Shakespeare, Newton and Beethoven – A talk by S. Chandrasekhar (Page 3/3)

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III

I now turn to Newton.

Isaac Newton, a posthumous child, born with no father on Christmas Day 1642, was, as Maynard Keynes has aptly written, “the last wonder child to whom the Magi could do sincere and appropriate homage.”

One of the most remarkable aspects of Newton’s most remarkable life is the explosive outburst of his genius. He was not an infant prodigy; and it is probable that when he went to Cambridge in 1661, he knew little more than elementary arithmetic. And it must be remembered that the new outlook on scientific thought that we associate with the names of Galileo, Kepler, and Descartes had hardly yet penetrated the walls of Oxford and Cambridge. Nevertheless, by 1664, when Newton was in his twenty-third year, his genius seems to have flowered. Thus, Newton recalled in his old age that he had “found the method of Infinite Series at such time (1664-65).” Newton, in fact, wrote out his notes as a connected essay entitled, “On Analysis of Equations with an Infinite Number of Terms” and allowed Barrow to send it to Collins, stipulating, however, that he remain anonymous.

This stipulation was withdrawn later; but we encounter here the first indication of a trait which was later to become an obsession with Newton.

By the summer of 1665, when Cambridge was evacuated on account of the plague and Newton had gone to Woolsthorpe, his genius was fully in flower. It manifested itself in a manner unsurpassed in the history of scientific thought. But it was not until many years later that the world was to know what happened during the two years that Newton was at Woolsthorpe.

For here at Woolsthorpe, Newton at the age of twenty-three made three of the greatest discoveries in science: the Differential Calculus, the Composition of Light, and the Laws of Gravitation. Writing towards the end of his life, Newton recalled his discovery of the laws of gravitation thus:

In the same year (1666) I began to think of gravity extending to the orb of the moon… I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty well. All this was in the two plague years 1665 and 1666, for in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since.

Notice, first, his statement that “in those days… I minded mathematics and philosophy [meaning science] more than at any time since.” Notice also the curious words “answer pretty well” to the agreement he had found with respect to the acceleration experienced by the moon in its orbit and as deduced – on the basis of his inverse square law – from the acceleration experienced by bodies on the earth, that is, the falling apple. Newton does not appear to have felt any urgency to verify if his prediction “answers” more than “pretty well.” Indeed, he does not seem to have experienced any special delight in having discovered so fundamental a law of nature. In actual fact, he dismissed the entire matter from his mind for a decade and more.

Newton returned to Cambridge early in 1667; and in 1669 he was appointed to the Lucasian Chair of Mathematics in succession to Barrow who had relinquished the Chair on Newton’s behalf.

Soon after his return to Cambridge, Newton appears to have completed to his satisfaction his experimental investigations on the composition of light and constructed his first reflecting telescope to avoid the chromatic aberrations of the then extant refracting telescopes. But he did not publish any of these results of his investigations for several years.

The news of Newton having constructed a telescope on a new principle soon spread and Newton was urged to exhibit it at the Royal Society. It is known that Newton sent at least two telescopes to the Royal Society and that the second of them was exhibited in 1671.

Farewell to a newly married Chandra with wife, Lalitha, at the Madras railway station (1936)

Farewell to a newly married Chandra with wife Lalitha
at the Madras railway station (1936)

Newton was elected to the Royal Society in January 1672. Stimulated perhaps by this recognition, Newton acceded to the request by Oldenburg, then the Secretary of the Royal Society, to communicate to the Society an account of his discoveries and in particular the principles underlying the construction of his telescope. In two successive letters, Newton replied to Oldenburg as follows:

I shall endeavour to testify my gratitude by communicating what my poor and solitary endeavlours can effect towards the promoting your philosophical designs. (January 6, 1672)

In the next letter he suggests communicating an account of his optical discoveries rather than a description of his telescope. He writes:

