Da jeg begynte i departementet høsten 1938, var det en fordel at jeg hadde et personlig kjennskap til så å si alle vitenskapelige institusjoner i landet. Og i folkeopplysnings-arbeidet hadde jeg hatt god kontakt med folkeakademiene.

Det var interessant å oppdage at prinsippene for departementets behandling av et sakskompleks i hovedsaken lignet de prinsipper som ligger til grunn for en vitenskapelig undersøkelse av et materiale. Den første oppgave er å undersøke så objektivt som mulig de fakta som har betydning i det foreliggende tilfelle. Den neste er å vurdere deres innbyrdes betydning, og den tredje er å forme en vel begrunnet konklusjon, hvor en også kan finne det nødvendig å vurdere de praktiske konsekvenser konklusjonen vil få.

Historians and philosophers of science have traditionally paid far too much attention to formal methodological pronouncements, often taking such statements at face value as adequate accounts of what past practitioners actually did when they went about making, assessing, and distributing scientific knowledge. In fact, the relation between any body of formal methodological directions and concrete natural philosophical practice in the seventeenth century is deeply problematic. For example, neither those whose methodological pronouncements professed radical disengagement between theorizing and fact gathering nor those who announced their systematic skeptical rejection of traditional culture wholly succeeded in their aims. There is much to commend a revisionist view that formal methodology is to be understood as a set of rhetorical tools for positioning practices in the culture and for specifying how those practices were to be valued. This is not, however, to deny formal methodology a role in seventeenth-century science. Methodology may be in part, as it has been called, a "myth," but myths may have real historical functions. Methodological pronouncements like Bacon's were avidly seized on by later, especially English, natural philosophers to justify a concerted collective program of observational and experimental fact collecting, while broadly deductive methodologies were used by other sorts of philosophers to justify the importance of rational theorizing over the accumulation of factual particulars. Formal methodology is important, therefore, in the same way that the justification of a practice is important to its recognized identity and worth. A practice without an attendant myth is likely to be weak, hard to justify, hard even to make visible as a distinct kind of activity.⁶ Justifications are not to be simply equated with the practice they justify, and we still need a more vivid picture of what a range of modern natural philosophers actually did when they set about securing a piece of knowledge. Modern natural philosophers did not just believe things about the natural world; they did things to secure, to justify, and to distribute those beliefs. Doing natural philosophy, that is, was a kind of work.

"Men De tror vel ikke for alvor," innvendte Einstein, "at man bare kan ha iakttagbare størrelser i en fysisk teori."

"Jeg trodde," kom det spørrende fra meg, "at nettopp De hadde denne tanke som forutsetning for Deres relativitetsteori? De hadde jo understreket at man ikke måtte snakke om absolutt tid, da den ikke kan iakttas. Kun urenes angivelser - hva enten i det bevegede eller hvilende referansesystem - er avgjørende for bestemmelsen av tiden."

"Muligens har jeg benyttet meg av denne type filosofi," svarte Einstein, "men den er ikke desto mindre nonsens. Eller jeg vil si litt forsiktigere at det kan ha heuristisk verdi å minne seg om det som man virkelig iakttar. Men prinsipielt er det helt galt å ville basere en teori utelukkende på iakttagbare størrelser. For i virkeligheten er det jo akkurat omvendt. Det er først teorien som avgjør hva man kan iaktta. De vet, iakttagelsen er jo vanligvis en meget komplisert historie.

I can hardly give here an outline of that outline which became my first published book.

But there are one or-two points I will mention. The book was meant to provide a theory

of knowledge and, at the same time, to be a treatise on method the method of science.

The combination was possible because I looked on human knowledge as consisting of

our theories, our hypotheses, our conjectures; as the product of our intellectual activities.

There is of course another way of looking at "'knowledge": we can regard "knowledge"

as a subjective "state of mind", as a subjective state of an organism. But I chose to

treat it as a system of statements-theories submitted to discussion. "Knowledge" in this sense is objective, and it is hypothetical or conjectural.

