Chapter 3

Read the last first. Begin with "Creative Evolution", for this is the most comprehensive exposition of his philosophy and is written in a less technical style than his earlier works. But the reader must remember that a knowledge of these is presupposed, and Bergson has here taken for granted what he has written two other large volumes to prove; namely, that time cannot be adequately represented in the forms of space, and that mind is not rigidly bound to matter. Bergson is unexcelled by any modern philosopher except William James in brilliancy of style and originality of illustration. "Creative Evolution" treats of such a variety of questions, biological, psychological, and metaphysical, that any intelligent reader will find something in it that will arouse new trains of thought. And if the intelligent reader finds passages which he cannot understand, he may console himself with the reflection that there are others who have been likewise baffled. Count Keyserling, who has the brain of a German metaphysician, says of Bergson that "his philosophy is perhaps the most original achievement since the days of Immanuel Kant", but he adds, "Many thoughts on which Bergson appears to lay great weight arouse in me not the shade of an idea." But he ascribes Bergson's obscurity to the fact that "he does not start from abstract principles; he begins in direct consciousness, in concrete life", so perhaps the ordinary reader may have in this respect an advantage over a Kantian student like Count Keyserling.

The student of philosophy may prefer to trace the development of Bergson's thought in its logical and chronological order. He will in that case begin with the "Essai sur les donnés immédiates de la conscience" (1889), and proceed to "Matière et Mémoire" (1896), and end with "Evolution créatrice" (1907). These are published by Félix Alcan, Paris, in his "Bibliothèque de Philosophie contemporaine." The "Essay on the Immediate Data of Consciousness" appears under the less cumbrous title of "Time and Free Will" in the translation of F. L. Pogson (Macmillan). "Matter and Memory" is translated by Nancy Margaret Paul and W. Scott Palmer (Macmillan). It may not be improper to note that the British edition of the Essay costs nearly four times as much as the French and is twice as heavy. "Creative Evolution", translated by Arthur Mitchell, is printed in this country by Henry Holt & Company. Bergson's lecture on Dreams, translated by E. E. Slosson, is published in book form by B. W. Huebsch, New York.

Those who read French but do not wish to attack one of the larger works will find convenient the summary of his philosophy with illustrative selections made by one of his former pupils, René Gillouin, and published in "Les Grands Philosophes" by Louis Michaud, Paris. The German reader will find in A. Steenbergen's "Bergsons Intuitive Philosophie", Jena, an epitome and critique.

"Time and Free Will" contains an admirable bibliography, including the most important discussions of Bergson's philosophy that have appeared in eight languages up to 1911. The most interesting introduction to Bergson is the article published by Professor James in theHibbert Journal, April, 1909, and reprinted in hisPluralistic Universe. This has the advantage of M. Bergson's indorsement, for when Professor Pitkin of Columbia attempted to show that James was wrong in claiming Bergson as an ally ("James and Bergson, or Who is Against Intellect?" inJournal of Philosophy, Psychology and Scientific Method, April 28, 1910), Bergson replied that James had not misinterpreted him but had said what he meant in better words than his (sameJournal, July 7, 1910). Other brief expositions of Bergson's philosophy are the articles by H. Wildon Carr inProc. Aristotelian Society, 1909 and 1910, andHibbert Journal, July, 1910; by J. Solomon inMind,January, 1911 (both these now in book form also); by Arthur Balfour on "Creative Evolution and Philosophic Doubt" in the decennial number of theHibbert Journal; "Bergson's Philosophy and the Idea of God," by H. C. Corrance, and "Syndicalism in its Relation to Bergson," by T. Rhondda Williams, both inHibbert Journalof January, 1914. Professor Arthur O. Lovejoy of Johns Hopkins criticizes "The Practical Tendencies of Bergsonianism" in theInternational Journal of Ethics, April and July, 1913. Bergson's London lectures on the soul are summarized in theEducational Review, January, 1912. Santayana's "Winds of Doctrine" (Scribner) contains an interesting chapter on Bergson's philosophy.

Of the voluminous controversial literature in France it is only possible to mention a few recent titles: R. Gillouin, "La Philosophie de Bergson" (Grasset); J. Segond, "L'Intuition Bergsonienne" (Alcan); J. Desaymard, "La Pensée d'Henri Bergson" (Mercure de France). The most conspicuous of the opponents of Bergson are: René Berthelot in "Un Romanticisme utilitaire," tome II, "Le Pragmatisme chez Bergson" (Alcan); and Julien Benda in "Le Bergsonisme ou une Philosophie de la Mobilité", and "Réponse aux Défenseurs du Bergsonisme" (Mercure de France).

"Bergson for Beginners", by Darcy B. Kitchin (Macmillan) gives a summary of his works and adds some interesting observations on the relation of Bergson to the English philosophers James Ward and Herbert Spencer. Other recent expositions and criticisms are "The Philosophy of Bergson", by A. D. Lindsay; "A Critical Examination of Bergson's Philosophy", by J. McKellar Stewart; "An Examination of Professor Bergson's Philosophy", by David Balsillie; "Bergson and the Modern Spirit", by G. R. Dodgson (American Unitarian Assoc., Boston). But the best volume to serve as an introduction to Bergson is that previously mentioned, "The New Philosophy of Henri Bergson", by Edouard Le Roy (Holt).