An account of a philosophical discovery – which I doubt not but will prove much more grateful than the communication of that instrument, being in my judgement the oddest, if not the most considerable detection, which has hitherto been made in the operation of nature. (January 18, 1672)

I should like to draw your attention especially to the words, “the oddest, if not the most considerable detection.” This is the first and the only time that Newton expresses a trace of enthusiasm with respect to any of his discoveries. But what followed the publication of Newton’s account of his experiments on the composition of light was nothing short of a disaster. A vigorous controversy ensued, and Newton appears to have been irritated beyond endurance by the inability of his critics even to comprehend what it was he had experimentally demonstrated. This lack of comprehension is apparent, for example, from Huygens – even Huygens – arguing that there “would still remain the great difficulty of explaining by mechanical principles, in what consists the diversity of colours, even supposing that Newton’s decomposition of white light into the colours of the spectrum is correct.”

At first Newton tried to persuade by clarifying his method:

For the best and safest method of philosophizing seems to be, first to enquire diligently into the properties of things, and of establishing those properties by experiments, and then to proceed more slowly to hypotheses for the explanation of them. For hypotheses should be subservient only in explaining the properties o f things, but not assumed in determining them; unless so far as they may furnish experiments…

(Parenthetically, we may notice that Newton is, here, enunciating what he was to formulate later in his famous aphorism:

Hypotheses non fingo – I frame no hypotheses.)

Newton’s failure to persuade resulted in the aversion he now formed to scientific publication, discussion, and arguments. Thus, he wrote to Oldenburg:

I have long since determined to concern myself no further about the promotion of philosophy. (December 5, 1672).

I see I have made myself a slave to Philosophy, but if I get free of Mr. Linus’ business I will resolutely bid adieu to it eternally, except what I do for my private satisfaction, or leave to come out after me. For I see, a man must either resolve to point out nothing new or to become a slave to defend it. (November 18, 1676)

This aversion to scientific publication, discussion, and argument was to find repeated expressions in later years. Here are two examples:

For I see not what there is desirable in public esteem, were I able to acquire and maintain it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline.

I am grown of all men the most shy of setting pen to paper about any thing that may lead into disputes. (September 12, 1682)

Soon after the publication of his optical discoveries, Newton receded into himself, and we do not know very much as to how he occupied himself during the following decade. But we do know that in 1679, Newton had proved for himself that under the influence of a central inverse-square attractive force an object will describe an elliptical orbit, with the center of attraction at one of its foci. But, again, he kept the result to himself.

At long last, in 1684, an incident, not of Newton’s making, was to change the course of scientific history. In January of that year, at a meeting in London between Christopher Wren, Robert Hooke, and Edmund Halley, the question arose as to the nature of the orbit a planet would describe under the influence of an inverse-square attractive gravitational force. Since none of them knew how the question could be resolved, Halley went to Cambridge in August of that year to inquire if Newton had any suggestions to offer. To Halley’s inquiry, Newton replied at once that the orbit would be an ellipse, and that he had established this result for himself some seven years earlier. Halley was overjoyed and wished to see Newton’s proof. On Newton finding that he had mislaid the piece of paper on which he had written out the proof, he promised to rework it and send it to him shortly.

The reworking of this old problem seems to have aroused Newton’s interest in the whole area. By October, he had worked out enough problems to serve as a basis for nine lectures which he gave during the Michaelmas term under the title De Motu Corporum in gyrum.

Halley, on receiving Newton’s promised proof at about this time and hearing also of Newton’s lectures, went to Cambridge once again, this time to persuade Newton to publish his lectures.

By now Newton’s mathematical genius seems to have been fully aroused, and Newton appears to have been caught in its grip. Newton now entered upon a period of the most intense mathematical activity. Against his will and against his preferences, Newton seems to have been propelled inexorably forward, by the pressure of his own genius, till, at last, he had accomplished the greatest intellectual feat of his life, the greatest intellectual feat in all of science.

