The Metaphysical Reach of Science by Michael Polanyi (As delivered on February 10, 1964 at Duke University) My subject.today will be the positivist theory of science ., ;-1?_;' • judged. on the evidence of a historical controversy, fought out at the very dawn of science over the system of Copernicus . . r,ilf:' .. ·~ . Rumours of his theory that the earth moves round the 'sun, had been current since 1515, twenty eight years before he published it ' '· in De Revolutionibus Orbium Celestium just before his death in 1543. Two years before this, in 1541, he received a latter from a Luther- an minister in Nuremberg, named Andreas Osiander, urging him not to regard his theory as true, but merely as a hypothesis, suitable to serve as a foundation for calcuia.t.ions. And when the book came ' .. -,\ out, it was prefaced by an Advice to the Reader, generally attri- buted to Osiander, in which he elaborated his warnings. He wrote that astronomy cannot B:_,rrive at the truth for it ignores the causes of stellar motion; it should only propose hypotheses in accordance .•. with observations and these hypotheses need not be true nor even probable. This view coincides substantially with the positivist theory of Ernst Mach, which regards science as a convenient functional re- lation between observed data. This theory purports to exclude all metaphysical claims of science by restricting it to the formulation0• of functional relations between observed data. We shall see that this intention was also present, though with an altogether differ- ent cotive, in the intervention of Osiander. To this intervention Copernicus replied in the First Dook of his volume by claiming that his system was true for it had symme- I
" tries, and harmonies exclusively its .01·m. The orders and magnitudes of all stars and spheres ••. become so bound together that nothing in any part thereof could be moved from its place without producing confusion in all other parts, and of the universe as a whole. .- ·t)~?-~ ~-~.:i This refers to the way major epicycles of Ptolemy ap~,re- , . ,. .,, . 1t 2 . ':-'\µ,~ ! ., placed by a pattern of suitably spaced circular orbits centering on the sun. The planet is observed at different points moving east~1ards '· against the firmament of fixed stars. Dut not steadily. It speeds up, sloHs down, retraces its step and resumes this oscillation at regular intervals·. This is explained by placing it on a circular orbit with a wheel attached to it: the epicycle. ' . - Copernicus shov1s that the same complex motion can be explained by placing earth on a circular orbit round the sun and the other planet on another orbit round which it moves faster or slower than the earth, The planet,. observed from the earth, will then be seen to pursue the same kind of periodically oscillating circular tra- .1ectory, as ~,as described before in terms of the epicyclical mech- anism (used by Ptolemy). Dut this does not suffice. In order to eliminate the epicycle, we must ascribe one particular orbital distance to the planet (as measu~ed in the earth 1s distance from the sun). So that, in the end, we shall have fixed the solar dis- tances of all five planets in terms of the earth's solar distance . .-' This was the triumph of Copernicus: the internal coherence of his system. It was enhanced further by the harmonious sequence of or- bital periods nou apparent for all six planets, the earth being placed among them. (See table), Osiander had attacl<ed the claims of Copernicus on the grounds
3 that science could no more than save the phenomena by a suitable hypothesis, which need not be true, nor even probable. This attaclc was continued later against the Copernicans. Galileo was attacked on these grounds and put on trial by Pope Urban the VIIIth. On behalf of the Roman church, Cardinal Dellarmine pressed him to ac- knoWl!::!dge ·ri;~::;.:,:., __ . that the heliocentric system was but a coniput;tl'.ig, .device, " but Galileo resisted this. I .. _' . :_ ,t, I have said that Osiander I i'lt'tack on the views·of Copernicus coincides with the positivist view that a scientific,theory is but a convenient description of observed facts. . ... . The coincidence of these two historically remote positions was borne out earlier in this century by a leading positivist writer, Paui Duhem, who declared that it was Cardinal Dellarmine and Osiander and not Galileo and Kepler who had grasped the precise significance of the experimental methog. I Henri Poincare too con- demned the "residual metaphysics" to which Galileo was adhering. Dut the grounds on which the clergy attacked Copernicanism were quite different from those on which the positivists objected to it. The clergy defended the medieval view, formulated by Aquinas, that empirical astronomy cannot speak of metaphysical re- ality. It defended the privilege of philosophic reason to speak of reality against encroachment by science. The positivists re- jected, on the contrary, any met~physical statements.as empty and confusing, and aimed at purifying science from any such claims. They demanded that science should refrain from claiming to be true- or to be bearing on reality. The position of the two different attacks on Copernicanism can be illustrated by a diagram. The medieval position shows rea- son bearing metaphysically on reality, while barring science from