A list of the most important of the books and articles on the subject in all languages up to 1913 comprising more than five hundred titles was published by the Columbia University Press on the occasion of Bergson's visit, "A Contribution to a Bibliography of Henri Bergson."

[1]Reported in theBulletin de la Société française de Philosophie, 1908.

[2]For his views on the possibility of scientific metaphysics, seeLe Parallélisme psycho-physique et la métaphysique positiveinBulletin de la Société française de Philosophie, June, 1901; andIntroduction à la métaphysiqueinRevue de Métaphysique et de Morale, January, 1903.

[3]Published in theRevue scientifique, June 8, 1901, and in English inThe Independent, October 23-30, 1913, and in book form, 1914.

[4]Articles on pragmatic Catholicism may be found in almost any volume of theRevue Philosophiqueand theRevue de Métaphysique et de Moraleduring the first twelve years of the twentieth century. See especially those by Edouard Le Roy, a disciple of James and Bergson. A brief account of the movement is contained in Lalande's "Philosophy in France, 1907",Philosophical Review, May, 1908.

[5]As representatives of the pragmatic syndicalists may be mentioned George Sorel and Edouard Berth. For an account of the philosophical side of the movement, seeSyndicalistes et Bergsoniensby C. Bougie inRevuedu Mois, April, 1909.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and of appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp. This it is which gives body, a structure so to speak, to the iridescent appearances which flatter our senses, and without this support the beauty of these fugitive dreams would be only imperfect, because it would be vague and always fleeting. On the contrary, intellectual beauty is sufficient unto itself, and it is for its sake, more perhaps than for the future good of humanity, that the scientist devotes himself to long and difficult labors.It is, therefore, the quest of this special beauty, the sense of the harmony of the cosmos, which makes us choose the facts most fitting to contribute to this harmony, just as an artist chooses from among the features of his model those which perfect the picture and give it character and life. And we need not fear that this instinctive and unavowed prepossession will turn the scientist aside from the search for the true. One may dream a harmonious world, but how far the real world will leave it behind! The greatest artists that ever lived, the Greeks, made their heavens; how shabby it is beside the true heavens, ours!—Poincaré's "The Value of Science," p. 8.

It is, therefore, the quest of this special beauty, the sense of the harmony of the cosmos, which makes us choose the facts most fitting to contribute to this harmony, just as an artist chooses from among the features of his model those which perfect the picture and give it character and life. And we need not fear that this instinctive and unavowed prepossession will turn the scientist aside from the search for the true. One may dream a harmonious world, but how far the real world will leave it behind! The greatest artists that ever lived, the Greeks, made their heavens; how shabby it is beside the true heavens, ours!—Poincaré's "The Value of Science," p. 8.

Such language as this is extremely disconcerting to those who hold the popular notion of science and scientists; regarding science as a vague impending mass of solid fact, immutable, inexorable, threatening the extinction of all such things as art, sentiment, poetry, and religion, only to be diverted by a determination to remain ignorant of it; regarding men of science as mere calculating machines, mechanically grinding out logical grist for utilitarian purposes. Mathematical astronomy is surely one of the sciences, the most rigid, remote, and recondite of the sciences. Yet here is the leading mathematical astronomer of the age talking about it as though it were one of the fine arts, a thing of beauty that the artist creates for his own delight in the making of it and shapes in accordance with his own ideas of what is harmonious.

Now we cannot throw out of consideration M. Poincaré's opinion, on the ground that he did not know what he was talking about. A man who has made as much science as he has ought to know how science is made, and what for. To most of us nature—or to avoid hurting our own feelings let us rather say, opportunity—has denied the privilege of knowing this by experience. Consequently M. Poincaré is an especially interesting man to study, for he has been willing to tell us not only what a man of science is, but also how it feels to be one. No other contemporary of equal eminence has been so frank and accommodating in the self-revelation of his methods or so willing to submit himself as a subject of observation. We are admitted to the laboratory of a mathematician, and we can watch the mechanism of scientific thought in action.

So far as he is concerned, he has repudiated the idea that science is purely utilitarian in the most emphatic language. August Comte said that it would be idle to seek to know the composition of the sun, since this knowledge would be of no use to sociology. Against such a charge of uselessness Poincaré eloquently defended his science by showing the practical value of astronomy even from Comte's point of view, but in conclusion asserted his own opinion very plainly:

Was I wrong in saying that it is astronomy which has made us a soul capable of comprehending nature; that under heavens always overcast and starless, the earth itself would have been for us eternally unintelligible; that we should there have seen only caprice and disorder; and that, not knowing the world, we should never have been able to subdue it? What science could have been more useful? And in thus speaking I put myself at the point of view of those who only value practical applications. Certainly, this point of view is not mine; as for me, on the contrary, if I admire the conquests of industry, it is, above all, because they free us from material cares, they will one day give to all the leisure to contemplate nature. I do not say: Science is useful, because it teaches us to construct machines. I say: Machines are useful, because in working for us, they will some day leave us more time to make science. But finally it is worth remarking that between the two points of view there is no antagonism, and that man having pursued a disinterested aim, all else has been added unto him.—"Value of Science", p. 88.

