THE CLASSICAL PHYSICIST'S EXPECTATION, FAR FROM BEING TRIVIAL, IS WRONG

Thus we have come to the conclusion that an organism and all the biologically relevant processes that it experiences must have an extremely ‘many-atomic’ structure and must be safeguarded against haphazard, ‘single-atomic’ events attaining too great importance. That, the ‘naïve physicist’ tells us, is essential, so that the organism may, so to speak, have sufficiently accurate physical laws on which to draw for setting up its marvellously regular and well-ordered working. How do these conclusions, reached, biologically speaking, a priori (that is, from the purely physical point of view), fit in with actual biological facts?

At first sight one is inclined to think that the conclusions are little more than trivial. A biologist of, say, thirty years ago might have said that, although it was quite suitable for a popular lecturer to emphasize the importance, in the organism as elsewhere, of statistical physics, the point was, in fact, rather a familiar truism. For, naturally, not only the body of an adult individual of any higher species, but every single cell composing it contains a ‘cosmical’ number of single atoms of every kind.

A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students.

‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc.’

Ladies and Gentlemen:

In a very primitive stage of development the human mind formed definite notions of space and time as the frame in which different events take place. These notions, without essential changes, have been carried forward from generation to generation, and, since the development of exact sciences, have been built into the foundations of the mathematical description of the universe. The great newton perhaps gave the first clear-cut formulation of the classical notions of space and time, writing in his Principia:

So strong was the belief in the absolute correctness of these classical ideas about space and time that they have often been held by philosophers as given a priori, and no scientist even thought about the possibility of doubting them.

However, just at the start of the present century it became clear that a number of results, obtained by most refined methods of experimental physics, led to clear contradictions if interpreted in the classical frame of space and time.

THE GENERAL PICTURE OF THE HEREDITARY SUBSTANCE

From these facts emerges a very simple answer to our question, namely: Are these structures, composed of comparatively few atoms, capable of withstanding for long periods the disturbing influence of heat motion to which the hereditary substance is continually exposed? We shall assume the structure of a gene to be that of a huge molecule, capable only of discontinuous change, which consists in a rearrangement of the atoms and leads to an isomeric molecule. The rearrangement may affect only a small region of the gene, and a vast number of different rearrangements may be possible. The energy thresholds, separating the actual configuration from any possible isomeric ones, have to be high enough (compared with the average heat energy of an atom) to make the change-over a rare event. These rare events we shall identify with spontaneous mutations.

The later parts of this chapter will be devoted to putting this general picture of a gene and of mutation (due mainly to the German physicist M. Delbrück) to the test, by comparing it in detail with genetical facts. Before doing so, we may fittingly make some comment on the foundation and general nature of the theory.

“JUMP-LIKE” MUTATIONS – THE WORKING-GROUND OF NATURAL SELECTION

The general facts which we have just put forward in evidence of the durability claimed for the gene structure, are perhaps too familiar to us to be striking or to be regarded as convincing. Here, for once, the common saying that exceptions prove the rule is actually true. If there were no exceptions to the likeness between children and parents, we should have been deprived not only of all those beautiful experiments which have revealed to us the detailed mechanism of heredity, but also of that grand, million-fold experiment of Nature, which forges the species by natural selection and survival of the fittest.

Let me take this last important subject as the starting-point for presenting the relevant facts – again with an apology and a reminder that I am not a biologist:

We know definitely, today, that Darwin was mistaken in regarding the small, continuous, accidental variations, that are bound to occur even in the most homogeneous population, as the material on which natural selection works. For it has been proved that they are not inherited. The fact is important enough to be illustrated briefly.

INTRODUCTION

Whereas the previous chapter tells us about mysteries surrounding the physical structure of the Universe from a largely observational point of view, in this essay I will approach the problem of space and time from a theoretical point of view. This is about the conceptual structure of physics, why in fact our current concepts of space and time are fundamentally flawed and how they might be improved. I will explain in detail why I think that spacetime is fundamentally not a smooth continuum at the pre-subatomic level due to quantum-gravity effects and why a better although still not final picture is one where there are no points, where everything is done by algebra much as in quantum mechanics, what I therefore call ‘quantum spacetime’.

The idea of ‘moving around’ in space in this theory is replaced by ‘quantum symmetry’ and I shall need to explain this to the reader. Symmetry is the deepest of all notions in mathematics and what emerged in the last two decades is that this very concept is really part of something even more fundamental. Indeed, these quantum symmetries not only generalise our usual notion of symmetry but have a deep self-duality in their very definition in which the role of the composition of symmetry transformations and a new structure called a ‘coproduct’ is itself symmetric. For our purposes, quantum symmetries are needed in order to extend Einstein's theory of Special Relativity to quantum spacetimes.

A scientist is supposed to have a complete and thorough knowledge, at first hand, of some subjects and, therefore, is usually expected not to write on any topic of which he is not a master. This is regarded as a matter of noblesse oblige. For the present purpose I beg to renounce the noblesse, if any, and to be freed of the ensuing obligation. My excuse is as follows:

We have inherited from our forefathers the keen longing for unified, all-embracing knowledge. The very name given to the highest institutions of learning reminds us, that from antiquity and throughout many centuries the universal aspect has been the only one to be given full credit. But the spread, both in width and depth, of the multifarious branches of knowledge during the last hundred odd years has confronted us with a queer dilemma. We feel clearly that we are only now beginning to acquire reliable material for welding together the sum total of all that is known into a whole; but, on the other hand, it has become next to impossible for a single mind fully to command more than a small specialized portion of it.

