Docstoc

WHAT-IS-LIFE-ERWIN-SCHRODINGER-First-published-1944-What-is-life-

Document Sample
WHAT-IS-LIFE-ERWIN-SCHRODINGER-First-published-1944-What-is-life- Powered By Docstoc
					WHAT IS LIFE?                                          numerous sections were originally intended to be
ERWIN SCHRODINGER                                      marginal summaries, and the text of every
First published 1944                                   chapter should be read in continuo. E.S.
                                                       Dublin September 1944
What is life? The Physical Aspect of the Living
Cell.                                                  Homo liber nulla de re minus quam de morte
Based on lectures delivered under the auspices of      cogitat; et ejus sapientia non mortis sed vitae
the Dublin Institute for Advanced Studies at           meditatio est. SPINOZA'S Ethics, Pt IV, Prop.
Trinity College, Dublin, in February 1943.             67
To the memory of My Parents
                                                       (There is nothing over which a free man ponders
Preface                                                less than death; his wisdom is, to meditate not on
A scientist is supposed to have a complete and         death but on life.)
thorough I of knowledge, at first hand, of some
subjects and, therefore, is usually expected not to    CHAPTER 1
write on any topic of which he is not a life,          The Classical Physicist's Approach to the Subject
master. This is regarded as a matter of noblesse
oblige. For the present purpose I beg to renounce      This little book arose from a course of public
the noblesse, if any, and to be the freed of the       lectures, delivered by a theoretical physicist to an
ensuing obligation. My excuse is as follows: We        audience of about four hundred which did not
have inherited from our forefathers the keen           substantially dwindle, though warned at the
longing for unified, all-embracing knowledge.          outset that the subject-matter was a difficult one
The very name given to the highest institutions        and that the lectures could not be termed popular,
of learning reminds us, that from antiquity to and     even though the physicist’s most dreaded
throughout many centuries the universal aspect         weapon, mathematical deduction, would hardly
has been the only one to be given full credit. But     be utilized. The reason for this was not that the
the spread, both in and width and depth, of the        subject was simple enough to be explained
multifarious branches of knowledge by during           without mathematics, but rather that it was much
the last hundred odd years has confronted us           too involved to be fully accessible to
with a queer dilemma. We feel clearly that we          mathematics. Another feature which at least
are only now beginning to acquire reliable             induced a semblance of popularity was the
material for welding together the sum total of all     lecturer's intention to make clear the fundamental
that is known into a whole; but, on the other          idea, which hovers between biology and physics,
hand, it has become next to impossible for a           to both the physicist and the biologist. For
single mind fully to command more than a small         actually, in spite of the variety of topics
specialized portion of it. I can see no other          involved, the whole enterprise is intended to
escape from this dilemma (lest our true who aim        convey one idea only -one small comment on a
be lost for ever) than that some of us should          large and important question. In order not to lose
venture to embark on a synthesis of facts and          our way, it may be useful to outline the plan very
theories, albeit with second-hand and incomplete       briefly in advance. The large and important and
knowledge of some of them -and at the risk of          very much discussed question is: How can the
making fools of ourselves. So much for my              events in space and time which take place
apology. The difficulties of language are not          within the spatial boundary of a living organism
negligible. One's native speech is a closely fitting   be accounted for by physics and chemistry? The
garment, and one never feels quite at ease when        preliminary answer which this little book will
it is not immediately available and has to be          endeavor to expound and establish can be
replaced by another. My thanks are due to Dr           summarized as follows: The obvious inability of
Inkster (Trinity College, Dublin), to Dr Padraig       present-day physics and chemistry to account for
Browne (St Patrick's College, Maynooth) and,           such events is no reason at all for doubting that
last but not least, to Mr S. C. Roberts. They were     they can be accounted for by those sciences.
put to great trouble to fit the new garment on me
and to even greater trouble by my occasional           STATISTICAL PHYSICS. THE
reluctance to give up some 'original' fashion of       FUNDAMENTAL W DIFFERENCE IN
my own. Should some of it have survived the            STRUCTURE
mitigating tendency of my friends, it is to be put     That would be a very trivial remark if it were
at my door, not at theirs. The head-lines of the       meant only to stimulate the hope of achieving in
                                                                                                                   sr
                                                    er
                          c

             e
                                       e
                         j 41 0 0 41 82100Tm ( ) Tj ET Q Q q 18.000002 33.000057 576 756 re Wn /Cs1 cs 0 0 0 sc q 0.23999999 0 0 0.23999999 90 5



                  h eh t
                                y                       a

                                                           o m
                                                                  t
                              ym

                   l                    g
                           y                               t


                                                                t
                                           e
                                          n            lp

                                m i                      i
                 the future what has not been achieved in the past.   sl
                 But the meaning is very much more positive, viz.


                             s
                         s      trl                 u s p.a
                 that the inability, up to the present moment, is
                                                               n
                              n


                                    s
                                                  n
                 amply accounted for. Today,ythanks to the
                                         e

                       r
                                                                                                                n


                                                r n
                 ingenious work of biologists, mainly of


              r
                                                i
                 geneticists, during the last thirty or e        r forty years,
                                                      e


               y                                      n
                 enougheisw a about y actual material t                 .
                             e known              s the s e

                          s
                 ct
                 l eg ee le of torganismsTt 41about their a347 (o) Tj 41 0 0 41 225 36Tm (e) Tj 41 0 0 41 207 37Tm ( ) Tj 41 0 0 41 4760 Tm (a) Tn 41
                 e
                 aa
                 tn
                 fofba sr el u auror i
                 structure  d hcc   se
                                     n              a ma 0 0 h 754
                                                   and a 41     h tn



                                      os l
                     h.
                     r




ioitfR41004136005m(i)Ta410041449353m(p)Tj41004161207Tm(u)Th41004139409Tm(a)Tj4100414330Tm(i)Te4100414320Tm()Tl4100414440Tm.a tpalcovsoe
        iTta41r 0o0a410754f157 5754t43mThftTj
        c re T a w 41 u 345 (e) T,(w) 0re 41
        resr nh t
        m ib r i a
        .nia eraaeinm t.h m trty rma o 41np i a y. hrob
        looo ao o i a
        ntrhltmnary tle ressa t firamp ldys0 0 t41s slieta
        ipps t n
        ein ac n
        taif athe i a u h r a i ae0
        aha osnlme o o vy l w y ooe t r suh
        nh
        d




         o
         ly
         s
         p




           r
           et
           i
           or
           c
           d
          mn
             n

               y



               p




               a
                 functioning to state that, and to tell precisely
                 why present-day physics and chemistry could not
                 h is l account tfor what a ot nf5Tt410 74 Tm(n)u410 5inTj2(iw106m )Tr410 7580m(n)sm4T10 360 respace and
                 p
                 t e .
                 possibly
                 de
                 l


                        e


                 time s h a living organism. The arrangements
                 .lt within
                 l
                 tr
                 re t
                 ofohni m
                 a
                 c olthe
                 o
                 rt




                 p




                 organism and the interplay e te
                 differ in a fundamental way from all those g
                 c epd r n lke a
                 ai
                 s
                 t
                 i
                  l
                     on u atomst in the mostafeec s partsr oss ian h s


                 arrangementsnofaatoms m th t physicists and
                 chemists have hitherto made t er object of their
                 experimental and theoretical research. Yet the
                 s
                 difference which I a 0 t 41 25t.t n
                 m
                 u
                 f




                Tt 41 0 0 41
                 a




                 n
                  n
                   e
                     a p s

                     a
                     t



                     a
                     r
                     n
                      e




                        mr r




                         a
                           i
                            n
                             i r


                           ae o
                            s




                               s
                               r


                         . tn h i
                                 .r 754 463m (e) o 41 0m
                                 s
                                 n
                                e a
                                 re

                               ta r
                               n e

                                 e
                                 n
                                     c i

                                    fr rht t en irvital ot att t


                                     n
                                     v


                                     a



                                      a
                                       n
                                       nr




                              0 e h0 0 s
                                         n




                                    etn a l

               ee lp a ur 41 0 0 41 b r s a
            p itt a h n aa i am h ra r r i
                                           i
                                           t



                                           a
                                            risp




                                           41
                                             o




                                              s
                                                is a
                                             h41 0




                        n o n e e nr wh ei nf s n
               a hro n Tt s ero uop 754 t587m i i
                                           er t i
                                                   po happens e o
                                                     t
                                                  r or ea




                                                   which i ea a
                                                   wi p e t f l t
                                                   o




                                                n Tj n

                                                  a na




              lse n eo r e 41 h i m e tsn ap 0a f r
                                                 41
                                                   e
                                                    i
                                                       i
                                                       yrmitt t of r




                                                   l nee


                                      j 41 0 0 41e 148m
                                                 l 44
                                               hn ie
                                                 a 0 oa
                             e a41 enw 4m 41e a(o) T
                        41 Tt t m nr i m s e p m.e 0 em
                                                      n
                                                      s
                                                        a




                                                        e
                                                         pa
                                                         cf




                                                         a
                                                         l


                                                       n i


                                aa 1Tm ( ) Tjw e e c41. i3
                                                           h




                                                           e
                                                             i


                                                          of these arrangements
                                                             h o t
                                                            the




                                                           nt n

                                                             t i
                                                           e m




                                                      ms i teoi
                                                 posapioa ltalr
                     ahie ntthac aattetanhTje41eh c0c41ta602
                           nierdnr hndni oTa pbcu y hec 359e
                                                               r



                                                               i
                                                             i en
                                                                r
                                                                 e



                                                                ia
                                                                                                          e
                                                                                                              l

                                                                                                              o o a
                                                                                                              e




                                                                                                               a
                                                                                                                 o
                                                                                                                   a



                                                                                                                   h
                                                                                                                      d




