THE METHOD OF SCIENCE.* HENRI POINCARE, who died two years
ago, was, according to Mr. Bertrand Russell, by general agreement the most eminent scientific man of his generation. In physics, astronomy, and, above all, in mathematics, he had few com- petitors, and be has left in sundry formidable treatises the results of his most original labours in these special depart- ments. But in addition be was that rare thing, a man of science who reflects upon the basis of his activities. and in four volumes of studies be has given the world, in a form more or lees popular, the fruits of his reflections. These volumes are La Science et l'Hypothese, La Valeur de la Science, Science et Nethode, and the posthumous collection issued last year under the title of Derrieres Ponies. The first is already se classic, if we may judge by the way in which its argument interpenetrates all recent writings on the subject, and the extent to which it is quoted. The book before us is a translation of the third, which is in some respects the most remarkable of the four. It is popular in the sense that it is brilliantly written, full of wit and illustrations at once mathematically exact and artistically effective, and as clear as only a great man who is also a Frenchman can make a difficult argument. For anyone who desires to understand the standpoint and some of the startling results of the most abstract science of to-day no better introduction could be found. Mr. Francis Maitland's translation is adequate— which is high praise in connexion with such an original—and Mr. Bertrand Russell in his preface pays a graceful tribute to a thinker who to him was at once master, fellow-labourer, and opponent.
An interesting treatise might be written on the new modesty of science. The old " High Church " party of Spencer and Huxley has been succeeded by a "Broad Church" movement, which discards all arrogant claims, and which tends to replace the conception of "laws of nature" by that of "working hypotheses." Men like Poincark M. Le Roy, and not least M. Bergson, who is man of science as well as philosopher, have gone very far in making the character of the proudest maxims provisional and tentative. One reason, perhaps, is to be tound in the success of our knowledge of and mastery over phenomena, which has tended to divert men's minds from large theoretical constructions. But the principal reason is the startling results those phenomena tend to give when we push our analysis far. Recent discoreries have compelled us to revise the old orthodoxies, and admit that, however excellent the " laws of nature" may be for the earlier stages of Inquiry, they simply do not work in the later—that the ultimate constitution of matter, for example, is something more fluent and variable than the old orthodoxy supposed. Poincare was driven by the exigencies of his work into some inquiry into these laws, but he was not a professional philosopher, and did not attempt a metaphysic. His aim was humbler, to contribute something towards the methodology of science. Generally speaking, he took his philosophy straight from Kant, though lie seems to shrink from the rigidity of the Kantian a priori "forms."- But he always maintained that experience is organized mainly by the use of principles which at any particular moment cannot find precise confirmation by experi- enoe—which is not far from the Kantian a priori synthetic judgment It is more important to notice that his position, while critical, is not sceptical. The temptation, when the orthodox reconstruction is found wanting, is to dispense with the need of a reconstruction at all, and to fall into a sort of positivism, which is content with empirical knowledge and shy of anything which has not an immediate "cash value." Poincare, in discarding the old dogmatism, insisted • &tease and Method. By Henri Poinsan6. Translated by Francis Maitland. With a Preface by the Hon. Bertrand Russell, F.R.S. Loudon: Thomas Xelsoa and Sons. tee. net.] • upon the utility of theoretical constructions and the rights of the constructive reason. As Mr. Russell well says— "He was. in truth, no sceptic; however conscious of the diffi- culty of attaining knowledge, he never admitted its impossibility. 'It is a mistake to believe,' he said, 'that the love of truth is indistinguishable from the love of certainty' ; and again, ' To doubt everything end to believe everything are two equally convenient solutions • both dispense with the necessity of reflection.' His Was the active, eager doubt that inspires a new scrutiny, not the idle doubt that acquiesces contentedly in nascience." .
