individualisation of artistic beauty, that consists in the advance of art to the sensuous realisation of its shapes and its self-completion as a system of the several arts and their genera and species.

2. With respect to the first part, we must begin by recalling to mind, in order to make the sequel intelligible, that the Idea qua the beautiful in art is not the Idea as such, in the mode in which a metaphysical logic apprehends it as the absolute, but the Idea as developed into concrete form fit for reality, and as having entered into immediate and adequate unity with reality. For the Idea as such, although it is the essentially and actually true, is yet the truth only in its generality which has not yet taken objective shape; but the Idea as the beautiful in art is at once the Idea when specially determined as in its essence individual reality, and also an individual shape of reality essentially destined to embody and reveal the Idea. This amounts to enunciating the requirement that the Idea, and its -plastic mould as concrete reality, are to be made completely adequate to one another. When reduced to such form the Idea, as a reality moulded in conformity with the conception of the Idea, is the Ideal. The problem of this conformity might, to begin with, be understood in the sense that any Idea would serve, so long as the actual shape, it did not matter what shape, represented this particular Idea and no other. But if so, the required truth of the Idea is confounded with mere correctness which consists in the expression of any meaning whatever in appropriate fashion so that its import may be readily recognised in the shape created. The Ideal is not to be thus understood. Any content whatever may attain to being represented quite adequately, judged by the standard of its own nature, but it does not therefore gain the right to claim the artistic beauty of the Ideal. Compared indeed with ideal beauty even the presentation will in such a case appear defective.

From this point of view we must remark to begin with, what cannot be proved till later, that the defects of a work of art are not to be regarded simply as always due, for instance, to individual unskillfulness. Defectiveness of form arises from defectiveness of content, for example, the Chinese, Indian and Egyptians in their artistic shapes, their forms of deities, and their idols, never got beyond a formless phase, or ore of a vicious and false definiteness of form, and were unable to attain genuine beauty; because their mythological ideas, the content and thought of their works of art, were as yet indeterminate in themselves, or of a vicious determinateness, and did not consist in the content that is absolute in itself. The more that works of art excel in true beauty of presentation, the more profound is the inner truth of their content and thought. And in dealing with this point, we have not to think merely perhaps of the greater or lesser skill with which the natural as given in external reality are apprehended and imitated. For in certain stages of art-consciousness and of representation, the distortion and disfigurement of natural structures is not unintentional technical inexpertness and want of skill, but intentional alteration, which emanates from the content that is in consciousness, and is required thereby. Thus, from this point of view, there is such a thing as imperfect art, which may be quite perfect, both technically and in other respects, in its determinate sphere, yet reveals itself to be defective when compared with the conception of art as such, and with the Ideal. Only in the highest art are the Idea and the representation genuinely adequate to one another, in the sense that the outward shape given to the Idea is in itself essentially and actually the true shape, because the content of the Idea, which that shape expresses, is itself the true and real content. It is a corollary from this, as we indicated above, that the Idea must be defined in and through itself as concrete totality, and thereby possess in itself the principle and standard of its particularisation and determination in external appearance. For example, the Christian imagination will be able to represent God only in human form and with man’s intellectual expression, because it is herein that God Himself is completely known in Himself as spirit. Determinateness is, as it were, the bridge to phenomenal existence. Where this determinateness is not totality derived from the Idea itself, where the Idea is not conceived as self-determining and self-particularising, the Idea remains abstract — and has its determinateness, and therefore the principle that dictates its particular and exclusively appropriate mode of presentation, not in itself but external to it. Therefore, the Idea when still abstract has even its shape external, and not dictated by itself. The Idea, however, which is concrete in itself hears the principle of its mode of manifestation within itself, and is by that means the free process of giving shape to itself. Thus it is only the truly concrete Idea that can generate the true shape, and this correspondence of the two is the Ideal.

3. Now because the Idea is in this fashion concrete unity, it follows that this unity can enter into the art consciousness only by the expansion and reconciliation of the particularities of the Idea, and it is through this evolution that artistic beauty comes to possess a totality of particular stages and forms. Therefore, after we have studied the beauty of art in itself and on its own merits, we must see how beauty as a whole breaks up into its particular determinations. This gives us our second part, the doctrine of the types of art. These forms find their genesis in the different modes of grasping the Idea as artistic content, whereby is conditioned a difference of the form in which it manifests itself. Hence the types of art are nothing but the different relations of content and shape, relations which emanate from the Idea itself, and furnish thereby the true basis of division for this sphere. For the principle of division must always be contained in that conception whose particularisation and division is in question.

We have here to consider three relations of the Idea to its outward shaping.

a. First, the Idea gives rise to the beginning of Art when being itself still in its indistinctness and obscurity, or in vicious untrue determinateness, it is made the import of artistic creations. As indeterminate it does not yet possess in itself that individuality which the Ideal demands; its abstractness and one-sidedness leave its shape to be outwardly bizarre and defective. The first form of art is therefore rather a mere search after plastic portrayal than a capacity of genuine representation. The Idea has not yet found the true form even within itself, and therefore continues to be merely the struggle and aspiration thereafter. In general terms we may call this form the Symbolic form of art. In it the abstract Idea has its outward shape external to itself in natural sensuous matter, with which the process of shaping begins, and from which, qua outward expression, it is inseparable.