                                                                                                                      e
to distribute the marked molecules uniformly            direct inspection. Must that be so? Is there an
throughout the seven seas; if then you took a           intrinsic reason for it? Can we trace back this
glass of water anywhere out of the ocean, you           state of affairs to some kind of first principle, in
would find in it about a hundred of your marked         order to ascertain and to understand why nothing
molecules. The actual sizes of atoms lie between        else is compatible with the very laws of
about 1/5000 and 1/2000 the wave-length of              Nature? Now this, for once, is a problem which
yellow light. The comparison is significant,            the physicist is able to clear up completely. The
because the wave-length roughly indicates the           answer to all the queries is in the affirmative.
dimensions of the smallest grain still
recognizable in the microscope. Thus it will be         THE WORKING OF AN ORGANISM
seen that such a grain still contains thousands of      REQUIRES EXACT PHYSICAL LAWS
millions of atoms. Now, why are atoms so                If it were not so, if we were organisms so
small? Clearly, the question is an evasion. For it      sensitive that a single atom, or even a few atoms,
is not really aimed at the size of the atoms. It is     could make a perceptible impression on our
concerned with the size of organisms, more              senses -Heavens, what would life be like! To
particularly with the size of our own corporeal         stress one point: an organism of that kind would
selves. Indeed, the atom is small, when referred        most certainly not be capable of developing the
to our civic unit of length, say the yard or the        kind of orderly thought which, after passing
metre. In atomic physics one is accustomed to           through a long sequence of earlier stages,
use the so-called Angstrom (abbr. A), which is          ultimately results in forming, among many other
the 10lOth part of a metre, or in decimal notation      ideas, the idea of an atom. Even though we select
0.0000000001 metre. Atomic diameters range              this one point, the following considerations
between 1 and 2A. Now those civic units (in             would essentially apply also to the functioning of
relation to which the atoms are so small) are           organs other than the brain and the sensorial
closely related to the size of our bodies. There is     system. Nevertheless, the one and only thing of
a story tracing the yard back to the humour of an       paramount interest to us in ourselves is, that we
English king whom his councillors asked what            feel and think and perceive. To the physiological
unit to adopt -and he stretched out his arm             process which is responsible for thought and
sideways and said: 'Take the distance from the          sense all the others play an auxiliary part, at least
middle of my chest to my fingertips, that will do       from the human point of view, if not from that of
all right.' True or not, the story is significant for   purely objective biology. Moreover, it will
our purpose. The king would naturally I indicate        greatly facilitate our task to choose for
a length comparable with that of his own body,          investigation the process which is closely
knowing that anything else would be very                accompanied by subjective events, even though
inconvenient. With all his predilection for the         we are ignorant of the true nature of this close
Angstrom unit, the physicist prefers to be told         parallelism. Indeed, in my view, it lies outside
that his new suit will require six and a half yards     the range of natural science and very probably of
of tweed -rather than sixty-five thousand               human understanding altogether. We are thus
millions of Angstroms of tweed. It thus being           faced with the following question: Why should
settled that our question really aims at the ratio      an organ like our brain, with the sensorial system
of two lengths -that of our body and that of the        attached to it, of necessity consist of an
atom - with an incontestable priority of                enormous number of atoms, in order that its
independent existence on the side of the atom,          physically changing state should be in close and
the question truly reads: Why must our bodies be        intimate correspondence with a highly developed
so large compared with the atom? I can imagine          thought? On what grounds is the latter task of the
that many a keen student of physics or chemistry        said organ incompatible with being, as a whole
may have deplored the fact that everyone of our         or in some of its peripheral parts which interact
sense organs, forming a more or less substantial        directly with the environment, a mechanism
part of our body and hence (in view of the              sufficiently refined and sensitive to respond to
magnitude of the said ratio) being itself               and register the impact of a single atom from
composed of innumerable atoms, is much too              outside? The reason for this is, that what we call
coarse to be affected by the impact of a single         thought (1) is itself an orderly thing, and (2) can
atom. We cannot see or feel or hear the single          only be applied to material, i.e. to perceptions or
atoms. Our hypotheses with regard to them differ        experiences, which have a certain degree of
widely from the immediate findings of our gross         orderliness. This has two consequences. First, a
sense organs and cannot be put to the test of           physical organization, to be in close
correspondence with thought (as my brain is           3, 4, 5, ...in mathematics. An entire newcomer
with my thought) must be a very well-ordered          should not expect to obtain from the following
organization, and that means that the events that     few pages a full understanding and appreciation
happen within it must obey strict physical laws,      of the subject, which is associated with the
at least to a very high degree of accuracy.           illustrious names of Ludwig Boltzmann and
Secondly, the physical impressions made upon          Willard Gibbs and treated in textbooks under the
that physically well-organized system by other        name of 'statistical thermodynamics'. If you fill
bodies from outside, obviously correspond to the      an oblong quartz tube with oxygen gas and put it
perception and experience of the corresponding        into a magnetic field, you find that the gas is
thought, forming its material, as I have called it.   magnetized. The magnetization is due to the fact
Therefore, the physical interactions between our      that the oxygen molecules are little magnets and
system and others must, as a rule, themselves         tend to orientate themselves parallel to the field,
possess a certain degree of physical orderliness,     like a compass needle. But you must not think
that is to say, they too must obey strict physical    that they actually all turn parallel. For if you
laws to a certain degree of accuracy.                 double the field, you get double the
                                                      magnetization in your oxygen body, and that
PHYSICAL LAWS REST ON ATOMIC                          proportionality goes on to extremely high field
STATISTICS AND ARE THEREFORE ONLY                     strengths, the magnetization increasing at the rate
APPROXIMATE                                           of the field you apply. This is a particularly clear
And why could all this not be fulfilled in the case   example of a purely statistical law. The
of an organism composed of a moderate number          orientation the field tends to produce is
of atoms only and sensitive already to the impact     continually counteracted by the heat motion,
of one or a few atoms only? Because we know           which works for random orientation. The effect
all atoms to perform all the time a completely        of this striving is, actually, only a small
disorderly heat motion, which, so to speak,           preference for acute over obtuse angles between
opposes itself to their orderly behaviour and does    the dipole axes and the field. Though the single
not allow the events that happen between a small      atoms change their orientation incessantly, they
number of atoms to enrol themselves according         produce on the average (owing to their enormous
to any recognizable laws. Only in the co-             number) a constant small preponderance of
operation of an enormously large number of            orientation in the direction of the field and
atoms do statistical laws begin to operate and        proportional to it. This ingenious explanation is
control the behaviour of these assemblies with an     due to the French physicist P. Langevin. It can
accuracy increasing as the number of atoms            be checked in the following way. If the observed
involved increases. It is in that way that the        weak magnetization is really the outcome of rival
events acquire truly orderly features. All the        tendencies, namely, the magnetic field, which
physical and chemical laws that are known to          aims at combing all the molecules parallel, and
play an important part in the life of organisms       the heat motion, which makes for random
are of this statistical kind; any other kind of       orientation, then it ought to be possible to
lawfulness and orderliness that one might think       increase the magnetization by weakening the
of is being perpetually disturbed and made            heat motion, that is to say, by lowering the
inoperative by the unceasing heat motion of the       temperature, instead of reinforcing the field. That
atoms.                                                is confirmed by experiment, which gives the
                                                      magnetization inversely proportional to the
THEIR PRECISION IS BASED ON THE                       absolute temperature, in quantitative agreement
LARGE OF NUMBER OF ATOMS                              with theory (Curie's law). Modern equipment
INTERVENING                                           even enables us, by lowering the temperature, to
FIRST EXAMPLE (PARAMAGNETISM)                         reduce the heat motion to such insignificance
Let me try to illustrate this by a few examples,      that the orientating tendency of the magnetic
picked somewhat at random out of thousands,           field can assert itself, if not completely, at least
and possibly not just the best ones to appeal to a    sufficiently to produce a substantial fraction of
reader who is learning for the first time about       'complete magnetization'. In this case we no
this condition of things -a condition which in        longer expect that double the field strength will
modern physics and chemistry is as fundamental        double the magnetization, but that the latter will
as, say, the fact that organisms are composed of      increase less and less with increasing field,
cells is in biology, or as Newton's Law in            approaching what is called 'saturation'. This
astronomy, or even as the series of integers, 1, 2,   expectation too is quantitatively confirmed by
experiment. Notice that this behaviour entirely       thing about this rather simple and apparently not
depends on the large numbers of molecules             particularly interesting process is that it is in no
which co-operate in producing the observable          way due, as one might think, to any tendency or
magnetization. Otherwise, the latter would not be     force driving the permanganate molecules away
an constant at all, but would, by fluctuating quite   from the crowded region to the less crowded one,
irregularly of from one second to the next, bear      like the population of a country spreading to
witness to the vicissitudes of pe the contest         those parts where there is more elbow-room.
between heat motion and field.                        Nothing of the sort happens with our
                                                      permanganate molecules. Every one of them
SECOND EXAMPLE (BROWNIAN                              behaves quite independently of all the others,
MOVEMENT, DIFFUSION)                                  which it very seldom meets. Everyone of them,
If you fill the lower part of a closed glass vessel   whether in a crowded region or in an empty one,
with fog, pt consisting of minute droplets, you       suffers the same fate of being continually
will find that the upper or boundary of the fog       knocked about by the impacts of the water
gradually sinks, with a well-defined velocity,        molecules and thereby gradually moving on in
determined by the viscosity of the air and the        an unpredictable direction -sometimes towards
size and the specific gravity of the droplets. But    the higher, sometimes towards the lower,
if you look at one of the droplets under the          concentrations, sometimes obliquely. The kind
microscope you find that it does not permanently      of motion it performs has often been compared
sink with constant velocity, but performs a very      with that of a blindfolded person on a large
irregular movement, the so-called Brownian            surface imbued with a certain desire of 'walking',
movement, which corresponds to a regular              but without any preference for any particular
sinking only on the average. Now these droplets       direction, and so changing his line
are not atoms, but they are sufficiently small and    continuously. That this random walk of the
light to be not entirely insusceptible to the         permanganate molecules, the same for all of
impact of one single molecule of those which          them, should yet produce a regular flow towards
hammer their surface in perpetual impacts. They       the smaller concentration and ultimately make
are thus knocked about and can only on the            for uniformity of distribution, is at first sight
average follow the influence of gravity. This         perplexing -but only at first sight. If you
example shows what funny and disorderly               contemplate in Fig. 4 thin slices of
experience we should have if our senses were          approximately constant concentration, the
susceptible to the impact of a few molecules          permanganate molecules which in a given
only. There are bacteria and other organisms so       moment are contained in a particular slice will,
small that they are strongly affected by this         by their random walk, it is true, be carried with
phenomenon. Their movements are determined            equal probability to the right or to the left. But
by the thermic whims of the surrounding               precisely in consequence of this, a plane
medium; they have no choice. If they had some         separating two neighbouring slices will be
locomotion of their own they might nevertheless       crossed by more molecules coming from the left
succeed in on getting from one place to another -     than in the opposite direction, simply because to
but with some difficulty, since the heat motion       the left there are more molecules engaged in
tosses them like a small boat in a rough sea. A       random walk than there are to the right. And as
phenomenon very much akin to Brownian                 long as that is so the balance will show up as a
movement is that of diffusion. Imagine a vessel       regular flow from left to right, until a uniform
filled with a fluid, say water, with a small          distribution is reached. When these
amount of some coloured substance dissolved in        considerations are translated into mathematical
it, say potassium permanganate, not in uniform        language the exact law of diffusion is reached in
concentration, but rather as in Fig. 4, where the     the form of a partial differential equation
dots indicate the molecules of the dissolved
substance (permanganate) and the concentration        §p/§t= DV2P
diminishes from left to right. If you leave this
system alone a very slow process of 'diffusion'       which I shall not trouble the reader by
sets in, the at permanganate spreading in the         explaining, though its meaning in ordinary
direction from left to right, that is, from the       language is again simple enough. The reason for
                                                          it
places of higher concentration towards the places     mentioning the stern 'mathematically exact' law
of lower concentration, until it is equally                                  u
                                                      here, is to emphasize that its physical exact
distributed of through the water. The remarkable
particular application. Being based on pure
chance, its validity is only approximate. If it is,
as a rule, a very good approximation, that is only
due to the enormous number of molecules that
co-operate in the phenomenon. The smaller their
number, the larger the quite haphazard deviations
we must expect and they can be observed under
favourable circumstances.