The book before us begins by discussing some of the methods of scientific inquiry in general, and then goes on to inquire into the methods, and occasionally into the results, of ' a few of the most recent speculations in mathematics, mechanics, and astronomy. The mathematical chapters are not always easy reading, except for the few who have habituated themselves to the modes of thought of Cantor and Hilbert, Peano and Dedekind. Poincare breaks a lance with Mr. Russell on his new mathematical logic, a dark mystery into which we do not dare to enter. He is not greatly in love with the language of symbols which Peano invented, in which the ordinary conjunctions of argument are represented by algebraical signs. "It is difficult," he says, "to admit that the word if acquires, when written ), a virtue it did not possess when written ' if.' " Signor Burali-Forti defines the number 1 thus :—
1=er'{ Ko n(u, ft) e (ue One},
a definition, says Poincare drily, "eminently fitted to give an idea of the number 1 to people who had never beard of it before." Some of his chapters might be described as "Just-so Stories" of science, explaining how we come by our simplest notions. Space, for example, is relative, for absolute space, in view of the movements of the earth and the solar system, is a phrase for mankind devoid of meaning. He explains why space for us must have three dimensions, and the reason lies not in anything in space by itself, but in our human intelligence. From our most elementary consciousness we derive certain spatial associations, and we resist any attempt to dissociate what has so long been associated, The evidence for what we call the truths of geometry rests on that resistance and on nothing else. But it is possible to "conceive of think- ing beings, living in our world, whose distribution board would have four dimensions, who would, consequently, think in hyperapace." Elsewhere he leads us within sight of some of the startling paradoxes of recent speculation. It is possible, according to Lorentz and Fitzgerald, that all bodies carried forward in the earth's motion undergo a deformation. A. yard measure of land parallel with the earth's motion is slightly smaller than if it were perpendicular. In physics, the discovery of radium has upset many doctrines, and rehabili- tated the old alchemist's dream of the transmutability of metals. It has also played havoc with the fundamental laws of mechanics. Mass, for example, instead of being a constant, is only an appearance. It increases with the velocity, and, "while apparently constant for velocities up to six hundred miles a second, it grows thenceforward, and becomes infinite for the velocity of light." Again, action and reaction are not always equal, for in certain cases there is no reaction. Even the famous doctrine of the conservation of energy under certain conceivable conditions becomes untrue. Such conclusions give the reader the sense of walking on the crust of a volcano, but Poineard has comfort for ,the plain man. If the tape which measures your carpet lying parallel to the earth's motion shrinks, so also does the carpet, so there is no inconvenience; and as for the laws of mechanics, they are still maintained in all the conditions under which man conducts his life. " Whatever be the progress of motoring, our cars will never attain the velocities at which its laws cease to be true." He only gives these instances to prove the need for humility in our theoretical constructions of the world.
These are questions in the methods of special sciences, but the most valuable part of the book to the ordinary reader is Poincare's discussion of the general method of all scientific discovery. His view may be best stated in his own words :— "There is a hierarchy of facts. Some are without any positive bearing, and teach in nothing but themselves. The scientist who ascertains them learns nothing but facts, and becomes no better able to foresee new facts. Such facts, it seems, occur but once, and are not destiaed to be repeated. There are, on the other band, facts that give a large return, each of which teaches ne a new law. And since he is obliged to make a selection, it is to these latter facts that the scientist must devote himself."
The facts that give ns small returns are those which appear complex, where the circumstances that influence them are endless The repaying facts appear simple, either because they are really influenced only by a few well-defined circum- stances, or because, if they are influenced by many, these many are controlled by the laws of chance. On chance Poincare has an exceedingly interesting and acute chapter. Chance is the salvation of the inquirer, and the operation of its laws is largely dependent upon the complexity of the circumstances. It is complex causes which produce a certain uniformity. The problem is most difficult when tbe conditions are too simple, for it means that something of the original state is preserved as an invariable, and this checks the approxima- tion towards uniformity which permits the laws of chance to be applied. In fact, in these inquiries it is in our very ignorance that our safety lies. If we approached omniscience and knew anything like all the conditions we should be baffled ; it is because we know so little that we can trust to the laws of probabilities. A manage r of an insurance company does.not know when each of the assured will die, but, resting on the law of large numbers, he makes no mistake so far as the general success of the business goes. If a very clever doctor gave him informa- tion about the chance of life of each person, he would know more, but the knowledge would not affect the dividends. The success of his business is based on a certain kind of know- ledge—the knowledge of general laws—and it is the complexity of the conditions which makes him have recourse to them, instead of muddling his head with special reports on each assured life from month to month. So in scientific inquiry our weakness turns out to be a very real convenience. Elsewhere Poincare insists upon the part which intuition and subconscious processes play in all investigations. His own account of bow he dis- covered Fuchsias functions is an illuminating picture of the mental processes of one who combined all the gifts of a man of science.
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