The Ascent of Man (34 page)

When an observer looks at a star, he knows that there is a multitude of causes for error. So he takes several readings, and he hopes, naturally, that the best estimate of the star’s position is the average – the centre of the scatter. So far, so obvious. But Gauss pushed on to ask what the
scatter
of the errors tells us. He devised
the Gaussian curve in which the
scatter
is summarised by the deviation, or spread, of the curve. And from this came a far-reaching idea: the scatter marks an area of uncertainty. We are not sure that the true position is the centre. All we can say is that it lies
in the area of uncertainty
, and the area is calculable from the observed scatter of the individual observations.

Having this subtle
view of human knowledge, Gauss was particularly bitter about philosophers who claimed that they had a road to knowledge more perfect than that of observation. Of many examples I will choose one. It happens that there is a philosopher called Friedrich Hegel, whom I must confess I specifically detest. And I am happy to share that profound feeling with a far greater man, Gauss. In 1800 Hegel presented
a thesis, if you please, proving that although the definition of planets had changed since the Ancients, there still could only be, philosophically, seven planets. Well, not only Gauss knew how to answer that: Shakespeare had answered that long before. There is a marvellous passage in
King Lear
, in which who else but the Fool says to the King: ‘The reason why the seven Starres are no mo then seuen,
is a pretty reason’. And the King wags sagely and says: ‘Because they are not eight’. And the Fool says: ‘Yes indeed, thou woulds’t make a good Foole’. And so did Hegel. On 1 January 1801, punctually, before the ink was dry on Hegel’s dissertation, an eighth planet was discovered – the minor planet Ceres.

History has many ironies. The time-bomb in Gauss’s curve is that after his death we discover
that there is no God’s eye view. The errors are inextricably bound up with the nature of human knowledge. And the irony is that the discovery was made in Göttingen.

Ancient university towns are wonderfully alike. Göttingen is like Cambridge in England or Yale in America: very provincial, not on the way to anywhere – no one comes to these backwaters except for the company of
professors. And the
professors are sure that this is the centre of the world. There is an inscription in the Rathskeller here which reads ‘Extra Gottingam non est vita’, ‘Outside Göttingen there is no life’. This epigram, or should I call it epitaph, is not taken as seriously by the undergraduates as by the professors.

The symbol of the University is the iron statue outside the Rathskeller of a barefoot goosegirl
that every student kisses at graduation. The University is a Mecca to which students come with something less than perfect faith. It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known but to question it.

Like every university town, the Göttingen landscape is criss-crossed with long walks that professors take
after lunch, and the research students are ecstatic if they are asked along. Perhaps Göttingen in the past had been rather sleepy. The small German university towns go back to a time before the country was united (Göttingen was founded by George II as ruler of Hanover), and this gives them a flavour of local bureaucracy. Even after the military might ended and the Kaiser abdicated in 1918, they were
more conformist than universities outside Germany.

The link between Göttingen and the outside world was the railway. That was the way the visitors came from Berlin and abroad, eager to exchange the new ideas that were racing ahead in physics. It was a by-word in Göttingen that science came to life in the train to Berlin, because that is where people argued and contradicted and had new ideas.
And had them challenged, too.

In the years of the First World War, science was dominated at Göttingen as elsewhere by Relativity. But in 1921 there was appointed to the chair of physics Max Born, who began a series of seminars that brought everyone interested in atomic physics here. It is rather surprising to reflect that Max Born was almost forty when he was appointed. By and large, physicists
have done their best work before they are thirty (mathematicians even earlier, biologists perhaps a little later). But Born had a remarkable personal, Socratic gift. He drew young men to him, he got the best out of them, and the ideas that he and they exchanged and challenged also produced his best work. Out of that wealth of names, whom am I to choose? Obviously Werner Heisenberg, who did his
finest work here with Born. Then, when Erwin Schrödinger published a different form of basic atomic physics, here is where the arguments took place. And from all over the world people came to Göttingen to join in.

It is rather strange to talk in these terms about a subject which, after all, is done by midnight oil. Did physics in the 1920s really consist of argument, seminar, discussion, dispute?
Yes, it did. Yes, it still does. The people who met here, the people who meet in laboratories still, only end their work with a mathematical formulation. They begin it by trying to solve conceptual riddles. The riddles of the sub-atomic particles – of the electrons and the rest – are mental riddles.

Think of the puzzles that the electron was setting just at that time. The quip among professors
was (because of the way university timetables are laid out) that on Mondays, Wednesdays, and Fridays the electron would behave like a particle; on Tuesdays, Thursdays, and Saturdays it would behave like a wave. How could you match those two aspects, brought from the large-scale world and pushed into a single entity, into this Lilliput,
Gulliver’s Travels
world of the inside of the atom? That is
what the speculation and argument was about. And that requires,
not calculation, but insight, imagination – if you like, metaphysics. I remember a phrase that Max Born used when he came to England many years after, and that still stands in his autobiography. He said: ‘I am now convinced that theoretical physics is actual philosophy’.

Max Born meant that the new ideas in physics amount to a different
view of reality. The world is not a fixed, solid array of objects, out there, for it cannot be fully separated from our perception of it. It shifts under our gaze, it interacts with us, and the knowledge that it yields has to be interpreted by us. There is no way of exchanging information that does not demand an act of judgment. Is the electron a particle? It behaves like one in the Bohr atom.
But de Broglie in 1924 made a beautiful wave model, in which the orbits are the places where an exact, whole number of waves closes round the nucleus. Max Born thought of a train of electrons as if each were riding on a crankshaft, so that collectively they constitute a series of Gaussian curves, a wave of probability. A new conception was being made, on the train to Berlin and the professorial
walks in the woods of Göttingen: that whatever fundamental units the world is put together from, they are more delicate, more fugitive, more startling than we catch in the butterfly net of our senses.

