Sience and Reality Polanyi

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    The British Society for the Philosophy of Science

    Science and RealityAuthor(s): Michael PolanyiReviewed work(s):Source: The British Journal for the Philosophy of Science, Vol. 18, No. 3 (Nov., 1967), pp.

    177-196Published by: Oxford University Press on behalf of The British Society for the Philosophy of ScienceStable URL: .

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    Brit. J. Phil. Sci. S18 1967), 177-196 Printed in Great Britain I77

    Science and Reality*by MICHAEL POLANYI

    The purpose of this essay is to re-introduce a conception which, havingserved for two millennia as a guide to the understanding of nature, hasbeen repudiated by the modern interpretation of science. I am speakingof the conception of reality. Rarely will you find it taught today, that thepurpose of science is to discover the hidden reality underlying the facts ofnature. The modern ideal of science is to establish a precise mathematicalrelationship between the data without acknowledging that if such relation-ships are of interest to science, it is because they tell us that we have hitupon a feature of reality. My purpose is to bring back the idea of realityand place it at the centre of a theory of scientific enquiry.The resurrected idea of reality will, admittedly, look different from itsdeparted ancestor. Instead of being the clear and firm ground underlyingall appearances, it will turn out to be known only vaguely, with an un-limited range of unspecifiable expectations attached to it.It is common knowledge that Copernicus overthrew the ancient viewthat the sun and the planets go round the Earth and that he establishedinstead a system in which it is the sun that is the centre around which allplanets are circling, while the Earth itself goes round the sun as one of theplanets. But we do not see it recognised that in the way Copernicusinterpreted this discovery, he and his followers established the metaphysicalgrounds of modern science. We cannot find this recognised, since thesegrounds of science are predominantly contested today.The great conflict between the Copernicans and their opponents,culminating in the prosecution of Galileo by the Roman hierarchy, is wellremembered. It should be clear also that the conflict was entirely aboutthe question, whether the heliocentric system was real. Copernicus and hisfollowers claimed that their system was a real image of the sun with theplanets circling around it; their opponents affirmed that it was no morethan a novel computing device.For thirty years Copernicus hesitated to publish his theory, largelybecause he did not dare to oppose the teachings of Aristotle by claimingthat the heliocentric system he had set up was real. Two years before the* Received I2.i.67


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    178 MichaelPolanyipublication of his book is I543, the protestant cleric Osiander respondedto preliminary publications of the Copernican system by a letter pressingCopernicus to acknowledge that science can only produce hypothesesrepresenting the phenomena without claiming to be true. Later, Osiandersucceeded in introducing an Address to the Reader into the publishedbook of Copernicus denying once more the reality of the Copernicansystem. The issue was still the same, more than half a century later, inKepler's defence of Tycho Brahe against his critic Ursus, and the sameagain when Galileo confronted Cardinal Bellarmine and afterwards PopeUrban VIII.

    The conflict was settled, at least for secular opinion, when the Copernicansystem was confirmed by Newton. Copernicus and his followers wererecognised then to have been right; and for the two following centuriestheir steadfastness in defending science was unquestioningly honouredamong modern educated people.I myself was still brought up on these sentiments; but by that time someeminent writers were already throwing cold water on them. The positivistcritique of science, initiated by Ernst Mach,1 and vigorously supportedby Henri Poincar6,2 declared that the claim which Copernicus, Keplerand Galileo so bitterly defended was illusory. This radical positivismtaught that science consisted merely in establishing functional relationsbetween the data observed by our senses and that any claim that wentbeyond this was undemonstrable. A reality underlying mathematicalrelations between observed facts was a metaphysical conception, withouttangible content.

    During the past half century these formulations of positivism have beenfirst sharpened into logical positivism, which claimed to establish strictcriteria for the meaning and validity of all empirical statements. Butlogical positivism, after reaching its highest prestige in the forties, presentlydeclined for its aims proved unattainable. Its theories were softened downthen by a series of qualifications, which amounted to abandoning anyattempt at establishing a formal criterion of the meaning and validity of ascientific statement. The rise of analytic philosophy confirmed thisabdication by abandoning the critique of science. Thus we are left todaywithout any accepted theory of the nature and justification of naturalscience.1 Ernst Mach, Die Mechanik in ihrer Entwicklung (1883).2 Henri Poincard, Science et Hypothese, Paris (I902), pp. I4o-I, and Henri Poincard, LaValeur de la Science, Paris (1914), pp. 271-4. In the latter book Poincard defends himselfagainst being taken to reject Galileo's affirmation that the Copernican system was true.He identifies convenience with coherence and ascribes to coherence the value of a

    greater truth than that which Galileo had claimed.

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    ScienceandReality I79There has been sharp opposition to the positivist movement by indivi-dual authors, among them Planck1 and Einstein,2 as well as the great

    historian of science, Alexandre Koyr ;3 but these authors supplied nostatement of the true metaphysical foundations of science. This is thesituation in which I shall examine the Copernican's claim that the helio-centric system was a true account of reality. And I shall show that in theirconception of reality we can find the actual grounds on which science hasrested ever since Copernicus established modern science on these grounds.