Let us pause for a moment to take full measure of the magnitude of this feat. By Newton’s own account, he began writing the Principia towards the end of December 1684, and he sent the completed manuscript of all three Books of the Principia to the Royal Society in May 1686, that is, in seventeen months. He had solved two of the propositions in the first Book in 1679, and he had also proved eight of the propositions in the second Book in June and July 1685. There are ninety-eight propositions in the first Book; fifty-three in the second; and forty-two in the third. By far the larger proportion of them was, therefore, enunciated and proved during the seventeen consecutive months that Newton was at work on the three Books. It is this rapidity of execution, besides the monumental scale of the whole work, that makes this achievement incomparable. If the problems enunciated in the Principia were the results of a lifetime of thought and work, Newton’s position in science would still be unique. But that all these problems should have been enunciated, solved, and arranged in logical sequence in seventeen months is beyond human comprehension. It can be accepted only because it is a fact: it just happens to be so!

It is only when we observe the scale of Newton’s achievement that comparisons, which have sometimes been made with other men of science, appear altogether inappropriate both with respect to Newton and with respect to the others. In fact, only in juxtaposition with Shakespeare and Beethoven is the consideration of Newton appropriate.

Now, a few remarks concerning the style of the Principia. Quite unlike his early communications on his optical discoveries, the Principia is written in a style of glacial remoteness which makes no concessions to his readers. As Whewell aptly wrote:

… As we read the Principia, we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them, we marvel what manner of men they were who could use as weapons what we can scarcely lift as a burden…

It is, however, clear that the rigid and the lamellated style of the Principia is deliberate. For after the publication of the Principia, Newton is reported to have told Rev. Dr. Derham:

To avoid being baited by little smatterers in mathematics, I designedly made the Principia abstruse; but yet so as to be understood by able mathematicians who, I imagine, by comprehending my demonstrations would concur with my theory.

Although Newton was only forty-two years of age when he finished writing the Principia and was, quite literally, at the height of his mathematical powers and was to remain in full possession of his faculties for another forty years, he never again seriously concerned himself with a scientific investigation. He turned to an utterly different way of living. And in time he became one of the principal sights of London for all visiting intellectuals: the Sir Isaac Newton of popular tradition.

No account of Newton’s life, however brief, can omit some indication of the manner of man he was. The subject is a complex and a controversial one. But this much can fairly be said: Newton seems to have been remarkably insensitive: impervious to the arts, tactless, and with no real understanding of others.

Newton’s most remarkable gift was probably his powers of concentration. As Keynes wrote:

His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted… I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret.

Besides, as De Morgan has said, he was:

…So happy in his conjectures as to seem to know more than he could possibly have any means of proving.

But the central paradox of Newton’s life is that he deliberately and systematically ignored his supreme mathematical genius and through most of his life neglected the one activity for which he was gifted beyond any man. This paradox can be resolved only if we realize that Newton simply did not consider science and mathematics as of any great importance; or, as Keynes has said:

… It seems easier to understand… this strange spirit, who was tempted by the Devil to believe, at the time when within these walls [of Trinity College] he was solving so much, that he could reach all the secrets of God and Nature by the pure power of mind – Copernicus and Faustus in one.

And finally, I cannot desist repeating Newton’s oft quoted evaluation of himself.

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

In view of Newton’s insensitiveness to others, doubts have sometimes been raised about the sincerity of this statement. I do not believe that such doubts are warranted: only someone, like Newton, who can view knowledge from his height, can have the vision of an “ocean of undiscovered truth.” As an ancient proverb of India says, “Only the wise can plumb the wells of wisdom.”

 

IV

From the foregoing accounts of the creative patterns of Shakespeare, Beethoven, and Newton, though very brief and very inadequate, two facts emerge with startling clarity: the remarkable similarity in the creative patterns of Shakespeare and Beethoven, on the one hand, and their stark contrast with that of Newton, on the other. Are the similarity and the contrast accidental? Or, are they manifestations of a general phenomenon which in the case of these giants only happens to be very sharply etched?