THIRD EXAMPLE (LIMITS OF ACCURACY
OF MEA
setting up its marvellously regular and well-           THE HEREDITARY CODE-SCRIPT
ordered working. How do these conclusions,              (CHROMOSOMES)
reached, biologically speaking, a priori (that is,      Let me use the word 'pattern' of an organism in
from the purely physical point of view), fit            the sense in be which the biologist calls it 'the
in with actual biological facts? At first sight one     four-dimensional pattern', meaning not only the
is inclined to think that the conclusions are little    structure and functioning of that organism in the
more than trivial. A biologist of, say, thirty years    adult, or in any other particular stage, but the
ago might have said that, although it was quite         whole of its ontogenetic development from the
suitable for a popular lecturer to emphasize the        fertilized egg the cell to the stage of maturity,
importance, in the organism as elsewhere, of            when the organism begins to reproduce itself.
statistical physics, the point was, in fact, rather a   Now, this whole four-dimensional pattern is
familiar truism. For, naturally, not only the body      known to be determined by the structure of that
of an adult individual of any higher species, but       one cell, the fertilized egg. Moreover, we know
every single cell composing it contains a               that it is essentially determined by the structure
'cosmical' number of single atoms of every kind.        of only a small part of that cell, its large nucleus.
And every particular physiological process that         This nucleus, in the ordinary 'resting state' of the
we observe, either within the cell or in its            cell, usually appears as a network of chromatine,
interaction with the cell environment, appears -or      distributed over the cell. But in the vitally
appeared thirty years ago -to involve such              important processes of cell division (mitosis and
enormous numbers of single atoms and single             meiosis, see below) it is seen to consist of a set
atomic processes that all the relevant laws of          of particles, usually fibre-shaped or rod-like,
physics and physical chemistry would be                 called the chromosomes, which number 8 or 12
safeguarded even under the very exacting                or, in man, 48. But I ought really to have written
demands of statistical physics in respect of large      these illustrative numbers as 2 X 4, 2 X 6, ..., 2 X
numbers; this demand illustrated just now by the        24, ..., and I ought to have spoken of two sets, in
\/n rule. Today, we know that this opinion would        order to use the expression in the customary
have been a mistake. As we shall presently see,         strict meaning of the biologist. For though the
incredibly small groups of atoms, much too              single chromosomes are sometimes clearly
small to display exact statistical laws, do play a      distinguished and individualized by shape and
dominating role in the very orderly and lawful          size, the two sets are almost entirely alike. As we
events within a living organism. They have              have shall see in a moment, one set comes from
control of the observable large-scale features          the mother (egg cell), one from the father
which the organism acquires in the course of its        (fertilizing spermatozoon). It is these
development, they determine important                   chromosomes, or probably only an axial skeleton
characteristics of its functioning; and in all this     fibre of what we actually see under the
very sharp and very strict me biological laws are       microscope as the chromosome, that contain in
displayed. I must begin with giving a brief             some kind of code-script the entire pattern of the
summary of the situation in biology, more               individual's future development and of its
especially in genetics -in other words, I have to       functioning in the mature state. Every complete
summarize the present state of knowledge in a           set of chromosomes contains the full code; so
subject of which I am not a master. This cannot         there are, as a rule, two copies of the latter in the
be helped and I apologize, particularly to any          fertilized egg cell, which forms the earliest stage
biologist, for the dilettante character of my           of the future individual. In calling the structure
summary. On the other hand, I beg leave to put          of the chromosome fibres a code-script we mean
the prevailing ideas before you more or less            that the all-penetrating mind, once conceived by
dogmatically. A poor theoretical physicist could        Laplace, to which every causal connection lay
not be expected to produce anything like a              immediately open, could tell from their structure
competent survey of the experimental evidence,          whether the egg would develop, under suitable
which consists of a large number of long and            conditions, into a black cock or into a speckled
beautifully interwoven series of breeding               hen, into a fly or a maize plant, a rhododendron,
experiments of truly unprecedented ingenuity on         a beetle, a mouse or a woman. To which we may
the one hand and of direct observations of the          add, that the appearances of the egg cells are
living cell, conducted with all the refinement of       very often remarkably similar; and even when
modern microscopy, on the other.                        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             of all his designs. If that is true (as it conceivably
added for obvious reasons. But the term                    might be, considering the high intelligence and
code-script is, of course, too narrow. The                 reliability of his troops) it provides an excellent
chromosome structures are at the same time                 analogy to our case, in which the corresponding
instrumental in bringing about the development             fact certainly is literally true. The most
they foreshadow. They are law-code and                     surprising fact is the doubleness of the
executive power -or, to use another simile, they           chromosome set, maintained throughout the
are architect's plan and builder's craft -in one.          mitotic divisions. That it is the outstanding
                                                           feature of the genetic mechanism is most
GROWTH OF THE BODY BY CELL                                 strikingly revealed by the one and only departure
DIVISION (MITOSIS)                                         from the rule, which we have now to discuss.
How do the chromosomes behave in
ontogenesis? The growth of an organism is                  REDUCTIVE DIVISION (MEIOSIS) AND
effected by consecutive cell met divisions. Such           FERTILIZATION (SYNGAMY)
a cell division is called mitosis. It is, in the life of   Very soon after the development of the
a cell, not such a very frequent event as one              individual has set in, a group of cells is reserved
might expect, considering the enormous number              for producing at a later stage the so-called
of cells of which our body is composed. In the             gametes, the sperm cells or egg cells, as the case
beginning the growth is rapid. The egg divides             may be, needed for the reproduction of the
into two 'daughter cells' which, at the next step,         individual in maturity. 'Reserved' means that
will produce a generation of four, then of 8, 16,          they do not serve other purposes in the meantime
32, 64, ..., etc. The frequency of division will not       and suffer many fewer mitotic divisions. The
remain exactly the same in all parts of the                exceptional or reductive division (called meiosis)
growing body, and that will break the regularity           is the one by which eventually, on maturity, the
of these numbers. But from their rapid increase            gametes posed to are produced from these
we infer by an easy computation that on the                reserved cells, as a rule only a short time before
average as few as 50 or 60 successive divisions            syngamy is to take place. In meiosis the double
suffice to produce the number of cells in a grown          chromosome set of the parent cell simply
man -or, say, ten times the number, taking into            separates into two single sets, one of which goes
account the exchange of cells during lifetime.             to each of the two daughter cells, the gametes. In
Thus, a body cell of mine is, on the average, only         other words, the mitotic doubling of the number
the 50th or 60th 'descendant' of the egg that was          of chromosomes does not take place in meiosis,
I.                                                         the number remains constant and thus every
                                                           gamete receives only half -that is, only one
IN MITOSIS EVERY CHROMOSOME IS                             complete copy of the code, not two, e.g. in man
DUPLICATED                                                 only 24:, not 2 X 24: = 4:8. Cells with only one
How do the chromosomes behave on mitosis?                  chromosome set are called haploid (from Greek
They duplicate -both sets, both copies of the              απλοϖχ, single). Thus the gametes are haploid,
code, duplicate. The process has been intensively          the ordinary body cells diploid (from Greek
studied under the microscope and is of                     Οπλϖχ, double). Individuals with three, four,
paramount interest, but much too involved to               ...or generally speaking with many chromosome
describe here in detail. The salient point is that         sets in all their body cells occur occasionally; the
each of the two 'daughter cells' gets a dowry of           latter are then called triploid, tetraploid, ...,
two further complete sets of chromosomes                   polyploid. In the act of syngamy the male
exactly similar to those of the parent cell. So all        gamete (spermatozoon) and the female gamete
the body cells are exactly alike as regards their          (egg), both haploid cells, coalesce to form the
chromosome treasure. However little we                     fertilized egg cell, which is thus diploid. One of
understand the device we cannot but think that it          its chromosome sets comes from the mother, one
must be in some way very relevant to the                   from the father.
functioning of the organism, that every single
cell, even a less important one, should be in              HAPLOID INDIVIDUALS
possession of a complete (double) copy of the              One other point needs rectification. Though not
code-script. Some time ago we were told in the             indispensable for our purpose it is of real
newspapers that in his African campaign General            interest, since it shows that actually a fairly
Montgomery made a point of having every                    complete code-script of the 'pattern' is contained
single soldier of his army meticulously informed           in every single set of chromosomes. There are
instances of meiosis not being followed shortly        in particular on one of them, say No.5. It is a
after by fertilization, the haploid cell (the          faithful replica either of the No.5 my father
'gamete') under- going meanwhile numerous              received from his father or of the No.5 he had
mitotic cell divisions, which result in building up    received from his mother. The issue was decided
a complete haploid individual. This is the case in     by a 50:50 chance in the meiosis taking place in
the male bee, the drone, which is produced             my father's body in November 1886 and
parthenogenetically, that is, from non-fertilized      producing the spermatozoon which a few days
and therefore haploid eggs of the queen. The           later was to be effective in begetting me. Exactly
drone has no father! All its body cells are            the same story could be repeated about
haploid. If you please, you may call it a grossly      chromosomes Nos. 1, 2, 3, ...,24 of my paternal
exaggerated spermatozoon; and actually, as             set, and mutatis mutandis about every one of my
everybody knows, to function as such happens to        maternal chromosomes. Moreover, all the 48
be its one and only task in life. However, that is     issues are fi entirely independent. Even if it were
perhaps a ludicrous point of view. For the case is     known that my paternal it chromosome No.5
not two quite unique. There are families of plants     came from my grandfather Josef Schrodinger,
in which the haploid gamete which is produced          the No.7 still stands an equal chance of being
by meiosis and is called a spore in the such cases     either also from him, or from his wife Marie, nee
falls to the ground and, like a seed, develops into    Bogner.
a the true haploid plant comparable in size with
the diploid.     Fig. 5 is a rough sketch of a moss,   CROSSING-OVER. LOCATION OF
well known in our forests. The leafy lower part is     PROPERTIES
the haploid plant, called the gametophyte,             But pure chance has been given even a wider
because at its upper end it develops sex organs        range in mixing the grandparental inheritance in
and gametes, which by mutual fertilization             the offspring than would appear from the
produce in the ordinary way the diploid plant,         preceding description, in which it has been
the bare stem with the capsule at the top. This is     tacitly assumed, or even explicitly stated, that a
called the sporophyte, because it produces, by         particular chromosome as a whole was either
meiosis, the spores in the capsule at the top.         from the grandfather or back to from the
When the capsule opens, the spores fall to the         grandmother; in other words that the single
ground and develop into a leafy stem, etc. The         chromosomes are passed on undivided. In actual
course of events is appropriately called               fact they are not, or on one of not always. Before
alternation of generations. You may, if you            being separated in the reductive division, No.5
choose, look upon the ordinary case, man and the       my say the one in the father's body, any two
animals, in the same way. But the 'gametophyte'        'homologous' chromosomes come into close
is then as a rule a very short-lived, unicellular      contact with each other, during chance in which
generation, spermatozoon or egg cell as the case       they sometimes exchange entire portions in the
may be. Our body corresponds to the sporophyte.        way illustrated in Fig. 6. By this process, called
Our 'spores' are the reserved cells from which, by     'crossing-over', days later two properties situated
meiosis, the unicellular generation springs.           in the respective parts of that chromosome will
                                                       be separated in the grandchild, who will follow
THE OUTSTANDING RELEVANCE OF                           the grandfather in one of them, the grandmother
THE REDUCTIVE DIVISION                                 in the other one. The act of crossing-over, being
The important, the really fateful event in the         neither very rare nor very issues are frequent, has
process of reproduction of the individual is not       provided us with invaluable information
fertilization but meiosis. One set of                  regarding the location of properties in the
chromosomes is from the father, one from the           chromosomes. For a full account we should have
mother. Neither chance nor destiny can interfere       to draw on conceptions not introduced before the
with that. Every man owes just half of his             next chapter (e.g. heterozygosy, dominance,
inheritance to his mother, half of it to his father.   etc.); but as that would take us beyond the range
That one or the other strain seems often to            of this little book, let me indicate the salient
prevail is due to other reasons which we shall         point right away. If there were no crossing-over,
come to later. (Sex itself is, of course, the          two properties for which the same chromosome
simplest instance of such prevalence.). But when       is responsible would always be passed on in
you trace the origin of your inheritance back to       mixing together, no descendant receiving one of
your grandparents, the case is different. Let me       them without receiving the other as well; but two
fix attention on my paternal set of chromosomes,       properties, due to different it has been
chromosomes, would either stand a 50:50 chance          notwithstanding the apparent linguistic out for
of being separated or they would invariably be          and logical contradiction of this statement. The
separated -the latter when they were situated in        differences of Its the properties actually are
homologous chromosomes of the same ancestor,            discrete, as will emerge in the next chapter when
which could never go together. These rules and          we have to speak of mutations and the dry
chances are interfered with by crossing-over.           scheme hitherto presented will, as I hope, acquire
Hence the probability of this event can be              more life each colour.
ascertained by registering carefully the
percentage composition of the off-spring in             MAXIMUM SIZE OF A GENE
extended breeding experiments, suitably laid out        We have just introduced the term gene for the
for at the purpose. In analysing the statistics, one    hypothetical same material carrier of a definite
accepts the suggestive working hypothesis that          hereditary feature. We must now the stress two
the 'linkage' between two properties situated in        points which will be highly relevant to our every
the same chromosome, is the less frequently             investigation. The first is the size -or, better, the
broken by crossing-over, the nearer they lie to         maximum size -of such a carrier; in other words,
each other. For then there is less chance of the        to how small a volume can we trace the location?
point of exchange lying between them, whereas           The second point will be the permanence of a
properties located near the opposite ends of the        gene, to be inferred from the durability of the
chromosomes are separated by every crossing-            hereditary pattern. As regards the size, there are
over. (Much the same applies to the                     two entirely independent estimates, one resting
recombination of properties located in                  on genetic evidence (breeding experiments), the
homologous chromosomes of the same ancestor.)           other on cytological evidence (direct microscopic
In this way one may expect to get from the              inspection). The first is, in principle, simple
'statistics of linkage' a sort of 'map of properties'   enough. After having, in the way described
within every chromosome. These anticipations            above, located in the chromosome a considerable
have been fully confirmed. In the cases to which        number of different (large-scale) features (say of
tests have been thoroughly applied (mainly, but         the Drosophila fly) within a particular one of its
not only, Drosophila) the tested properties             chromosomes, to get the required estimate we
actually divide into as h many separate groups,         need only divide the measured length of that
with no linkage from group to group, as there are       chromosome by the number of features and
different chromosomes (four in Drosophila).             multiply by the cross-section. For, of course, we
Within every group a linear map of properties           count as different only such features as are
can be drawn up which accounts quantitatively           occasionally separated by crossing-over, so that
for the degree of linkage it between any two of         they cannot be due to the same (microscopic or
that group, so that there is little doubt h that they   molecular) structure. On the other hand, it is
actually are located, and located along a line, as      clear that our estimate can only give a maximum
the rod-like shape of the chromosome suggests.          size, because the number of features isolated by
Of course, the scheme of the hereditary                 in this genetic analysis is continually increasing
mechanism, as drawn up here, is still rather            as work goes on. The other estimate, though
empty and colourless, even slightly naive. For          based on microscopic inspection, is really far
we have not said what exactly we understand by          less direct. Certain cells of Drosophila (namely,
a property. It seems neither adequate nor               those of its salivary glands) are, for some reason,
possible to dissect into discrete 'properties' the      enormously enlarged, and so are their
pattern of an organism which is essentially a           chromosomes. In them you distinguish a
unity, a 'whole'. Now, what we actually state in        crowded pattern of transverse dark bands across
any particular case is, that a pair of ancestors        the fibre. C. D. Darlington has remarked that the
were different in a certain well-defined respect        number of these bands (2,000 in the case he
(say, one had blue eyes, the other brown), and          uses) is, though, considerably larger, yet roughly
that the offspring follows in this respect either       of the same order of magnitude as the number of
one or the other. What we locate in                     genes located in that chromosome by breeding
the chromosome is the seat of this difference.          experiments. He inclines to regard these bands as
(We call it, in technical language, a 'locus', or, if   indicating the actual genes (or separations of
we think of the hypothetical material structure         genes). Dividing the length of the chromosome,
underlying it, a 'gene'.) Difference of by              measured in a normal-sized cell by their number
property, to my view, is really the fundamental         (2,000) he finds the volume of a gene equal to a
concept rather than property itself,                    cube of edge 300 A. Considering the roughness
of the estimates, we may regard this to be also         different plane. I mean the fact that we, whose
the size obtained by the first method.                  total being is entirely based on a marvellous
                                                        interplay of this very kind, yet if all possess the