    PTOLEMY Planet


    FIG. I.

    In order to explain what made Copernicus feel that the new system heproposed was real, I shall give an outline of an important feature of the oldsystem and show the way the new system dealt with this feature.When you watch a planet night after night you see its position shiftingthrough the firmament of fixed stars. Seen from a point in the northernhemisphere, it moves predominantly from west to east, but does not movesteadily. It speeds up, slows down, retraces its path and continues eastwardsagain. It passes through these loops at regular intervals. The Ptolemaicsystem explained these loopings by assuming that the planet-instead ofsimply moving round its orbit-is carried round this orbit, as it were, onthe edge of a wheel. While the wheel moves round the planet's orbit, itx See footnote to p. 17.2 Albert Einstein, Biographical Notes in Albert Einstein Philosopher-Scientist, ed. P. A.Schilpp, New York (1949), p. 49, writes about Ostwald and Mach:'The antipathy of these scholars towards atomic theory can indubitably be tracedback to their positivistic philosophical attitude. This is an interesting example of thefact that even scholars of audacious spirit and fine instinct can be obstructed in theinterpretation of facts by philosophical prejudices. The prejudice-which has by nomeans died out in the meantime-consists in the faith that facts by themselves canand should yield scientific knowledge without free conceptual construction.'3 Alexandre Koyr6, Les Origines de la Science Moderne, Diogene, October I956, no. 16,attacks positivism for denying that science has knowledge of reality.

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    I80 MichaelPolanyikeeps turning around its own axle and thus-when seen from the Earth-produces the loops in the planet's journey round its orbit. Such wheelsare known as epicycles, and the particular type I have described, are themajor epicycles. (Fig. I.) The path along which the epicycles are carriedround is known as the deferent.


    ':" :.:":....... ::. ? :


    EarthFIG. 2.

    The effect of epicyclic motion can be analysed more closely by assumingthat the planet has for a moment discontinued its main eastward motionaround its orbit. Viewed from the Earth at rest, the image of the planetamong the fixed stars would oscillate then at the rate of its passage around

    Oscillation + Circling

    = Looping

    FIG. 3.the epicycle. (Fig. 2.) Add then to the oscillation once more the orbitalmotion from west to east and you obtain the looping as observed from theEarth. (Fig. 3.)

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    Scienceand Reality 181The fundamental idea of Copernicus was that instead of having the

    planets circling on epicyclical wheels, we can get the same effect by puttingthe Earth into a circular motion round the sun. You can see how this worksif you imagine once more, a planet arrested for a moment in its orbitalmotion and then trace its image against the firmament of stars. The imageoscillates in the same way as the planet was seen to oscillate in thePtolemaic system. (Fig. 4.) And if we again add to this oscillation the east-ward orbital motion of the planet, we see arising the observed looping.But the loops are now mere illusions, without any underlying epicyclicalmotion.




    SunFIG. 4.

    Let me add some further features of the Ptolemaic system which wereknown before Copernicus. First, all the wheels representing major epi-cycles were seen to go round at the same rate, and this common period ofthe epicycles was found to equal oneyear. Hence a planet like Mars, withan orbit of about two years, passes through one loop in rounding itsorbit; while Jupiter, which completes its orbit in twelve years, passesthrough eleven loops, and Saturn, taking about thirty years to go round,makes twenty-nine loops on its way.' Second, it was observed and noted'in reply to an enquiry, Professor S. Sambursky of the Hebrew University of Jerusalemwrote as follows: 'The Almagest in fact does mention the relevant figures for the epicyclicloops of the planets and their amplitudes (in Book IX, ch. 3, and Book XII), but Ptolemyof course fails to interpret these data, and their numerical relations are mere coincidencesfor him.' The knowledge of this relationship is clearly taken for granted by Rheticus inthe Oratio Prima (1540), but I could find no mention of it in De Revolutionibus.

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    182 MichaelPolanyithat the apparent size of the loops decreases with the increasing length oforbital periods from Mars, through Jupiter to Saturn.

    To these two observations about the major epicycles, we may add as athird point a widespread speculative idea about the size of the orbitsaround which the planets and the sun were thought to circle round theEarth. In order to understand, however roughly, the grounds for thisidea, suppose for a moment that all these circling bodies go round theirorbit at the same speed, so that the time each takes to get round its orbitwould be proportional to the radius of its orbit. The orbit of Saturn shouldthen be the largest, Jupiter's smaller and Mars's smaller still. More will besaid later about the derivation of this sequence.



    ~Sun EatIyr

    FIG. 5.Turning now to the heliocentric theory of Copernicus, we find that thethree main features of the Ptolemaic system fit in well with the new theory.