It is this insistence upon the æsthetic value of science that caused him to shrink from being called a "pragmatist", although those who accept that name have always laid unusual stress upon the æsthetic factor in thinking. But in his theory of knowledge Poincaré is decidedly pragmatic, and no one has given a clear exposition or stronger expression to the practical mode of thought by which the natural sciences have made their progress and which is now being extended to the fields of metaphysics, religion, ethics, and sociology. Poincaré's favorite word is "convenient" (commode). Theories are strictly speaking not to be classed as true or false. They are merely more or less convenient. For example:

Masses are coefficients it is convenient to introduce into calculations. We could reconstruct all mechanics by attributing different values to all the masses. This new mechanics would not be in contradiction either with experience or with the general principles of dynamics. Only the equations of this new mechanics would beless simple.—"Science and Hypothesis", p. 76.We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them. But what is the nature of these rules? No general rule, no rigorous rule; a multitude of little rules applicable to each particular case. These rules are not imposed upon us, and we might amuse ourselves by inventing others; but they could not be cast aside without greatly complicating the laws of physics, mathematics, and astronomy. We therefore choose these rules, not because they are true, but because they are most convenient, and we may recapitulate them as follows: "The simultaneity of two events or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible; in other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."—"Value of Science", p. 35.Time should be so defined that the equations of mechanics may be as simple as possible. In other words, there is not one way of measuring time more true than another. That which is generally adopted is only moreconvenient. Of two watches, we have no right to say that one goes true, the other wrong: we can only say that it is advantageous to conform to the indications of the first.—"Value of Science", p. 30.Behold then the rule we follow and the only one we can follow: when a phenomenon appears to us as the cause of another, we regard it as anterior. It is therefore by cause we define time.—"Value of Science", p. 32.Experience does not prove to us that space has three dimensions. It only proves to us that it is convenient to attribute three dimensions to it.—"Value of Science", p. 69.It has often been observed that if all the bodies in the universe were dilated simultaneously and in the same proportion we should have no means of perceiving it, since all our measuring instruments would grow at the same time as the objects themselves which they serve to measure. The world, after this dilatation, would continue on its course without anything apprising us of so considerable an event. —"Value of Science", p. 39.

We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them. But what is the nature of these rules? No general rule, no rigorous rule; a multitude of little rules applicable to each particular case. These rules are not imposed upon us, and we might amuse ourselves by inventing others; but they could not be cast aside without greatly complicating the laws of physics, mathematics, and astronomy. We therefore choose these rules, not because they are true, but because they are most convenient, and we may recapitulate them as follows: "The simultaneity of two events or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible; in other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."—"Value of Science", p. 35.

Time should be so defined that the equations of mechanics may be as simple as possible. In other words, there is not one way of measuring time more true than another. That which is generally adopted is only moreconvenient. Of two watches, we have no right to say that one goes true, the other wrong: we can only say that it is advantageous to conform to the indications of the first.—"Value of Science", p. 30.

Behold then the rule we follow and the only one we can follow: when a phenomenon appears to us as the cause of another, we regard it as anterior. It is therefore by cause we define time.—"Value of Science", p. 32.

Experience does not prove to us that space has three dimensions. It only proves to us that it is convenient to attribute three dimensions to it.—"Value of Science", p. 69.

It has often been observed that if all the bodies in the universe were dilated simultaneously and in the same proportion we should have no means of perceiving it, since all our measuring instruments would grow at the same time as the objects themselves which they serve to measure. The world, after this dilatation, would continue on its course without anything apprising us of so considerable an event. —"Value of Science", p. 39.

But Poincaré goes farther and shows not only that two such worlds of different sizes would be absolutely indistinguishable, but that they would be equally indistinguishable if they were distorted in any manner so long as they corresponded with each other point by point. This conception of the relativity of space may be thought a little hard to grasp, but M. Poincaré is kind enough to suggest a way by which any one may see it for himself if he has ten cents to admit him to one of those hilarious resorts where life-size concave and convex mirrors are to be seen.[1]You may think yourself a gentleman of proper figure, that is to say, somewhat portly, and you look upon the tall slim shape that confronts you in the cylindrical mirror as absurdly misshapen. But you would find it difficult to convince him of his deformity. His legs, as well as yours, fulfill the requirement that Lincoln laid down as their proper length; that is, they reach from the body to the ground. If you touch your chin with your thumb and your brow with your forefinger, so does he. It occurs to you that here is a case where your knowledge of geometry would, if ever, prove useful, but when you appeal to it, you will find that the geometry of his queer-looking world is just as good as yours; in fact, is just the same. You get a foot rule and measure yourself; 70 inches high, 14 inches in diameter at the equator, ratio 5:2. But meanwhile the mirror man is also measuring himself, and his dimensions come out exactly the same as yours, 70 and 14 and 5:2, for when he holds the rule perpendicular it lengthens and when horizontal it shrinks. Lines that in your world are straight are curved in his, but you cannot prove it to him, for when he lays his straightedge against these curves of his, behold it immediately bends to correspond. By this time, finding it so difficult to prove to the mirror man that you are right and he is wrong, it occurs to you that perhaps he isn't, that he may have just as much reason as you for believing that his is the normal, well-proportioned world, and yours the distorted image of it. Since, then, you have no way of perceiving the absolute length, direction, or curvature of a line, your space may be as irregularly curved and twisted as it looks to be in the funniest of the mirrors, and you would not know it. Now the principle of the pragmatist is that anything that does not make any difference to anything else is not real. The reason why we have not been able to discover any differences between the mirror space and our space, each considered by itself, is because there is none. Or to return to the language of Poincaré, "space is in reality amorphous and the things that are in it alone give it a form." Why do we say that space has three dimensions instead of two or four or more? Why do we stick to an old fogy like Euclid when Riemann and Lobachevski proffer us new and equally self-consistent systems of geometry wherein parallels may meet or part? Because:

by natural selection our mind hasadapteditself to the conditions of the external world. It has adopted the geometrymost advantageousto the species or, in other words,the most convenient. Geometry is not true, it is advantageous.

Such language may pass without notice in university halls, for all scientists are more or less clearly conscious of the provisional and practical nature of the hypotheses and conventions they employ. But to the outside world it sounds startling. To some it seemed that the foundations of the universe were being undermined. Others saw in it a confession of what Brunetière had called "the bankruptcy of science" and openly rejoiced over the discomfiture of the enemy of the Church. Now Poincaré had chanced to use in discussing the relativity of motion the following illustration:

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence. Hence this affirmation "the earth turns round" has no meaning, since it can be verified by no experiment; since such an experiment not only could not be either realized or dreamed by the boldest Jules Verne but cannot be conceived of without contradiction. Or rather these two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.—"Science and Hypothesis", p. 85.

This remark was at once seized upon by the Catholic apologists, and the Galileo case, once closed by the voice of Rome, was reopened for the admission of this new evidence. If the Ptolemaic and the Copernican theories are equally true, and the choice between them is merely a matter of expediency, was not the Holy Inquisition justified in upholding the established theory in the interests of religion and morality? Monsignor Bolo, an eminent and sagacious theologian, announced inLe Matinof February 20, 1908, that M. Poincaré, the greatest mathematician of the century, says that Galileo was wrong in his obstinacy. To this Poincaré replied in the whispered words of Galileo:

"E pur si muove, Monseigneur"?

In a later discussion of the point, he explains that what he said about the rotation of the earth could be equally well applied to any other accepted hypothesis, even the very existence of an external world, for "these two propositions, 'the external world exists' or 'it is more convenient to suppose that it exists' have one and the same meaning." The Copernican theory is the preferable because it has a richer, more profound content, since if we assume the earth is stationary we have to invent other explanations for the flattening at the poles, the rotation of Foucault's pendulum, the trade winds, etc., while the hypothesis of a revolving earth brings all these together as the effects of a single cause.

M. Le Roy, a Catholic pragmatist and a disciple of Bergson's, goes much further than Poincaré in regard to the human element in science, holding that science is merely a rule of action and can teach us nothing of truth, for its laws are only artificial conventions. This view Poincaré considered to be dangerously near to absolute nominalism and skepticism, and in his controversy with Le Roy[2]he showed that the scientist does not "create facts as Le Roy said, but merely the language in which he enunciates them." Of the contingence upon which Le Roy and Boutroux insist, Poincaré would admit only that scientific laws can never be more than approximate and probable. Even in astronomy, where the single and simple law of gravitation is involved, neither absolute certainty nor absolute accuracy can be attained. Therefore we cannot safely say that at a particular time Saturn will be at a certain point in the heavens. We must limit ourselves to the prediction that "Saturn willprobablybenear" such a point.

In an address before the International Philosophical Congress at Bologna in April, 1910, Professor Poincaré discussed again the question of whether the laws of nature may not change. He admitted that there is not a sole law that we can enunciate with the certainty that it has always been true in the past. Nevertheless, he concluded, there is nothing to hinder the man of science from keeping his faith in the principle of immutability, since no law can descend to the level of a secondary and limited law without being replaced by another law more general and more comprehensive. He considered in particular the possibility that in the remote past the fundamental laws of mechanics would not hold, for since the energy of the world has been continually dissipating in the form of heat there must have been a time when bodies moved faster than they do now. But according to the recent theories of matter, no body can travel faster than light, and with velocities approaching that of light its mass is no longer constant but increases with its velocity. This, of course, would play havoc with all of Newton's laws, which then we should have to regard as limited in their scope to such ordinary conditions and moderate motion as we see about us now.

But even at present we can hardly regard them with the same implicit confidence as formerly. Take, for example, Newton's law that action and reaction are equal and opposite. When a ball is fired from a cannon, the cannon recoils at the same time and with the same momentum that the ball goes forward. But suppose instead of a cannon we have a lamp with a reflector sending a beam of light into space. It has been deduced mathematically and proved experimentally that light exerts a minute but measurable pressure on an object which it strikes. The reflector therefore recoils like the cannon, but where is the ball if light is an immaterial wave motion? To be sure, if the ray of light strikes some planet out in space, it would give it an impulse equal and opposite to that originally imparted to the reflector on our earth. But what if the light goes on through vacant space and never hits anything at all? A law that may have to wait several thousand years for its validation and may even fail of it altogether is not what the layman has in mind when he thinks of immutable and infrangible laws governing the universe.