,, 4 such bearing. The positivist position is shown isolating science both from reason and reality, self contained in strict empiricism. Copernicanism is sho.wn, thirdly, claiming to exercise reason through science with a bearing on reality. DI,\GRAMS ·t):,S:-_ .. ; In this three cornered dispute I shall side witJi,,..t~, Coperni- cans"; I agree with the posit:tvists in pointing out that:'~fu~ Coper- nicans were making metaphysical claims, but I side against them by agreeing with the medievalists, that such claims are not empty \ but, on the contrary, essential to all true knowledge. Seen in this light, the medievalists were right, in recognising empirical science as encroaching on their domain, but wrong in contesting that science was competent to do so. The Copernicans·were right in every respect. The difficulty in meeting the positivist criticism of Coperni- canism lies in the fact that there is such an obvious answer to it, namely, that the Copernicans were right, because the earth does in ~ fact go round the sun. Dut, of course, Duhem and ?oincare could not have overlool{ed this fact. They must have meant that Kepler and Galileo were wrong, and Copernicus himself even more wrong, in asserting this fact on the grounds of evidence which could be rep- resented also by an earth centered system. To this we may obJect that Kepler and Galileo--though not Copernicus--had one strong reason for asserting the reality of the,.. heliocentric system. They may have felt that it must be real, since it l'las by relying on the Copernican system to be real, that they had made their own great discoveries. Dut we must ask vhether any such feeling could possibly be
5 justified. If we are to accept the connection to be other than accidental, we must see clear1y how the Copernican system could exercise such heuristic powers, which the Ptolemaic system would lack. The first point to note in this connection is,~ful.t,, .. ,Qopernicus .. , ..... : : , and his followers clearly felt a deficiency· in thei; s;~t~fu which • ·, •1; ..... ~hey tried to remedy. They felt that there must be some good rea- son for the central position of the sun l"lith the planets going . \ round it. ··-Copernicus argued that the sun as giver of all light must be the center of the Universe. Kepler insisted on the natural pre_-eminence of the sun and came near the truth by assuming that the sun emits a motive spirit (anima motrix) which keeps the plan- ets going round. Thus the problem·wa-s kept open and alive until Newton solved it by the discovery of general gravitation .. This shows how Copernicus and his followers were guided by ' the heliocentric system to their enquiries. They pursued the prob- lems suggested by a Copernican layout of the Universe. Kepler's Third Law, relating the square of planetary periods inversely to the cube of planetary distances from the_ sun, also elaborated a problem set by Copernicus, by observing how orbital periods steadi- ly increase with the planet's distance from the sun. The First and Second Laws introducing the elliptic paths, with the sun in one focus·of them, could hardly have been conceived by anyone who ig- / nored the heliocentric system; for it made no sense in the Ptole- maic system. i\nd it was of course Kepler's laus, combined 1·1ith findings of Galileo, that set Newton his task and prepared his tri- umph, Vle can take it as a fact then that the Copernican system did
