The question what LIFE is and NOT, is a
basic question in the evolution of the human mind
and reflects also the different states of the human mind.
Through recorded history it,s well known that
there are different states of understanding life
itself it,s conditions and it,s so called laws.
The emerging of the sciences from way back
before ancient greek to much older type of civilistations
show remarkable efforts in understanding LIFE by
systematic analytic techniques.
From a spohisticated point of view the noble reader
may take the Text below as an neo-philosophic
approach to the essence of reality.
(R51 Ed.)
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
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 10throughout 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.
dence 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 cooperation
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.
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.
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.
–
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.
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
ap…., single). Thus the gametes are haploid,
the ordinary body cells diploid (from Greek
.p…, 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.
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,
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. 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 (fourdimensional)
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!
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.
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.
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 .-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-ray26-9, 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-rayproduced
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 .-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.
-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.
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!
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.
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.
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
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 wellordered
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.
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.) 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.
‘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. 6974
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.
s: 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.
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.).
h 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.
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-fromorder’
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 ‘orderhave 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 ‘orderfrom-
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 ‘clockothers -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 ‘clockworks’.
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(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-rayinduced
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
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.
A World,s Heritage Of Native Music 
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