    Firstly, once epicycles are replaced by an illusory oscillation correspondingto the annual motion of the Earth around the sun, all these oscillationsmust occur at the same rate equalling one year. Secondly, we can see that,in the Copernican system, differences in the observed angles of oscillationsimply that the planets are at different distances from the sun. (Fig. 5.)The observed decrease in the angles of oscillations in the sequence ofMars, Jupiter and Saturn yields then the conclusion that the orbital radiiof these planets increase in this order, which accords with the ancientsurmise, that the size of planetary orbits steadily increases as the orbitalperiod gets longer.

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    ScienceandReality 183I have so far based the transformation of the Ptolemaic system into

    Copernican terms on the three outer planets known to Copernicus, andmust now introduce the two inner planets Venus and Mercury. Whenapplied to the inner planets, the meaning of Fig. I is inverted. The periodof the epicycle becomes the orbital period of the planet, and the period ofthe deferent becomes the period of the planet's oscillation, i.e. of itsillusory motion due to the Earth's annual passage round the sun. ForVenus and Mercury the amplitude of these oscillations is found to fall inline with that of the outer planets, and accordingly the calculated solardistance of Venus comes out smaller than that of Mars and the solar dis-tance of Mercury smaller still than that of Venus. All three features of thePtolemaic system are thus confirmed for the inner planets, when theirdeferents are taken as equivalent to the major epicycles of the outer planets.Looking at this result with the eyes of a modern scientist, I would saythat the most striking achievement of the new theory was that it explainedthe strange fact that the observed periods of loopings were all identicaland equal to one terrestrial year. But these coincidences strike us asstrange only because they areinexplicable in terms of mechanics. Copernicushad no idea that planetary motions were due to mechanical causes andhence his explanation of these coincidences, which is a triumph to ourway of thinking, made no such impression on him. To us the very factthat the Copernican system eliminates the major epicycles by whichPtolemy explained the loopings of the planets, is a great achievement. ButCopernicus does not explicitly mention this, presumably because he usedepicycles readily in other parts of his system, and so they were nothingstrange to him.To the scientist today the mere prediction of the relative orbital radiiof the planets is a great achievement of the Copernican system. ButCopernicus sees it mainly in relation to the sequence of planetary distancesderived from a mistaken theory.His theory of this sequence is stated in De Revolutionibus, book I,chapter io, in two passages, one at the beginning the other later. I quotethe second passage first for it is more explicit.Quapropterprima ratione salve manente, nemo enim conventiorem allegabit,quam ut magnitudinemorbium multitudo temporis metiatur, ordo sphaerumsequiturin huncmoduma summocapiens nitium... (Capiens jcapientesMS.)(De Revolutionibus, d. Thoruni 1873, L. Prowe, E. de Losson, Boethke,Hagemann,p. 28.)This reads in translation:Therefore,if the first law is still safe-for no one will bringforwarda better onethan that, the magnitude of the orbital circles should be measured by the

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    184 MichaelPolanyimagnitudeof time-then the order of the planetswill follow in this way...(C. G. Wallis, GreatBooksof the WesternWorld,vol. 16, Chicago(1952)).

    To say that the radii are 'measured by the magnitude of time' is toassert that the linear velocity of all planets is the same.1 The words at theopening of the chapter appear to bear this out.Errantium vero seriem penes revolutionum suarum magnitudinem acciperevoluissepriscosphilosophosvidemus, assumptaratione,quod aequaliceleritatedelatorum, quae longius distant, tardius ferri videntur, ut apud Euclidem inOpticis demonstratur.'aequali celeritate delatorum', i.e. 'objects moving with equal speed',could conceivably be construed as a hypothetical statement by Euclid,but as it fits in with the subsequent description of the planets, this des-cription appears to be its meaning.

    Copernicus rejoices that the sequence of the planets computed by himconforms to the law derived from the equality of linear speeds. But, ofcourse, the same sequence is obtained by Kepler's Third Law underwhich it is the squaresof times that are proportional to the cube of the radii.The relation from which Copernicus derived the sequence of the planetswas grossly erroneous. Could he have failed to notice the error?I think heknew his mistake.

    In his Commentariolus,composed a number of years before De Revolu-tionibus, Copernicus presents the computation of the relative radii for thethree outer planets as follows:Saturn's deferentrevolvesin 30 years, Jupiter's n I2 years,andthat of Marsin29 months; it is as though the size of the circles delayedthe revolutions.For ifthe radiusof the greatcircleis dividedinto 25 units, the radiusof Mars' deferentwill be 38 units, Jupiter's i 30 and Saturn's 230G. By 'radius of the deferent' Imean the distance from the centre of the deferent to the centre of the firstepicycle. (ThreeCopernicanTreatises, ranslatedwith introductionby E. Rose,2nd edn., Dover Publications,New York, p. 74. Note that the 'great circle'means the orbit of the Earth.)The ratios of the figures 230ok : 130 : 38 : 25 agree within about 2 per centwith Kepler's Third Law, but they greatly differ from the correspondingratios of the orbital periods, which are 29.5 : I2 : 2 : i. Comparing theratios for Saturn and Earth, that is the ratio 230k : 25 with the ratio29.5 : I, the discrepancy between them amounts to about a factor three,and when we extend these ratios to include Mercury, the deviation from1J. F. Dobson and S. Brodetsky, Nicolaus Copernicus, De Revolutionibus, Preface andbook I, Roy. Astron. Soc. I947, translate 'prima ratione salve manente' as 'given theabove view' which seems better than 'if the first law is still safe'. They translate 'quamut magnitudinem orbium multitudo temporis metiatur' as 'that the periodic times areproportional to the sizes of the orbits' which is perhaps too free, even though substantiallyright.