Consider in juxtaposition the following statements that have been made concerning the creativity of mathematicians and of poets.

G. H. Hardy, an outstanding English mathematician of this century, in his essay A Mathematician’s Apology – an essay which has been described by C.P. Snow as “the most beautiful statement of the creative mind ever written or ever likely to be written” – writes:

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game… Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty three, Riemann at forty. There have been men who have done great work a good deal later; … [but] I do not know an instance of a major mathematical advance initiated by a man past fifty…. A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

And with respect to Ramanujan’s early death, Hardy has further written:

The real tragedy about Ramanujan was not his early death. It is, of course, a disaster that any great man should die young; but a mathematician is comparatively old at thirty, and his death may be less of a catastrophe than it seems…

Place beside these statements of Hardy the following one of A. L. Rowse on the death of Christopher Marlowe at the age of twenty nine:

What would he not have achieved if he had lived! – his was the greatest of all losses to English Literature.

Or, of Desmond King-Hele’s on the death of Shelley at the age of thirty:

The rule that a poet is at his best after the age of 30 might have applied as well to him as to Shakespeare, Milton, Wordsworth, Byron, Tennyson, and indeed almost every major English poet who lived to be over 30.

In a more negative vein, there is the statement attributed to Thomas Huxley that a man of science past sixty does more harm than good.

I do not doubt that these statements will be challenged or, at least, subjected to qualifications. But consider this.

In 1817, at the age of forty-seven, when the long period of meditation, during which Beethoven composed very little, was coming to an end, he said to Cipriani Potter with transparent sincerity, “Now, I know how to compose.” I do not believe that there has been any scientist, past forty, who could have said, “Now, I know how to do research.” And this to my mind is the center and the core of the difference: the apparent inability of a scientist to continually grow and mature.

 

V

If one should wish to establish with some degree of certainty that a contrast does exist in the patterns of creativity among the practitioners in the arts and the practitioners in the sciences, then one should undertake a survey of an extent and a depth which is far beyond my resources. At the same time it does not seem entirely proper that I leave the matter without some further examples. I shall consider four examples taken from science.

My first example is James Clerk Maxwell who is generally considered the greatest physicist of the nineteenth century. Maxwell’s principal contributions to physics are his founding of the kinetic theory of gases and the dynamical theory of the electromagnetic field. The new physical concepts which Maxwell introduced in formulating his equations of the electromagnetic field – Maxwell’s equations which every student of physics knows – have been described by Einstein as “the most fruitful and profound that physics has experienced since the time of Newton.”

The four great memoirs which encompass Maxwell’s contributions to the two areas were published during the five years 1860-65 when he was between the ages, of thirty and thirty-five and was a professor at King’s College, London. At the end of this period of intense activity, Maxwell resigned his professorship in London and retired to his country home in Glenlair in Scotland (Maxwell’s biographers never really “explain why Maxwell felt it necessary to take these actions.) In Glenlair, for the following six years, Maxwell seems to have lived in quietness, occupied, principally, with the planning of his two-volume Treatise on Electricity and Magnetism (which was eventually completed and published in 1873). In 1871, Maxwell was persuaded to leave his retirement in Glenlair and return to academic life in Cambridge as the first Cavendish Professor of Experimental Physics. He died in 1878 at the age of forty-eight. Maxwell’s eight years in Cambridge were devoted mostly to editing the scientific papers of Henry Cavendish, organizing and establishing the Cavendish Laboratory, and other diverse university matters. While Maxwell’s early death was a tragedy, it must be admitted that his work did not rise again to the heights it had in his early thirties.