SMALL NUMBERS                                           power of acquiring considerable knowledge
A full discussion of the bearing of statistical         about it. I think it possible that this knowledge
physics on all the facts I am recalling -or             may advance to little just a short of a complete
perhaps, I ought to say, of the bearing of these        understanding -of the first marvel. The second
facts on the use of statistical physics in the living   may well be beyond human understanding.
cell will follow later. But let me draw attention at
this point to the fact that 300 A is only about 100     CHAPTER 3
or 150 atomic distances in a liquid or in a solid,      Mutations
so that a gene contains certainly not more than
about a million or a few million atoms. That            'JUMP-LIKE' MUTATIONS -THE
number is much too small (from the \/v point of         WORKING- GROUND OF NATURAL
view) to entail an orderly and lawful behaviour         SELECTION
according to statistical physics -and that means        The general facts which we have just put forward
according to physics. It is too small, even if all      in evidence of the durability claimed for the gene
these atoms played the same role, as they do in a       structure, are perhaps too familiar to us to be
gas or in a drop of liquid. And the gene is most        striking or to be regarded as convincing. Here,
certainly not just a homogeneous drop of liquid.        for once, the common saying that exceptions
It is probably a large protein molecule, in which       prove the rule is actually true. If there were no
every atom, every radical, every heterocyclic           exceptions to the likeness between children and
ring plays an individual role, more or less             parents, we should have been deprived not only
different from that played by any of the other          of all those beautiful experiments which have
similar atoms, radicals, or rings. This, at any         revealed to us the detailed mechanism of
rate, is the opinion of leading geneticists such as     heredity, but also of that grand, million-fold
Haldane and Darlington, and we shall soon have          experiment of Nature, which forges the species
to refer to genetic experiments which come very         by natural selection and survival of the fittest.
near to proving it.                                     Let me take this last important subject as the
                                                        starting-point for presenting the relevant facts -
PERMANENCE                                              again with an apology and a reminder that I am
Let us now turn to the second highly relevant           not a biologist. We know definitely, today, that
question: What degree of permanence do we               Darwin was mistaken in regarding the small,
encounter in hereditary properties and what must        continuous, accidental variations, that are bound
we therefore attribute to the material structures       to occur even in the most homogeneous
which carry them? The answer to this can really         population, as the material on which natural
be given without any special investigation. The         selection works. For it has been proved that they
mere fact that we speak of hereditary properties        are not inherited. The fact is important enough to
indicates that we recognize the permanence to be        be illustrated briefly. If you take a crop of
of the almost absolute. For we must not forget          pure-strain barley, and measure, ear by ear, the
that what is passed on by the parent to the child       length of its awns and plot the result of your
is not just this or that peculiarity, a hooked nose,    statistics, you will get a bell-shaped curve as
short fingers, a tendency to rheumatism,                shown in Fig. 7, where the number of ears with a
haemophilia, dichromasy, etc. Such features we          definite length of awn is plotted against the
may conveniently select for studying the laws of        length. In other words: a definite medium length
heredity. But actually it is the whole (four-           prevails, and deviations in either direction occur
dimensional) pattern of the 'phenotype', the all        with certain frequencies. Now pick out a group
the visible and manifest nature of the individual,      of ears (as indicated by blackening) with awns
which is reproduced without appreciable change          noticeably beyond the average, but sufficient in
for generations, permanent within centuries -           number to be sown in a field by themselves and
though not within tens of thousands of years -and       give a new crop. In making the same statistics
borne at each transmission by the material in a         for this, Darwin would have expected to find the
structure of the nuclei of the two cells which          corresponding curve shifted to the right. In other
unite to form the fertilized egg cell. That is a        words, he would have expected to produce by
marvel -than which only one is greater; one that,       selection an increase of the average length of the
if intimately connected with it, yet lies on a          awns. That is not the case, if a truly pure-bred
strain of barley has been used. The new               are a suitable material on which natural selection
statistical curve, obtained from the selected crop,   may work and produce the species as described
is identical with the first one, and the same         by Darwin, by eliminating the unfit and letting
would be the case if ears with particularly short     the fittest survive. In Darwin's theory, you
awns had been selected for seed. Selection has        just have to substitute 'mutations' for his 'slight
no effect -because the small, continuous              accidental variations' (just as quantum theory
variations are not inherited. They are obviously      substitutes 'quantum jump' for 'continuous
not based on the structure of the hereditary          transfer of energy'). In all other respects little
substance, they are accidental. But about forty       change was necessary in Darwin's theory, that is,
years ago the Dutchman de Vries discovered that       if I am correctly interpreting the view held by the
in the offspring even of thoroughly pure-bred         majority of biol ogists.
stocks, a very small number of individuals, say
two or three in tens of thousands, turn up with       LOCALIZATION, RECESSIVITY AND
small but 'jump-like' changes, the expression         DOMINANCE
‘jump-like' not meaning that the change is so         We must now review some other fundamental
very considerable, but that there is a                facts and notions about mutations, again in a
discontinuity inasmuch as there are no                slightly dogmatic manner, without showing
intermediate forms between the unchanged and          directly how they spring, one by one, from the
the few changed. De Vries called that a mutation.     experimental evidence. We should expect a
The significant fact is the discontinuity. It         definite observed mutation to be caused by a
reminds a physicist of quantum theory -no             change in a definite region in one of the
intermediate energies occurring between two           chromosomes. And so it is. It is important to
neighbouring energy levels. He would be               state that we know definitely, that it is a change
inclined to call de Vries's mutation theory,          in one chromosome only, but not in the
figuratively, the quantum theory of biology. We       corresponding 'locus' of the homologous
shall see later that this is much more                chromosome. Fig. 8 indicates this schematically,
than figurative. The mutations are actually due to    the cross denoting the mutated a locus. The fact
quantum jumps in the gene molecule. But               that only one chromosome is affected is revealed
quantum theory was but two years old when de          when the mutated individual (often called
Vries first published his discovery, in 1902.         'mutant') is crossed with a non-mutated one. For
Small wonder that it took another generation to       exactly half of the offspring exhibit the mutant
discover the intimate connection!                     character and half the normal one. That is what is
                                                      to be expected as a consequence of the
THEY BREED TRUE, THAT IS, THEY ARE                    separation of the two chromosomes on meiosis
PERFECTLY INHERITIED                                  in the mutant as shown, very schematically, in
Mutations are inherited as perfectly as the           Fig. 9. This is a 'pedigree', representing every
original, correctly unchanged characters were.        individual (of three consecutive generations)
To give an example, in the first crop of barley       simply by the pair of chromosomes in question.
considered above a few ears might turn up             Please realize that if the mutant had both its
with awns considerably outside the range of           chromosomes affected, all the children would
variability shown in Fig. 7, say with no awns at      receive the same (mixed) inheritance, different
all. They might represent a de Vries mutation         from that of either parent. But experimenting in
and would then breed perfectly true, that is to       this domain is not as simple as would appear
We must say, all their descendants would be           from what has just been said. It is complicated
equally awnless. Hence a mutation is definitely a     by the second important fact, viz. that mutations
change in the hereditary without treasure and has     are very often latent. What does that mean? In
to be accounted for by some change in the             the mutant the two copies of the code-script are
hereditary substance. Actually most of the            no longer identical; they present two different
important breeding experiments, which have            'readings' or 'versions', at any rate in that one
revealed to us the mechanism of by a heredity,        place. Perhaps it is well to point out at once that,
consisted in a careful analysis of the                while it might be tempting, it would nevertheless
offspring obtained by crossing, according to a        be entirely wrong to regard the original version
preconceived plan, mutated (or, in many cases,        as 'orthodox', and the mutant version as 'heretic'.
multiply mutated) with non-mutated or with            We have to is regard them, in principle, as being
differently mutated individuals. On the other         of equal right -for the normal characters have
hand, by virtue of their breeding true, mutations     also arisen from mutations. What actually
happens is that the 'pattern' of the individual, as a   brief, but highly technical statement: A recessive
general rule, follows either the one or the other       allele influences the phenotype only when the
rte version, which may be the normal or the             genotype is homozygous. We shall use these
mutant one. The -version which is followed is           technical expressions occasionally, but shall
called dominant, the other, recessive; in other         recall their meaning to the reader where
words, the mutation is called dominant or               necessary.
recessive, according to whether it is immediately
effective in changing the pattern or not.               THE HARMFUL EFFECT OF
Recessive mutations are even more frequent than         CLOSE-BREEDING
dominant ones and are very important, though at         Recessive mutations, as long as they are only
first they do not show up at all. To affect the         heterozygous, are of course no working-ground
pattern, they have to be present in both                for natural selection. If they are detrimental, as
chromosomes (see Fig. 10). Such individuals can         mutations very often are, they will nevertheless
be produced when two equal recessive mutants            not be eliminated, because they are latent. Hence
happen to be crossed with each other or when a          quite a host of unfavourable mutations may
mutant is crossed with itself; this is possible in      accumulate and do no immediate damage. But
hermaphroditic plants and even happens                  they are, of course, transmitted to that half of the
spontaneously. An easy reflection shows that in         offspring, and that has an important application
these cases about one-quarter of the offspring          to man, cattle, poultry or any other species, the
will be of this type and thus visibly exhibit the       good physical qualities of which are of
mutated pattern.                                        immediate concern to us. In Fig. 9 it is assumed
                                                        that a male individual (say, for concreteness,
INTRODUCING SOME TECHNICAL                              myself) carries such a recessive detrimental
LANGUAGE                                                mutation heterozygously, so that it does not
I think it will make for clarity to explain here a      show up. Assume that my wife is free of it. Then
few technical terms. For what I called 'version of      half of our children (second line) will also carry
the code-script' -be it the original one or a mutant    it -again heterozygously. If all of them are again
one -the term 'allele' has been; adopted. When          mated with non-mutated partners (omitted from
the versions are different, as indicated in Fig. 8,     the diagram, to avoid reed confusion), a quarter
the individual is called heterozygous, with             of our grandchildren, on the average, will be
respect to that locus. When they are equal, as in       affected in the same way. No danger of the evil
the non-mutated individual or in the case of Fig.       ever becoming manifest arises, unless of equally
10, they are called homozygous. Thus a recessive        affected individuals are crossed with each other,
allele influences the pattern only when                 when, as an easy reflection shows, one-quarter of
homozygous, whereas a dominant allele                   their children, being homozygous, would
produces the same pattern, whether homozygous           manifest the damage. Next to self-fertilization
or only heterozygous. Colour is very often              (only possible in hermaphrodite plants) the
dominant over lack of colour (or white). Thus,          greatest danger would be a marriage between a
for example, a pea will flower white only when it       son and a daughter of mine. Each of them
has the 'recessive allele responsible for white' in     standing an even chance of being latently
both chromosomes in question, when it is                affected or not, one-quarter of these incestuous
'homozygous for white'; it will then breed true,        unions would be dangerous inasmuch as
and all its descendants will be white. But one 'red     one-quarter of its children would manifest the
allele' (the other being white; 'heterozygous') will    damage. The danger factor for an incestuously
make it flower red, and so will two red alleles         bred child is thus 1: 16. In the same way the
('homozygous'). The difference of the latter two        danger: factor works out to be 1 :64 for the
cases will only show up in the offspring,               offspring of a union between two ('clean-bred')
when the heterozygous red will produce some             grand- children of mine who are first cousins.
white descendants, and the homozygous red will          These do not seem to be but overwhelming odds,
breed true. The fact that two individuals may be        and actually the second case is usually tolerated.
exactly alike in their outward appearance, yet          But do not forget that we have analysed the
differ in their inheritance, is so important that an    consequences of only one possible latent injury
exact differentiation is desirable. The geneticist      in one partner of the ancestral couple ('me and
says they have the same phenotype, but different        my wife'). Actually both of them are quite likely
genotype. The contents of the preceding                 to harbour more than one latent deficiency of this
paragraphs could thus be summarized in the              kind. If you know that you yourself harbour a
definite one, you have to reckon with l out of 8      would in the twentieth century become the
of your first cousins sharing it! Experiments with    lodestar of an entirely new branch of science,
plants and animals seem to indicate that in           easily the most interesting of our days. His paper
addition to comparatively rare deficiencies of a      was forgotten and was only rediscovered in
serious kind, there seem to be a host of minor        1900, simultaneously and independently, by
ones whose chances combine to deteriorate the         Correns (Berlin), de Vries (Amsterdam) and
offspring of close-breeding as a whole. Since we      Tschermak may (Vienna).
are no longer inclined to eliminate failures in the
harsh way the Lacedemonians used to adopt in          THE NECESSITY OF MUTATION BEING A
the Taygetos mountain, we have to take a              RARE EVENT
particularly serious view about these things in       So far we have tended to fix our attention on
the case of man, were natural selection of the        harmful mutations, which may be the more
fittest is largely retrenched, nay, turned to the     numerous; but it must be definitely stated that we
contrary. The anti-selective effect of the modern     do encounter advantageous mutations as well. If
mass slaughter of the healthy youth of all nations    a spontaneous mutation is a small step in the
is hardly outweighed by the consideration that in     development of the species, we get the
more primitive conditions war may have had a          impression that some change is 'tried out' in
positive value in letting the fittest survive.        rather a haphazard fashion at the risk n, as of its
                                                      being injurious, in which case it is automatically
GENERAL AND HISTORICAL REMARKS                        eliminated. This brings out one very important
The fact that the recessive allele, when              point. In order to be suitable material for the
heterozygous, is completely overpowered by the        work of natural selection, mutations must be rare
dominant and produces no visible effects at all,      events, as they actually are. If they were so
is amazing. It ought at least to mentioned that       frequent that there was a considerable chance of,
there are exceptions to this behaviour. When          say, a dozen of different mutations occurring in
a homozygous white snapdragon is crossed with,        the same individual, the injurious ones would, as
equally homozygous, crimson snapdragon, all           a rule, predominate over the advantageous ones
the immediate descendants are intermediate in         and the species, instead of being improved by
colour, i.e. they are pink (not crimson, as might     selection, would remain unimproved, or would
be expected). A much more important case of           perish. The comparative conservatism which
two alleles exhibiting their influence                results from the high degree of permanence of
simultaneously occurs in blood-groups -but we         the genes is essential. An analogy might be
cannot enter into that here. I should not be          sought in the working of a large manufacturing
astonished if at long last recessivity should turn    plant in a factory. For developing better
our to be capable of degrees and to depend on         methods, innovations, even if as yet unproved,
the sensitivity of the tests we apply to examine      must be tried out. But in order to ascertain
the ‘phenotype’. This is perhaps the place for a      whether the innovations improve or decrease the
word on the early history of genetics. The            output, it is essential that they should be
backbone of the theory, the law of inheritance, to    introduced one at a time, while all the other parts
successive generations, of properties in which        of the mechanism are kept constant.
the parents differ, and more especially the
important distinction recessive-dominant, are due     MUTATIONS INDUCED BY X-RAYS
to the now world famous Augustininan Abbot            We now have to review a most ingenious series
Gregor Mendel (1822-84). Mendel knew nothing          of genetical research work, which will prove to
about mutations and chromosomes. In his               be the most relevant feature of our analysis. The
cloister gardens in Brunn (Brno) he made              percentage of mutations in the offspring, the
experiments on the garden pea, of first which he      so-called mutation rate, can be increased to a
reared different varieties, crossing them and         high multiple of the Small natural mutation rate
watching their offspring in the 1st, 2nd, 3rd, ...,   by irradiating the parents with X-rays or γ-rays.
generation. You might say, he experimented with       The mutations produced in this way differ in no
mutants which he found ready-made in nature.          way (except by being more numerous) from
The results he published as early as 1866 in the      those occurring spontaneously, and one has the
Proceedings of the Naturforschender Verein in         impression that every ‘natural’ mutation can also
Brunn. Nobody seems to have been particularly         be induced by X-rays. In Drosophila many
interested in the abbot's hobby, and nobody,          special mutations recur spontaneously again and
certainly, had the faintest idea that his discovery   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', THE
       SECOND LAW. LOCALIZATION OF that is to say, two or more
                              different 'versions' and 'readings' -in addition to
                              the normal, non-mutated one -of the same place
                                the rays
       you vary the quality ofin the chromosome code; that means not only                                                     (wave-length)
                              two, but three or more alternatives in that                                                    -
                              particular one 'locus', any two of which are to                     γ-rays, the coefficient remains constant,
                              each other in the relation 'dominant-recessive'                                                         -called
                              when they occur simultaneously in their                        r
     -units,haoyprvdem