Natural objects are thus primarily left unaltered, and yet at the same time invested with the substantial Idea as their significance, so that they receive the vocation of expressing it, and claim to be interpreted as though the Idea itself were present in them. At the root of this is the fact that natural objects have in them an aspect in which they are capable of representing a universal meaning. But as an adequate correspondence is not yet possible, this reference can only concern an abstract attribute as when a lion is used to mean strength.

On the other hand, this abstractness of the relation brings to consciousness no less strongly the foreignness of the Idea to natural phenomena; and the Idea, having no other reality to express it, expatiates in all these shapes, seeks itself in them in all their unrest and disproportion, but nevertheless does not find them adequate to itself. Then it proceeds to exaggerate natural shapes and the phenomena of reality into indefinitenessess and disproportion, to intoxicate itself in them, to seethe and ferment in them, to do violence to them, to distort explode them into unnatural shapes, and strives by the variety, hugeness and splendour of the forms employed to exalt the phenomenon to the level of the idea. For the idea is here still more or less indeterminate and non-plastic, but the natural objects are in their shape thoroughly determinate.

Here, in view of the unsuitability of the two elements to each other, the relation of the Idea to objective reality becomes a negative one, for the former, as in its nature inward, is unsatisfied with such an externality, and as being its inner universal substance persists in exaltation or Sublimnity beyond and above all this inadequate abundance of shapes. In virtue of this sublimnity the natural phenomena and the human shapes and incidents are accepted, and left as they were, though at the same time understood to be inadequate to their significance, which is exalted far above every earthly content.

These aspects may be pronounced in general terms to constitute the character of the primitive artistic pantheism of the East, which either charges even the meanest objects with the absolute import, or again coerces nature with violence into the expression of its view. By this means it becomes bizarre, grotesque, and tasteless, or turns the infinite but abstract freedom of the substantive Idea disdainfully against all phenomenal being as null and evanescent. By such means the import cannot be completely embodied in the expression, and in spite of all aspirations and endeavour the reciprocal inadequacy of shape and Idea remains insuperable. This may be taken as the first form of art — symbolic art with its aspiration its disquiet, its mystery and its sublimnity.

b. In the second form of art, which we propose to call “Classical,” the double defect of symbolic art is cancelled. The plastic shape of symbolic art is imperfect, because, in the first place, the Idea in it only enters into consciousness in an abstract determinateness or indeterminateness, and, in the second place, this must always make the conformity of shape to import defective, and in its turn merely abstract. The classical form of art is the solution of this double difficulty; it is the free and adequate embodiment of the Idea in the shape that, according to its conception is peculiarly appropriate to the Idea itself. With it, therefore, the Idea is capable of entering into free and complete accord. Hence, the classical type of art is the first to afford the production and intuition of the completed Ideal, and to establish it as a realised fact.

The conformity, however, of notion and reality in classical art must not be taken in the purely formal sense of the agreement of a content with the external shape given to it, any more than this could be the with the Ideal itself. Otherwise every copy from nature, and every type of countenance, every landscape, flower, or scene, etc., which forms the purport of any representation, would be at once made classical by the agreement which it displays between form and content. On the contrary, in classical art the peculiarity of the content consists in being itself concrete idea, and as such, the concrete spiritual; for only the spiritual is the truly inner self. To suit such a content, then, we must search out that in Nature which on its own merits belongs to the essence and actuality of the mind. It must be the absolute notion that invented the shape appropriate to concrete mind, so that the subjective notion — in this case the spirit of art — has merely found it, and brought it, as an existence possessing natural shape, into accord with free individual spirituality. This shape, with which the Idea as spiritual — as individually determinate spirituality — invests itself when manifested as a temporal phenomenon, is the human form. Personification and anthropomorphism have often been decried as a degradation of the spiritual; but art, in as far as its end is to bring before perception the spiritual in sensuous form, must advance to such anthropomorphism, as it is only in its proper body that mind is adequately revealed to sense. The migration of souls is in this respect a false abstraction (ed. if it represents the soul as independent of an appropriate body) and physiology ought to have made it one of its axioms that life had necessarily in its evolution to attain to the human shape, as the sole sensuous phenomenon that is appropriate to mind (Spirit). The human form is employed in the classical type of art not as mere sensuous existence, but exclusively as the existence and physical form corresponding to mind, and is therefore exempt from all the deficiencies of what is merely sensuous, and from the contingent finiteness of phenomenal existence. The outer shape must be thus purified in order to express in itself a content adequate to itself; and again, if the conformity of import and content is to be complete, the spiritual meaning which is the content must be of a particular kind. It must, that is to say, be qualified to express itself completely in the physical form of man, without projecting into another world beyond the scope of such an expression in sensuous and bodily terms. This condition has the effect that Mind is by it at once specified as a particular case of mind, as human mind, and not as simply absolute and eternal, inasmuch as mind in this latter sense is incapable of proclaiming and expressing itself otherwise than as intellectual being (ed. Geistigkeit should be translated here as spiritual).

Out of this latter point arises, in its turn, the defect which brings about the dissolution of classical art, and demands a transition into a third and higher form, viz., into the romantic form of art.

c. The romantic form of art destroys the completed union of the Idea and its reality, and recurs, though in a higher phase, to that difference and antagonism of two aspects which was left unvanquished by symbolic art. The classical type attained the highest excellence, of which the sensuous embodiment of art is capable; and if it is in any way defective, the defect is in art as a whole, i.e., in the limitation of its sphere. This limitation consists in the fact that art as such takes for its object Mind — the conception of which is infinite concrete universality — in the shape of sensuous concreteness, and in the classical phase sets up the perfect amalgamation of spiritual and sensuous existence as a Conformity of the two. Now, as a matter of fact, in such an amalgamation Mind cannot be represented according to its true notion. For mind is the infinite subjectivity of the Idea, which, as absolute inwardness, is not capable of finding free expansion in its true nature on condition of remaining transposed into a bodily medium as the existence appropriate to it.