But it is rather important just now that the layman gets to understand what the scientist means when he talks of laws, theories, and hypotheses. For we are in the midst of a stupendous revolution in science. Our nicely arranged nineteenth century cosmos seems to be dissolving into chaos again. We have seen the elements melt with fervent heat and we can no longer rely upon the uniformity of atomic weights. The laws of the conservation of matter and energy, which were the guiding stars of research to the last generation, are becoming dimmed. The old-fashioned ether, in its time a useful but never entirely satisfactory contrivance, for it had to be patched up repeatedly with divers new properties to enable it to bear the various duties thrust upon it, seems no longer competent to stand the strain and may have to be sent to the scientific scrap-heap at any moment. We hear physicists of supposed sanity assert that all bodies contract in the direction of their motion and that their weight varies with their speed and the direction in which they are going. We read of "atoms of light," and of corpuscles of electricity which, though they are but a thousandth part of the hydrogen atom, are caught and counted and weighed one by one.

Now what puzzles the lay mind is the calmness with which the scientists survey this crash of worlds and shock of systems. They do not have the mien of exposed impostors. They are not, like the augurs of decadent Rome, unable to meet without laughing in each other's faces. They do not resent the overthrow of their former idols. They have no fear of heretics, consequently no hatred for them. They regard all this iconoclasm with a mild curiosity quite in contrast to their intense and personal interest in science generally. It is hard to get out a quorum at the Association for the Advancement of Science to hear a discussion of the principle of relativity with all its revolutionary consequences.

Compare this apparent indifference to the fate of fundamental principles in scientific circles with what would happen in a Presbyterian assembly if it should be proposed to eliminate predestination from the Westminster Confession or in an Episcopal convocation if the Virgin Birth were denied; with what would happen in a stockholders' meeting if doubt were expressed as to the rights of capital, or in a socialist convention if the class conflict were questioned. Now the existence of the ether has the same importance to scientific thought that predestination has to theological or capitalism to economic thought. Its refutation or modification would be quite as upsetting to faith and practice. Yet scientists are men; they have red blood in their veins, and it not infrequently shows in their cheeks when they debate something that seems to them worth while. Pure theory rarely seems to them worth while because it is recognized as pure conventionality and convenience.

The scientific man, especially the scientific investigator, holds his theories with a light hand, but keeps a firm grip on his facts. This is just the opposite of the lay attitude toward science. If the layman is interested in knowing the speed of light, it is because he thinks that he learns from it that all space is filled with a rigid elastic solid, at which he cannot but wonder. The scientist is interested in the ether because it helps him in his calculation of the speed of light.

A lecturer on wireless telegraphy will use in the course of the hour two or three more or less contradictory conceptions of electricity. If afterward you call his attention to the inconsistency and ask him which is right and which is wrong, you will not get a very satisfactory answer. He does not know and obviously does not care. You insist upon his telling you which theory he personally believes in. He really had not thought of "believing" in any of them. If he uses white chalk on the blackboard in preference to red, it is not because he denies the existence of red chalk and its occasional usefulness. So, too, the astronomer will speak of the sun's rising and in the next breath of the earth's turning toward the sun, quite innocent of his inconsistency. The botanist alludes to a certain flower as a poppy and again as Eschscholtzia. He means the same thing but is using different languages; in the first case English, in the second case I don't know what.

It is eminently desirable that people should have faith in science, but in order to do that they must have the same sort of faith in it that the scientist has. Otherwise they will regard it as a lot of ingenious fancies which are proved false by each succeeding generation. Science is moulting just now and looks queer. The public ought to understand clearly that the process means growth and not disease. There is another reason now for the popularization of the scientific mode of thought. It is beginning to be applied where entirely different conceptions have so far prevailed—to art, ethics, religion, sociology, and the like. This is already arousing a great commotion and will cause more before the process is complete. It will, for example, involve the rewriting and to a large extent the reinvestigation of history. Poincaré has hinted at this in a passage which seems to me of very great significance:

Carlyle has somewhere said something like this: "Nothing but facts are of importance. John Lackland passed by here. Here is something that is admirable. Here is a reality for which I would give all the theories in the world." Carlyle was a fellow countryman of Bacon, but Bacon would not have said that. That is the language of the historian. The physicist would say rather: "John Lackland passed by here. That makes no difference to me for he never will pass this way again."—"Science and Hypothesis", p. 102.

The aim of science is prevision, and I believe that this will eventually be recognized as the true aim of all knowledge. The historian, or let me say rather the antiquarian, for the historian may have the scientific temperament, values facts for their rarity. The scientist values facts for their commonness. A unique fact, if there be such, would have no possible interest to him. The antiquarian goes about looking for things, facts, or furniture, which have been of importance in the past. The scientist is looking only for things that will be of importance in the future.