                              corresponding loci of the two homologous                       dosage by the total amount standard substance
                              chromosomes. The experiments on X-ray-
       parents are exposed to produced mutations give the impression that
                               the r                                                                                     ays. As standard
       substance one choosesevery particular 'transition', say from the normal
                               air not only for
                              individual to particular mutant, or conversely,
       convenience, but also for the reasonathat organic
                              has its individual same
       tissues are composed of elements of the 'X-ray coefficient', indicating
                              the percentage of the
       atomic weight as air. A lower limit for the offspring which turns out to
                              have mutated in that
       amount of ionizations or allied processes particular way, when a unit
       (excitations) in th    dosage of X-ray has been applied to the parents,                                 e tissue is obtained simply by
                              before the offspring was
       multiplying the number of ionizations in air by engendered.

                                 FIRST LAW. MUTATION IS A SINGLE                             and is confirmed by a more critical investigation,
                                 EVENT
       that the single event, causing a mutation, is just
       an ionization (or si      Furthermore, the laws governing the induced                                    milar process) occurring
                                 mutation rate are extremely simple and                      within some 'critical' volume of the germ cell.
                                  critical volume? It can I follow here the report
       What is the size of thisextremely illuminating. be
                                 of N. mutation rate in a
       estimated from the observedW. Timofeeff, by Biological Reviews, vol.
                                 IX, if a dosage of 50,000
       consideration of this kind: 1934. To a considerable extent it refers to
                                 that author's own beautiful work. The first law is    ions per cm3 produces a chance of           only 1:1000
                                 (I) The increase is exactly proportional to the       for any particular gamete (that finds itself in the
                                 dosage of rays, so that one can actually speak (as          irradiated district) to mutate in that particular
                                 I did) of a coefficient of increase. We are so used         way, we conclude that the critical volume, the
       'target' which has to beto simple proportionality that we are liable to
                                  'hit' by an ionization
       for                       underrate the far-reaching consequences of this
    thamuioncr,sly1/0f




       1                         simple law. To grasp them, we may remember                                                             -
     /50ofacm3,this