This way of looking at knowledge made it possible for me to reformulate Hume's problem of induction. In this objective reformulation the problem of induction is no longer a problem of our beliefs-or of the rationality of our beliefs-but a problem of the logical relationship between singular statements (descriptions of "observable" singular facts) and universal theories.

In this form, the problem of induction becomes soluble: ¹⁰⁸ there is no induction, because universal theories are not deducible from singular statements. But they may be refuted by singular statements, since they may clash with descriptions of observable facts.

Moreover, we may speak of "better" and of "worse" theories in an objective sense even before our theories are put to the test : the better theories are those with the greater content and the greater explanatory power (both relative to the problems we are trying to solve). And these. I showed, are also the better testable theories; and-if they stand up to tests-the better tested theories.

This solution of the problem of induction gives rise to a new theory of the method of science, to an analysis of the critical method, the method of trial and error : the method of proposing bold hypotheses, and exposing them to the severest criticism, in order to detect where we have erred.

It may be mentioned (although this was not a thesis of Logik der Forschung) that the proposed solution of the problem of induction also shows the way to a solution of the older problem-the problem of the rationality of our beliefs. For we may first replace the idea of belief by that of action; and we may say that actions (or inactions) are "rational" if they are carried out in accordance with the state, prevailing at the time, of the critical scientific discussion. There is no better synonym for "rational" than "critical".

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We must be careful to observe, however, that this description is so far strictly limited. It is only when we have performed a large number of similar experiments in widely separated places, at widely separated intervals with widely separated initial conditions .. and using gases of different chemical composition, that our description begins to be felt as having a greater a greater range of application and validity. In every such case the symbolic description .. .. we say that we have established a physical law .

….

The possibility indeed lies open that, among certain symbols representing primitive concepts, a few mathematical relations may exist from which can be deduced, by purely mathematical operations, a whole group of physical laws .. Now when such a state of affairs exists we say we have a physical theory.

One may ask: what is the relation of the fundamental asumption of mechanics to Newton’s laws of motion? The answer is that Newton’s laws, however phrased, constitute the hypotheses at the basis of mechanics.

..

Incidentally, it will be found that many so-called "laws" of physics are really hypotheses of theories and not laws in the sense of the present text.

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It may be desirable from the logical standpoint, however, to ditinguish as sharply as possible between law and theory.

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Physical theories will allways be based on hypotheses, but the deduction from these hypotheses must allways have a readily identifiable relation with experience.

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We have so far, indeed, overlooked one point, and that is the power of a physical theory to predict physical observations previously unknown. This is a remarkable faculty.

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It is easy to sympathize with modern theoretical physicist who are inclined to emphasize the power of prediction as the really crucial test of a theory.

When, therefore, I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? If now we examine the matter carefully we find no addition or increment more simple than that which repeats itself always in the same manner. This we readily understand when we consider the intimate relationship between time and motion; for just as uniformity of motion is defined by and conceived through equal times and equal spaces (thus we call a motion uniform when equal distances are traversed during equal time-intervals), so also we may, in a similar manner, through equal time-intervals, conceive additions of speed as
taking place without complication; thus we may picture to our [198] mind a motion as uniformly and continuously accelerated when, during any equal intervals of time whatever, equal increments of speed are given to it.

THEOREM I, PROPOSITION I

The time in which any space is traversed by a body starting from rest and uniformly accelerated is equal to the time in which that same space would be traversed by the same body moving at a uniform speed whose value is the mean of the highest speed and the speed just before acceleration began.

Dette er middelverdisatsen brukt til å finne tilbakelagt veistrekning, slik vi gjør det med elever før de kan integrere.

