appendix: on the discovery of general facts

The problem to be discussed in this note is: how are discoveries of facts made, and why do we find it strange that a given discovery was not made earlier? The three views answering the problem which we consider are as follows:

1.

2. William Whewell: Discoveries are verifications of new ideas. They could not be made before the hypotheses which they verified were conceived. Discoverers conjecture explanatory hypotheses and try to verify them.

3. Karl Popper: Discoveries are refutations of scientific hypotheses. They could not be made before the hypotheses which they refute (and the specific attempts to criticize these hypotheses) were conceived. Discoverers conjecture explanatory hypotheses and try to criticize them.

Long Struggle

For logical reasons these are all the possible cases: if a discovery is neither a verification nor a refutation of a prediction deducible from any existing hypothesis, then by definition it is independent of any existing hypothesis and is thus accidental. Naturally, the views I have mentioned above are deeply connected with much wider issues of logic and scientific method. In particular, they are connected with the issue of theoretical discoveries. I shall not enter these issues, and only discuss discoveries of facts, using the word ‘facts’ in its ordinary sense, or in the sense of ‘generalizations’ or ‘low-level generalizations’ or ‘observable facts’. The following example should make this clear. I put forward this example in order to show, in an intuitive way, that even a most simple and obvious fact had to be discovered after a long struggle.

If you have an electric torch and a compass - a toy compass will do - you will hardly find any difficulty in observing that the electric current in the torch deflects the needle of the compass.

The same difficulty arises when we consider even the latest discoveries, though, naturally, in a somewhat less obvious manner. Take the dis­covery of the non-conservation of parity. Professor Abdus Salam pointed out in his inaugural lecture at the University of London, “that the results could have been discovered 10 years back, for the evidence existed on all photographic plates with 7i-//-e decay”. Why then were they not observed 10 years earlier?

Bacon's View

This question was already posed in the early 17th century by Francis Bacon. His answer was this. The chief obstacle to discovery is people’s self-assuredness in their belief that they know all that there is to know, while in fact they are merely blinded by their prejudices and superstitions. In order to be a discoverer one has to forget all that one was taught and to realize the need for more factual knowledge. A discoverer doubts everything and takes nothing for granted. A discoverer merely observes facts diligently, collecting as many of them as he can. This is all he can do. The rest is up to Mother Nature, or accident, or luck, or call it what you will. As the discoverer does not rely on any opinion but only on what he sees, he cannot foretell what his eyes will tell him. (The theoretician can evolve demonstrable theories out of the discoverer’s findings, and he can predict. But this is a totally different matter.)

Bacon has a very strong argument in favour of his view that dis­coveries are unpredictable. Discoveries, he observed, are surprising. If you could tell people of previous generations about today’s discoveries, they would not believe you, or they would consider your tales miraculous.

Discoveries to Timetable

Some discoverers resented the doctrine that no thinking, no theorizing, was involved in the process of discovery. When Bacon’s views were most popular - in the early 19th century - some discoverers tried to show that their discoveries went along preconceived plans, by trying to make dis­coveries in public lectures. Davy wrote in a letter to a friend that he was going to decompose nitrogen - which he (erroneously) thought was a compound - in a public lecture. Oersted made his discovery in a public lecture. Ampere, too, made his discovery shortly afterwards in a public lecture. Yet people remained unconvinced. The fact that Oersted made his discovery in a lecture was taken as evidence that his discovery was accidental, and the fact that Ampere had predicted his discovery was taken as evidence that it was no discovery at all. It was therefore necessary to show the error in Bacon’s reasoning rather than to perform a discovery in public. This was done by the great Cambridge philosopher of the 19th century, William Whewell.

Whewell’s Qualification

Whewell agreed with Bacon that new discoveries cannot be predicted on the basis of established theories, but he claimed that they must be pre­dicted or else they would not be seen at all. It follows then, that a dis­covery is predicted on the basis of a new, not yet established theory. An investigator conjectures an explanatory hypothesis and then tests it. He refutes it and starts all over again. This process is repeated many times. Eventually, though very rarely, and even then only with the aid of in­tuition and luck, he succeeds in verifying a prediction based on a hypoth­esis, thus rendering that hypothesis into an established scientific theory.

The great merit of Whewell is that while rejecting Bacon’s anti- intellectualist view he retained its most significant element - the idea that scientific discoveries are surprising.

Yet Whewell’s view does not fit discoveries which do not come out according to plan, and refute seemingly well-established theories in an unexpected manner. I am referring to the famous crisis in physics of the turn of the last century. As atomism was considered to be well established, radioactivity seemed quite perplexing, even to its discoverers. And as both Newton’s theory and Maxwell’s theory were claimed to have been verified, it was plain that Michelson’s experiment should indicate ether drift. But it did not. With this the whole philosophy of verification col­lapsed. Most philosophers are at present concerned with a rescue opera­tion trying to substitute high probability for verification. The most im­portant exception is Karl Popper, who suggested that we learn from experience by refuting our hypotheses experimentally. Surprising facts are those which, according to existing views, are quite impossible.