As an escape from such condition the romantic form of art in its turn dissolves the inseparable unity of the classical phase, because it has won a significance which goes beyond the classical form of art and its mode of expression. This significance we may — if we may recall familiar ideas — coincides with what Christianity declares to be true of God as Spirit, in contradistinction to the Greek faith in gods which forms the essential and appropriate content for classical art. In Greek art the content import is potentially, but not explicitly, the unity of the human and divine nature; a unity which, just because it is purely immediate and not explicit, is capable of adequate manifestation in an immediate and sensuous mode. The Greek god is the object of naive intuition and sensuous imagination. His shape is, therefore, the bodily shape of man. The circle of his power and of his being is individual and individually limited. In relation with the subject, he is, therefore, an essence and a power with which the subject’s inner being is merely latent unity, not itself possessing this unity as inward subjective knowledge. Now the higher stage is the knowledge of this latent unity, which as latent is the import of the classical form of art, and capable of perfect representation in bodily shape. The elevation of the latent or potential into self-conscious knowledge produces an enormous difference. It is the infinite difference which, e.g., separates man as such from the animals. Man is animal, but even in his animal functions he is not confined within the latent and potential as the animal is, but becomes conscious of them, learns to learns to know them, and raises them — as for instance, the process of digestion — into self conscious science. By this means Man breaks the boundary of merely latent and immediate consciousness, so that just for the reason that he knows himself be animal, he ceases to be animal, and as mind, attains to self-knowledge.

If in the above fashion the unity of the human and divine nature, which in the former phase was potential, is raised from an immediate to a conscious unity, it follows that true medium for the reality of this content is no longer the sensuous immediate existence of spiritual, the human bodily shape, but self-conscious inward intelligence (Innerlichkeit, lit. “inwardness”). Now Christianity brings God before our intelligence as spirit, or mind — not as particularised individual spirit, but as absolute, in spirit and in truth. And for this reason Christianity retires from the sensuousness of imagination into intellectual inwardness, and makes this, not bodily shape, the medium and actual existence of its significance. So, too, the unity of the human and divine nature is a conscious unity, only to be realised by spiritual knowledge and in spirit. Thus the new content, won by this unity, is not inseparable from sensuous representation, as if that were adequate to it, but is freed from this immediate existence which has to be posited as negative, absorbed, and reflected into the spiritual unity. In this way, romantic art must be considered as art transcending itself, while remaining within the artistic sphere and in artistic form.

Therefore, in short, we may abide by the statement that in this third stage the object (of art) is free, concrete intellectual being, which has the function of revealing itself as spiritual existence for the inward world of spirit. In conformity with such an object-matter, art cannot work for sensuous perception. It must address itself to inward mind, which coalesces with, its object as though this were itself, to the subjective inwardness, to the heart, the feeling, which, being spiritual, aspires to freedom within itself, and seeks and finds its reconciliation only in the spirit within. It is this inner world that forms the content of the romantic, and must therefore find its representation as such inward feeling, and in the show or presentation of such feeling. The world of inwardness celebrates its triumph over the outer world, and actually in the sphere of the outer and in its medium manifests this its victory, owing to which the sensuous appearance sinks into worthlessness.

But, on the other hand, this [romantic] type of Art, like every other, needs an external vehicle of expression. Now the spiritual has withdrawn into itself out of the external and its immediate oneness therewith. For this reason, the sensuous externality of concrete form is accepted and represented, as in Symbolic art, as something transient and fugitive. And the same measure is dealt to the subjective finite mind and will, even including the peculiarity or caprice of the individual, of character, action, etc., or of incident and plot. The aspect of external existence is committed to contingency, and left at the mercy of freaks of imagination, whose caprice is no more likely to mirror what is given as it is given, than to throw the shapes of the outer world into chance medley, or distort them into grotesqueness. For this external element no longer has its notion and significance, as in classical art, in its own sphere, and in its own medium. It has come to find them in the feelings, the display of which is in themselves instead of being in the external and its form of reality, and which have the power to preserve or to regain their state of reconciliation with themselves, in every accident, in every unessential circumstance that takes independent shape, in all misfortune and grief, and even in crime. Owing to this, the characteristics of symbolic art, in difference, discrepancy, and severance of Idea and plastic shape, are here reproduced, but with an essential difference. In the sphere of the romantic, the Idea, whose defectiveness in the case of the symbol produced the defect of external shape, has to reveal itself in the medium of spirit and feelings as perfected in itself. And it is because of this higher perfection that it withdraws itself from any adequate union with the external element, inasmuch as it can seek and achieve its true reality and revelation nowhere but in itself.

This we may take as in the abstract the character of the symbolic, classical, and romantic forms of art, which represent the three relations of the Idea to its embodiment in the sphere of art. They consist in the aspiration after, and the attainment and transcendence of the Ideal as the true Idea of beauty.