Beviset til Galilei kan sammenfattes slik:

Her er tidsaksen vertikal. Hastigheten er avsatt vinkelrett på tidsaksen. Konstant fart gir et rektangel som mål på tilbakelagt veistrekning. Ved jevnt økende hastighet får vi en trekant med samme areal. Farten ved I er middelverdien av farten ved A og B.

Galilei brukte figur 49 i beviset for "COROLLARY I".

THEOREM II, PROPOSITION II

The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time-intervals employed in traversing these distances.

Figuren og beviset Galilei bruker her er litt mer vrient å gjennomskue. En konsekvens av setningen er lettere.

COROLLARY I

Hence it is clear that if we take any equal intervals of time whatever, counting from the beginning of the motion, such as AD, DE, EF, FG, in which the spaces HL, LM, MN, NI are traversed, these spaces will bear to one another the same ratio as the series of odd numbers, 1, 3, 5, 7; for this is the ratio of the differences of the squares of the lines [which represent time], differences which exceed one another by equal amounts, this excess being equal to the smallest line [vie. the one representing a single time-interval] : or we may say [that this is the ratio] of the differences of the squares of the natural numbers beginning with unity.

Suppose we have found out that the angle of refraction r of a light ray depends on the angle of incidence i (relatedness hypothesis). We wish to

find the precise law relating these two variables in the case of a given transparent medium and a given light color. We may then proceed as follows. We first perform angle measurements at intervals of 10 degrees with, say, 1 minute accuracy, and tabulate the results of our measurements. In this way we get a table like Table 6.1, which displays our findings. But this table, a summary of experimental results, is clearly insufficient: (i) it contains a finite number of data only, and (ii) it does not help to explain the refraction phenomenon. Consequently we search for a formula of the form "r= f (i) " covering infinitely many possible pairs <i, r> of angles. To this end we first plot the data on the i- r plane and join the "empirical points" with a smooth line: this will give us an intuitive representation of the formula. (See Fig. 6.4.) We see that, up to about 30°, the linear approximation - dotted line representing the function " r= 0.5 i " - is quite good. From then on the discrepancy increases noticeably, reaching 40 per cent at 90°. Before the law was found KEPLER had guessed that a linear relation between the angle of incidence and the angle of refraction holds. This is common in the history of science

first-order approximations, i.e. the simplest hypotheses, are usually (not

always) the first to be conjectured.

To improve on the first-order approximation we may add a quadratic term to the previous expression, i.e. we may put r=0.5 i---a i², where a should be a small negative number to curb the curve downwards. But we need not grope at random: GREGORY and NEWTON, among others, bequeathed upon us a mechanical interpolation technique by means of which our ten pairs of numbers in Table 6.1 can be made to fit a 9th degree polynomial. This procedure can be improved without limits other than those set by the sensitivity of our measuring instruments. In fact, we may next take one degree intervals, then one minute intervals, and so on until we hit the afore-mentioned limitations (which are both technical and physical). We accordingly get better and better fits though at the

price of dull complexity. For example, with one reading every one-tenth of a second, and some patience, we could obtain a polynomial with 54,000 terms. But this would take us no single step nearer the true hypothesis, which is SNELL'S law.

I distinguished three main types of learning process, of which the first was the fundamental one:

(1) Learning in the sense of discovery: (dogmatic) formation of theories or expectations, or regular behavior, checked by (critical) error elimination.

(2) Learning by imitation. This can be interpreted as a special case of (1).

(3) Learning by "repetition" or "practicing", as in learning to play an instrument or to drive a car.

Meg'et rommer selvfølgelig ikke bare vakre og vidunderlige dansetrinn og geniale pasninger i fotball. Meg'et rommer store mengder sterkt negative trekk, som ikke minst psykoanalysen har gjort klart. På samme måte rommer Jeg'et ikke bare vetoer og kontroll, men også evnen til å kommunisere og fastholde tanker livet igjennom og venner imellom. De to sidene av mennesket er avgjort rikere på både skitt og kanel enn det fremgår av den "fenomenologiske" analysen ovenfor.