                                 that the price not the
       millionth of a cm3. The numbers areof a commodity, for example, is                                                                      right
                                  by way of illustration. to
       ones, but are used onlynot always proportionalIn its amount. In
       the actual estimate we ordinary times a shopkeeper may be so
                                 follow M. Delbruck, in a
                                 much every impressed by your having bought six              paper by Delbruck, N.W. Timofeeffand K.G.
       Zimmer, which will als    oranges from him, that, on your deciding to take                                 o be the principal source
                                 after all a the following
       of the theory to be expounded in whole dozen, he may give it to you for
                                 less than double the price
       two chapters. He arrives there at a size of only of the six. In times of
       about                     scarcity the opposite may happen. In the present                  ten average atomic distances cubed,
                                 case, we conclude that the first half-dosage of             containing thus only about 103 = a thousand
                                 radiation, while causing, say, one out of a                 atoms. The simplest interpretation of this result
                                 thousand descendants
       is that there is a fair chance of producing thatto mutate, has not
                                 influenced the rest at all, either in the way of            mutation when an ionization (or excitation)
                                 predisposing them for, or of immunizing them                occurs not more
  thanabout'10atomsaway'from




       some particular spot inagainst, mutation. For otherwise the second
                                  the chromosome. We
                                 half-dosage would not cause again just one out              shall discuss this in more detail presently. The
                                 of a thousand to mutate. Mutation is thus not an            Timofeeff report contains a practical hint which I
                                 accumulated effect, brought about by
       cannot refrain from mentioning here, though it
       has, of course,           consecutive small portions of radiation                                     no bearing on our present
                                 reinforcing each other. It must consist in some             investigation. There are plenty of occasions in
       modern life when a human being has to be




       duringeventthe andfrom kindX where the If
       provided you give the sameis chromosome
       within the occurring theIt thus fairly
       This irradiation. at in one of event?
       single answered by the place
       EVENT
       hard is wide limits,What softdosage viz. (2)
       the ratio oftimedensities.second law,in soobvious,                                                                     rays to fairly
say,onefifty
exposed to X-rays. The direct dangers involved,        responsible for the abnormal feature, has been
as burns, X-ray cancer, sterilization, are well        carried on from generation to generation through
known, and protection by lead screens, lead-           the centuries, faithfully reproduced at every one
loaded aprons, etc., is provided, especially for       of the not very numerous cell divisions that lie
nurses and doctors who have to handle the rays         between. Moreover, the number of atoms
regularly. The point is, that even when these          involved in the responsible gene structure is
imminent dangers to the individual are                 likely to be of the same order of magnitude as in
successfully warded off, there appears to be the       the cases tested by X-rays. The gene has been
indirect danger of small detrimental mutations         kept at a temperature around 98°F during all that
being produced in the germ cells -mutations of         time. How are we to understand that it has
the kind envisaged when we spoke of the                remained unperturbed by the disordering
unfavourable results of close-breeding. To put it      tendency of the heat motion for centuries? A
drastically, though perhaps a little naively, the      physicist at the end of the last century would
injuriousness marriage between first cousins           have been at a loss to answer this question, if he
might very this well be increased by the fact that     was prepared to draw only on those laws of
their grandmother had served for a long period as      Nature which he could explain and which he
an X-ray nurse. It is not a point that need worry      really understood. Perhaps, indeed, after a short
any individual personally. But any possibility of      reflection on the statistical situation he would
gradually infecting the human race with                have answered (correctly, as we shall see): These
unwanted latent mutations ought to be a matter         material structures can only be molecules. Of the
of concern to the community.                           existence, and sometimes very high stability, of
                                                       these associations of atoms, chemistry had
CHAPTER 4                                              already acquired a widespread knowledge at the
The Quantum-Mechanical Evidence                        time. But the knowledge was purely empirical.
Thus, aided by the marvellously subtle                 The nature of a molecule was not understood -
instrument of X-rays (which, as the physicist          the strong mutual bond of the atoms which keeps
remembers, revealed thirty years ago really the        a molecule in shape was a complete conundrum
detailed atomic lattice structures of crystals), the   to everybody. Actually, the answer proves to be
united efforts of biologists and physicists have of    correct. But it is of limited value as long as the
late succeeded in reducing the upper limit for the     enigmatic biological stability is traced back only
size of the microscopic structure, being               to an equally enigmatic chemical stability. The
responsible for a definite large-scale feature of      evidence that two features, similar in appearance,
the individual- the 'size of a gene' -and reducing     are based on the same principle, is always
it far below the estimates obtained on pp. 29-30.      precarious as long as the principle itself is
We are now seriously faced with the question:          unknown.
How can we, from the point of view of statistical
physics, reconcile the facts that the gene             EXPLICABLE BY QUANTUM THEORY
structure seems to involve only a comparatively        In this case it is supplied by quantum theory. In
small number of atoms (of the order of 1,000 and       the light of present knowledge, the mechanism of
possibly much less), and that value nevertheless       heredity is closely related to, nay, founded on,
it displays a most regular and lawful activity -       the very basis of quantum theory. This theory
with a durability or permanence that borders           was discovered by Max Planck in 1900. Modern
upon the miraculous? Let me throw the truly            genetics can be dated from the rediscovery of
amazing situation into relief once again. Several      Mendel's paper by de Vries, Correns and
members of the Habsburg dynasty have a                 Tschermak (1900) and from de Vries's paper on
peculiar disfigurement of the lower lip                mutations (l901-3). Thus the births of the two
('Habsburger Lippe'). Its inheritance has been         great theories nearly coincide, and it is small
studied carefully and published, complete with         wonder that both of them had to reach a certain
historical portraits, by the Imperial Academy In       maturity before the connection could emerge. On
Vienna, under the auspices of the family. The          the side of quantum theory it took more than a
feature proves to be a genuinely Mendelian             quarter of a century till in 1926-7 the quantum
'allele' to the normal form of the lip. Fixing our     theory of the chemical bond was outlined in its
attention on the portraits of a member of the          general principles by W. Heitler and F. London.
family in the sixteenth century and of his             The Heitler-London theory involves the most
descendant, living in the nineteenth, we may           subtle and intricate conceptions of the latest
safely assume that the material gene structure,        development of quantum theory (called 'quantum
mechanics' or 'wave mechanics'). A presentation          state as meaning a definite configuration of all
without the use of calculus is well-nigh                 the corpuscles. The transition from one of these
impossible or would at least require another little      configurations to another is a quantum jump. If
volume each like this. But fortunately, now that         the second one has the greater energy ('is a
all work has been done and has served to clarify         higher level'), the system must be supplied from
our thinking, it seems to be possible to point out       outside with at least the difference of the two
in a more direct manner the connection between           energies to make the transition possible. To a
'quantum jumps' and mutations, to pick out at the        lower level it can change spontaneously on the
moment the most conspicuous item. That is what           spending the surplus of energy in radiation.
we attempt here.
                                                         MOLECULES
QUANTUM THEORY -DISCRETE STATES –                        Among the discrete set of states of a given
QUANTUM JUMPS                                            selection of atoms in such a state form a
The great revelation of quantum theory was that          molecule. The point to stress here is, that the
features of a discreteness were discovered in the        molecule will of necessity have a certain
Book of Nature, in context in which anything             stability; the configuration cannot change, unless
other than continuity seemed to be absurd                at least the energy difference, necessary to 'lift' it
according to the views held until then. The first        to the next higher level, is supplied from outside.
case of this kind concerned energy. A body on            Hence this level difference, which is a well-
the large scale changes its energy continuously.         defined quantity, determines quantitatively the
A pendulum, for instance, that is set swinging is        degree of stability of the molecule. It will be
gradually slowed down by the resistance of the           observed how intimately this fact is linked with
air. Strangely enough, it proves necessary               the very basis of quantum theory, viz. with the
to admit that a system of the order of the atomic        discreteness of the level scheme. I must beg the
scale behaves differently. On grounds upon               reader to take it for granted that this order of
which we cannot enter here, we then have to              ideas has been thoroughly checked by chemical
assume that a small system can by its very nature        facts; and that it has proved successful in
possess only certain discrete amounts of energy,         explaining the basic fact of chemical valency and
called its peculiar energy levels. The transition        many details about the structure of molecules,
from one state to another is a rather mysterious         their binding-energies, their stabilities at
event, which is usually called a quantum Jump.           different temperatures, and so on. I am speaking
But energy is not the only characteristic of a           of the Heitler- London theory, which, as I said,
system. Take again our pendulum, but think of            cannot be examined in detail here.
one that can perform different kinds of
movement, a heavy ball suspended by a string             THEIR STABILITY DEPENDENT ON
from the ceiling can be made to swing in a north-        TEMPERATURE
south or east-west or any other direction or in a        We must content ourselves with examining the
circle or in an ellipse. By gently blowing the ball      point which is of paramount interest for our
with a bellows, it can be made to pass                   biological question, namely, the stability of a
continuously from one state of motion to other.          molecule at different temperatures. Take our
For small-scale systems most of these or similar         system of atoms at first to be actually in its state
characteristics -we cannot enter into details -          of lowest energy. The physicist would call it a
change discontinuously. They are 'quantized',            molecule at the absolute zero of temperature. To
just as the energy is. The result is that a number       lift it to the next higher state or level a definite
of atomic nuclei, including their bodyguards of          supply of energy is required. The simplest way
electrons, when they find themselves close to            of trying to supply it is to 'heat up' your
each other, forming 'a system', are unable by            molecule. You bring it into an environment of
their very nature to adopt any arbitrary                 higher temperature ('heat bath'), thus allowing
configuration we might think of. Their very              other systems (atoms, molecules) to impinge
nature leaves them only a very numerous but              upon it. Considering the entire irregularity of
discrete series of 'states' to choose from. We           heat motion, there is no sharp temperature limit
usually call them levels or energy levels, because       at which the 'lift' will be brought about with
the energy is a very relevant part of the                certainty and immediately. Rather, at any
characteristic. But it must be understood that the       temperature (different from absolute zero) there
complete description includes much more than             is a certain smaller or greater chance for the lift
just the energy. It is virtually correct to think of a   to occur, the chance increasing of course with the
temperature of the heat bath. The best way              every vibration', that is to say, about 1013 or 1014
to express this chance is to indicate the average       times during every second.
time you will have to wait until the lift takes
place, the 'time of expectation'. From an               FIRST AMENDMENT
investigation, due to M. Polanyi and E. Wigner,         In offering these considerations as a theory of the
the 'time of expectation' largely depends on the        stability of the molecule it has been tacitly
ratio of two energies, one being just the energy        assumed that the quantum jump which we called
difference itself that is required to effect the lift   the 'lift' leads, if not to a complete disintegration,
(let us write W for it), the other one                  at least to an essentially different
characterizing the intensity of the heat motion at      configuration of the same atoms -an isomeric
the temperature in question (let us write T for the     molecule, as the chemist would say, that is, a
absolute temperature and kT for the                     molecule composed of the same atoms in a
characteristic energy). It stands to reason that the    different arrangement (in the application to
chance for effecting the lift is smaller, and hence     biology it is going to represent a different 'allele'
that the time of expectation is longer, the higher      in the same 'locus' and the quantum jump will
the lift itself compared with the average heat          represent a mutation). To allow of this
energy, that is to say, the greater the ratio W:kT.     interpretation two points must be amended in our
What is amazing is how enormously the time of           story, which I purposely simplified to make it at
expectation depends on comparatively small              all intelligible. From the way I told it, it might be
changes of the ratio W:kT. To give an example           imagined that only in its very lowest state does
(following Delbruck): for W 30 times kT the             our group of atoms form what we call a molecule
time of expectation might be as short as 1\10s.,        and that already the next higher state is
but would rise to 16 months when W is 50 times          'something else'. That is not so. Actually the
kT, and to 30,000 years when W is 60 times kT!          lowest level is followed by a crowded series of
                                                        levels which do not involve any appreciable
MATHEMATICAL INTERLUDE                                  change in the configuration as a whole, but only
It might be as well to point out in mathematical        correspond to those small vibrations among the
language -for those readers to whom it appeals -        atoms free which we have mentioned above.
the reason for this enormous sensitivity to             They, too, are 'quantized', but with
changes in the level step or temperature, and to        comparatively small steps from one level to the
add a few physical remarks of a similar kind.           next. Hence the impacts of the particles of the
The reason is that the time of expectation, call it     'heat bath' may suffice to set them up already at
t, depends on the ratio W/kT by an exponential          fairly low temperature. If the molecule is an
function, thus t = teW/kT. t is a certain small         extended structure, you may conceive these
constant of the order of 10-13 or 10-14S. Now, this     vibrations as high-frequency sound waves,
particular exponential function is not an               crossing the molecule without doing it any harm.
accidental feature. It recurs again and again in        So the first amendment is not very serious: we
the statistical theory of heat, forming, as it were,    have to disregard the 'vibrational fine-structure'
its backbone. It is a measure of the improbability      of the level scheme. The term 'next higher level'
of an energy amount as large as W gathering             has to be understood as meaning the next level
accidentally in some particular part of the             that corresponds to a relevant change of
system, and it is this improbability which              configuration.
increases so enormously when a considerable
multiple of the 'average energy' kT is required.        SECOND AMENDMENT
Actually a W = 30kT (see the example quoted             The second amendment is far more difficult to
above) is already extremely rare. That it does not      explain, involve because it is concerned with
yet lead to an enormously long time of                  certain vital, but rather complicated, features of
expectation (only 1/10s. in our example) is, of         the scheme of relevantly different levels. The
course, due to the smallness of the factor T. This      atoms free passage between two of them may be
factor has a physical meaning. It is of the order       obstructed, quite apart from the required energy
of the period of the vibrations which take place        supply; in fact, it may be obstructed even from
in the system all the time. You could, very             the higher to the lower state. Let us start from the
broadly, describe this factor as meaning that the       empirical facts. It is known to the chemist that
chance of accumulating the required amount W,           the same group of atoms can unite in more than
though very small, recurs again and again 'at           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                  THE GENERAL PICTURE OF THE
alternatives are offered. Fig. II shows one of the      HEREDITARY SUBSTANCE
simplest cases, the two kinds of propyl alcohol,        From these facts emerges a very simple answer
both consisting of 3 carbons (C), 8 hydrogens           to our question, namely: Are these structures,
(H), 1 oxygen (0). The latter can be interposed         composed of comparatively few atoms, capable
between any hydrogen and its carbon, but only           of withstanding for long periods the disturbing
the two cases shown in our figure are different         influence of heat motion to which the hereditary
substances. And they really are. All their              substance is continually exposed? We shall
physical and chemical constants are distinctly          assume the structure of a gene to be that of a
different. Also their energies are different, they      huge molecule, capable only of discontinuous
represent 'different levels'. The remarkable fact is    change, which consists in a rearrangement of the
that both molecules are perfectly stable, both          atoms and leads to an isomeric molecule. The
behave as though they were 'lowest states'.             rearrangement may affect only a small region of
There are no spontaneous transitions from either        the gene, and a vast number of different
state towards the other. The reason is that the         rearrangements may be possible. The energy
two configurations are not neighbouring                 thresholds, separating the actual configuration
configurations. The transition from one to the          from any possible isomeric ones, have to be high
other can only take place over intermediate             enough (compared with the average heat energy
configurations which have a greater energy than         of an atom) to make the change-over a rare
either of them. To put it crudely, the oxygen has       event. These rare events we shall identify with
to be extracted from one position and has to            spontaneous mutations. The later parts of this
be inserted into the other. There does not seem to      chapter will be devoted to putting this general
be a way of doing that without passing through          picture of a gene and of mutation (due mainly
configurations of considerably higher energy.           to! the German physicist M. Delbruck) to the
The state of affairs is sometimes figuratively          test, by comparing it in detail with genetical
pictured as in Fig. 12, in which I and 2 represent      facts. Before doing so, we may fittingly make
the two isomers, 3 the 'threshold' between them,        some comment on the foundation and general
and the two arrows indicate the 'lifts', that is to     nature of the theory.
say, the energy supplies required to produce the
transition from state I to state 2 or from state 2 to   THE UNIQUENESS OF THE PICTURE
state I, respectively. Now we can give our              Was it absolutely essential for the biological
'second amendment', which is that transitions of        question to dig up the deepest roots and found
this 'isomeric' kind are the only ones in which we      the picture on quantum mechanics? The
shall be interested in our biological application.      conjecture that a gene is a molecule is today, I
It was these we had in mind when explaining             dare say, a commonplace. Few biologists,
'stability' on pp. 49-51. The 'quantum jump'            whether familiar with quantum theory or not,
which we mean is the transition from one                would disagree with it. On p. 47 we ventured to
relatively stable molecular configuration to            put it into the mouth of a pre-quantum physicist,
another. The energy supply required for the             as the only reasonable explanation of the
transition (the quantity denoted by W) is not the       observed permanence. The subsequent
actual level difference, but the step from the          considerations about isomerism, threshold
initial level up to the threshold (see the arrows       energy, the paramount role of the ratio W:kT in
in Fig. 12). Transitions with no threshold              determining the probability of an isomeric
interposed between the initial and the final state      transition -all that could very well be introduced
are entirely uninteresting, and that not only in        to our purely empirical basis, at any rate without
our biological application. They have actually          drawing on quantum theory. Why did I so
nothing to contribute to the chemical stability of      strongly insist on the quantum-mechanical
the molecule. Why? They have no lasting effect,         periods the point of view, though I could not
they remain unnoticed. For, when they occur,            really make it clear in this little book and may
they are almost immediately followed by a               well have bored many a reader? Quantum
relapse so into the initial state, since nothing        mechanics is the first theoretical aspect which
prevents their return.                                  accounts from first principles for all kinds of
                                                        aggregates of atoms actually encountered in
CHAPTER 5                                               Nature. The Heitler-London bondage is a unique,
Delbruck's Model Discussed and Tested                   singular feature of the theory, not invented for
the purpose of explaining the chemical bond. It         of the single molecule is sometimes
comes in quite by itself, in a highly interesting       recognizable, as in the case of alcohol, and most
and puzzling manner, being forced upon us by            organic compounds, while in other crystals, e.g.
entirely different considerations. It proves to         rock-salt (NaCI), NaCI molecules cannot be
correspond exactly with the observed chemical           unequivocally delimited, because every Na atom
facts, and, as I said, it is a unique feature, well     is symmetrically surrounded by six CI atoms,
enough understood to tell with reasonable               and vice versa, so that it is largely arbitrary what
certainty that 'such a thing could not happen           pairs, if any, are regarded as molecular partners.
again' in the further development of quantum            Finally, we have been told that a solid can be
theory. Consequently, we may safely assert that         crystalline or not, and in the latter case we call it
there is no alternative to the molecular                amorphous.
explanation of the hereditary substance. The
physical aspect leaves no other possibility to          DIFFERENT STATES OF MATTER
account for itself and of its permanence. If the        Now I would not go so far as to say that all these
Delbruck picture should fail, we would have to          statements and distinctions are quite wrong. For
give up further attempts. That is the first point I     practical purposes they are sometimes useful.
wish to make.                                           But in the true aspect of the structure of matter
                                                        the limits must be drawn in an entirely different
SOME TRADITIONAL MISCONCEPTIONS                         way. The fundamental distinction is between the
But it may be asked: Are there really no other          two lines of the following scheme of 'equations':
endurable structures composed of atoms except
molecules? Does not a gold coin, for example,           molecule = solid = crystal.
buried in a tomb for a couple of thousand years,        gas = liquid = amorphous.
preserve the traits of the portrait stamped on it? It
is true that the coin consists of an enormous           We must explain these statements briefly. The
number of atoms, but surely we are in this case         so-called amorphous solids are either not really
not inclined to attribute the mere preservation of      amorphous or not really solid. In 'amorphous'
shape to the statistics of large numbers. The           charcoal fibre the rudimentary structure of the
same remark applies to a neatly developed batch         graphite crystal has been disclosed by X-rays. So
of crystals we find embedded in a rock, where it        charcoal is a solid, but also crystalline. Where
must have been for geological periods without           we find no crystalline structure we have to
changing. That leads us to the second point I           regard the thing as a liquid with very high
want to elucidate. The cases of a molecule, a           'viscosity' (internal friction). Such a substance
solid crystal are not really different. In the light    discloses by the absence of a well-defined
of present knowledge they are virtually the             melting temperature and of a latent heat of
same. Unfortunately, school teaching keeps up           melting that it is not a true solid. When heated it
certain traditional views, which have been out of       softens gradually and eventually liquefies
date for many years and which obscure the               without discontinuity. (I remember that at the
understanding of the actual state of                    end of the first Great War we were given in
affairs. Indeed, what we have learnt at school          Vienna an asphalt-like substance as a substitute
about molecules does not give the idea that they        for coffee. It was so hard that one had to use a
are more closely akin to the solid state than to        chisel or a hatchet to break the little brick into
the liquid or gaseous state. On the contrary, we        pieces, when it would show a smooth, shell-like
have been taught to distinguish carefully               cleavage. Yet, given time, it would behave as a
between a physical change, such as melting or           liquid, closely packing the lower part of a vessel
evaporation in which the molecules are                  in which you were unwise enough to leave it for
preserved (so that, for example, alcohol, whether       a couple of days.). The continuity of the gaseous
solid, liquid or a gas, always consists of the same     and liquid state is a well-known story. You can
molecules, C2H6O), and a chemical change, as,           liquefy any gas without discontinuity by taking
for example, the burning of alcohol, C2H6O +            your way 'around' the so-called critical point. But
302 = 2C02 + 3H2O, where an alcohol molecule            we shall not enter on this here.
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            THE DISTINCTION THAT REALLY
three-fold periodic lattices, in which the structure    MATTERS
We have thus justified everything in the above         Indeed, the number of atoms in such a structure
scheme, except the main point, namely, that we         need not be very large to produce an almost
wish a molecule to be regarded as a solid =            unlimited number of possible arrangements. For
crystal. The reason for this is that the atoms         illustration, think of the Morse code. The two
forming a molecule, whether there be few or            different signs of dot and dash in well-ordered
many of them, are united by forces of exactly the      groups of not more than four allow thirty
same nature as the numerous atoms which build          different specifications. Now, if you allowed
up a true solid, a crystal. The molecule presents      yourself the use of a third sign, in addition to dot
the same solidity of structure as a crystal.           and dash, and used groups of not more than ten,
Remember that it is precisely this solidity on         you could form 88,572 different 'letters'; with
which we draw to account for the permanence of         five signs and groups up to 25, the number is
the gene! The distinction that is really important     372,529,029,846,19 1,405. It may be objected
in the structure of small matter is whether atoms      that the simile is deficient, because our two
are bound together by those Heitler-London             Morse signs may have different composition
forces or whether they are not. In a solid and in a    (e.g. .--and .-) and thus they are a bad analogue
molecule they all are. In a gas of single atoms (as    for isomerism. To remedy this defect, let us pick,
e.g. think mercury vapour) they are not. In a gas      from the third example, only the combinations of
composed of molecules, only the atoms within           exactly 25 symbols and only those containing is
every molecule are linked in this thirty way.          exactly 5 out of each of the supposed 5 types (5
                                                       dots, 5 dashes, etc.). A rough count gives you the
THE APERIODIC SOLID                                    number of combinations as more
A small molecule might be called 'the germ of a        62,330,000,000,000, where zeros on the right
solid'. Starting from such a small solid germ,         stand for figures which I have not taken the
there seem to be two different ways of building        trouble to compute. Of course, in the actual case,
up larger and larger associations. One is the          by no means 'every' arrangement of the group of
comparatively dull way of repeating the same           atoms will represent a possible molecule;
structure in three directions again and again.         moreover, it is not a question of a code to be
That is the way followed in a growing crystal.         adopted arbitrarily, for the code-script must itself
Once the periodicity is established, there is no       be the operative factor bringing about the
definite limit to the size of the aggregate. The       development. But, on the other hand, the number
other way is that of building up a more and more       chosen in the example (25) is still very small,
extended aggregate without the dull device of          and we have envisaged only the simple
repetition. That is the case of the more and more      arrangements in one line. What we wish to
complicated organic moleculein which every             illustrate is simply that with the molecular
atom, and every group of atoms, plays an               picture of the gene it is no longer inconceivable
individual role, not entirely equivalent to that of    that the miniature code should precisely
many others (as is the case in a periodic              correspond with a highly complicated and
structure). We might quite properly call that an       specified plan of development and should
aperiodic crystal or solid and express our             somehow contain the means to put it into
hypothesis by saying: We believe a gene -or            operation.
perhaps the whole chromosome fibre -to be an
aperiodic solid.                                       COMPARISON WITH FACTS: DEGREE OF
                                                       STABILITY; DISCONTINUITY OF
THE VARIETY OF CONTENTS                                MUTATIONS
COMPRESSED IN THE MINIATURE CODE                       Now let us at last proceed to compare the
It has often been asked how this tiny speck of         theoretical picture cha with the biological facts.
material, nucleus of the fertilized egg, could         The first question obviously is, whether it can
contain an elaborate code-script involving all the     really account for the high degree of permanence
future development of the organism. A well-            we observe. Are threshold values of the required
ordered association of atoms, endowed with             amount -high multiples of the average heat
sufficient resistivity to keep its order               energy kT - reasonable, are they within the range
permanently, appears to be the only conceivable        known from ordinary chemistry? That question
material structure that offers a variety of possible   is trivial; it can be answered in the affirmative
('isomeric') arrangements, sufficiently large          without inspecting tables. The molecules of any
to embody a complicated system of                      substance which the chemist is able to isolate at a
'determinations' within a small spatial boundary.      given temperature must at that temperature have
a lifetime of at least minutes. That is putting it
mildly; as a rule they have much more. Thus the
threshold values the chemist encounters are of
necessity precisely of the order of magnitude
required to account for practically any degree of
permanence the biologist may encounter; for we
recall from p. 51 that thresholds varying within a
range of about 1:2 will account for lifetimes
ranging from a fraction of a second to tens of
thousands of years. But let me mention figures,
for future reference. The ratios W/kT mentioned
by way of example on p. 51, viz.
          W/kT = 30,50,60,
producing lifetimes of 1/10s, 16 months, 30,000
years, respectively, correspond at room
temperature
2.5, is what in an ordinary chemical reaction we      is a little larger or a little smaller, say 1 or 1.3
call the van't Hoff factor.)                          volts.