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    ScienceandReality 185proportionality rises nearly to afactor five. I believe it was these deviationsfrom proportionality that Copernicus had in mind when he wrote: 'It isas though the size of the circles delayed the revolutions.' This delaywould, e.g. have to reduce the speed of Saturn to close on one-fifth of thevalue predicted by Copernicus in order to make its actual speed agreewith the observed speed of Mercury. This could not have gone unnoticedby Copernicus.Consultations with historians have failed to reveal a place in literaturementioning this error; it seems to have been overlooked. My pointin bringing it up is to suggest that Copernicus disregardedthis discrepancy,because his conception of physical magnitudes in the celestial domain wasbut vague and that this vagueness must have been worsened still furtherby his knowledge of this discrepancy. Seen against this background, hisprediction of the radii could not have for him the solidity which it has forthe modern scientist, for whom most other details of the Copernican systemare, by contrast, mere fictions.What remained then for Copernicus to convince him of the reality ofhis system? We can sum it up in one sentence. He had succeeded inexplaining planetary loopings by a theory which, when introducing theactually observed periods and amplitudes of oscillations, predicts a plausiblesequence of orbital radii. It was this achievement to which Copernicusfastened his hopes during thirty years of travail and on the grounds ofwhich he and his followers claimed, against bitter opposition, that theheliocentric system was real.In his preface addressed to Pope Paul III Copernicus writes that he hasat last discoveredthat, if the motions of the rest of the planetsbe brought intorelationwith the circulationof the Earthand be reckoned n proportionto theorbit of each planet, not only do their phenomenapresently ensue, but theorders and magnitudes of all stars and spheres, nay the heavens themselves,become so bound together that nothing in any part thereof could be movedfrom its place without producing confusion of all the other parts and of theUniverse as a whole.Everything is now bound together, he claims, and this is a sign that thesystem is real.1

    But why did this claim evoke such protest among his contemporaries,particularly by the clergy? The objection was not raised primarily indefence of the bible, but of the medieval philosophy held by clerics and1 'The motion of the Earth, therefore, suffices to explain so many apparent inequalities inthe heavens' wrote Copernicus in Commentariolus. That coherence is a token of reality,is expressed by Rheticus in his Narratio Prima (1540) by the words: 'So wise is ourmaker, that each of his works has not one use, but two or three or often more.'

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    186 MichaelPolanyilay scholars alike, since the day of Aquinas 300 years before. The philoso-phic view which clerics from Osiander to Bellarmine and lay scholars likeMelanchton defended, goes back to Aristotle. It assumed that all basicfeatures of the universe can be derived from necessary first principles; forexample, the perfection of the universe required that the course of allheavenly bodies be represented by steady circular motions. Such viewsexcluded the possibility of discovering basic features of nature by theempirical observations of the astronomer; any theory established byrepresenting astronomical observations could only be regarded as a merecomputing device, and this applied as much to the Ptolemaic system as tothat of Copernicus. Only philosophy was competent to arrive at an under-standing of essential reality in nature.Centuries later the positivists declared once more that science can saynothing about ultimate reality, but theirs was a very different reason,namely that they though any such claim to be meaningless. Theirpurpose was not to preserve to philosophy the competence for meta-physical theories, but on the contrary, to purify science from making anysuch empty claims.The meaning of these two different attacks on Copernicanism, themedieval and the positivist attacks, and the position of Copernicus himself,can be illustrated by a diagram as follows.

    Three Views of ScienceFirstFirst Science RealityPrinciples


    Positivist O +OCopernican - " ' 4 " ' 4 '

    Note, the term 'science' is used here in the modern sense as applying to astronomy.

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    ScienceandReality 187(I) In the medieval position first principles bear directly on reality,while excluding science from such bearing. (2) The positivist movement is

    shown isolating science on the one hand from any extra-scientific firstprinciples and on the other hand from reality, since neither of these isrecognised. Science, regarded merely as a convenient summary of givenfacts, is strictly self-contained. (3) Copernicanism is shown, thirdly,claiming to apply basic principles through empiricalsciencefor discoveringreality.