According to Poincaré, the proper choice of facts is the first duty of the scientist. He must be able to pick out the significant and reject all the rest. "Invention consists in avoiding the constructing of useless combinations and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose." It is most desirable to bring together elements far distant from one another. Such unions are mostly sterile, but when this is not the case, they are the most fruitful of all. The successful scientist does not, like a shopper, look over one by one all available samples and pick out what he wants. Life is too short. The unsuitable ideas do not even present themselves to his mind. It is as if he were an examiner of second resort who only concerns himself with the candidates who have passed the first test. This preliminary sifting and sorting process is done largely by the unconscious mind, as Poincaré shows by telling how he came to make his first mathematical discoveries:

For a fortnight I labored to demonstrate that there could exist no function analogous to those that I have since called the fuchsian functions.[3]I was then very ignorant. Every day I seated myself at my work table and spent an hour or two there, trying a great many combinations, but I arrived at no result. One night when, contrary to my custom, I had taken black coffee and I could not sleep, ideas surged up in crowds. I felt them as they struck against one another until two of them stuck together, so to speak, to form a stable combination. By morning I had established the existence of a class of fuchsian functions, those which are derived from the hyper-geometric series. I had merely to put the results in shape, which only took a few hours.—"Science et Méthode", p. 52.

After working out the deductions from this discovery, he went on a geological excursion of the School of Mines. The distractions of travel took his mind from his mathematical labor. But at Constance, just as he was stepping into an omnibus for some excursion, the idea occurred to him, without any connection with his previous thoughts, that his fuchsian functions were identical in their transformations with those of the non-Euclidian geometry. He took his seat in the omnibus and continued his conversation, feeling absolutely certain of his discovery, which he worked out at his leisure on his return to his home at Caen.

He next devoted himself to the study of arithmetical questions, without reaching any results of importance and without suspecting that this subject could have the slightest connection with his earlier researches. Disgusted at his lack of success, he went to pass some days at the seashore, where he was occupied with other things. One day as he was walking on the cliff, the thought came to him, brief, sudden, and certain as usual, that he had been employing the same transformations in his arithmetical and geometrical work.

He thereupon went back to Caen and undertook the systematic application of his theory. But he was stopped by an insurmountable obstacle, and while in this perplexity he was called away to his military service at Mont-Valérien, where he had no time for mathematics. One day while walking on the street, the solution of the difficulty appeared to him in a flash. He did not try to think it out at the time, but after his release from the army, he completed his memoir without trouble.

These fascinating glimpses into the soul of a mathematician will remind the reader of many other instances of such subconscious assistance on record and doubtless of personal experiences as well. We think of Alfred Russel Wallace at Ternate, his brain inflamed with tropical fever, seized with the sudden inspiration of the theory of natural selection, the key to the biological problems which had perplexed him for so many months. How fortunate that his clerical opponents did not know of this and so could not dismiss evolution as the dream of a diseased imagination. But as James says in his "Varieties of Religious Experience", we have no right to discountenance unwelcome theories as feverish fancies, since for all we know 102° may be a more favorable temperature for truth to germinate and sprout in than the ordinary bloodheat of 98°.

We are reminded, too, of Kekulé of Bonn puzzling over the constitution of benzene, trying in vain to satisfy six carbon atoms with six hydrogen atoms when they wanted fourteen. In the evening as he sat by the fire, his wearied brain refused to rest, and he seemed to see the four-handed carbon imps dancing with their one-armed hydrogen partners on the floor. Suddenly six of them joined hands in a ring and the problem was solved. Since then the benzene sextet has been dancing through hundreds of volumes and has added millions annually to the wealth of Germany. Professor Hilprecht of the University of Pennsylvania has told how a Chaldean priest, custodian of the "Temple Library", appeared to him in a dream and showed him how to put together the fragments of a cuneiform inscription which he had for a long time been striving in vain to translate.

Then there was Stevenson in Samoa, writing for dear life, but not failing to give credit to his "brownies" for doing a large part of his work for him. But the brownies do not work unbidden, and they will not make bricks without straw. Poincaré insists upon the necessity of the preliminary period of conscious effort without which these subliminal inspirations never come and the subsequent period of verification, development, and application, without which they are fruitless. Such ideas came to him most often in the evening or morning when he was in bed and half awake. He did not regard the operations of his unconscious mind as merely mechanical. On the contrary, it is distinguished by the power of choice, selecting and presenting to the conscious ego only those combinations that seem profitable and important. This choice is made, in Poincaré's opinion, under the guidance of the artistic instinct.

The usual combinations are precisely the most beautiful; I mean those which can best charm that special sensibility which all mathematicians recognize but at which the profane are tempted to smile. Among the numerous combinations which the subliminal self has blindly formed, almost all are without interest and without utility. For that reason they have no action upon the æsthetic sensibility and never come into consciousness. Only those that are harmonious and consequently both useful and beautiful are capable of moving that special sensibility of the geometrician of which I spoke, and which, once excited, calls our attention to them and so gives them the chance to become conscious.—"Science et Méthode", p. 58.