HOW X-RAYS PRODUCE MUTATION                           REVERSIBLE MUTATIONS
Turning now to the X-ray-induced mutation rate,       In some cases a transition was studied in both
we have already inferred from the breeding            directions, say from a certain 'wild' gene to a
experiments, first (from the proportionality of       specified mutant and back from that mutant to
mutation rate, and dosage), that some single          the wild gene. In such cases the natural mutation
event produces the mutation; secondly (from           rate is sometimes nearly the same, sometimes
quantitative results and from the fact that the       very different. At first sight one is puzzled,
mutation rate is determined by the integrated         because the threshold to be overcome seems to
ionization density and independent of the             be the same in both cases. But, of course, it need
wave-length), that this single event must be an       not be, because it has to be measured from the
ionization, or similar process, which has to take     energy level of the starting configuration, and
place inside a certain volume of only about 10        that may be different for the wild and the
atomic-distances-cubed, in order to produce a         mutated gene. (See Fig. 12 on p. 54, where 'I'
specified mutation. According to our picture, the     might refer to the wild allele, '2' to the mutant,
energy for overcoming the threshold must              whose lower stability would be indicated by the
obviously be furnished by that explosion-like         shorter arrow.) On the whole, I think, Delbruck's
process, ionization or excitation. I call it          'model' stands the tests fairly well and we are
explosion-like, because the energy spent in one       justified in using it in further considerations
ionization (spent, incidentally, not by the X-ray
itself, but by a secondary electron it produces) is   CHAPTER 6
well known and has the comparatively enormous
amount of 30 electron-volts. It is bound to be        Order, Disorder and Entropy
turned into enormously increased heat motion
around the point where it is discharged and to        A REMARKABLE GENERAL CONCLUSION
spread from there in the form of a 'heat wave', a     FROM THE MODEL
wave of intense oscillations of the atoms. That        Let me refer to the phrase on p. 62, in which I
this heat wave should still be able to furnish the    tried to explain that the molecular picture of the
required threshold energy of 1 or 2 electron-volts    gene made it at least conceivable that the
at an average 'range of action' of about ten          miniature code should be in one-to-one
atomic distances, is not inconceivable, though it     correspondence with a highly complicated and
may well be that an unprejudiced physicist might      specified plan of development and should
have anticipated a slightly lower range of action.    somehow contain the means of putting it into
That in many cases the effect of the explosion        operation. Very well then, but how does it do
will not be an orderly isomeric transition but a      this? How are we going to turn ‘conceivability’
lesion of the chromosome, a lesion that becomes       into true understanding? Delbruck's molecular
lethal when, by ingenious crossings, the              model, in its complete generality, seems to
uninjured partner (the corresponding                  contain no hint as to how the hereditary
chromosome of the second set) is removed              substance works, Indeed, I do not expect that any
and replaced by a partner whose corresponding         detailed information on this question is likely to
gene is known to be itself morbid -all that is        come from physics in the near may future. The
absolutely to be expected and it is exactly what is   advance is proceeding and will, I am sure,
observed.                                             continue to do so, from biochemistry under the
                                                      guidance of physiology and genetics. No detailed
THEIR EFFICIENCY DOES NOT DEPEND                      information about the functioning of the
ON SPONTANEOUS MUTABILITY                             genetical mechanism can emerge from a
Quite a few other features are, if not predictable    description of its structure so general as has been
from the picture, easily understood from it. For      given above. That is obvious. But, strangely
example, an unstable mutant does not on the           enough, there is just one general conclusion to be
average show a much higher X-ray mutation rate        obtained from it, and that, I confess, was my
than a stable one. Now, with an explosion             only motive for writing this book. From
furnishing an energy of 30 electron-volts you         Delbruck's general picture of the hereditary
would certainly not expect that it makes a lot of     subustance it emerges that living matter, while
difference whether the required threshold energy      not eluding the 'laws of physics' as established
up to date, is likely to involve 'other laws of      LIVING MATTER EVADES THE DECAY
physics' hitherto unknown, which, however, once      TO EQUILIBRIUM
they have been revealed, will form just as           What is the characteristic feature of life? When
integral a part of this science as the former.       is a piece of matter said to be alive? When it
                                                     goes on 'doing something', moving, exchanging
ORDER BASED ON ORDER                                 material with its environment, and so forth, and
This is a rather subtle line of thought, open to     that for a much longer period than we would
misconception in more than one respect. All the      expect of an inanimate piece of matter to 'keep
remaining pages are concerned with making it         going' under similar circumstances. When a
clear. A preliminary insight, rough but not          system that is not alive is isolated or placed in a
altogether erroneous, may be found in the            uniform environment, all motion usually comes
following considerations: It has been explained      to a standstill very soon as a result of various
in chapter 1 that the laws of physics, as we know    kinds of friction; differences of electric or
them, are statistical laws. They have a lot to do    chemical potential are equalized, substances
with the natural tendency of things to go over       which tend to form a chemical compound do so,
into disorder. But, to reconcile the high            temperature becomes uniform by heat
durability of the hereditary substance with its      conduction. After that the whole system fades
minute size, we had to evade the tendency to         away into a dead, inert lump of matter. A
disorder by 'inventing the molecule', in fact, an    permanent state is reached, in which no
unusually large molecule which has to be a           observable events occur. The physicist calls this
masterpiece of highly differentiated order,          the state of thermodynamical equilibrium, or of
safeguarded by the conjuring rod of quantum          ‘maximum entropy'. Practically, a state of this
theory. The laws of chance are not invalidated by    kind is usually reached very rapidly.
this 'invention', but their outcome is modified.     Theoretically, it is very often not yet an absolute
The physicist is familiar with the fact that the     equilibrium, not yet the true maximum of
classical laws of physics are modified by            entropy. But then the final approach to
quantum theory, especially at low                    equilibrium is very slow. It could take anything
temperature. There are many instances of this.       between hours, years, centuries,... To give an
Life seems to be one of them, a particularly         example -one in which the approach is still fairly
striking one. Life seems to be orderly and lawful    rapid: if a glass filled with pure water and a
behaviour of matter, not based exclusively on its    second one filled with sugared water are placed
tendency to go over from order to disorder, but      together in a hermetically closed case at constant
based partly on existing order that is kept up. To   temperature, it appears at first that nothing
the physicist -but only to him -I could hope to      happens, and the impression of complete
make my view clearer by saying: The living           equilibrium is created. But after a day or so it is
organism seems to be a macroscopic system            noticed that the pure water, owing to its higher
which in part of its behaviour approaches to that    vapour pressure, slowly evaporates and
purely mechanical (as contrasted with                condenses on the solution. The latter overflows.
thermodynamical) conduct to which all systems        Only after the pure water has totally evaporated
tend, as the temperature approaches absolute         has the sugar reached its aim of being equally
zero and the molecular disorder is removed. The      distributed among all the liquid water
non-physicist finds it hard to believe that really   available. These ultimate slow approaches to
the ordinary laws of physics, which he regards as    equilibrium could never be mistaken for life, and
the prototype of a part inviolable precision,        we may disregard them here. I have referred to
should be based on the statistical tendency of       them in order to clear myself of a charge
matter to go over into disorder. I have given        of Inaccuracy.
examples in chapter 1. The general principle
involved is the famous Second Law of                 IT FEEDS ON 'NEGATIVE ENTROPY'
Thermodynamics (entropy principle) and its           It is by avoiding the rapid decay into the inert
equally famous statistical foundation. On pp. 69-    state of 'equilibrium' that an organism appears so
74 I will try to sketch the bearing of the entropy   enigmatic; so much so, that from the earliest
principle on the large-scale behaviour of a living   times of human thought some special
organism -forgetting at the moment all that is       non-physical or supernatural force (vis viva,
known about chromosomes, inheritance, and so         entelechy) was claimed to be operative in the
on.                                                  organism, and in some quarters is still claimed.
                                                     How does the living organism avoid decay? The
obvious answer is: By eating, drinking, breathing     chemical nature) the entropy increases by an
and (in the case of plants) assimilating. The         amount which is computed by dividing every
technical term is metabolism. The Greek word ()       little portion of heat you had to supply in that
means change or exchange. Exchange of what?           procedure by the absolute temperature at which it
Originally the underlying idea is, no doubt,          was supplied -and by summing up all these small
exchange of material. (E.g. the German for            contributions. To give an example, when you
metabolism is Stoffwechsel.) That the exchange        melt a solid, its entropy increases by the amount
of material should be the essential thing is          of the heat of fusion divided by the temperature
absurd. Any atom of nitrogen, oxygen, sulphur,        at the more melting-point. You see from this,
etc., is as good as any other of its kind; what       that the unit in which entropy is measured is
could be gained by exchanging them? For a             cal./C (just as the calorie is the unit of heat or the
while in the past our curiosity was silenced by       centimetre the unit of length).
being told that we feed upon energy. In some
very advanced country (I don't remember               THE STATISTICAL MEANING OF
whether it was Germany or the U.S.A. or both)         ENTROPY
you could find menu cards in restaurants              I have mentioned this technical definition simply
indicating, in addition to the price, the energy      in order to remove entropy from the atmosphere
content of every dish. Needless to say, taken         of hazy mystery that frequently veils it. Much
literally, this is just as absurd. For an adult       more important for us here is the bearing on the
organism the energy content is as stationary as       statistical concept of order and disorder, a
the material content. Since, surely, any calorie is   connection that was revealed by the
worth as much as any other calorie, one cannot        investigations of Boltzmann and Gibbs in
see how a mere exchange could help. What then         statistical physics. This too is an exact
is that precious something contained in our food      quantitative connection, and is expressed by
which keeps us from death? That is easily                        entropy = k log D,
answered. Every process, event, happening -call       where k is the so-called Boltzmann constant ( =
it what you will; in a word, everything that is       3.2983 . 10-24 cal./C), and D a quantitative
going on in Nature means an increase of the           measure of the atomistic disorder of the body in
entropy of the part of the world where it is going    question. To give an exact explanation of this
on. Thus a living organism continually increases      quantity D in brief non-technical terms is
its entropy -or, as you may say, produces             well-nigh impossible. The disorder it indicates is
positive entropy -and thus tends to approach the      partly that of heat motion, partly that which
dangerous state of maximum entropy, which             consists in different kinds of atoms or molecules
is of death. It can only keep aloof from it, i.e.     being mixed at random, instead of being neatly
alive, by continually drawing from its                separated, e.g. the sugar and water molecules in
environment negative entropy -which is                the example quoted above. Boltzmann's equation
something very positive as we shall immediately       is well illustrated by that example. The gradual
see. What an organism feeds upon is negative          'spreading out' of the sugar over all the water
entropy. Or, to put it less paradoxically, the        available increases the disorder D, and hence
essential thing in metabolism is that the             (since the logarithm of D increases with D) the
organism succeeds in freeing itself from all the      entropy. It is also pretty clear that any supply of
entropy it cannot help producing while alive.         heat increases the turmoil of heat motion, that is
                                                      to say, increases D and thus increases the
WHAT IS ENTROPY?                                      entropy; it is particularly clear that this should be
Let me first emphasize that it is not a hazy          so when you melt a crystal, since you thereby
concept or idea, but a measurable physical            destroy the neat and permanent arrangement of
quantity just like of the length of a rod, the        the atoms or molecules and turn the crystal
temperature at any point of a body, the heat of       lattice into a continually changing random
fusion of a given crystal or the specific heat of     distribution. An isolated system or a system in a
any given substance. At the absolute zero point       uniform environment (which for the present
of temperature (roughly -273°C) the entropy of        consideration we do best to include as the part of
any substance is zero. When you bring the             the system we contemplate) increases its entropy
substance into any other state by slow, reversible    and more or less rapidly approaches the inert
little steps (even if thereby the substance changes   state of maximum entropy. We now recognize
its physical or chemical nature or splits up into     this fundamental law of physics to be just the
two or more parts be of different physical or         natural tendency of things to approach the
chaotic state (the same tendency that the books         take free as more or less an epitheton
of a library or the piles of papers and                 ornans without much relevance, while actually
manuscripts on a writing desk display) unless we        the concept is a rather intricate one, whose
obviate it. (The analogue of irregular heat             relation to Boltzmann's order-disorder principle
motion, in this case, is our handling those objects     is less easy to trace than for entropy and 'entropy
now and again to without troubling to put them          taken with a negative sign', which by the way is
back in their proper places.                            not my invention. It happens to be precisely the
                                                        thing on which Boltzmann's original
ORGANIZATION MAINTAINED BY                              argument turned. But F. Simon has very
EXTRACTING 'ORDER' FROM THE                             pertinently pointed out to me that my simple
ENVIRONMENT                                             thermodynamical considerations cannot account
How would we express in terms of the statistical        for our having to feed on matter 'in the extremely
theory the marvellous faculty of a living               well ordered state of more or less complicated
organism, by which it delays the decay into             organic compounds' rather than on charcoal or
thermodynamical equilibrium (death)? We said            diamond pulp. He is right. But to the lay reader I
before: 'It feeds upon negative entropy',               must explain that a piece of un-burnt coal or
attracting, as it were, a stream of negative            diamond, together with the amount of oxygen
entropy upon itself, to compensate the entropy          needed for its combustion, is also in an
increase it produces by living and thus to              extremely well ordered state, as the physicist
maintain itself on a stationary and fairly low          understands it. Witness to this: if you allow the
entropy level. If D is a measure of disorder, its       reaction, the burning of the coal, to take place, a
reciprocal, l/D, can be regarded as a direct            great amount of heat is produced. By giving it
measure of order. Since the logarithm of l/D is         off to the surroundings, the system disposes of
just minus the logarithm of D, we can write             the very considerable entropy increase entailed
Boltzmann's equation thus:                              by the reaction, and reaches a state in which it
           -(entropy) = k log (l/D).                    has, in point of fact, roughly the same entropy as
Hence the awkward expression 'negative entropy'         before. Yet we could not feed on the carbon
can be he replaced by a better one: entropy,            dioxide that results from the reaction. And so
taken with the negative sign, is itself a measure       Simon is quite right in pointing out to me, as he
of order. Thus the device by which an organism          did, that actually the energy content of our food
maintains itself stationary at a fairly high level of   does matter; so my mocking at the menu cards
he orderliness ( = fairly low level of entropy)         that indicate it was out of place. Energy is
really consists continually sucking orderliness         needed to replace not only the mechanical energy
from its environment. This conclusion is less           of our bodily exertions, but also the heat we
paradoxical than it appears at first sight. Rather      continually give off to the environment. And that
could it be blamed for triviality. Indeed, in the       we give off heat is not accidental, but essential.
case of higher animals we know the kind of              For this is precisely the manner in which we
orderliness they feed upon well enough, viz. the        dispose of the surplus entropy we continually
extremely well-ordered state of matter in more or       produce in our physical life process. This seems
less complicated organic compounds, which               to suggest that the higher temperature of the
serve them as foodstuffs. After utilizing it they       warm-blooded animal includes the advantage of
return it in a very much degraded form -not             enabling it to get rid of its entropy at a quicker
entirely degraded, however, for plants can still        rate, so that it can afford a more intense life
make use of it. (These, of course, have their most      process. I am not sure how much truth there is in
power supply of ‘negative entropy’ the sunlight)        this argument (for which I am responsible, not
                                                        Simon). One may hold against it, that on the
NOTE TO CHAPTER 6                                       other hand many warm-blooders are protected
The remarks on negative entropy have met with           against the rapid loss of heat by coats of fur or
doubt and Opposition from physicist colleagues.         feathers. So the parallelism between body
Let me say first, that if I had been law catering       temperature and 'intensity of life', which I
for them alone I should have let the discussion         believe to exist, may have to be accounted for
turn on free energy instead. It is the more             more directly by van't Hoff’s law, mentioned on
familiar notion in this context. But this highly        p. 65: the higher temperature itself speeds up the
technical term seemed linguistically too near to        chemical reactions involved in living. (That it
energy for making the average reader alive to the       actually does, has been confirmed
contrast between the two things. He is likely to
     eyn
  experimentally in species which take the
  temperature of the surroundings.).