    Copernicus did not contest the competence of philosophy to arrive atnecessary conclusions about the nature of things. When Osiander remindedhim that his astronomy fails to explain the motions of the planets,1 hemust have agreed that these motions could be understood only from firstprinciples and not from his astronomy. His strict adherence to the steadycircular motion of heavenly bodies, which made his system inordinatelycomplicated and clumsy, showed him to be basically an Aristotelian. Buthe was irresistibly compelled by the appearance of his own system to claimthat this particular feature of the celestial order, though derived essentiallyfrom experience, was true and real. Thus did he make for the first timethe metaphysical claim that science can discover new knowledge aboutfundamental reality and thus did this claim eventually triumph in theCopernican revolution.Such is the claim of science to know reality, that positivism disownedin our time; and it is this same metaphysical claim, now widely discredited,that I want to re-establish today.Let me start by asking, what Copernicus meant by saying, that hissystem was real? What had he actually in mind when believing that theplanets really circle the sun? We shall find a clue to this question if wefirst look at the more active form of this belief which Kepler and Galileomanifested when undertaking their enquiries. They testified to their beliefthat the Copernician system was real, by relying on it as a guide to dis-covery.I shall show this for Kepler. His Third Law, discovered seventy-sixyears after the death of Copernicus, developed the feature of the helio-centric system, which Copernicus had mentioned as its most strikingharmony, namely the fact that all six planets recede steadily further fromthe sun in the sequence of their longer orbital periods. Kepler lent precisionto this relationship by showing that the cube of solar distances is pro-portional to the square of the orbital periods. His other great discovery-1 In his Address to the Reader prefacing the De Revolutionibus, Osiander says of the celes-tial movements, that the astronomer '... cannot by any line of reasoning reach the truecauses of these movements ...'

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    188 MichaelPolanyiten years earlier-of his First and Second Laws, was in some sense adeparture from Copernicus. It broke away from the doctrine of steadycircular planetary motions and introduced instead an elliptic path and alaw of variable velocities related to the ellipse. Yet this elliptic path, withthe sun in one focus of it, was firmly tied to the heliocentric system. It couldnot have been discovered from Ptolemy's image of the planetary system.I would not hesitate to say that these discoveries proved the reality ofthe Copernicus system, but this is only because I know that Newtondiscovered towards the end of the same century that these threelaws of Kepler were expressions of the law of universal gravitation. Atthe time at which Kepler put his laws forward, mixed up with a number ofother numerical rules that were to prove fallacious, the effect of his threelaws was not widely convincing; Galileo himself was unimpressed by them.But for the moment I can set these questions aside, for I am only tryingto understand what Kepler and Galileo themselves believed about theCopernican system, when they relied on their conviction that it was realand thus a proper guide to their enquiries.At first glance it seems easy to see what happened in Kepler's andGalileo's minds. Relying on the reality of the Copernican system, theyrecognised the presence of problems,which by many years of labour theyproved to have been fruitful. But this leaves open the question, how theCopernican system could indicate to them good problems that were notvisible in the Ptolemaic system.We meet here a general issue, which to my knowledge, has never beensystematically examined. We must ask: What is a problem? Not the kindof problem set to students of mathematics, or to chemists in practicalclasses, but a scientific problem the solution of which is unknown, and onwhich the scientist may yet embark with a reasonable hope of discoveringsomething that is new and that will prove also worth the labour and expenseof the search.

    I would answer that to have such a problem, a good problem, is tosurmise the presence of something hidden, and yet possibly accessible,lying in a certain direction. Problems are evoked in the imagination bycircumstances suspected to be clues to something hidden; and when theproblem is solved, these clues are seen to form part of that which is dis-covered, or at least to be proper antecedents of it. Thus the clues to a prob-lem anticipate aspects of a future discovery and guide the questing mindto make the discovery.We may say then that Kepler's conviction that the Copernican systemwas real, was expressed by his belief that its image anticipated aspects ofsomething hidden and possibly accessible by an enquiry in a certain direc-

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    ScienceandReality I189tion. And we may add that he confirmedthese anticipations when, byfollowing their guidance, he discovered his three laws.

    Nor was this all. For in their turn, Kepler's discoveries raised newproblems in Newton's mind, insofar as they anticipated aspects of the stillhidden laws of gravitation, which Newton was to discover. Thus Newtonwas guided still further by a belief in the reality of the Copernican system.The confidence which the followers of Copernicus placed in the realityof the Copernican system consisted, then, in surmising still hidden im-plications in it, as were suggested to them by certain features of the system.Their belief in the system's reality was an act of their imagination thatspurred and guided them to discovery.Let us take stock of the position we have reached so far. In the historyof the Copernican Revolution we have found it possible to discriminatethe explicit statements of a theory from its anticipatory powers. Thecelestial time-table set out by Copernicus was not markedly different fromthat of Ptolemy. Close on to a century following the death of Copernicus,all efforts to discriminate convincingly between the two systems on thegrounds of their observable quantitative predictions had failed. While thediscoveries of Kepler and Galileo based on the heliocentric system greatlyincreased its plausibility and eventually convinced most astronomers, thegeneral effect, judged for example by the critical responses of Bacon orMilton, was far from conclusive. Yet all this time the theory of Copernicuswas exercising heuristic powers absent in the system of Ptolemy.We are faced with the question then how one of two theoretical systems,having virtually the same explicit content, could vastly exceed the otherin its anticipations.In a way I have given the answer to this question in the anticipatorysuggestions offered by the Copernicansystem to the followers of Copernicus.Its anticipatory powers lay in the new image by which Copernicus recast thecontent of the Ptolemaic system. It is in the appearanceof the new system thatits immense superiority lay; it is this image that made the Copernicanrevolution.