My second example is George Gabriel Stokes. Stokes was elected to the Lucasian Chair of Mathematics (in Cambridge) in 1849 when he was just past thirty. He held this Chair until his death in 1903 – a Chair that was once held by Newton. Stokes is one of the great figures of nineteenth-century physics and mathematics. His name continues to be associated with several current notions and concepts. Thus, we have the Navier-Stokes equations governing viscous flow in hydrodynamics; the Stokes law giving the asymptotic rate of fall of small spherical bodies in a viscous medium – a law which provides the basis for Millikan’s “oil-drop experiment” for determining the charge on the electron; the Stokes parameters for characterizing polarized radiation which are relevant to most current measurements in radio astronomy; the Stokes law of fluorescence, that the wavelength of the fluorescing light must exceed that of the exciting light; and the Stokes theorem which, in addition to being a very fundamental theorem, provides a key element for modern developments in the calculus of differential forms.

Now Stokes’s scientific papers are collected in five medium-sized volumes. The first three volumes contain all the important concepts and notions that I have just enumerated and cover the ten-year period 1842-52; the remaining two volumes suffice to cover his entire scientific work of the following fifty years.

G. Evelyn Hutchinson (the distinguished zoologist at Yale University), whose father was a close associate of Stokes during his last years, makes the remarkable statement: “Stokes, however, quite possibly, emulated his great predecessor [in the Lucasian Chair] consciously…What Newton did, Stokes deemed appropriate for him to do also.”

My third example is Einstein. The year 1905 was the annus mirabilis both for Einstein and for physics. It was in that year that Einstein, at the age of twenty-six, published three papers, each epoch-making in its own way: the first laid the foundations for his special theory of relativity with remarkable clarity, conciseness, and coherence; the second provided a rational molecular basis (independently of Smoluchowski) for accounting for Brownian motion; and the third carried Planck’s hypothesis of the quantum to its logical limit to formulate the concept of the light quantum. In the decade that followed, Einstein was constantly preoccupied with the resolution of the basic inconsistency between Newton’s law of gravitation, with its postulate of instantaneous action at a distance, and his own special theory of relativity, with its postulate that no signal can be propagated with a velocity exceeding that of light. After many detours and false starts, Einstein finally arrived triumphantly at his general theory of relativity in 1915. As Hermann Weyl later expressed, Einstein’s general theory of relativity is “one of the great examples of the power of speculative thought. ”

In the years following the founding of his general theory of relativity, Einstein made a number of important contributions to the further ramifications of his own general theory as well as to certain aspects of statistical physics. But already by 1925, Einstein was letting the newer developments in the quantum theory, initiated by Heisenberg, pass him by. Thus, Heisenberg records that at the Solvay Congress in 1927, Paul Ehrenfest, Einstein’s friend, said to him, “Einstein, I am ashamed of you: you are arguing against the new quantum theory just as your opponents argue about relativity theory.” Heisenberg adds sadly that this friendly admonition went unheeded. As Einstein’s great admirer Cornelius Lanczos observes

From 1925 on his interest in the current affairs of physics begins to slacken. He voluntarily abdicated his leadership as the foremost physicist of his time, and receded more and more into voluntary exile from his laboratory, a state into which only a few of his colleagues were willing to follow. During the last thirty years of his life he became more and more a recluse who lost touch with the contemporary developments of physics.

I should like to conclude with an example which in some ways appears counter to Hardy’s general rule: the case of Lord Rayleigh, perhaps the greatest pillar of classical mathematical physics. Rayleigh’s productivity was remarkably steady and uniform all through his fifty years of scientific publication. His scientific work is encompassed in a two-volume treatise on The Theory of Sound and the six large volumes of his Scientific Papers.

In a memorial address, delivered in Westminster Abbey in December 1921, J.J. Thomson evaluated Rayleigh’s scientific contributions in the following terms:

Among the 446 papers which fill these volumes [the six volumes of his Scientific Papers], there is not one that is trivial, there is not one which does not advance the subject with which it deals, there is not one which does not clear away difficulties; and among that great number there are scarcely any which time has shown to require correction… Lord Rayleigh took physics for his province and extended the boundary of every department of physics. The impression made by reading his papers is not only due to the beauty of the new results attained, but to the clearness and insight displayed, which gives one a new grasp of the subject…

This is a remarkable testimony; and anyone who has had occasion to use Rayleigh’s Scientific Papers will testify to its accuracy.