  CHAPTER 7
  Is Life Based on the Laws of Physics?

  NEW LAWS TO BE EXPECTED IN THE
  ORGANISM
  What I wish to make clear in this last chapter is,
  in short, that from all we have learnt about the
  structure of living matter, we must be prepared to
  find it working in a manner that cannot be
  reduced to the ordinary laws of physics. And that
  not on the ground that there is any 'new force' or
  what not, directing the behaviour of the single
  atoms within a living organism, but because the
  construction is different from a anything we have
  yet tested in the physical laboratory. To put it




       ae
  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 e c rtnfilTm (d) Tj 41 999999 90 Tj 41 0 0 41 175 ,632 0 Tm (n) Tj 41 0 0 41 623 0 Tm (m) Tj41 0 0 48




yh shhcnSe
            a       t  n
                  tnad h d dr here ketyfof
                                       y




                                                                                                  s
movement give rise to the regular phenomenon            of acting in this manner, the situation is
of diffusion. The disintegration of a single            unprecedented, it is unknown anywhere else
radioactive atom is observable (it emits a              except in living matter. The physicist and the
projectile which causes a visible scintillation on      chemist, investigating inanimate matter, have
a fluorescent screen). But if you are given a           never witnessed phenomena which they had to
single radioactive atom, its probable lifetime is       interpret in this way. The case did not arise and
much less certain than that of a healthy sparrow.       so our theory does not cover it -our beautiful
Indeed, nothing more can be said about it than          statistical theory of which we were so justly
this: as long as it lives (and that may be for          proud because it allowed us to look behind the
thousands of years) the chance of its blowing up        curtain, to watch the magnificent order of exact
within the next second, whether large or small,         physical law coming forth from atomic and
remains the same. This patent lack of individual        molecular disorder; because it revealed that the
determination nevertheless results in the exact         most important, the most general, the
exponential law of decay of a large number of           all-embracing law of entropy could be
radioactive atoms of the same kind.                     understood without a special assumption ad hoc,
                                                        for it is nothing but molecular disorder itself.
THE STRIKING CONTRAST
In biology we are faced with an entirely different      TWO WAYS OF PRODUCING
situation. A single group of atoms existing only        ORDERLINESS
in one copy produces orderly events,                    The orderliness encountered in the unfolding of
marvellously tuned in with each other and us            life springs from a different source. It appears
number of with the environment according to             that there are two different 'mechanisms' by
most subtle laws. I said existing only in one           which orderly events can be produced: the
copy, for after all we have the example of the          'statistical mechanism' which produces
egg and of the unicellular organism. In the             order from disorder and the new one, producing
following stages of a higher organism the copies        order from order. To the unprejudiced mind the
are multiplied, that is true. But to what extent?       second principle appears to be much simpler,
Something like 1014 in a grown mammal, I                much more plausible. No a doubt it is. That is
understand. What is that! Only a millionth of the       why physicists were so proud to have fallen in
number of molecules in one cubic inch of air.           with the other one, the 'order-from-disorder'
Though comparatively bulky, by coalescing they          principle, which is actually followed in Nature
would form but a tiny drop of liquid. And look at       and which alone conveys an understanding of the
the way they are actually distributed. Every cell       great line of natural events, in the first place of
harbours just one of them (or two, if we bear in        their irreversibility. But we cannot expect that
mind diploidy). Since we know the power this            the 'laws of physics' derived from it suffice
tiny central office has in the isolated cell, do they   straightaway to explain the behaviour of
not resemble stations of local government               living matter, whose most striking features are
dispersed through the body, communicating with          visibly based to a large extent on the 'order-from-
each other with great ease, thanks to the code          order' principle. You would not expect two
that is common to all of them? Well, this is a          entirely different mechanisms to bring about the
fantastic description, perhaps less becoming a          same type of law -you would not expect your
scientist than a poet. However, it needs no             latch-key, to open your neighbour's door as well.
poetical imagination but only clear and sober           We must therefore not be discouraged by the
scientific reflection to recognize that we are here     difficulty of interpreting life by the ordinary laws
obviously faced with events whose regular and           of physics. For that is just what is to be expected
lawful unfolding is guided by a 'mechanism'             from the knowledge we have gained of the
entirely different from the 'probability                structure of living matter. We must be prepared
mechanism' of physics. For it is simply a fact of       to find a new type of physical law prevailing in
observation that the guiding principle in every         it. Or are we to term it a non-physical, not to say
cell is embodied in a single atomic association         a super-physical, law?
existing only one copy (or sometimes two) -and
a fact of observation that it may results in            THE NEW PRINCIPLE IS NOT ALIEN TO
producing events which are a paragon of                 PHYSICS
orderliness. Whether we find it astonishing or          No. I do not think that. For the new principle that
whether we find it quite plausible that a small         is involved is a genuinely physical one: it is, in
but highly organized group of atoms be capable          my opinion, nothing else than the principle of
quantum theory over again. To explain this, we          wrong, but it has to be taken 'with a very big
have to go to some length, including a                  grain of salt'.
refinement, not to say an amendment, of the
assertion previously made, namely, that all             THE MOTION OF A CLOCK
physical laws are based on statistics. This             Let us analyse the motion of a real clock
assertion, made again and again, could not fail         accurately. It is not at all a purely mechanical
to arouse contradiction. For, indeed, there are         phenomenon. A purely mechanical clock would
phenomena whose conspicuous features are                need no spring, no winding. Once set in motion,
visibly based directly on the 'order-from-order'                                      real (a) Tj 41 0 0 a
                                                        it would go on forever. A0 Tmclock without41 42
principle and appear to have nothing to do with         spring stops after a few beats of the pendulum,
statistics or molecular disorder. The order of the      its mechanical energy is turned into heat. This is
solar system, the motion of the planets, is             an infinitely complicated atomistic process. The
maintained for an almost indefinite time. The           general picture the physicist forms of it compels
constellation of principle this moment is directly      him to admit that th inverse process is not
connected with the constellation at any particular      entirely impossible: a springless clock might
moment in the times of the Pyramids; it can             suddenly begin to move, at the expense of the
be traced back to it, or vice versa. Historical         heat energy of its own cog wheels and of the
eclipses have been calculated and have been             environment. The physicist would have to say:
found in close agreement with historical records        The clock experiences an exceptionally in tense
or have even in some cases served to correct the        fit of Brownian movement. We have seen in
accepted chronology. These calculations do not          chapter 2 (p. 16) that with a very sensitive
imply any statistics, they are based solely on          torsional balance (electrometer or galvanometer)
Newton's law of universal attraction. Nor does          that sort of thing happens all the time. In the case
the regular motion of a good clock or any similar       of a clock it is, of course, infinitely unlikely.
mechanism appear to have anything to do with            Whether the motion of a clock is to be assigned
statistics. In short, all purely mechanical events      to the dynamical or to th statistical typ of
seem to follow distinctly and directly the 'order-      lawful events (to use Planck's expressions)
from-order' principle. And if we say                    depends on our attitude. In calling it a dynamical
'mechanical', the term must be taken in a wide          phenomenon we fix attention on the regular
sense. A very useful kind of clock is, as you           going that can be secured by a compara ively
know, based on the regular transmission of              weak spring, which overcomes th small
electric pulses from the power station. I               dis urbances by heat motion, so tha we may
remember an interesting little paper by Max                                    if we phenomenon.
                                                        dis egard them. Bu istical r member that Tm 41 0 0 41 676 0 Tm ( ) Tj 4
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       However insignificant the frictional and heating
from order' and 'order from disorder'. The object       effects in a clock may be from the p actical point
of that paper was to show how the interesting           of view, there can be no doubt that the second
statistical type of law, controlling large-scale        attitude, which does not neglect them, is the
events, is constituted from the dynamical laws          more fundamental one, even when we are faced
supposed to govern the small-scale events, the          with the based on a regular motion of a clock
interaction of the single atoms and molecules.          that is driven by a spring. For it must not be
The latter type is illustrated by large-scale           believed that the driving m chanism really does
mechanical phenomena, as the motion of the              away with the statistical na ure of the process.
planets or of a clock, etc. Thus it would appear        The true physical picture includes the possibility
that the 'new' principle, the order- from-order         that even a regularly going clock should all at
principle, to which we have pointed with great          once invert its motion and, working backward,
solemnity as being the real clue to the                 rewind its own spring -at the expense of the heat
understanding of life, is not at all new to physics.    of the environment. The event is just a little less
Planck's attitude ev n vindicates priority for it.      likely than a 'Brownian fit' of a clock w thout
We seem to arrive at the ridiculous conclusion          driving mechanism.
that the clue to the understanding of life is that it
is based on a pure mechanism, a 'clock-work' in         CLOCKWORK AFTER ALL STATISTICAL
the sense of Planck's paper, The conclusion is          Let us now review the situation. The 'simple'
not ridiculous and is, in my opinion, not entirely
case we have analysed is representative of many       insignificant role in many chemical reactions
others -in fact of all such appear to evade the       (Let me recall that entropy is a direct measure of
all-embracing principle of molecular statistics.      molecular disorder, viz. its logarithm.).
Clockworks made of real physical matter (in
contrast to imagination) are not true 'clock-         THE PENDULUM CLOCK IS VIRTUALLY
works'. The element of chance may be more or          AT ZERO TEMPERATURE
less reduced, the likelihood of the clock suddenly    What about a pendulum clock? For a pendulum
going altogether wrong may be infinitesimal, but      clock room temperature is practically equivalent
it always remains in the background. Even in the      to zero. That is the reason why it works
motion of the celestial bodies irreversible           'dynamically'. It will continue to work as it does
frictional and thermal torsional influences are not   if you cool it (provided that you have removed
wanting. Thus the rotation of the earth is slowly     all traces of oil!). But it does not continue to
diminished by tidal friction, and along with          work if you heat it above room temperature, for
this of course, reduction the moon gradually          it will eventually melt.
recedes from the earth, which would not happen
if the earth were a completely rigid                  THE RELATION BETWEEN CLOCKWORK
rotating sphere. Nevertheless the fact remains        AND ORGANISM .
that 'physical clock-works' visibly display very      That seems very trivial but it does, I think, hit the
prominent 'order-from-order' features - the type      cardinal point. Clockworks are capable of
that aroused the physicist's excitement when he       functioning 'dynamically', because they are built
encountered them in the organism. It seems            of solids, which are kept in shape by London-
likely that the two cases have after all something    Heider forces, strong enough to elude the
in common. It remains to be seen what this is         disorderly tendency of heat motion at ordinary
and what is the striking difference which makes       temperature. Now, I think, few words more are
case of the organism after all novel and              needed to disclose the point of resemblance
unprecedented.                                        between a clockwork and an organism. It is
                                                      simply and solely that the latter also hinges upon
NERNST'S THEOREM                                      a solid –the aperiodic crystal forming the
When does a physical system -any kind of              hereditary substance, largely withdrawn from the
association atoms -display 'dynamical law' (in        disorder of heat motion. But please do not accuse
Planck's meaning) 'clock-work features'?              me of calling the chromosome fibres just the
Quantum theory has a very short answer to this        'cogs of the organic machine' -at least not
question, viz. at the absolute zero of temperature.   without a reference to the profound physical
As zero temperature is approached the molecular       theories on which the simile is based. For,
disorder ceases to have any bearing on physical       indeed, it needs still less rhetoric to recall the
events. This fact was, by the way, not discovered     fundamental difference between the two and to
by theory, but by carefully investigating             justify the epithets novel and unprecedented in
chemical reactions over a wide range of               the biological case. The most striking features
temperatures and extrapolating the results to zero    are: first, the curious distribution of the cogs in a
temperature -which cannot actually be reached.        many-celled organism, for which I may refer to a
This is Walther Nernst's famous 'Heat Theorem',       very the somewhat poetical description on p. 79;
which is sometimes, and not unduly, given the         and secondly, by fact that the single cog is not of
proud name of the 'Third Law of                       coarse human make, but is the finest masterpiece
Thermodynamics' (the first being the energy           ever achieved along the lines of the Lord's
principle, the second the entropy principle).         quantum mechanics.
Quantum theory provides the rational foundation
of Nernst's empirical law, and also enables us to     Epilogue
estimate how closely a system must approach to        On Determinism and Free Will
the absolute zero in order to display an              As a reward for the serious trouble I have taken
approximately 'dynamical' behaviour. What             to expound the purely scientific aspects of our
temperature is in any particular case already         problem sine ira et studio, I beg leave to add my
practically equivalent to zero? Now you must not      own, necessarily subjective, view of the
believe that this always has to be a very low         philosophical implications. According to the
temperature. Indeed, Nernst's discovery was           evidence put forward in the preceding pages the
induced by the fact that even at room                 space-time events in the body of a living being
temperature entropy plays a astonishingly             which correspond to the activity of its mind, to
its self conscious or any other actions, are           into the happenings of the world. The striving of
(considering also their complex structure and the      all the scholars of Vedanta was, after having
accepted statistical explanation of                    learnt to pronounce with their lips, really to
physico-chemistry) if not strictly deterministic at    assimilate in their mi s this grandest of all
any rate statistico-deterministic. To the physicist    thoughts. Again, the mystics of many centuries,
I wish to emphasize that in my opinion, and            independently, yet in perfect harmony with each
contrary to the opinion upheld in some quarters,       other (somewhat like the particles in an ideal
quantum indeterminacy plays no biologically            gas) have described, each of them, the
relevant role in them, except perhaps by               unique experience of his or her life in terms that
enhancing their purely accidental character in         can be condensed in the phrase: DEUS FACTUS
such events as meiosis, natural and X-ray-             SUM (I have become God). To Western
induced mutation and so on -and this is in any         ideology the thought has remained a stranger, in
case obvious and well recognized. For the sake         spite of Schopenhauer and others who stood for
of argument, let me regard this as a fact, as I        it and in spite of those true lovers who, as they
believe every unbiased biologist would, if there       look into each other's eyes, become aware that
were not the well-known, unpleasant feeling            their though and their joy are numerically one -
about 'declaring oneself to be a pure mechanism'.      not merely similar or identical; but they, as a
For it is deemed to contradict Free Will as in         rule, are emotionally too busy to indulge in clear
warranted by direct introspection. But immediate       thinking, which respect they very much resemble
experiences in themselves, however various and         the mystic. Allow me a few further comments.
disparate they be, are logically incapable of          Consciousness is never experienced in the plural,
contradicting each other. So let us see whether        only in the singular. Even in the pathological
we cannot draw the correct, non-contradictory          cases of spli consciousness or double
conclusion from the following two premises: (i)        personality the two persons alternate, they are
My body functions as a pure mechanism                  never manifest simultaneously. In a dream we do
according to the Laws of Nature. (ii) Yet I know,      perform several characters at the same time, but
by incontrovertible direct experience, that I am       not indiscriminately: we are one of them; in
directing its motions, of which I foresee the          him we act and speak directly, while we often
effects, that may be fateful and all-important, in     eagerly await answer or response of another
which case I feel and take full responsibility for     person, unaware of the fact tha it is we who
them. The only possible inference from these           control his movements and his speech just as
two facts is, I think, that I –I in the widest         much as our own. How does the idea of plurality
meaning of the word, that is to say, every             (so emphatically opposed by the Upanishad
conscious mind that has ever said or felt 'I' -am      writers) arise at all? Conscious ess finds itself
the person, if any, who controls the 'motion of        intimately connected with, and dependent on, the
the atoms' according to the Laws of                    physical state of a limited region of matter, the
Nature. Within a cultural milieu (Kulturkreis)         body. (Consider the changes of mind during the
where certain conceptions (which once had or           developmen of the body, at puberty, ageing,
still have a wider meaning amongst other               dotage, etc., or consider the effects of fever
peoples) have been limited and specialized, it is      intoxication, narcosis, lesion of the brain and so
daring to give to this conclusion the simple           on.) Now there is a great plurality of similar
wording that it requires. In Christian terminology     bodies. Hence the pluralization of
to say: 'Hence I am God Almighty' sounds both          consciousnesses or minds seems a very
blasphemous and lunatic. But please disregard          sugges ive hypothesis. Probably all simple,
these connotations for the moment and consider         ingenuous people, as well as the great majority
whether the above inference is not the closest a       of Western philosophers, have accepted it. It
biologist can get to proving also their God and        leads almost immedia ely to the invention of
immortality at one stroke. In itself, the insight is   souls, as many as there are bodies, and to the
not new. The earliest records to my knowledge          question whether they are mortal as the body is
date back some 2,500 years or more. From the           or whether they are immortal a d capable of
early great Upanishads the recognition                 existing by themselves. The former alternative is
ATHMAN = BRAHMAN upheld in (the                        distasteful while the latter frankly forgets,
personal self equals the omnipresent,                  ignores or disowns the fact upon which the
all-comprehending eternal self) was in Indian          plurality hypothesis rests. Much sillier questions
thought considered, far from being blasphemous,        have been asked: Do animals a so have souls? It
to represent the quintessence of deepest insight       has even been questioned whether women, or
only men, have souls. Such consequences, even          person, indeed the protagonist of the novel you
if only tentative, must make us suspicious of the      are reading is probably nearer to your heart,
plurality hypothesis, which is common to all           certainly more intensely alive and better known
official Western creeds. Are we not inclining to       to you. Yet there has been no intermediate break,
much greater nonsense, if in discarding their          no death. And even if a skilled hypnotist
gross superstitions we retain their naive idea of      succeeded in blotting out entirely all your earlier
plurality of souls, but 'remedy' it by declaring the   reminiscences, you would not find that he had
souls to be perishable, to be annihilated with the     killed you. In no case is there a loss of personal
respective bodies? The only possible alternative       existence to deplore. Nor will there ever be.
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

				
DOCUMENT INFO
Shared By:
Tags: WHAT-, IS-LI
Stats:
views:49
posted:11/30/2009
language:English
pages:32
Description: WHAT-IS-LIFE-ERWIN-SCHRODINGER-First-published-1944-What-is-life-