Man comes into the world with a cry: a burst of light, a slap, initiate him into the universe of sensation. The material of science is this: our experience of the natural world, the world that is – not the ones that might be. Somehow in the mind this raw experience is ordered, and this order is the substance of science. What happens there is the application to a great diversity of the phenomena of the world of many of those elements called common sense, used every day and resting on certain suppositions we make concerning the world about us. Some of these are probably universal to man and beast. Others are more particular. We tend to accept them without special awareness, and some are so well hidden we are scarcely conscious of their existence.

The foremost supposition is the belief that the world outside ourselves, outside our own mind, exists. This belief is so primitive that it is very likely shared by all, except animals lowest on the evolutionary scale and some philosophers (whose position on the evolutionary scale we cannot guess).

Since I am a card-carrying member of the scientific establishment, and might possibly be accepted as one of the “Eastern Intellectual Elite,” my position on the current, somewhat astonishing “debate” on the teaching of evolution should be as predictable as the orbit of Mars calculated according to Newtonian physics. And it probably is. But today, we are quantum physicists; there may be a degree of uncertainty or unpredictability in our positions.

If Darwinian evolution is not a theory what could it be? It was proposed by Darwin as an explanation for an astonishing variety of facts concerning the interrelatedness of the many species now existent as well as the origins of these species and the evolution of life on Earth. It explains anatomical progressions, DNA, protein and other chemical similarities between different species.

It is one of the more remarkable theoretical structures created by the human mind; Darwin's evolution stands with the great theories of the physical world: remarkable structures that explain and connect vast varieties of phenomena – from the behavior of electrons at the lowest temperatures to the origin of the matter in the fiery instants after the creation of our present universe in what is called the Big Bang.

Over sixty years ago, Alan Turing proposed to test the hypothesis that a machine might think in the following way. Put either a machine or a person into a closed room, and communicate from outside this room in a manner that either the person or the machine can understand. (Let us say, by typing on a keyboard.) If one poses questions to whatever or whoever is in the room and if the responses do not allow one to distinguish between human and machine, then according to Turing, we can say that the machine (or the person) thinks.

Suppose, however, the entity in the room answers all questions with “I don't know,” or “I don't understand what you are saying.” Human being or machine? Could be a programmed computer. Could be one of our denser colleagues. Suppose the questions concern next best moves in the game of tic-tac-toe.

Once upon a time, not so long ago, neural networks were as easy to sell as Rhode Island wine in France. Reading the newspapers and trade journals, one might conclude that things have changed. To a certain extent this is the case. Scientific fashion has undergone one of its seasonal flip-flops. From the wintery opinion that neural networks could do nothing, we have, among the current summertime excesses, the suggestion that they will do everything. But the jury is still out. Commercial enterprises, sensing the possibilities and experiencing success, are beginning to move into the field. A recent study from the Defense Advanced Research Projects Agency, hailing this new technology, endorsing its potential importance and supporting applications to real-world problems, cautiously encourages benchmark tests and comparisons between neural networks and more conventional techniques.

What's all the fuss about? Put somewhat simplistically, we're talking about machines that can think. Now that kind of statement generates anticipation as well as a certain anxiety.

On this fiftieth anniversary of BCS (Superconductivity, not the Bowl Championship Series) it's hard to recapture the very great difficulty (even conjectured insolubility) this problem appeared to present just half a century ago. Many of the greatest names in physics had tried or were trying their hand – Einstein, Bohr, Heisenberg, and Feynman, among many others. The contrast between then (impossible) and now (safely ensconced in textbooks) leads me to reflect a bit about problems, past and present, thought to be insoluble.

Problems are thought to be insoluble for different reasons: it may be too soon, as Newton's attempts to understand the properties of matter, or Einstein's 1922 attempt to construct a theory of superconductivity before a quantum theory of metals was in place. It maybe that existing science does not contain the solution – a new postulate or law of nature is required, as Max Planck's 1901 quantum hypothesis. Or might it sometimes be that no solution is possible? Put another way: Are there limits to what we can understand? Are there limits to science as we do it? Are some questions inaccessible to human intellect?

I regard the public lectures which the statute of the Institute prescribes for us to deliver every year as one of the means for establishing and keeping up this contact in our small domain. Indeed I consider this to be their exclusive scope. The task is not very easy. For one has to have some kind of background to start from, and, as you know, scientific education is fabulously neglected, not only in this or that country—though, indeed, in some more than in others. This is an evil that is inherited, passed on from generation to generation. The majority of educated persons are not interested in science, and are not aware that scientific knowledge forms part of the idealistic background of human life. Many believe—in their complete ignorance of what science really is—that it has mainly the ancillary task of inventing new machinery, or helping to invent it, for improving our conditions of life. They are prepared to leave this task to the specialists, as they leave the repairing of their pipes to the plumber. If persons with this outlook decide upon the curriculum of our children, the result is necessarily such as I have just described it.

There are, of course, historical reasons why this attitude still prevails. The bearing of science on the idealistic background of life has always been great—apart perhaps from the Dark Ages, when science practically did not exist in Europe.