Poincaré, if we may believe what he says on this point, was a poor chess player and absolutely incapable of adding up a column of figures correctly. But the reader should beware of the common fallacy of reversing a proposition of this kind and assuming that if he, too, makes mistakes in addition he has the mind of a great mathematician. Poincaré's memory was, however, exceptionally good, especially for figures and formulas. On returning from a walk he was able to recall the numbers of the carriages he had met. When he was in the Polytechnic School he followed the courses in mathematics without taking a note and without looking at the syllabus provided by the professor. He was a rapid mental calculator, using auditive imagery rather than visual. He associated colors with the sound of words.[4]

In this connection may be quoted an anecdote told by M. Jules Sageret:[5]At aconférencein the Superior School of Telegraphy the director called upon him to discuss a very difficult problem in the propagation of the electric current. Poincaré complied and solved the problem without taking any time in preparation. After theconférencethe director felicitated him on the solution. "Yes," said Poincaré, "I found the value ofx, but is it in kilograms or kilometers?"

Poincaré did not find it profitable to work more than two hours at a time. His custom was to stay at his desk from ten o'clock to noon and from five to seven in the afternoon, never working in the evening after dinner. He drank wine at meals, but never smoked. He went to bed at ten and rose at seven, but did not sleep soundly.

He was a blond, five feet five inches in height and weighed 154 pounds. His head was unusually large, especially in breadth. His eyes were myopic and unsteady. He stood stoopingly with his wrinkled forehead upturned. He spoke somewhat slowly and with a distraught air, as though he were thinking of something else, even though he might be at the time interested and keenly observant. He talked English and German readily and read Latin and Italian. He was fond of music, especially Wagner.

Of the absent-mindedness that had been characteristic of him from youth, many stories are told. Like most mathematicians he was fond of walking while thinking, his fingers opening and closing in an unconscious gesture. One day on his return from a walk he was surprised to find that he was carrying a wicker cage, new and happily empty. He could not imagine how he had got it, but retracing his steps he found upon the sidewalk the stock of the basket maker whom he had innocently despoiled.

When as an engineering student he made a trip to Austria, his mother was afraid he would drop his portfolio sometime without noticing it. So, realizing doubtless that his memory was auditory, she sewed little bells on it. The plan was successful. His mother found on his return that he had brought back in his valise not only the portfolio but also an Austrian bed sheet neatly folded, which, some morning, he had mistaken for his night clothes.

These and similar anecdotes were told by M. Frédéric. Masson when he welcomed M. Poincaré into the Académie Française, January 28, 1909,[6]and it must have been a trifle embarrassing to the new member to listen to such a minute analysis of his life and character addressed to him in the second person. How deftly the director of the Academy mingled eulogy and raillery may be seen from a quotation:

"You did not delay revealing your vocation and will be justly cited as the most precocious of infant prodigies. You were nine months old when for the first time as night came your eyes were directed toward the sky. You saw there a star light up. You persistently pointed it out to your mother, who was also your nurse. Then you discovered another with some astonishment, and your reason cried 'Enco lo la bas!' A third, a fourth, more cries of joy and equal enthusiasm. You had to be put to bed because you became so excited discovering stars. That evening was your first contact with the infinite, and you had inaugurated your courses in astronomy, the youngest professor known."

Henri Poincaré was born April 29, 1854, at Nancy, where his ancestors had long been established. His grandfather was a pharmacist and his father a physician of more than usual scholarship. The name, he said, was originally Pontcaré, for, one can imagine a square bridge but not a square point. But the philologists who took the question up discovered in the register of the university a student named "Petrus Pugniquadrati" in 1403 and "Jehan Poing-quarré" in 1418, so the name Poincaré meant "clenched-fist." His cousin, Raymond Poincaré, son of a distinguished engineer, has long been one of the most prominent figures in the political world, a member of the Academy, senator, minister, and is now president of the French republic.

In the Nancylycéehe led all his classes and showed a special aptitude for history and literature. At the age of thirteen he composed a five-act tragedy in verse, and since he was a Lorrainer, the heroine was of course Jeanne d'Arc. But as soon as he caught sight of a geometry, his true vocation became apparent. His instructor ran to his home and announced to his mother: "Madame, your son will be a mathematician."

Passing through the Polytechnic School he entered the National School of Mines, and for a few years after graduation he served as engineer in the Government departments of mines and railroads. At the age of twenty-seven he was called to a chair of mathematics in the University of Paris, where he remained, also filling the positions of Professor of Astronomy in the Polytechnic School and Professor of Theoretical Electricity in the Professional School of Posts and Telegraphs. He was received into the Academy of Sciences at the early age of thirty-two, and at the time of his election to the French Academy he had been honored by election to membership by thirty-five foreign academies. He took his seat in the Académie française very appropriately as the successor of Sully-Prudhomme, who likewise was an engineer by profession and a philosopher by temperament. To Poincaré as well as to Sully-Prudhomme, science appealed to the æsthetic sense as a thing of beauty and an inspiration to the imagination.

He married at the age of twenty-seven and had four children, three daughters and a son. His younger sister is the wife of the philosopher, Émile Boutroux, well known in this country from the lectures he gave at Harvard and Princeton.

Poincaré was influential in introducing improved methods in teaching mathematics, promoting the use of natural and dynamical methods instead of the abstract and static methods of Euclid and Legendre. He was skeptical in regard to religion and indifferent to politics. When called upon to contribute to a symposium on the old question of the scholar in politics,[7]he responded that savants like all citizens ought to interest themselves in the affairs of the country. But politics has become a profession, and a savant who entered into it would have to devote half his time to public business if he would be useful and the other half to his constituents if he wished to keep his seat, so he would have no time for science.