6 indicate good problems which were not visib.le in the Ptolemaic system. Let us no\'1 try to identify the process by which Coperni- canism suggested such good problems. This brings up an awl<ward question, which to my knowledge, has never been systematically examined, 'l.'he questioi'l-Tu.:...,, What is a ·,,· ♦ . .,..~ ••• f ...,-.,. problem? Not the kind of problem set to students o;f};1~thematics or '-.. to chemists in practical classes but a scientific problem the solu- tion of \·rhich is unlmown; the l<ind of problem a scientist embarks on with a reasonable hope to discover something new that will be \ '• worth the labour and expenses of the search for it. I would answer that to have such a problem, a good problem, is to surmise the presence of something hidden, and yet possibly accessible, lying in a certain oireqtion. A gooo problem--let me repeat--is a surmise of something h.1dclen yet accessible by an en- quiry in a certain direction. Such a surmise·is evoked in the imagination of a scientist by a set of circumstances which come to be seen as clues to a hioden thing. When the problem is solved, these clues will seem to form part of the hidden thing that is now discovered, The clL.tes of a problem thus anticipate parts or aspects of a future discovery. The heliocentric system of Copernicus could raise a problem to be answered by the discovery of general gravitation because it was itself an aspect of the theory of general gravitation; and the,; same is true of Kepler 1s discoveries which lay on the way to Newton 1s work. Copernicus anticipated important aspects of Kep- ler's three·1aws. The anticipations contained in the heliocentric theory are sharply distinct from its explicit predictions. The celestial
7 timetable set out by Copernicus was not markedly different from that of Ptolemy. Close on to a century and a half following the death of Copernicus all efforts to discriminate between the two systems on the grounds of their observable quantitative predic- tions have failed. 1'/hile the discoveries of Keplei-.:;;a~, Galileo ·~ ~rt.;-' ba~ed on the heliocentric system greatly increased it_~_.p:-i'ausibility, . ' ·~ a medieval thinker like Delarmine and such distinguished scien- tists of our 01-m days, as Duhem anci Poinca.re, from a. positivist point. of ,View, could still regard the factual content of the two '· . rival-system as having been identical, And they were right. Faced with this fact we may as!{ once more, How can one of' two systems having the same predictive content, so vastly exceed the other in its anticipations? The ansr1er is given already in what I have just. described in detail. Th~-• a_nticipatory powers of the Copernican system lay in the new image by which it represented the ' predictive content of the Ptolemaic system. It is in the appear- ance of the new system that lay its immense superiority; it is this image that originated the Copernican revolution. I am drawing here a distinction which will prove decisive. I distinguish between the precise predictive content of a mathemati- cal theory consisting in a functional relation of measured vari- ables and a meaning of the theory which goes beyond this. While these functional relations remain the same, whatever symbols are ;- used for presenting them, the surplus of meaning which goes beyond this depends on the appearance of the theory. The way this may come about can be illustrated from everyday life. Suppose \'Te have a list of all the towns of England, each with its precise longitude and latitude, and the number of its in-
8 habitants, and we represent these data in a map, each town being marked by a circle corresponding to it in size. The mapping of the list adds .no new data to it, yet it conveys a far better under- standing of these data. It reveals for example the 1~-~ the popula- . -·.-~-, . ·-;j-~! i.' tion".is distributed through the country and suggests Cl;tJ~~t_ions about the reasons of physical geography and history wh1qh will ac- count for this distribution. The map will guide the imagination \ to enter on fruitful enquiries to which the original list v10uld leave us blind. We can, in fact, give a fairly close analogy between the Ptolemaic and the Copernican system in such terms. Suppose you are interested only in a certain number of itineraries. They could . , .. " . be conveniently represented separately ~n several lines. You some- times find this kind of indication in guide bo.ol<s; Dut the travel- ler may use instead a map on which he can trace the itineraries for himself. The first representation corresponds to the Ptolemaic, the second to the Copernican system, It is clear that the latter, though not more convenient for the original purpose, is far richer in possible implications beyond this purpose. Returning then to the context of my argument, I shall nail down as my first result to have·established and clearly identified a surplus of meaning contained in a scientific theory beyond its explicit predictions, This non explicit surplus consists in the anticipatory powers of the theory which it exercises by its general outline and appearance. This appearance appeals to the imagination of future minds and invites them to explore its possible ,·rider im- plications. It suggests problems to them that lead to future dis~ coveries. Since a precise positivist interpretation of a scientific