4. The third part of our subject, in contradistinction to the two just described, presupposes the conception of the Ideal, and the general types of art, inasmuch as it simply consists of their realisation in particular sensuous media. Hence we have no longer to do with the inner development of artistic beauty in conformity with its general fundamental principles. What we have to study is how these principles pass into actual existence, how they distinguish themselves in their external aspect, and how they give actuality to every element contained in the idea of beauty, separately and by itself as a work of art, and not merely as a general type. Now, what art transfers into external existence are the differences proper to the idea of beauty and immanent therein. Therefore, the general types of art must reveal themselves in this third part, as before, in the character of the fundamental principle that determines the arrangement and definition of the several arts; in other words, the species of art contain in themselves the same essential modifications as those with which we become acquainted as the general types of art. External objectivity, however, to which these forms are introduced through the medium of a sensuous and therefore particular material, affects these types in the way of making them separate into independent and so particular forms embodying their realisation. For each type finds its definite character in some one definite external material, and its adequate actuality in the mode of portrayal which that prescribes. But, moreover, these types of art, being for all their determinateness, its universal forms, break the bounds of particular realisation by a determinate form of art, and achieve existence in other arts as well, although in subordinate fashion. Therefore, the particular arts belong each of them specifically to one of the general types of art, and constitutes its adequate external actuality; and also they represent, each of them after its own mode of external plasticity, the totality of the types of art.

Then, speaking generally, we are dealing in this third principal division with the beautiful of art, as it unfolds itself in the several arts and in their creations into a world of actualised beauty. The content of this world is the beautiful, and the true beautiful; as we saw, is spiritual being in concrete shape, the Ideal, or, more closely looked at, the absolute mind, and the truth itself. This region, that of divine truth artistically represented to perception and to feeling, forms the center of the whole world of art. It is the independent, free, and divine plasticity, which has thoroughly mastered the external elements of form and of medium, and wears them simply as a means to manifestation of itself. Still, as the beautiful unfolds itself in this region in the character of objective reality, and in so doing distinguishes within itself its individual aspects and elements, permitting them independent particularity, it follows that this center erects its extremes, realised in their peculiar actuality, into its own antitheses. Thus one of these extremes comes to consist in an objectivity yet devoid of mind, in the merely natural vesture of God. At this point the external element takes plastic shape as something that has its spiritual aim and content, not in itself, but in another.

The other is the divine as inward, as something known, as the variously particularised subjective existence of the Deity; it is the truth as operative and vital in sense, heart, and mind of individual subjects, not persisting in the mould of its external shapes, but as having returned into subjective individual inwardness. In such a mode, the Divine is at the same time distinguished from its first manifestation as Deity, and passes thereby into the diversity of particulars which belongs to all subjective knowledge — emotion, perception, and feeling. In the analogous province of religion, with which art at its highest stage is immediately connected, we conceive this same difference as follows. First, we think of the earthly natural life in its finiteness as standing on one side; but, then, secondly, consciousness makes God its object, in which the distinction of objectivity and subjectivity is done away. And at last, thirdly, we advance from God as such to the devotion of the community, that is, to God as living and present in the subjective consciousness. Just so these three chief modifications present themselves in the world of art in independent development.

a. The first of the particular arts with which, according to their fundamental principle, we have to begin, is architecture as a fine art. Its task lies in so manipulating external inorganic nature that it becomes cognate to mind, as an artistic outer world. The material of architecture is matter itself in its immediate externality as a heavy mass subject to mechanical laws, and its forms do not depart from the forms of inorganic nature, but are merely set in order in conformity with relations of the abstract understanding, i.e., with relations of symmetry. In this material and in such forms the ideal as concrete spirituality does not admit of being realised. Hence the reality which is represented in them remains contrasted with the Idea, as something external which it has not penetrated, or has penetrated only to establish an abstract relation.

For these reasons the fundamental type of the fine art of building is the symbolical form of art. It is architecture that pioneers the way for the adequate realisation of the God, and in this its service bestows hard toil upon existing nature, in order to disentangle it from the jungle of finitude and the abortiveness of chance. By this means it levels a space for the God, gives form to his external surroundings, and builds him his temple as a fit place for concentration of spirit, and for its direction to the mind’s absolute objects. It raises an enclosure round the assembly of those gathered together, as a defence against the threatening of the storm, against rain, the hurricane, and wild beasts, and reveals the will to assemble, although externally, yet in conformity with principles of art. With such import as this it has power to inspire its material and its forms more or less effectively, as the determinate character of the content on behalf of which it sets to work is more or less significant, more concrete or more abstract, more profound in sounding its own depths, or more dim and more superficial. So much, indeed, may architecture attempt in this respect as even to create an adequate artistic existence for such an import in its shapes and in its material. But in such a case it has already overstepped its own boundary, and is leaning to sculpture, the phase above it. For the limit of architecture lies precisely in this point, that it retains the spiritual as inward existence over against the external forms of the art, and consequently must refer to what has soul only as to something other than its own creations.