Men før vi kaster oss ut i en nærmere undersøkelse av hva Jeg'et og Meg'et er for slags størrelser, kan det være grunn til å peke på at vi i hvert fall har fått løst ett problem: Boltzmanns spørsmål om hvem det var som skrev Maxwells ligninger.

Da James Clerk Maxwell ikke kunne utrette mer, men lå kreftsyk på dødsleiet, sa han til sin venn, professor Hort: "Det som gjøres av det som kalles meg selv, gjøres, føler jeg, av noe som er større enn meg selv i meg."

Det var ikke ment slik, men det var svaret til fysikerkollegaen Ludwig Boltzmann, som i ærefrykt spurte om opphavet til de vidunderlige maxwellske ligningene.

Vitenskapens skjønnhet har ofte slått vitenskapsmennene med undring. Men den vitenskapelige tradisjon er grunnlagt i et forsøk på å forstå de guddommelige prinsippene bak verden. Vitenskapens opprinnelse ligger etter Julian Jaynes' syn i studiet av varsler, som ble innledet i Assyria under det tokamrede sinns sammenbrudd. Pythagoras studerte matematikk i det gamle Hellas fordi han ville oppsøke tallenes uttrykk for det guddommelige prinsipp. De store navnene i moderne naturvitenskap var ofte dypt religiøst motiverte i sitt arbeid: Kepler, Newton, Einstein. Som Jaynes formulerer det: "Galilei kalte matematikken Guds tale." ³²

Tenkning er ikke bevisst; vitenskapelig tenkning er heller ikke bevisst, men vårt begrep om bevissthet rommer alt det vi mennesker er stolte av ved oss selv, hvilket ikke minst vil si vitenskapen.

Men kanskje er det ikke så underlig at skjønnheten kan spille en så stor rolle i det vitenskapelige arbeidet. For det er slett ikke det bevisste Jeg som tenker, men det ikkebeviste Meg. Alt det Jeg'et ikke kan redegjøre for.

Vi kan derfor fortsette replikkskiftet fra slutten av kapittel 10: Boltzmann: Var det en gud som skrev disse tegn? Maxwell: Nei, det var meg!

Vårherre: Ja, det var meg.

Feynman treated the attempt to discover the laws of nature by giving the following analogy. Imagine that the gods are playing some great game of chess and we don't know the rules of the game, but we are allowed to look at the board, in a little corner perhaps, from time to time. From these observations we try to figure out what the rules of the game are, what rules are obeyed by the moving pieces. After a while we might discover, for example, that when there is only one bishop around on the board that it maintains its color. Later on we might discover that the bishop moves along the diagonal, which would explain the law that we understood before that it maintains its color; this would give us a deeper understanding of the motion of the bishop on the chessboard. Then other things can happen. Everything is going well, we've got all the laws, and then all of a sudden some strange phenomenon occurs in the corner; so we investigate that: it's castling, something we didn't expect.

In fundamental physics, we are always trying to investigate those things in which we don't understand the conclusions. We're not trying to check our conclusions all the time; after we have checked them enough we are OK. The thing that doesn't fit is the thing that's the most interesting, the part that doesn't go according to what you expected. There could also be revolutions in our understanding of the game of chess, which are comparable to revolutions in physics. For instance, after we have noticed that the bishops maintain their color and they move along the diagonal for such a long time that everybody knows that that's true; then we suddenly discover one day in a chess game that the bishop doesn't maintain its color, it changes its color. Only later do we discover a new possibility: that a bishop is captured and that a pawn went down all the way to the queen's end to produce a new bishop. That can happen, but we didn't know it. So it's very analogous to the way the laws of nature are. They keep on working and, all of a sudden, some little gimmick shows that they are wrong. And then we have to investigate the conditions under which this bishop's change of color happened and so forth, and gradually learn the new rule that explains things more deeply.