Is the ancient atomic theory, which is attached to the names of Leucippus and Democritus (born around 460 b.c.), the true forerunner of the modern one? This question has often been asked and very different opinions about it are on record. Gomperz, Cournot, Bertrand Russell, J. Burnet say: Yes. Benjamin Farrington says that it is, ‘in a way’, and that the two have a lot in common. Charles Sherrington says: No, pointing to the purely qualitative character of ancient atomism and to the fact that its basic idea, embodied in the word ‘atom’ (uncuttable or indivisible), has made this very name a misnomer. I am not aware that the negative verdict has ever passed the lips of a classical scholar. And when it comes from a scientist, he always shows by some remark that he regards chemistry—not physics—as the proper domain of the notions of atoms and molecules. He will mention the name of Dalton (born 1766) and omit, in this context, the name of Gassendi (born 1592). It was the latter who definitively reintroduced atomism into modern science, and he came to it after studying the fairly substantial extant writings of Epicurus (born around 341 b.c.), who had taken up the theory of Democritus, of which only scarce original fragments have come down to us.

The two great men of whom I wish to tell in this section have this in common, that they both give you the impression of walkers-alone—deep original thinkers, influenced by others, but not pledged to any ‘school’. The most probable period for Xenophanes' life is the century after about 565 b.c. At the age of ninety-two he describes himself as having wandered through the Greek countries (including, of course, Magna Graecia) for the last sixty-seven years. He was a poet, and the fragments of his fine verse that have come down to us make one deeply regret that his, as well as Empedocles' and Parmenides', hexameters and elegiacs were mostly lost, while the war-songs of the Iliad were preserved. Even so, what is extant of all these philosophical poems would in my opinion make a more interesting, a worthier and a more suitable subject for our school reading than the Wrath of Achilles (if you think what it is about). According to Wilamowitz, Xenophanes ‘upheld the only real monotheism that has ever existed upon earth’.

He was the same who discovered and correctly interpreted fossils in the rocks of south Italy—in the sixth century b.c.! I wish to quote here some of his famous fragments that give us an idea of the attitude of the advanced thinkers of that period towards religion and superstition.

When, early in 1948, I set out to deliver a course of public lectures on the subject dealt with here, I still felt the urgent need of prefacing them with ample explanations and excuses. What I was expounding then and there (to wit, at University College, Dublin) has come to form a part of the little book before you. Some comment from the standpoint of modern science was added, and a brief exposition of what I deem to be the peculiar fundamental features of the present-day scientific world-picture. To prove that these features are historically produced (as against logically necessitated), by tracing them back to the earliest stage of Western philosophic thought, was my real objective in enlarging on the latter. Yet, as I said, I did feel a little uneasy, particularly since those lectures arose from my official duty as a professor of theoretical physics. There was need to explain (though I was myself not so thoroughly convinced of it) that in passing the time with narratives about ancient Greek thinkers and with comments on their views I was not just following a recently acquired hobby of mine; that it did not mean, from the professional point of view, a waste of time, which ought to be relegated to the hours of leisure; that it was justified by the hope of some gain in understanding modern science and thus inter alia also modern physics.

The situation is rather disconcerting. You will ask: What are these particles then, if they are not individuals? And you may point to another kind of gradual transition, namely that between an ultimate particle and a palpable body in our environment, to which we do attribute individual sameness. A number of particles constitute an atom. Several atoms go to compose a molecule. Molecules there are of various sizes, small ones and big ones, but without there being any limit beyond which we call it a big molecule. In fact there is no upper limit to the size of a molecule, it may contain hundreds of thousands of atoms. It may be a virus or a gene, visible under the microscope. Finally we may observe that any palpable object in our environment is composed of molecules, which are composed of atoms, which are composed of ultimate particles … and if the latter lack individuality, how does, say, my wrist-watch come by individuality? Where is the limit? How does individuality arise at all in objects composed of non-individuals?

It is useful to consider this question in some detail, for it will give us the clue to what a particle or an atom really is–what there is permanent in it in spite of its lack of individuality.

Let me now, at last, approach the answer to the question which was put at the outset.

Remember the lines of Burnet's preface—that science is a Greek invention; that science has never existed except among peoples who came under Greek influence. Later in the same book he says: ‘The founder of the Milesian School and therefore [!] the first man of science was Thales.’ Gomperz says (I quoted him extensively) that our whole modern way of thinking is based on Greek thinking; it is therefore something special, something that has grown historically over many centuries, not the general, the only possible way of thinking about Nature. He sets much store on our becoming aware of this, of recognizing the peculiarities as such, possibly freeing us from their wellnigh irresistible spell.

What are they then? What are the peculiar, special traits of our scientific world-picture?

About one of these fundamental features there can be no doubt. It is the hypothesis that the display of Nature can be understood. I have touched on this point repeatedly. It is the non-spiritistic, the non-superstitious, the non-magical outlook. A lot more could be said about it. One would in this context have to discuss the questions: what does comprehensibility really mean, and in what sense, if any, does science give explanations?

In this we must, of course, take shape (or Gestalt) in a much wider sense than as geometrical shape. Indeed there is no observation concerned with the geometrical shape of a particle or even of an atom. It is true that in thinking about the atom, in drafting theories to meet the observed facts, we do very often draw geometrical pictures on the black-board, or on a piece of paper, or more often just only in our mind, the details of the picture being given by a mathematical formula with much greater precision and in a much handier fashion than pencil or pen could ever give. That is true. But the geometrical shapes displayed in these pictures are not anything that could be directly observed in the real atoms. The pictures are only a mental help, a tool of thought, an intermediary means, from which to deduce, out of the results of experiments that have been made, a reasonable expectation about the results of new experiments that we are planning. We plan them for the purpose of seeing whether they confirm the expectations—thus whether the expectations were reasonable, and thus whether the pictures or models we use are adequate. Notice that we prefer to say adequate, not true. For in order that a description be capable of being true, it must be capable of being compared directly with actual facts. That is usually not the case with our models.