Refuted Theories

Thus Popper retains and even fortifies Bacon’s idea of discovery as a surprise, while allowing, at the same time, for the case of two investigators discovering independently the same fact (by criticizing the same well- known theory). He also retains Whewell’s idea that discovery involves more thinking than observing. Bacon and Whewell had concluded from the idea that discoveries do not follow from previous theories, that they are independent of them. In doing this they just ignored refuted theories. But refuted theories are very important because they led to discoveries which were made as refutations of them. Whewell was right in claiming that a fact must bear some relation to our theories in order to be observed. But the relation need not be that of agreement - if we are critically minded we may see facts which disagree with our anticipations.

Oersted's Sudden Thought

Many people (including Oersted’s pupil Hansteen) viewed Oersted’s discovery as accidental. Others (including Whewell) used this discovery as an example for a planned experiment. The latter party could not ex­plain why it took Oersted over 10 years to make his discovery, and neither parties could explain what is its significance. The answer to these ques­tions can be given only if the discovery is viewed as a refutation. Although the effect can be repeated with any weak battery, Oersted failed again and again to perform it while using stronger and stronger batteries. Why? We know that the only way to fail is to place the conductor perpendicular to the needle of the compass, i.e. in the east-west direction. Oersted, as well as Young, Davy, and quite possibly other investigators, repeated this mistake many times and systematically. Why? From Popper’s view­point the answer is pretty obvious: it was due to a theory which they all took for granted. For if you assume, with Newton, that all forces are central (i.e. either pull or push), then even if you do not know whether the electro-magnetic force is attractive or repulsive, or where the centres of force in the conductor lie, though you know that it is cylindrically symmetrical, you can see that the best position of the conductor must be in the east-west direction. For as you do not know whether it will make the needle rotate clockwise or anti-clockwise, you must put it in a position where this question matters least - in the east-west direction.

A Modern Instance

A particularly simple and beautiful modern discovery is Anderson’s dis­covery of the position. Curved lines looking like antennae of some insects are in fact clouds which were created by charged particles moving through cold vapour. These tracks are curved because at the time a magnet was present in the vicinity. Lorentz’s theory of force enables us to say that two tracks curve in opposite directions either if the two particles having the same charge move in opposite directions or if the two particles having opposite charges move in the same direction. Before Anderson everyone naturally agreed that two tracks curving in opposite directions are of two electrons which have the same charge and which moved in opposite directions. The reason for it is the hypothesis - call it prejudice if you like - that all electrons are negatrons. The hypothesis that positrons exist, and are created and annihilated together with negatrons, was made by Dirac as a part of a stop-gap hypothesis designed to overcome a severe difficulty in his theory of the electron.

The difficulty exists no more, and the stop-gap hypothesis was never taken seriously anyhow. But the idea of positrons struck Millikan and Anderson and they decided to check the assumption that the two particles which formed oppositely curved tracks moved in opposite directions. Anderson checked the direction by putting a lead plate in the particles’ way. Lorentz’s theory of force tells us that the more curved path belongs to a slower particle. Assuming that the particle lost rather than gained speed when meeting the obstacle, we can determine the direction of its motion. In this way Anderson refuted the received hypothesis. Refuting also the hypothesis that the positively charged particle was a proton, he was left with the hypothesis that it was a positron. We now know of many other possibilities (mesons) which Anderson did not consider. Thus Anderson proved nothing. But he disproved the previously accepted hypothesis. By now pair creations are repeated much more easily than in Anderson’s day, so if Dirac’s and Anderson’s hypothesis is false its refutation will be quite a revolution of the greatest order of magnitude.

A Rational Attitude

I have discussed these two examples in some detail in order to show that Popper’s way of viewing discoveries allows a better interpretation of them. I should stress again that the choice is only between interpreting a discovery to be a verification, or a refutation, or an accident. This is so simply because the relation between two statements (theory and an ob­servation report) is by definition either deducibility (the report is a verification of a prediction based on the theory), contradiction (the report is of a refutation of the theory), or independence (accidental discovery). When we claim that a discovery is accidental we are totally unable, I think, to explain the intellectual significance which a discovery has when it is announced. When we claim that it is a verification of a predic­tion we can only claim that it is intellectually significant if we can show that it was a verification of a theory. But then we cannot explain why discoveries - like Oersted’s or Anderson’s - are intellectually significant, although they are verifications of predictions based on theories which were not accepted at all. Nor can we explain the immense impact of experimental refutations like those of Michelson and Morley and of Lee and Yang.

This, however, is only one of the reasons why I accept Popper’s view. The main reason why I accept it is that it is inspired by the faith that we learn from criticism, namely, from finding out our own mistakes. Popper has shown the surprising power and fruitfulness of this modest form of rationalism.