9 theory insists on limiting its content to its explicit observa- tional predictions (this being indeed the very essence of the posi- tivist idea) it necessarily ignores its anticipatory powers and reduces it thus to s'cerility. Dut before going further, I must yet enter a caveat,. .. ;, The dis- .: ., t~ :.• tinction between explicit content and informal heuristi,~-¥g.qJiers is ·. -·~ . profound, but not absolute, No mathematical formula mean[! anything except as understood by him who applies it, and such an act of ' understanding and applying is necessarily informal. When I speak of the explicit content of a theory, I mean such applications of it which, though informal, are quite obvious. These I distinguish from the yet indeterminate meaning of the theory that may be re- ·vealed only much later, by a creative act of a scientist 1s imagina- tion. Dut I have still to show, if I am to justify Copernicus, that in expressing his belief in the reality of the heliocentric sys- tern, as distinct from the Ptolemaean, he was in fact asserting the presence of its anticipatory powers, This is far from obvious,. since, for one thing, it is not clear how anticipatory powers can be known at all, It is clear that they cannot be explicitly !{no~m. Copernicus certainly did not knm~ that his system represented an aspect of Kepler I s lai·rn and of Newton I s theory of general gravi ta- t ion, Indeed, being wedded to an explanation of the planetary sys- / tern in terms of steady circular motions, he would have absolutely rejected Kepler's Laws and Newton's theory based on them. Yet, in my view, he did show that he had this knowledge and expressed it by his affirmation that his system was real. For he based this claim on the very features of the system which were to
10 serve as clues to the problems of Kepler and Newton and lead to their discoveries. He gloried in the internal coherence of his system and felt particularly gratified by the regular increase of orbital periods with the increasing distance of the planets from . ·! ~1?:~;:: .... -. the sun. He said that this orderliness was reasonabl,e ~.fld, ,elaimed that it was a unique quality of his system. .J~.i, l t. t· He also trl'.fid' ·to show that it was reasonable that the sun, as the sole provider of light to the universe, should be situated at its center. What he meant . \ . . by asserting that the heliocentric system was real, must have in- cluded an anticipation of the fact that these features of his sys- tem; and perhaps others too, might yet serve as clues to future problems and that such problems may lead to yet unthinl,able further ... -~ ~ discoveries. '>~.-- We shall see more clearly what Copernicus.meant, if we align him with his successors to whose purposes the reality of his system was even more essential than it ~,as to him. Tbe results of Copernicus would have remained valid and interesting, even if Osiander had been right in calling his theory a mere computing device, The followers of Copernicus were much more deeply com- mitted. The enquiries on which Kepler spent his life, would have been altogether non-sensical, if the-heliocentric system were not . . real, He elaborated the distinctive image of the Copernican system, basing himself on the belief that it represented a fact. Galileo.< was of course equally involved, The hostility and danger which he faced, -added to the rislrn of his commitment, but a scientist pur- suing a solitary problem for years is hazarding his.existence as a scientist and this hazard is fearful enough by itself. The be- lief of Copernicus in the reality of his system thus acquired an
11 overwhelming practical meaning for Kepler and Galileo in the form of their conviction that the problems suggested by the heliocentric image were good problems, pointing to important hidden truths. The manifest continuity between Copernicus·1s b~:tri:t;~n the ~~ . -~ i~~;"? reality of his system and the heuristic commitment of hi\!i~f>ollowers · .. -~ .. leads me to conclude that their commitment was but an intensifica- tion of Copernicus's belief. It demonstrates that his belief in \ the reality of his system expressed the same kind of expectation which his followers expressed in embarking on their problems. The difference was mainly that his belief in the reality of his system was less dynamic and less pointed, than their belief in the sound- ness of their problems. De lief in t~e:;;eality of a theory entails the expectation that any of its statements