b. Architecture, however, as we have seen, has purified the external world, and endowed it with symmetrical order and with affinity to mind; and the temple of the God, the house of his community, stands ready. Into this temple, then, in the second place, the God enters in the lightning-flash of individuality which strikes and permeates the inert mass, while the infinite and no longer merely symmetrical form belonging to mind itself concentrates and gives shape to the corresponding bodily existence. This is the task of Sculpture. In as far as in this art the spiritual inward being which architecture can but indicate makes itself at home in the sensuous shape and its external matter, and in as far as these two sides are so adapted to one another that neither is predominant, sculpture must be assigned the classical form of art as its fundamental type. For this reason the sensuous element itself has here no expression which could not be that of the spiritual element, just as, conversely, sculpture can represent no spiritual content which does not admit throughout of being adequately presented to perception in bodily form. Sculpture should place the spirit before us in its bodily form and in immediate unity therewith at rest and in peace; and the form should be animated by the content of spiritual individuality. And so the external sensuous matter is here no longer manipulated, either in conformity with its mechanical quality alone, as a mass possessing weight, nor in shapes belonging to the inorganic world, nor as indifferent to colour, etc.; but it is wrought in ideal forms of the human figure, and, it must be remarked, in all three spatial dimensions. In this last respect we must claim for sculpture, that it is in it that the inward and spiritual are first revealed in their eternal repose and essential self completeness. To such repose and unity with itself there can correspond only that external shape which itself maintains its unity and repose. And this is fulfilled by shape in its abstract spatiality. The spirit which sculpture represents is that which is solid in itself, not broken up in the play of trivialities and of passions; and hence its external form too is not abandoned to any manifold phases of appearance, but appears under this one aspect only, as the abstraction of space in the whole of its dimensions.

c. Now, after architecture has erected the temple, and the hand of sculpture has supplied it with the statue of the God, then, in the third place, this god present to sense is confronted in the spacious halls of his house by the community. The community is the spiritual reflection into itself of such sensuous existence, and is the animating subjectivity and inner life which brings about the result that the determining principle for the content of art, as well as for the medium which represents it in outward form, comes to be particularisation (dispersion into various shapes, attributes, incidents, etc.), individualisation, and the subjectivity which they require. The solid unity which the God has in sculpture breaks up into the multitudinous inner lives of individuals, whose unity is not sensuous, but purely ideal.

It is Only in this stage that God Himself comes to be really and truly spirit — the spirit in His (God’s) community; for He here begins to be a to-and-fro; an alternation between His unity within himself and his realisation in the individual’s knowledge and in its separate being, as also in the common nature and union of the multitude. In the community, God is released from the abstractness of unexpanded self-identity, as well as from the simple absorption in a bodily medium by which sculpture represents Him. And He is thus exalted into spiritual existence and into knowledge, into the reflected appearance which essentially displays itself as inward and as subjectivity. Therefore the higher content is now the spiritual nature, and that in its absolute shape. But the dispersion of which we have spoken reveals this at the same time as particular spiritual being, and as individual character. Now, what manifests itself in this phase as the main thing is not the serene quiescence of the God in Himself, but appearance as such, being which is for another, self-manifestation. And hence, in the phase we have reached, all the most manifold subjectivity in its living movement and operation — as human passion, action, and incident, and, in general, the wide realm of human feeling, will, and its negation — is for its own sake the object of artistic representation. In conformity with this content the sensuous element of art has at once to show itself as made particular in itself, and as adapted to subjective inwardness. Media that fulfil this requirement we have in colour, in musical sound, and finally in sound as the mere indication of inward perceptions and ideas; and as modes of realising the import in question by help of these media we obtain music and poetry. In this region the sensuous medium displays itself as divided in its own being and universally set down as ideal. Thus it has the highest degree of conformity with the content of art, which, as such, is spiritual, and the connection of intelligible import and sensuous medium develops into closer intimacy than was possible in the case of architecture and sculpture. The unity attained, however, is a more inward unity, the weight of which is thrown wholly on the subjective side, and which, in as far as form and content are compelled to particularise themselves and give themselves merely ideal existence, can only come to pass at the expense of the objective universality of the content and also of its amalgamation with the immediately sensuous element. The arts, then, of which form and content exalt themselves to ideality, abandon the character of symbolic architecture and the classical ideal of sculpture, and therefore borrow their type from the romantic form of art, whose mode of plasticity they are most adequately adapted to express. And they constitute a totality of arts, because the romantic type is the most concrete in itself.

(1) The articulation of this third sphere of the individual arts may be determined as follows. The first art in it, which comes next to sculpture, is painting. It employs as a medium for its content and for the plastic embodiment of that content visibility as such in as far as it is specialised in its own nature, i.e., as developed into colour. It is true that the material employed in architecture and sculpture is also visible and coloured; but it is not, as in painting, visibility as such, not the simple light which, differentiating itself in virtue of its contrast with darkness, and in combination with the latter, gives rise to colour. This quality of visibility, made subjective in itself and treated as ideal, needs neither, like architecture, the abstractly mechanical attribute of mass as operative in the properties of heavy matter, nor, like sculpture, the complete sensuous attributes of space, even though concentrated into organic shapes. The visibility and the rendering visible which belong to painting have their differences in a more ideal form, in the several kinds of colour, and they liberate art from the sensuous completeness in space which attaches to material things, by restricting themselves to a plane surface.

On the other hand, the content also attains the most comprehensive specification. Whatever can find room in the human heart, as feeling, idea, and purpose; whatever it is capable of shaping into act — all this diversity of material is capable of entering into the varied content of painting. The whole realm of particular existence, from the highest embodiment of mind down to the most isolated object of nature, finds a place here. For it is possible even for finite nature, in its particular scenes and phenomena, to make its appearance in the realm of art, if only some allusion to an element of mind endows it with affinity to thought and feeling.