But why was Rayleigh so different from Maxwell and Einstein? Perhaps the clue is to be found in what Thomson said in the same memorial address:

There are some great men of science whose charm consists in having said the first word on a subject, in having introduced some new idea which has proved fruitful; there are others whose charm consists perhaps in having said the last word on the subject, and who have reduced the subject to logical consistency and clearness. I think by temperament Lord Rayleigh belonged to the second group.

And perhaps there is a clue also in Rayleigh’s response to his son (also a distinguished physicist) when he asked him to comment on Huxley’s remark I quoted earlier, “that a man of science past sixty does more harm than good.” Rayleigh was sixty-seven at that time, and his response was

That may be, if he undertakes to criticize the work of younger men, but I do not see why it need be so if he sticks to the things he is conversant with.

Perhaps there is a moral here for all of us!

 

VI

I now pass on to some cognate matters.

First, may I say that I am frankly puzzled by the difference that appears to exist in the patterns of creativity among the practitioners in the arts and the practitioners in the sciences: for, in the arts as in the sciences, the quest is after the same elusive quality: beauty. But what is beauty?

In a deeply moving essay on “The Meaning of Beauty in the Exact Sciences,” Heisenberg gives a definition of beauty which I find most apposite. The definition, which Heisenberg says goes back to antiquity, is that “beauty is the proper conformity of the parts to one another and to the whole.” On reflection, it does appear that this definition touches the essence of what we may describe as “beautiful”: it applies equally to King Lear, the Missa Solemnis, and the Principia.

There is ample evidence that in science, beauty is often the source of delight. One can find many expressions of such delight scattered through the scientific literature. Let me quote a few examples.

Kepler:

Mathematics is the archetype of the beautiful.


David Hilbert (in his memorial address for Hermann Minkowski):

Our Science, which we loved above everything, had brought us together. It appeared to us as a flowering garden. In this garden there were well-worn paths where one might look around at leisure and enjoy one self without effort, especially at the side of a ongenial companion. But we also liked to seek out hidden trails and discovered many an unexpected view which was pleasing to our eyes; and when the one pointed it out to the other, and we admired it together, our joy was complete.

Hermann Weyl (as quoted by Freeman Dyson):

My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.

Heisenberg (in a discussion with Einstein):

If nature leads us to mathematical forms of great simplicity and beauty – by forms I am referring to coherent systems of hypothesis, axioms, etc. – to forms that no one has previously encountered, we can not help thinking that they are ‘true,’ that they reveal a genuine feature of nature… You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.

Chandra with friends (1945 and 1981)

Chandra with friends (1945 and 1981)

All these quotations express thoughts that may appear vague or too general. Let me try to be concrete and specific.

The discovery by Pythagoras, that vibrating strings, under equal tension, sound together harmoniously if their lengths are in simple numerical ratios, established for the first time a profound connection between the intelligible and the beautiful. I think we may agree with Heisenberg that this is “one of the truly momentous discoveries in the history of mankind.”

Kepler was certainly under the influence of the Pythagorean concept of beauty when he compared the revolution of the planets about the sun with a vibrating string and spoke of the harmonious concord of the different planetary orbits as the music of the spheres. It is known that Kepler was profoundly grateful that it had been reserved for him to discover, through his laws of planetary motion, a connection of the highest beauty. A more recent example of the reaction of a great scientist, to this aspect of beauty at the moment of revelation of a great truth, is provided by Heisenberg’s description of the state of his feelings when he found the key that opened the door to all the subsequent developments in the quantum theory.