or aspects may become a clue to new problems and discoveries. Then, ~hen this expecta- tion materialises and~new problems are discovered on these lines, these will entail more definite expectations of a hidden truth lying in a particular direction, and this expectation will lead to action in quest of the hidden truth. We may say that in rejecting Osiander 1s view that his theory was merely a new computing device, Copernicus vaguely anticipated the kind of concrete anticipations, called problems, which he evolrnd in Kepler, Galileo, and Newton. We can generalise this result. i'lhat Copernicus meant by at-/ tributing reality to his system, is but an instance of what is com- monly meant by saying that something is real and no mere figment of the mind. \'/hen we say that an object is real, we mean that it will not dissolve like a dream, but that, for better or worse, it will yet manifest its existence, inexhaustibly. We feel that it is there, outside, whether we believe it or not, existing independently of
12 us, and hence never fully predictable in its consequences, I propose to define reality and truth, accordingly, as follows. If anything is believed to be capable of a largely indeterminate range of future manifestations it is thus believed t.6:,;p.e .real. A ··. -·-.•~·- ., ~t ,:, statement about nature is believed to be true if it is iqeJ!-ieved . • .. •1~--.,,. , .. · .. ., to disclose an aspect of something real in nature. A true physical theory is, therefore, no mere functional relation between pointer . ' readings, out represents an aspect of a reality, which may yet manifest itself inexhaustibly in the future. I agree therefore with positivism in the view that if a scientific theory could be reduced to a bare functional relation · between obse:i:-vable facts, it would ·have no bearing on reality nor claim to be true; but I deny that such a functional relation can constitute a scientific theory. The difference between the scope of a statement that is only explicitly grounded and one that is claimed to be true, is shown in the deductive sciences. According to Godel 1s famous theorem, a sentence which says of itself that it is not demonstrable merely reflects on its origins, while a sentence which says of itself that it is not true, can be shOl'm to be· self-contradictory. The reason is that by contrast to explicit demonstration, the establishment of truth entails an unlimited commitment, Dut we have still to show the ultimate grounds on which such unlimited commitments are entered upon. We may still ask why the internal harmony of the heliocentric system made Copernicus and his followers believe that it was real. The clue to the answer, and in- deed most of the answer itself, may be found in the fact that the existence of a ha~monious order is a denial of randomness. Some-
-· 13 thing that is random is meaningless, and, by contrast, anything that is orderly, is meaningful. Take the difference between a tune and a noise .. Or, more generally, between a message and a noise. Communic_a_tion theory ·: )~~-.;.:-t.,41P._:, def~nes a noise, by contrast to any as a random sequence and says that, distinctive seri•es 0cff;:signals, J ,.. -l' . , :~~;jt-.;. t.., as such, noise conv~ys no in- formation, means nothing. This shows that order is strictly com- plementarY',to randomness; each starts where the other ends and each . '• can be conceived only as the denial of the other. There is a very import"ant difference in the identifiability of an ordered sequence as compared with a noise·. Any single message is represented ideal- ly by only one configuration of signals, while for a noise the very ... opposite holds. No significance musf ·,be attached to any particular configuration of signals that are a mere noise. We must indis- ' criminately identify any particular configuration of a noise, with any other configurat:fon of them. And this is true of any random aggregate: the chance events which compose it could have as well happened otherwise. Dy contrast, once we have recognised an ag- gregate as orderly an,;! meaningful, we cannot think that it might just as 1·1ell have happened differently. It is deemed an identifi- able thing, possessing reality in the sense I have defined it, name- ly that, being real, it may yet manifest itself inexhaustibly in the future. <' To distinguish meaningful patterns from random ag- · gregates is therefore rightly described as the power for structur- ing reality. Our capacity for discerning meaningful aggregates as distinct from chance aggregates is an ultimate power of personal judgment. It can be aided by explicit argument but never determined by it.