    I am drawing here a distinction which will prove decisive. I distinguishbetween the precise predictive content of a mathematical theory consistingin a functional relation of measured variables and a meaning of the theorywhich goes beyond this. While the functional relations remain the same,the surplus of meaning which goes beyond them may vary, as manifestedin this case by the appearance of the theory.The way this may come about can be illustrated from everyday life.Suppose we have a list of all the towns of England, each with its preciselongitude and latitude, and the number of its inhabitants, and we now

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    190 Michael Polanyirepresent these data in a map, each town being marked by a circle corres-ponding to its size. The mapping of the list adds no new data to it, yet itconveys a far deeper understanding of these data. It reveals, for example,the way the population is distributed through the country and suggestsquestions about the reasons of physical geography and history which willaccount for this distribution. The map will guide the imagination to enteron fruitful enquiries to which the original list would leave us blind.E. M. Forster has shown a similar difference between two kinds ofcharacters in a novel. There are fiat characters whose behaviour can beprecisely predicted and round characters which develop creatively; thelatter, says Forster, are more real and hence have the power convincinglyto surprise us. By bearing on reality, scientific theories too have the powerconvincingly to surprise us.But here I must enter a warning. The distinction between explicitcontent and informal heuristic powers is profound, but not absolute. Nomathematical theory means anything except as understood by him whoapplies it, and such an act of understanding and applying is no explicitoperation; it is necessarily informal. Indeed, great discoveries can be madeby merely finding novel instances to which an accepted theory applies.For example, Van t'Hoff's demonstration that the mass action law ofchemistry was an instance of the Second Law of thermodynamics was afundamental discovery. When I speak of the explicit content of a theory,I refer to such applications of it which are fairly obvious, and I distinguishthese from a yet indeterminate meaning of a theory that may be revealedonly much later, through a scientist's imagination.But was Copernicus himself, when expressing his belief in the realityof his system, in fact asserting that it had anticipatory powers, which thePtolemaic system had not?It is not clear how anticipatory powers can be known at all, apart fromrelying on them as clues to an enquiry. Copernicus obviously did not knowthat his system represented an aspect of Kepler's laws and of Newton'stheory of general gravitation; indeed, being wedded to an explanationof the planetary system in terms of steady circular motions, he wouldhave strictly rejected Kepler's laws and Newton's theory based on theselaws. Yet his belief that his system was real, was basically akin to that ofhis great successors. For he saw the essence of his system in those featuresof it which were to serve as clues to the problems of Kepler and Newton.He saw in the increase of orbital periods with increasing solar distancethe characteristic feature of a system in which the sun centrally controlsthe order of planets, and this is the feature on which Kepler and Newtonwere to build their discoveries.

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    ScienceandReality 191But there is actually a more general kinship between the commitment

    of Copernicus to his belief that his system was real and that of his followersrelying on it for their problems. What Copernicus believed of this systemwas what we all mean by saying that a thing is real and not a merefigment of the mind. What we mean is that the thing will not dissolvelike a dream, but that, in some ways it will yet manifest its existence, in-exhaustibly, in the future. For it is there, whether we believe it or not,independently of us, and hence never fully predictable in its consequences.The anticipatory powers which Kepler, Galileo and Newton revealed inthe heliocentric system, were as many particulars of the general antici-pations that are intrinsic to any belief in reality.This defines reality and truth. If anything is believed to be capable ofa largely indeterminate range of future manifestations, it is thus believedto be real. A statement about nature is believed to be true if it is believedto disclose an aspect of something real in nature. A true physical theory istherefore believed to be no mere mathematical relation between observeddata, but to represent an aspect of reality, which may yet manifest itselfinexhaustibly in the future.We can ask then why the general appearance of the heliocentric systemmade Copernicus and his followers believe that it was real-why its closecoherence, its intellectual harmonies had such power to convince them ofits reality. And to this we reply that the existence of a harmonious order isa denial of randomness, and order and randomness are mutually exclusive.Moreover, anything that is random is meaningless, while anything that isorderly is significant. 1To recognise the principle at work here, think of the difference betweena tune and a noise; or, more generally, between a message and a noise.Communication theory defines a noise, in contrast to any distinctive seriesof signals, as random sequence, and it says that, being random, noiseconveys no information-means nothing. This implies an importantdifference in the identifiability of an ordered sequence, as compared witha noise. Any single message is represented ideally by only one configurationof signals, while for a noise the very opposite holds. No significance mustbe attached to any particular configuration of signals that are a noise; wemust indiscriminately identify any one configuration of a noise with anyother configuration of it.This is true of any aggregate deemed random: we must assume that thechance events which compose it could have as well happened otherwise.And, by contrast, once we have recognised an aggregate of events as1 I disregard here statistical laws, as they apply to another level of reality. (See my PersonalKnowledge, p. 390.)