Towards the end of May 1925, Heisenberg, ill with hay fever, went to Heligoland to be away from flowers and fields. There by the sea, he made rapid progress in resolving the difficulties in the quantum theory as it was at that time. He writes:

Within a few days more, it had become clear to me what precisely had to take the place of the Bohr-Sommerfeld quantum conditions in an atomic physics working with none but observable magnitudes. It also became obvious that with this additional assumption, I had introduced a crucial restriction into the theory. Then I noticed that there was no guarantee that… the principle of the conservation of energy would apply… Hence I concentrated on demonstrating that the conservation law held; and one evening I reached the point where I was ready to determine the individual terms in the energy table [Energy Matrix]… When the first terms seemed to accord with the energy principle, I became rather excited, and I began to make countless arithmetical errors. As a result, it was almost three o’clock in the morning before the final result of my computations lay before me. The energy principle had held for all the terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structure nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble, and waited for the sun to rise.

May I allow myself at this point a personal reflection? In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein’s equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful,” this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound. Indeed, everything I have tried to say in this connection has been stated more succinctly in the Latin mottos:

Simplex sigillum veri – The simple is the seal of the true.

and

Pulchritudo splendor veritatis – Beauty is the splendour of truth.

 

VII

But I must return to my question: why is there a difference in the patterns of creativity among the practitioners in the arts and the practitioners in the sciences? I shall not attempt to answer this question directly; but I shall make an assortment of remarks which may bear on the answer. First, I should like to consider how scientists and poets view one another. When one thinks of the attitude of the poets to science, one almost always thinks of Wordsworth and Keats and their oft-quoted lines:

A fingering slave,
One that would peep and botanize
Upon his mother’s grave?

A reasoning self-sufficing thing,
An intellectual All-in-all!

Sweet is the lore which Nature brings;
Our meddling intellect
Misshapes the beauteous forms of things:
We murder to dissect.
(Wordsworth)

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings.
(Keats)

These lines, perhaps, find an echo in a statement of Lowes Dickinson, “When Science arrives, it expels Literature.”

It is to be expected that one should find scientists countering these views. Thus, Peter Medawar counters Lowes Dickinson by

The case I shall find evidence for is that when literature arrives, it expels science… The way things are at present, it is simply no good pretending that science and literature represent complementary and mutually sustaining endeavours to reach a common goal. On the contrary, where they might be expected to cooperate, they compete.

It would not seem to me that one can go very far in these matters by pointing accusing fingers at one another. So, let me only say that the attitudes of Wordsworth and Keats are by no means typical. A scientist should rather consider the attitude of Shelley. Shelley is a scientist’s poet. It is not an accident that the most discriminating literary criticism of Shelley’s thought and work is by a distinguished scientist, Desmond King-Hele. As King-Hele has pointed out, “Shelley’s attitude to science emphasizes the surprising modern climate of thought in which he chose to live,” and Shelley “describes the mechanisms of Nature with a precision and a wealth of detail unparalleled in English poetry.” And here is A.N. Whitehead’s testimony:

Shelley’s attitude to Science was at the opposite pole to that of Wordsworth. He loved it, and is never tired of expressing in poetry the thoughts which it suggests. It symbolizes to him joy, and peace, and illumination …

I should like to read two examples from Shelley’s poetry which support what has been said about him. The first example is from his Cloud which “fuses together a creative myth, a scientific monograph, and a gay picaresque tale of cloud adventure”:

I am the daughter of Earth and Water,
And the nursling of the Sky;
I pass through the pores of the ocean and shores;
I change, but I cannot die.
For after the rain when with never a stain
The pavilion of Heaven is bare,
And the winds and sunbeams with their convex gleams
Build up the blue dome of air,
I silently laugh at my own cenotaph,
And out of the caverns of rain,
Like a child from the womb, like a ghost from the tomb,
I arise and unbuild it again.

The second example is from Prometheus Unbound, which has been described by Herbert Read as “the greatest expression ever given to humanity’s desire for intellectual light and spiritual liberty:

The lightning is his slave; heaven’s utmost deep
Gives up her stars, and like a flock of sheep
They pass before his eye, are numbered, and roll on!
The tempest is his steed, he strides the air;
And the abyss shouts from her depth laid bare,
Heaven, hast thou secrets? Man unveils me; I have none.