14 The final decision will always remain tacit. Such a distinction may of course be so obvious, that our tacit powers are used effort- lessly and their use remains unnoticed. Our eyes and ears make such decisions almost automatically for us. Dut dec:Uq;.9,,11.s, of this . . ~·· ~_:: ;;, kind may be hard and momentous. A jury may be presenteq, 1j:\i:j.):;h a . :-: ·~r~-' pattern of circumstantial evidence pointing to the accuse.a. It is always conceivable that this pattern may be due to chance. Just I how unlikely a chance should they admit as possible? What degree of coincidence should be deemed to be quite unbelievable? The prisoner's life will depend on the decision, and there is no rule by which this can be decided. Admittedly, rules for setting a· limit to the improbability of chances which a scientist might properly assume to have ociurred have been widely accepted among scientists. nut.these rules have no other foundation than a vague feeling for what a scientist may regard as an unreasonable chance. The late Enrico Fermi is re- ported to have said that a miracle is an· event the chances of 1Ihich are less than one in ten, The rule which R, A. Fisher in his book, The Design of Experiments, has made widely current is a little more cautious; it rejects as illusory only patterns for which the odds of having been formed by chance is less than one in tl'lenty. Dut if anyone were to suggest that the limit should be set at one in / five or at one in two hundred, nothing more could be said against this than that it does not seem reasonable. Such decisions will also greatly depend on the kind .of connec- tions we deem plausible on gene1•a1 grounds. We shall accept much less substantial evidence for plausible patterns or regularities than we would require for connections which we consider highly im-
15 probable. Kepler has put forward along with his three laws, and just as triumphantly, other regularities in the Solar system which we brush aside today, for we no longer believe that that kind of connection could be real. A curious numerical lawq;o.v..erning the .- '.,. -;:.~!._. spacing of the planets, usually known for about two centuries. described as Dode Is L<J.,llf...- ,has been . · .. ·,:~ .. ' .. -~ Long since discredited:,. it was recently given currency once more by C. F. von Weizsacl(er, for he thought he.had an explanation for it. A very substantial body of evidence which I produced aboµt 50 years for my theory of the ad- sorption of gases on solids, was brushed aside soon after its publi- cation, because the theory which this evidence supported was found incompatible with the electrical- structure of matter as discovered ?~. . by Dohr, Debye and the Draggs. Later when Fritz London, late of this university, revised this view of molecular forces on the grounds of the new quantum mechanics, the evidence became once more acceptable, while other experimentai evidence--put forward by no less a man than Irving Langmuir--1•Ihich-had supported the previously held view concerning molecular forces, now turned out to be er- roneous. I have reported this story in the September 13th issue of Science, published in Washington. I have said that reality in nature was something that persists outside and may yet manifest itself inexhaustibly, far beyond our ;' .. '6 present ken. Something must be added to this description, if the pursuit of natural science is to be justified. Consider that the Copernican revolution was but a continuation of a structuring that had its origins in antiquity. Copernicus deepened and beautifully clarified a coherence transmitted by Ptolemy. imd this triumph pointed beyond itself in the mind of Copernicus himself. In Kepler,
16 passionately embracing the system of Copernicus, its image evoked anew the same kind of creative hunger which Copernicus had satisfied by discovering it. And still the presence of yet hidden truth worked its way ever further. To Newton, Kepler's .,l<l-WS appeared in- , ~· :''!'"'~~--~- ., .. -.. ~- ·., coherent and he responded by developing the theory of !§:eTf!ral '·: •1~ ....... ~ gravitation in which Kepler's three laws were.Jointly ·derived .from the me.chanics o.f Galileo. Nor was this the end, for a quarter of a millenni.~ later, Einstein was to find unsatis.fying the relation o.f the Newtonian system to the electromagnetic theory of light and to discover an even deeper coherence to reconcile the two. The continued pursuit o.f science is possible, because the structure of nature and the capac~ty of the human mind to grasp .... - this structure, are .frequently such ·a:ti is exemplified by this se- quence of discoveries during the past two thousand years. It seems .frequently to be the case that nature is capable o.f being grasped in successive stages; each of v1hich can be reached only by the high- est powers of the human mind. Consequently, to discover a true coherence in nature is in general not only to discern something which by the mere .fact of being real, necessarily points beyond it- sel.f, but to anticipate that future discoveries may prove such reality to be far deeper still than our present thought. can an- ticipate. ,> It may sound strange that I insist on a belie.fin the reality o.f theoretical suppositions as the driving force to discovery. It would seem a conservative conviction rather than a source of innova- tion. The positivist view of science would claim that the major discoveries of modern physics were based on a sceptical attitude towards the framework of hitherto accepted scienti.fic theories. The