(2) The second art in which the romantic type realises itself is contrasted with painting, and is music. Its medium, though still sensuous, yet develops into still more thorough subjectivity and particularisation. Music, too, treats the sensuous as ideal, and does so by negating, and idealising into the individual isolation of a single point, the indifferent externality of space, whose complete semblance is accepted and imitated by painting. The single point, qua such a negativity (excluding space) is in itself a concrete and active process of positive negation within the attributes of matter, in the shape of a motion and tremor of the material body within itself and in its relation to itself. Such an inchoate ideality of matter, which appears no longer as under the form of space, but as temporal ideality, is sound, the sensuous set down as negated, with its abstract visibility converted into audibility, in as much as sound, so to speak liberates the ideal content from its immersion in matter. This earliest inwardness of matter and inspiration of soul into it furnishes the medium for the mental inwardness itself as yet indefinite and for the soul into which mind concentrates itself; and finds utterance in its tones for the heart with its whole gamut of feelings and passions. Thus music forms the center of the romantic arts, just as sculpture represents the central point between architecture and the arts of romantic subjectivity. Thus, too, it forms the point of transition between abstract spatial sensuousness, such as painting employs, and the abstract spirituality of poetry. Music has within itself, like architecture, a relation of quantity conformable to the understanding, as the antithesis to emotion and inwardness; and has also as its basis a solid conformity to law on the part of the tones, of their conjunction, and of their succession.

(3) As regards the third and most spiritual mode of representation of the romantic art-type, we must look for it in poetry. Its characteristic peculiarity lies in the power with which it subjects to the mind and to its ideas the sensuous element from which music and painting in their degree began to liberate art. For sound, the only external matter which poetry retains, is in it no longer the feeling of the sensuous itself, but is a sign, which by itself is void of import. And it is a sign of the idea which has become concrete in itself, and not merely of indefinite feeling and of its nuances and grades. This is how sound develops into the Word, as voice articulate in itself, whose import it is to indicate ideas and notions. The merely negative point up to which music has developed now makes its appearance as the completely concrete point, the point which is mind, the self conscious individual, which, producing out of itself the infinite space of its ideas, unites it with the temporal character of sound. Yet this sensuous element, which in music was still immediately one with inward feeling, is in poetry separated from the content of consciousness. In poetry the mind determines this content for its own sake, and apart from all else, into the shape of ideas, and though it employs sound to express them, yet treats it solely as a symbol without value or import. Thus considered, sound may just as well be reduced to a mere letter, for the audible, like the visible is thus depressed into a mere indication of mind. For this reason the proper medium of poetical representation is the poetical imagination and intellectual portrayal itself. And as this element is common to all types of art, it follows that poetry runs through them all and develops itself independently in each. Poetry is the universal art of the mind which has become free in its own nature, and which is not tied to its final realisation in external sensuous matter, but expatiates exclusively in the inner space and inner time of the ideas and feelings. Yet just in this its highest phase art ends by transcending itself, in as much as it abandons the medium of a harmonious embodiment of mind in sensuous form, and passes from the poetry of imagination into the prose of thought.

5. Such we may take to be the articulated totality of the particular arts, viz., the external art of architecture, the objective art of sculpture, and the subjective art of painting, music and poetry. Many other classifications have been attempted, for a work of art presents so many aspects, that, as has often been the case, first one and then another is made the basis of classification. For instance, one might take the sensuous medium. Thus architecture is treated as crystallisation; sculpture, as the organic modelling of the material in its sensuous and spatial totality; painting, as the coloured surface and line; while in music, space, as such, passes into the point of time possessed of content within itself, until finally the external medium is in poetry depressed into complete insignificance. Or, again, these differences have been considered with reference to their purely abstract attributes of space and time. Such abstract peculiarities of works of art may, like their material medium, be consistently explored in their characteristic traits; but they cannot be worked out as the ultimate and fundamental law, because any such aspect itself derives its origin from a higher principle, and must therefore be subordinate thereto.

This higher principle we have found in the types of art – symbolic, classical, and romantic – which are the universal stages or elements of the Idea of beauty itself. For symbolic art attains its most adequate reality and most complete application in architecture, in which it holds sway in the full import of its notion, and is not yet degraded to be, as it were, the inorganic nature dealt with by another art. The Classical type of art, on the other hand, finds adequate realisation in sculpture, while it treats architecture only as furnishing an enclosure in which it is to operate, and has not acquired the power of developing painting and music as absolute form for its content. The romantic type of art, finally, takes possession of painting and music, and in like manner of poetic representation, as substantive and unconditionally adequate modes of utterance. Poetry, however, is conformable to all types of the beautiful, and extends over them all, because the artistic imagination is its proper medium, and imagination is essential to every product that belongs to the beautiful, whatever it type may be.

And, therefore, what the particular arts realise in individual works of art, are according to their abstract conception simply universal types which constitute the self-unfolding Idea of beauty. It is as the external realisation of this Idea that the wide Pantheon of art is being erected, whose architect and builder is the spirit of beauty as it awakens to self-knowledge, and to complete which the history of the world will need its evolution of ages.

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Ellen Fullman: how to play a 100ft stringed instrument. by Ben Beaumont-Thomas

‘Playing it can be ecstatic’ … Ellen Fullman with her Long String Instrument. Photograph: Robert Szkolnicki

The Long String Instrument is exactly that – and then some. Stainless steel and phosphor bronze strings, 100-feet-long, are stretched taut across a room. Ellen Fullman, the instrument’s creator, places her fingers on the strings, pressing down as she moves the length of the instrument. A droning sound sweeps out like a prairie wind. “I feel like I’ve been miniaturised when I’m playing it,” Fullman says. “My whole body is a finger moving along a fretboard.”