Nine years ago I put forward two general principles that form the basis of the scientific method, the principle of the understandability of nature, and the principle of objectivation. Since then I have touched on this matter now and again, last time in my little book Nature and the Greeks. I wish to deal here in detail with the second one, the objectivation. Before I say what I mean by that, let me remove a possible misunderstanding which might arise, as I came to realize from several reviews of that book, though I thought I had prevented it from the outset. It is simply this: some people seemed to think that my intention was to lay down the fundamental principles which ought to be at the basis of scientific method or at least which justly and rightly are at the basis of science and ought to be kept at all cost. Far from this, I only maintained and maintain that they are – and, by the way, as an inheritance from the ancient Greeks, from whom all our Western science and scientific thought has originated.

The misunderstanding is not very astonishing. If you hear a scientist pronounce basic principles of science, stressing two of them as particularly fundamental and of old standing, it is natural to think that he is at least strongly in favour of them and wishes to impose them.

During many months of unusual adventures, in the course of which the professor tried to introduce Mr Tompkins to the secrets of physics, Mr Tompkins became more and more enchanted by Maud and finally, and rather sheepishly, made a proposal of marriage. This was readily accepted, and they became man and wife. In his new role of father-in-law, the professor considered it his duty to enlarge the knowledge of his daughter's husband in the field of physics and of its most recent progress.

One Sunday afternoon Mr and Mrs Tompkins were resting in armchairs in their comfortable flat, she being engulfed in the latest issue of Vogue, he reading an article in Esquire.

‘Oh,’ Mr Tompkins exclaimed suddenly, ‘here is a chance game system which really works!’

‘Do you really think, Cyril, that it will?’ asked Maud, raising her eyes reluctantly from the pages of the fashion magazine. ‘Father has always said that there can't be such a thing as a surefire gambling system.’

‘But look here, Maud,’ answered Mr Tompkins, showing her the article he had been studying for the last half hour. ‘I don't know about other systems, but this one is based on pure and simple mathematics, and I really don't see how it could possibly go wrong.’

Mr Tompkins was very amused about his adventures in the relativistic city, but was sorry that the professor had not been with him to give any explanation of the strange things he had observed: the mystery of how the railway brakeman had been able to prevent the passengers from getting old worried him especially. Many a night he went to bed with the hope that he would see this interesting city again, but the dreams were rare and mostly unpleasant; last time it was the manager of the bank who was firing him for the uncertainty he introduced into the bank accounts… so now he decided that he had better take a holiday, and go for a week somewhere to the sea. Thus he found himself sitting in a compartment of a train and watching through the window the grey roofs of the city suburb gradually giving place to the green meadows of the countryside. He picked up a newspaper and tried to interest himself in the Vietnam conflict. But it all seemed to be so dull, and the railway carriage rocked him pleasantly.…

When he lowered the paper and looked out of the window again the landscape had changed considerably. The telegraph poles were so close to each other that they looked like a hedge, and the trees had extremely narrow crowns and were like Italian cypresses.

In the winter of 1938 I wrote a short, scientifically fantastic story (not a science fiction story) in which I tried to explain to the layman the basic ideas of the theory of curvature of space and the expanding universe. I decided to do this by exaggerating the actually existing relativistic phenomena to such an extent that they could easily be observed by the hero of the story, C. G. H.* Tompkins, a bank clerk interested in modern science.

I sent the manuscript to Harper's Magazine and, like all beginning authors, got it back with a rejection slip. The other half-a-dozen magazines which I tried followed suit. So I put the manuscript in a drawer of my desk and forgot about it. During the summer of the same year, I attended the International Conference of Theoretical Physics, organized by the League of Nations in Warsaw. I was chatting over a glass of excellent Polish miod with my old friend Sir Charles Darwin, the grandson of Charles (The Origin of Species) Darwin, and the conversation turned to the popularization of science. I told Darwin about the bad luck I had had along this line, and he said: ‘Look, Gamow, when you get back to the United States dig up your manuscript and send it to Dr C. P. Snow, who is the editor of a popular scientific magazine Discovery published by the Cambridge University Press.’

Can science vouchsafe information on matters of religion? Can the results of scientific research be of any help in gaining a reasonable and satisfactory attitude towards those burning questions which assail everyone at times? Some of us, in particular healthy and happy youth, succeed in shoving them aside for long periods; others, in advanced age, have satisfied themselves that there is no answer and have resigned themselves to giving up looking for one, while others again are haunted throughout their lives by this incongruity of our intellect, haunted also by serious fears raised by time-honoured popular superstition. I mean mainly the questions concerned with the ‘other world’, with ‘life after death’, and all that is connected with them. Notice please that I shall not, of course, attempt to answer these questions, but only the much more modest one, whether science can give any information about them or aid our – to many of us unavoidable – thinking about them.

To begin with, in a very primitive way it certainly can, and has done so without much ado. I remember seeing old prints, geographical maps of the world, so I believe, including hell, purgatory and heaven, the former being placed deep underground, the latter high above in the skies.

THE GENERAL CHARACTER AND THE PURPOSE OF THE INVESTIGATION

This little book arose from a course of public lectures, delivered by a theoretical physicist to an audience of about four hundred which did not substantially dwindle, though warned at the outset that the subject-matter was a difficult one and that the lectures could not be termed popular, even though the physicist's most dreaded weapon, mathematical deduction, would hardly be utilized. The reason for this was not that the subject was simple enough to be explained without mathematics, but rather that it was much too involved to be fully accessible to mathematics. Another feature which at least induced a semblance of popularity was the lecturer's intention to make clear the fundamental idea, which hovers between biology and physics, to both the physicist and the biologist.

For actually, in spite of the variety of topics involved, the whole enterprise is intended to convey one idea only – one small comment on a large and important question. In order not to lose our way, it may be useful to outline the plan very briefly in advance.