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    I92 Michael Polanyiorderly and meaningful, we may not believe that they might as well havehappened differently. Such an aggregate is an identifiable thing, possessingreality in the sense I have defined it; namely, that it may yet manifestitself inexhaustibly in the future. To distinguish meaningful patterns fromrandom aggregates is therefore to exercise our power for recognisingreality.Our capacity for discerning meaningful aggregates, as distinct fromchance aggregates, is an ultimate power of our personal judgment. It canbe aided by explicit argument but never determined by it: our finaldecision will always remain tacit. Such a decision may be so obvious, thatin it our tacit powers are used effortlessly and thus their use remainsunnoticed; our eyes and ears continuously commit us to such effortlessdecisions. But other decisions of the same class may be hard and moment-ous. A jury may be presented with a pattern of circumstantial evidencepointing to the accused. It is always conceivable that this pattern may bedue to chance; but how unlikely a chance should they admit to be possible?Or else, what degree of coincidence should be deemed quite unbelievable?The prisoner's life and the administration of justice will depend on thedecision, and there is no rule by which it can be decided. This is preciselywhy it is left to the jury to decide it.I have said that reality in nature is a thing that may yet manifest itselfinexhaustibly, far beyond our present ken. Something must be added tothis description, if the pursuit of natural science is to be justified. Considerthat the Copernican revolution was but a continuation of a structuringthat had its origins in antiquity. Copernicus deepened and beautifullyclarified a coherence transmitted to him by Ptolemy. And this triumphpointed further beyond itself in the mind of Copernicus. In Kepler,passionately embracing the system of Copernicus, its image was to evokeanew the kind of creative hunger which Copernicus had satisfied by dis-covering it. And the presence of yet hidden truth worked its way further.To Newton, Kepler's three laws appeared to hang covertly together andhe established this fact by his theory of gravitation, which derived all threelaws jointly from the mechanics of Galileo. Nor was this the end, for aquarter of a millennium later, Einstein was to find unsatisfying the co-existence of the Newtonian system with the electromagnetic theory oflight, and was to discover an even deeper coherence reconciling the two.The continued pursuit of science is possible, because the structure ofnature and man's capacity to grasp this structure, can be such as isexemplified by this sequence of discoveries covering two millennia. It doeshappen, that nature is capable of being comprehended in successivestages, each of which can be reached only by the highest powers of the

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    ScienceandReality 193human mind. Consequently, to discover a true coherence in nature is oftennot only to discern something which, by the mere fact of being real,necessarily points beyond itself, but to surmise that future discoveriesmay prove the reality of the thing to be far deeper than we can at presentimagine.It may seem strange that I insist on a belief in the reality of theoreticalsuppositions as the driving force to discovery. Such belief would seem aconservative assumption, rather than a source of innovation. The positivistview of science would indeed claim that the major discoveries of modernphysics were based on a sceptical attitude towards the framework ofhitherto accepted scientific theories. The discovery of relativity involvedthe abandonment of the current conceptions of space and time, and quantummechanics achieved its breakthrough by discarding Bohr's planetarysystem of electrons circling the nucleus. Einstein himself acknowledgedthat Mach's positivist philosophy had inspired his work and Heisenberg'squantum mechanics was deliberately framed to reduce atomic theory to afunctional relation of observable quantities.These revolutionary heresies may seem to contradict my thesis, but Ithink they fall in line with it, once I make clearer the opposite extreme ofcreative procedure, based on a firm belief in the reality of the currentframework of scientific theory. We may recognise the prototype of such afeat in the discovery of America by Columbus. He triumphed by takingliterally, and as a guide to action, that the earth was round, which hiscontemporaries held vaguely and as a mere matter of speculation. Theegg of Columbus is the proverbial symbol for such breath-taking originalityguided by a crudely concrete imagination. I remember having this feelingwhen first hearing of Einstein's theory of Brownian motion. The idea thatthe meandering oscillations of small floating particles seen by a botanistunder the microscope, should reveal the impact of molecules hitting theparticles in tune with the highly speculative equations of the kinetictheory of gases, impressed me as grossly incongruous. I experienced thesame shock of a fantastic idea, when I heard Elsasser suggesting (in 1925)that certain anomalies observed in the scattering of electrons by solidsmay be due to the optical interference of their de Broglie waves. We hadall heard of these waves since 1923, yet were astounded by the fact thatthey could be taken literally as Elsasser did.'1 This paper was delivered as a lecture at Duke University, Durham, N.C., in February1964. James Franck lived at that time in Durham and we met to discuss my talk. Franckbegan very quietly, almost in a whisper, saying: 'You know, I am one of those literals.'He clearly was very pleased. During his great career, spent among conceptual revolu-tionaries like Planck, Einstein, Bohr, Heisenberg, Schrodinger, Born, he must have oftendoubted the quality of his own genius and he was glad to find its place acknowledged in


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    I94 Michael PolanyiThis should remind us that the first great move towards the discoveryof quantum mechanics was de Broglie's idea of the wave nature of matter.