Let me turn to a slightly different aspect of the matter. What are we to make of the following confession of Charles Darwin:

Up to the age of thirty, or beyond it, poetry of many kinds, such as the works of Milton, Gray, Byron, Wordsworth, Coleridge, and Shelley, gave me great pleasure; and even as a school boy I took intense delight in Shakespeare, especially historical plays… I have also said that formerly pictures gave me considerable, and music very great delight. But now for many years I cannot endure to read a line of poetry; I have tried lately to read Shakespeare, and found it so intolerably dull that it nauseated me. I have almost lost my taste for pictures or music… My mind seems to have become a kind of machine for grinding general laws out of large collections of facts, but why this should have caused the atrophy of that part of the brain alone on which the higher tastes depend, I cannot conceive.

Or, consider this: Faraday discovered the laws of electromagnetic induction, and his discoveries led him to formulate concepts such “lines of force” and “fields of force” which were foreign to the then prevailing modes of thought. They were in fact looked askance by many of his contemporaries. But of Faraday’s ideas Maxwell wrote with prophetic discernment:

The way in which Faraday made use of his idea of lines of force in coordinating the phenomenon of magneto-electric induction shows him to have been in reality a mathematician of a very high order – one from whom the mathematicians of the future may derive valuable and fertile methods. We are probably ignorant even of the name of the science which will be developed out of the materials we are now collecting, when the great philosopher next after Faraday makes his appearance.

And yet when Gladstone, then the Chancellor of the Exchequer, interrupted Faraday in his description of his work on electricity by the impatient inquiry, “But after all, what use is it?” Faraday’s response was, “Why, Sir, there is every probability that you will soon be able to tax it.” And Faraday’s response has always been quoted most approvingly.
It seems to me that to Darwin’s confession and to Faraday’s response, what Shelley has said about the cultivation of the sciences in his A Defence of Poetry is apposite:

The cultivation of those sciences which have enlarged the limits of the empire of man over the external world, has, for want of the poetical faculty, proportionally circumscribed those of theinternal world; and man, having enslaved the elements, remains himself a slave.

Lest you think that Shelley is not sensitive to the role of technology in modern society, let me quote what he has said in that connection:

Undoubtedly the promoters of utility, in this limited sense, have their appointed office in society. They follow the footstep of poets, and copy the sketches of their creations into the book of common life. They make space, and give time.

Shelley’s A Defence of Poetry from which I have just quoted is one of the most moving documents in all of English literature. W.B. Yeats has called it “the profoundest essay on the foundation of poetry in the English language.” The essay should be read in its entirety; but allow me to read a selection:

Poetry is the record of the best and happiest moments of the happiest and best minds.

Poetry thus makes immortal all that is best and most beautiful in the world; it arrests the vanishing apparitions which haunt the interlunations of life…

Poetry is indeed something divine. It is at once the centre and circumference of knowledge; it is that which comprehends all science, that to which all science must be referred. It is at the same time the root and blossom of all other systems of thought.

Poets are the hierophants of an unapprehended inspiration; the mirrors of the gigantic shadows which futurity casts upon the present; the words which express what they understand not; the trumpets which sing to battle, and feel not what they inspire; the influence which is moved not, but moves. Poets are the unacknowledged legislators of the world.

On reading Shelley’s A Defence of Poetry, the question insistently occurs why there is no similar A Defence of Science written by a scientist of equal endowment. Perhaps in raising this question I have, in part, suggested an answer to the one I have repeatedly asked during the lecture.

I began this lecture by asking your forbearance for addressing myself to matters which are largely outside the circumference of my comprehension. Allow me then to conclude by quoting from Shakespeare’s epilogue to the second part of his Henry IV.

First, my fear; then my curtsy; last my speech. My fear, is your displeasure, my curtsy, my duty, and my speech, to beg your pardon.

 
 

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