17 discovery of relativity involved the abandonment of the current con- ceptions of space and time and quantum mechanics achieved its break- through by discarding the planetary system of electrons circling the nucleus from which Niels Dohr had derived the th~9ry of atomic . ·::_-<'!'""-:-,-;~~ spectra. Einstein himself acknowledged that Mach's posi,fiv.:tst ':~\~.:. ~., philosophy inspired his work and Heisenberg I s quantum me·chanics was deliberately framed to reduce atomic theory to a functional rela- \ tion of observable quantities. It was with this in mind that one spoke of the modern epistemological method in science . . These facts seem to contradict my thesis, but I think they will fall into line with it, if I first make clearer the opposite ex- treme of creative procedure, based on .a firm belief in the reality . ····~~ of the current framework of scientific theory. We may recognise the prototype of such a feat in the discovery of America by Colum- bus. He triumphed by taking literally, and as guide to action, that the earth was round, which his contemporaries held vaguely and as a mere matter of speculation. The egg of Columbus is the proverbial symbol for such breath-taking originality guided by a crudely concrete imagihation. I remember having the same feeling when first hearing of Einstein's theory of Drownian motion. The idea that the meandering motion of small floating particles seen under the microscope, should show us the impact of molecules knock- > ing them about in accordance with the equations by which Doltzman··· and Maxwell had derived the kinetic theory of gases, impressed me as grossly incongruous--like something out of science fiqtion. I had the same kind of feeling that I was listening to something grossly fantastic, when I heard Elsasser suggesting (in 1925) that certain anomalies observed in the scattering of electrons by solids
18 may be due to the optical interference of their de Droglie waves. He had all heard of the waves since 1923, yet were astounded by the fact that they could be taken literally as Elsasser did. This may remind us that the first great move towards the dis- ·:jt~;;-t;, .. ~, cover~ of quantum mechanics was de Droglie 1s idea of the41'ave nature . . }~f ~ v· of matter. This revolutionary idea and Schrodinger Is de've)';pment .. of it into wave mechanics, shows no trace of any positivistic in- fluences-. J.dd to this that Max Planck, the founder of quantum .. theory was an active opponent of Mach's analysis of science and dis- sented also-from Heisenberg's claim of basing physical theories on directly observable quantities, It appears then that the pre-domi- nant principle that shaped modern Ph,~sical theory was not the posi- tivist program but the transition from··a mechanical conception of reality to a mathematical conception of it, which sometimes coin- cided with positivistic aims. We can bring then-the revolution of the twentieth century into line with the Copernican revolution of t_he 16th and 17th century. They both consisted in a decisive deepening of coherence with a simultaneous extension"of its range. The modern re~olution differed from its precursor in establishing mathematical harmonies in place of beautiful mechanical systems .. The mathematical image of reality is more abstract than the mechanical but its capacity to point beyond its immediate predictive content is similar to that of the mechanical image. The idea that the wave nature of particles postulated by de Droglie could be con- firmed by diffraction experiments came as a fantastic surprise to physicists. The discovery of the positron came about just as unex- pectedly to confirm a prediction contained unnoticed by its author
19 in a mathematical theory of Dirac. Generally speaking, the trans- formation of modern physics started with the discovery of quantum theory by Planck in 1900 and continued after that by a series of attempts to restore the coherence of the this discovery. Each successive step in image brut'a:1-4.y*,l.>roken by . .•;' • -~~ :J this process)vlil.