    This revolutionary idea and Schrodinger's development of it into wavemechanics, shows no trace of positivistic influences. Add to this, that MaxPlanck, the founder of quantum theory, actively opposed Mach's analysisof science and also dissented from Heisenberg's claim of basing physicaltheories on directly observable quantities1; and that Einstein himself,whose principle of relativity served as an inspiration to modern positivism,was sharply critical of Mach's analysis of science as a mere relation ofobserved facts.2 It appears then, that the predominant principle that shapedmodern physical theory was not the positivist programme, but the transitionfrom a mechanical conception of reality to a mathematical conception ofit, which sometimes coincided with the positivistic programmefor the purifi-cation of science.

    We can thus bring the revolution of the twentieth century in line withthe Copernican revolution of the sixteenth and seventeenth centuries.Both revolutions consisted in a stepwise deepening of coherence with asimultaneous extension of its range. The modern revolution differed fromits precursor only in establishing mathematical harmonies in place ofbeautiful mechanical systems.The mathematical image of reality is more abstract than the mechanical,but its capacity to point beyond its immediate predicative content is similarto that of the mechanical image. I have said that the fact that the wavenature of particles postulated by de Broglie could be confirmed bymy analysis. I think that among great discoveries the one most purely based on a literalacceptance of current ideas, was Laue's discovery of the diffraction of X rays; butLangmuir too triumphed by the powers of a literal imagination, and many of Rutherford'sdiscoveries were based on daringly primitive conceptions.1 Max Planck, Scientific Autobiography and Other Papers, Philosophical Library, NewYork (1949), P. I29, Tr. Fr. Gaynor. (Original title of this essay was 'Der Causalbegriffin der Physic' first published in 1948.) 'It is absolutely false, although it is often asserted,that the world picture of physics contains, or may contain, directly observable magni-tudes only. On the contrary, directly observable magnitudes are not found at all in theworld picture. It contains symbols only.' In this essay (p. 139) he also objects to theelimination of seemingly unverifiable statements: 'I must take exception to the view(a very popular one these days, and certainly a very plausible one on the face of it)that a problem in physics merits examination only if it is established in advance that adefinite answer to it can be obtained. If physicists had always been guided by thisprinciple, the famous experiment of Michelson and Morley undertaken to measure theso-called absolute velocity of the earth, would never have taken place, and the theoryof relativity might still be nonexistent.'

    2 In his Autobiographical Notes I. c, p. 53, Einstein writes about his re-definition ofreality as follows: 'The type of critical reasoning which was required for the discoveryof this central point was decisively furthered, in my case, especially by the reading ofDavid Hume's and Ernst Mach's philosophical writings.' But Einstein did not confirmMach's teaching that the Newtonian doctrine of absolute rest is meaningless; Einsteinproved, on the contrary, that Newton's doctrine, far from being meaningless, was false.

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    Scienceand Reality I95diffraction experiments, came as a fantastic surprise to physicists. Thediscovery of the positron occurred just as unexpectedly in confirmation ofa prediction contained unnoticed in Dirac's quantum theory of the electron(1928).In my account of the Copernican revolution and of the modern revolu-tion in physics, I have mentioned only in passing the contributions madeby new experimental observations. But the examples I gave were typicalof the way at this time experiments often followed their theoreticalanticipation, the connection being sometimes not recognised at first.Usually, theoretical speculation and experimental probing enter jointlyinto the quest towards an ever broader and deeper coherence.This brings up the question, how the actual process of discovery isperformed. Much has been written about this with which I disagree, butfor the moment I can put my own views only quite summarily. To see agood problem is to see something hidden and yet accessible. This is doneby integrating some raw experiences into clues pointing to a possible gapin our knowledge. To undertake a problem is to commit one-self to thebelief that you can fill in this gap and make thereby a new contact withreality. Such a commitment must be passionate; a problem which doesnot worry us, that does not excite us, is not a problem; it does not exist.Evidence is cast up only by a surmise filled with its own particular hopeand fervently bent on fulfilling this hope. Without such passionate commit-ment no supporting evidence will emerge, nor failure to find suchevidence be felt; no conclusions will be drawn and tested-no quest willtake place.Thus the anticipatory powers that we have seen at work in historicalperspective, arouse and guide individual creativity. These powers areever at work in the scientist's mind, because he believes that science offersan aspect of reality and may therefore manifest its truth ever again by newsurprises.In this essay I have tried to define the mental powers by which coherenceis discovered in nature. But the coherence achieved by the CopernicanRevolution filled with dismay those brought up on the medieval order ofthe universe. The Earth's central position which had been the symbol ofman's destiny as the only thinking morally responsible being, was lost.Gone was the divine perfection of an immutable firmament encirclingthe place where fallen man was ever to strive for salvation beyond thisplace. 'It is all in pieces, all coherence gone', wrote John Donne as early as1611.

    The destruction was deepened by the revival of atomism. Dante hadsaid of Democritos that he 'abandoned the world to chance'. And Dante

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