The LSI has been Fullman’s obsession for more than 30 years, but is only now beginning to make waves. Having secured a major US arts grant last year, Fullman has “a very busy schedule” taking it to festivals in Paris and Bologna in the coming months. Its sound recalls Indian raga, with harmonies sliding over one another. Fullman says playing it “can be an ecstatic feeling, a floating sensation. Music is bigger than me: there are pitch relationships, shapes of notes beautiful beyond the level of human expression. I like that feeling of being a conduit. I don’t like egotistical thrashing. I like trying to give a gift.”

In effect, she turns herself into a human bow

The strings are connected to wooden resonators that act like the body of a guitar to amplify the sound. To bring it out further, Fullman rubs her fingers with rosin, the same substance used on bows. In effect, she turns herself into a human bow. The strings are 2cm apart and she can have up to 28 on each of the two sides of the instrument: “The number is only limited by the length of my arms: 60cm.”

The LSI began life in New York in 1983, after Fullman heard about composer Alvin Lucier’s Music on a Long Thin Wire. An early version, which featured a single wire with a mixing bowl full of water as a resonator, made “a chaotic, noisy sound”. She worked by day as a bookkeeper and chef to an art materials supplier “who only ate goat meat – these legs of goat boiled in the department where they mixed all the paint”, says Fullman. “He ate very loudly, with lots of slurping, on a desk covered in rat droppings. It was so New York.”
‘I don’t like egotistical thrashing’ … Fullman plays the LSI

‘I don’t like egotistical thrashing’ … Fullman plays the LSI

Born in Memphis and kissed by Elvis as a baby, Fullman went to art school in Kansas and moved to Minneapolis before New York; she’s since lived in Austin, Seattle, Tokyo and Berlin, working as a graphic designer, an electrician and in building maintenance. “It’s only in the last few years that I’ve started to feel a kind of financial viability in music,” she says, having now settled in Berkeley, California. “Graphic design gave me skills I’ve used in my notation, and being an electrician demystified some of the equipment I work with. It’s great to feel self-sufficient as an artist, having an idea of plumbing, how to construct walls, how the world works.”

She was also initially a sculptor, making such one-off pieces as the 1980 work Streetwalker: a metal skirt with strings that connect to the wearer’s shoes. “This triangular skirt made me look like a female stick figure, and the strings were puppet-like, so I looked like Pinocchio.” She turned heads walking through Minneapolis. “One man leaned out of a phone booth and said, ‘D’ya need some oil?’ Another asked what planet I was from. I like something funny to be in my work, funny and serious. The Long String Instrument has a ridiculous aspect to it too – it’s absurd!”

And the serious side of Streetwalker? “As a young female wearing a skirt, you’re very vulnerable,” she says. “So the skirt was like armour. I’ve been sexually assaulted in public wearing a skirt. Women always have to deal with being victims – you have to protect yourself. Skirts are also stereotypically female, and the female stereotype is that you are less capable than a male, so I rejected that. It was the last time I wore a skirt.”

I’ve designed it to fit into my luggage

In fact, she rejected everything that society expected her to be as a woman, including heterosexuality. “When I saw women serving the food and clearing the dishes the way they do, especially in Europe – taking on that stereotypical gender role – it was enough to make me want to go gay. It’s kind of a crass way to put it. But I couldn’t stand that feeling of being subjected, of being less equal.”

Fullman continues to finesse the LSI. “Sometimes when I’m playing, it seems like something special is happening,” she says. “Other times, it seems more of a failure.” What about transportation costs? Does an instrument this large not need roadies? “I’ve designed it to fit into my luggage,” she says proudly, “and to weigh just under the baggage limit. But I’m not a huge person – and dragging this sack, it’s is not very freeing.”

She laughs. “I sometimes think, ‘Could I have found more mainstream success if I were a man?’ But on the other hand, I am dragging around this 100-foot-long instrument wherever I go. And it requires five days of installation. I’ve got this monkey on my back.”

Ellen Fullman plays the Sonic Protest festival, Paris, 6 April, and the Angelica festival, Bologna, 5-6 May.

http://www.theguardian.com/music/2016/mar/01/100-foot-instrument-long-string-ellen-fullman?CMP=share_btn_fb#_=_

Typographical Experiments And Sound Waves Become Geometric Landscapes By Erica Gonsales — Nov 23 2012

Typographical Experiments And Sound Waves Become Geometric Landscapes

“I think art is about making people think and dream. But what is to dream? It’s also a way of seeing things differently,” said artist Angela Detanico in an interview to Parisian museum Jeu de Paume.

This attempt to define art, suggesting a question and maybe even some incertitude, says a lot about the work of Paris-based Brazilian artists Angela Detanico and Rafael Lain. For them questioning is a constant and also the starting point for their creations, which invariably investigate the symbols and means of communication, graphic design, maps, typography, and language.

Some of the duo’s most famous creations experiment with typography and cartography, like the alphabetic system Utopia (above) based on Oscar Niemeyer’s work. And a map of the world that is aligned left, centered, right, and justified as if it were text in a Word document in The World Justified (2008) below.