$}'.antici- - :· pated in part by its antecedents and thus testified to its bearing on reality far beyond its explicit content. It was in the course of this enterprise that mathematical beauty manifestly became a guide to discovery and was recognised as the final token of truth. Paul Dirac has repeatedly observed this fact. My account of the Copernican revolution and of the modern revolution in physics has mentioned only in passing the contribu- tions made by new experimental observations. Dut the examples I have given were typical of the way experiments·duripg this period often followed the theoretical anticipation of them, the connection being often not recognized at first. Theoretical speculation and experimental probing entered Jointly into a persistent quest towards an ever wider and deeper coherence. · This remark brings up the question, how the actual process of discovery is performed. Much has·been written about this with which I disagree, but I can put my own views only quite summarily at this stage. To see a good problem is to see something hidden and yet/ accessible. This is done by integrating some raw experiences into clues pointing to a gap, To undertake a problem is to corrmit one- self to the belief that you can fill in this gap and make thereby a new contact with reality. Such a commitment must be passionate. A problem which does not worry us and the prospects of which do not excite us is not a problem; it does not exist. A problem is
20 discerned by integrating bits of experience to a fragmentary pat- tern which, if completed, \'Till touch upon reality. Completion, which solves the problem, is achieved by a sustained quest for deeper coherence. Every move towards this aim is pr?i~pt,eg, by an . - ~~ : . , .., I ; ·: ~ ;, intense desire evoked and guided by a sense of approachijlj;Jdis - covery. Such is the dynamic form of the anticipatory powers seen before \ in a historical perspective. Without them no research can succeed; cannot even be said to take place. ·Natural ability for discerning the incipient coherence of things and sen~ing the direction towards deeper coherence, varies 'to about the same extent among men· as. aoe~ the ability for boxing, . ·,.,~ . ballet dancing or playing chess. Theories of discovery which off'er no decisive role to scientific genius have no bearing on discovery. This is true also for theories in which hypotheses arise unaccount- ably and are entertained for no better reason than to try everything once. Nor is it true that we could sele.ct from such hypotheses those which are false by letting them be knocked out by a fact which • contradicts them. Any contradictory evidence can be Judged only within the context of the quest; Judgment must ultimately depend on our sense of approaching coherence. tions cannot produce a discovery. In any case, ulterior refuta- The dynamics of discovery are brought into action by committing ourselves to certain anticipations. Without such commitment no supporting evidence will turn up; no failure to find such evidence will be felt; no conclusions will be drawn and tested; no quest will take place. Evidence can be mobilised only by a surmise, which being a vision of the truth we are after, necessarily seeks its own
21 confirmation. Such commitment exposes us to possible failure, but to risk failure is not to aim at it. To say that in this process we are seeking the refutation of the hypothesis we are entertaining, as K. R. Popper often says, is misleading. A mounta1h~.r.may risk . . ··. ~-,' -~f\' _::,' disaster, but he does not set out to meet with disaster:~,$.:;:t:· When distinguished minds arrive at conclusions which.·seem quite unacceptable, we may be sure that the fault lies deeply buried in their premises. In these lectures and seminars I shall introduce a principle that is missing in these premises. I want to define and recognise the powers of the mind by which coherence is discovered in nature. This will place on solid grounds the progression of dis- covery; guided by anticipations of' reality, of which I have spoken. ·, ··,"•-.,,. And it should do more. The triumph _of coherence achieved by the Copernican Revolution filled those brought up in the Medieval tradition with dismay. The earth's central position had been the ~ symbol of man's destiny as the only thinking, morally responsible being in the universe. The providential-meaning of nature, which had confirmed man in the ordering of his life, was lost in the new, symbolically meaningless image of the universe. "It is all in pieces, all coherence gone", wrote John Donne already_in 1611. This conflict has steadily widened up to this day. The destruc- tion of the ancient cosmic hierarchy has spread into a theoretical ,, denial of all higher forms of existence. The ultimate components of things, including those that make up man and his thoughts were all placed on an identical level of being. Just as the harmonies of Copernicus disappear in the Neutonian equations and become mere ac- cidental formations of them, so must all complex entities now be re- duced to the law governing their components. Then, truly, all
' . 22 coherence is gone. Dut once we credit ourselves with genuine powers of integra- tion, the structure of our comprehension will re-appear in that which we comprehend, This will restore stratificati:0'.ti;tQ..,, the uni- .• . t,;;;;· : . ~ " verse: we shall recognise a set of logically identificj.~fitievels . , of existence. In such a hierarchy man takes his place as· the creature by which the universe knows itself, And so eventually, •, he may be able to make himself at home again in the universe.