All those woodland walks and conversations came to a brilliant climax in 1927. Early that year Werner Heisenberg gave a new characterisation of the electron. Yes, it is a particle, he said, but
a particle which yields only limited information. That is, you can specify where it is at this instant, but then you cannot impose on it a specific speed and direction at the setting-off. Or conversely, if you insist that you are going to fire it at a certain speed in a certain direction, then you cannot specify exactly what its starting-point is – or, of course, its end-point.

That sounds like
a very crude characterisation. It is not. Heisenberg gave it depth by making it precise. The information that the electron carries is limited in its totality. That is, for instance, its speed
and
its position fit
together
in such a way that they are confined by the tolerance of the quantum. This is the profound idea: one of the great scientific ideas, not only of the twentieth century, but in
the history of science.

Heisenberg called this the Principle of Uncertainty. In one sense, it is a robust principle of the everyday. We know that we cannot ask the world to be exact. If an object (a familiar face, for example) had to be
exactly
the same before we recognised it, we would never recognise it from one day to the next. We recognise the object to be the same because it is much the
same; it is never exactly like it was, it is tolerably like. In the act of recognition, a judgment is built in – an area of tolerance or uncertainty. So Heisenberg’s principle says that no events, not even atomic events, can be described with certainty, that is, with zero tolerance. What makes the principle profound is that Heisenberg specifies the tolerance that can be reached. The measuring rod
is Max Planck’s quantum. In the world of the atom, the area of uncertainty is always mapped out by the quantum.

Yet the Principle of Uncertainty is a bad name. In science or outside it, we are not uncertain; our knowledge is merely confined within a certain tolerance. We should call it the Principle of Tolerance. And I propose that name in two senses. First, in the engineering sense. Science
has progressed step by step, the most successful enterprise in the ascent of man, because it has understood that the exchange of information between man and nature, and man and man, can only take place with a certain tolerance. But second, I also use the word passionately about the
real world. All knowledge, all information between human beings can only be exchanged within a play of tolerance.
And that is true whether the exchange is in science, or in literature, or in religion, or in politics, or even in any form of thought that aspires to dogma. It is a major tragedy of my lifetime and yours that, here in Göttingen, scientists were refining to the most exquisite precision the Principle of Tolerance, and turning their backs on the fact that all around them tolerance was crashing to the
ground beyond repair.

The sky was darkening all over Europe. But there was one particular cloud which had been hanging over Göttingen for a hundred years. Early in the 1800s Johann Friedrich Blumenbach had put together a collection of skulls that he got from distinguished gentlemen with whom he corresponded throughout Europe. There was no suggestion in Blumenbach’s work that the skulls were to
support a racist division of humanity, although he did use anatomical measurements to classify the families of man. All the same, from the time of Blumenbach’s death in 1840 the collection was added to and added to and became a core of racist, pan-Germanic theory, which was officially sanctioned by the National Socialist Party when it came into power.

When Hitler arrived in 1933, the tradition
of scholarship in Germany was destroyed, almost overnight. Now the train to Berlin was a symbol of flight. Europe was no longer hospitable to the imagination – and not just the scientific imagination. A whole conception of culture was in retreat: the conception that human knowledge is personal and responsible, an unending adventure at the edge of uncertainty. Silence fell, as after the trial of
Galileo. The great men went out into a threatened world. Max Born. Erwin Schrödinger. Albert Einstein. Sigmund Freud. Thomas Mann. Bertolt Brecht. Arturo Toscanini. Bruno Walter. Marc Chagall. Enrico Fermi. Leo Szilard, arriving finally after many years at the Salk Institute in California.

The Principle of Uncertainty or, in my phrase, the Principle of Tolerance fixed once for all the realisation
that all knowledge is limited. It is an irony of history that at the very time when this was being worked out there should rise, under Hitler in Germany and other tyrants elsewhere, a counter-conception: a principle of monstrous certainty. When the future looks back on the 1930s it will think of them as a crucial confrontation of culture as I have been expounding it, the ascent of man, against
the throwback to the despots’ belief that they have absolute certainty.

I must put all these abstractions into concrete terms, and I want to do so in one personality. Leo Szilard was greatly engaged in them, and I spent many afternoons in the last year or so of his life talking with him about them at the Salk Institute.

Leo Szilard was a Hungarian whose university life was spent in Germany. In 1929 he had published an important and pioneer paper on what would now be called Information Theory, the relation between knowledge, nature and man. But by then Szilard was certain that Hitler would come to power, and that war was inevitable. He kept two
bags packed in his room, and by 1933 he had locked them and taken them to England.

It happened that in September of 1933 Lord Rutherford, at the British Association meeting, made some remark about atomic energy never becoming real. Leo Szilard was the kind of scientist, perhaps just the kind of good-humoured, cranky man, who disliked any statement that contained the word ‘never’, particularly
when made by a distinguished colleague. So he set his mind to think about the problem. He tells the story as all of us who knew him would picture it. He was living at the Strand Palace Hotel – he loved living in hotels. He was walking to work at Bart’s Hospital, and as he came to Southampton Row he was stopped by a red light. (That is the only part of the story I find improbable; I never knew Szilard
to stop for a red light.) However, before the light turned green, he had realised that if you hit an atom with one neutron, and it happens to break up and release two, then you would have a chain reaction. He wrote a specification for a patent which contains the words ‘chain reaction’ which was filed in 1934.