The outcome of their latest investigations are currently showing at Sao Paulo’s Vermelho Gallery, featuring the animation Wave Horizon (One and Two mediums) which is composed of a piece of printed sheet music and two black and white projections. The piece combines geometric tracks of sine waves, which have a similar shape to sea, sound, and light waves. Here’s a small sample of it:

Eight tracks of graphic and sonic elements glide in the field of the image, creating a moving horizon for the installation. Each track is composed of three elements corresponding to each wave’s behavior. Tracks that appear closer to viewers move faster and have a higher pitch while ones that look farther away move more slowly and have a lower pitch. The combination of these elements builds a geometric landscape of sound waves. The projection is followed by a map that describes the structure of the composition as a palindrome, that is, it can be read right to left or left to right.

Wave Horizon (One and Two Mediums) (2012)

In the Compound Words installation (below), Portuguese words and their opposite meanings—such as yes/no, always/never, or full/empty—are combined in order to create one image. To do so, the duo use the upper half of each word and places them exactly over their opposites, creating abstract images made of antonyms.

Claro/Escuro (Bright/Dark) (2012)

Dentro/Fora (In/Out) (2012)

Sempre/Nunca (Always/Never) (2012)

You can check more works from Angela Detanico and Rafael Lain on their website.

@CreatorsProject
By Erica Gonsales Tags: Music, Design, Angela Detanico, Rafael Lain, Typography, Sound Art

http://thecreatorsproject.vice.com/blog/typographical-experiments-and-sound-waves-become-geometric-landscapes

The limits of social engineering. Nicholas Carr

https://www.technologyreview.com/s/526561/the-limits-of-social-engineering/

First Laser Measurements of Magnetic Fields of Single Nerves

First Laser Measurements of Magnetic Fields of Single Nerves

Physicists have worked out how to measure the magnetic fields generated by single nerves from outside the body and at room temperature.

Biologists have known that nerves produce and respond to electrical signals since the 18th century, when Luigi Galvani discovered that the muscles in a frog’s leg twitch when stimulated by a spark.

However, the systematic study of the electrical signals that nerves produce had to wait until the early 20th century for the development of sensitive electrical recording equipment such as the cathode ray oscilloscope.

This development revolutionized the understanding of nervous function. The ways nerves conduct signals can be a powerful indicator for diseases such as multiple sclerosis and can even detect certain types of intoxication.

And yet the method has some drawbacks. For example, measuring electrical signals in nerves by inserting a needle-like electrode is somewhat invasive, and the mere act of attaching an electrode to a nerve can change the signal, making the results hard to interpret. So neuroscientists have long hoped for a noninvasive technique that could do the job instead.

That may be about to happen thanks to the work of Kasper Jensen at the University of Copenhagen in Denmark and a few pals who have developed a way to easily measure the magnetic fields associated with electrical signals in nerves. The technique could pave the way for a new generation of diagnostic tools for spotting diseases linked to nervous function and for understanding the basic function of nerves.

First, some basics. When a nerve fires, it sends an electrical signal called an action potential along its length. This electrical pulse also generates a magnetic field. Scientists have been able to measure this pulse since the 1980s using SQUID magnetometers that need to be carefully cooled to superconducting temperatures.

The sensing part of the device is a tiny coil through which the nerve has to run. So this technique cannot be used for in vivo measurement. And although these devices have become more practical, they still rely on superconducting technology which is costly to translate into a clinical setting.

So a way of measuring these magnetic fields at a distance and at room temperature would be hugely useful. And that’s exactly what Jensen and co have done.

These guys have built a sensor that uses a laser beam to detect the effect of a magnetic field on gaseous caesium atoms, which polarize light when they are magnetized. So-called optical magnetometers are hugely powerful devices that are limited in sensitivity only by quantum effects such as the quantum shot noise of light.

That’s important because, at least in theory, it allows them to detect the fields associated with nerves at a distance of several millimeters. So they can sit outside the body while measuring a field produced inside it.

There’s another important advantage. Optical magnetometers work perfectly well at room temperature and even better and body temperature. The sensors are also small—just a few millimeters across—so they are ideal for clinical settings. Indeed, they have been used on various occasions for just this purpose.

However, until now, these clinical devices have never worked at the quantum limit and so have not been sensitive enough to detect the fields from individual nerve fibers.

The breakthrough that Jensen and co have achieved is to operate an optical magnetometer at the quantum limit at room temperature for the first time in this biological setting.

Jensen and co put the device through its paces by sensing the magnetic fields generated by frog sciatic nerves from a few millimeters away. This field turns out to be in the region of a few picoTesla but sub-picoTesla measurements are possible. By comparison, the Earth’s magnetic field is some three orders of magnitude stronger.

The device can operate continuously which allowed the team to measure the shape of the magnetic field generated by the nerve as it is stimulated. “We have performed noninvasive detection of nerve impulses from the frog sciatic nerve by measuring the magnetic field generated by the nerve with a room-temperature sensor with near quantum limited sensitivity,” say Jensen and co.

That’s interesting work that will have important applications in medical diagnostics. “The magnetometer [is] perfect for medical diagnostics in physiological/clinical areas such as cardiography of fetuses, synaptic responses in the retina, and magnetoencephalography,” say the team.

It surely won’t be long before this team, or another, begins to make just these kinds of measurements in human subjects. So it’s just possible that this development will have a similar impact on the study of nerve conduction as the development of sensitive electrical recording equipment in the 1920s.

Ref: arxiv.org/abs/1601.03273 : Non-Invasive Detection of Animal Nerve Impulses with an Atomic Magnetometer Operating Near Quantum Limited Sensitivity