When asked for his opinion on woman suffrage,[8]he replied as follows:

I see no theoretical reason for refusing the political suffrage to women, married or not. They pay taxes the same as men, and they contribute their sons, so it is even heavier upon them than upon men. Perhaps woman suffrage is the sole means of combating alcoholism. I fear only the clerical influence over women.

Of the achievements that have given M. Poincaré his world-wide fame I am not competent to speak. Readers who would know the significance and value of his work on fuchsian, hyper-fuchsian, theta-fuchsian, abelian, and elliptical functions must go further for the information. I can only quote the opinions of those most competent to express an opinion as to his contributions to science. In 1905 he received the Bolyai Prize of ten thousand crowns, which is awarded by the Hungarian Academy of Sciences every five years for the best work in mathematics done during that period. The official report by Gustave Rados begins as follows:

"Henri Poincaré is incontestably the first and most powerful investigator of the present time in the domain of mathematics and mathematical physics. His strongly marked individuality permits us to recognize in him a savant endowed with intuition, who knows how to draw from the exhaustless well of geometrical and mechanical intuitions the elements and the origins of his profound and penetrating researches, yet using besides the most admirable logical power in working out his conceptions. In addition to his brilliant inventive genius we must recognize in him an ability for the finest and most fruitful generalizations of mathematical relations, which has often enabled him to push back, far beyond the point where others have hitherto been stopped, the limits of our knowledge in different branches of pure and applied mathematics. This was shown already in his first work on automorphic functions with which he began the series of his brilliant publications which must be classed with the greatest mathematical discoveries of all time."

In this country Poincaré has become known largely through the efforts of Professor George Bruce Halsted of the State Normal School of Greeley, Colorado, who has translated his philosophical works and has for many years been indefatigable in spreading the new gospel of the non-Euclidian geometry. Professor Halsted has at my request kindly contributed the following account of one of Poincaré's astronomical triumphs and of the visit that Professor Sylvester of Johns Hopkins paid to Poincaré many years ago:

"The kernel of Poincaré's power lies in an oracle Sylvester often quoted from Hesiod: Only the genius knows how much more the part is than the whole. He penetrates at once the divine simplicity of the perfectly general case, and thence descends, as from Olympus, to the special concrete earthly particulars. Thus his memoir of 1885, which Sir George Darwin says came to him as a revelation, on a rotating fluid mass, and his book 'Les Méthodes nouvelles de la Mécanique céleste,' 1892-1899, were ready with prevision when the shocking special case occurred of Phoebe, ninth satellite of Saturn, discovered in 1900, afterward found, incredible as it seemed, to be revolving in the direction contrary to that of all the others. It follows that Saturn himself originally rotated in the reverse direction. Again, on February 29, 1908, was found an eighth satellite of Jupiter, Jviii, revolving round Jove in the shocking Phoebe retrograde direction. Zeus must have turned over. All the planets have turned over, and some are now making another somersault. Moreover, Jviii does not even revolve in a closed orbit; its path is an open twister of unreturning turns.

"For Poincaré the inexhaustible source, the lamp of Aladdin, has ever been the non-Euclidian geometry. In him the Bolyai-Lobachevski-Riemann germ flowers fair.

"Personally Poincaré is the most lovable of men. At our very first meeting I realized that I had already been intimately associated with him for two years in the person of Sylvester. I told him the story of Sylvester's discovery of him, and he showed me how vividly and tenderly reconnaissant he was toward the great old master.

"Midsummer, and up a stuffy Paris stairway labors a giant gnome, beard on enormous chest, fortunately no neck, for no neck could upbear such a monstrous head, bald but for the inverted halo of hair collaring its juncture with the broad shoulders; small inefficient hands holding big hat and damp handkerchief; breath puffing with the heat and exertion. It is Sylvester, self-driven to seek out the source of new creations strangely akin to his own. At the sought door, open, he pauses, seized by doubt, the person within is so young, so slight, so dazed. Can this be the new incarnation of the eternal world-genius of geometry? But the aloof sensitiveness of the face, the broad sphericity of the head reassure him. This is Henri Poincaré. And so the old King finds the True Prince, who in turn finds himself at last truly comprehended, anointed to the succession, and given high heart to establish his dominion."

The sudden death of Henri Poincaré, July 18, 1912, at the age of fifty-eight, shocked the scientific world. This marvelous thinking machine was stopped, this repository of the exact sciences was lost to the world, by the trifling accident of a clot of blood catching in one of the valves of the heart. He had gone to the hospital for a minor operation which was apparently successful. Ten days later he was pronounced well enough to leave and was dressing when he was struck down.

The funeral service at the church of Saint-Jacques-du-Haut-Pas was attended by a remarkable assemblage of men of science and letters, government officials, and representatives of foreign countries. At the Montparnasse cemetery orations were delivered by M. Guist'hau, Minister of Public Instruction, Jules Claretie of the Académie française, M. Appell, dean of the Faculty of Sciences, M. Bigourdan of the Observatory, Paul Painlevé of the Academy of Sciences, and General Cornille, Commandant of the École polytechnique. M. Painlevé said of him:

"The life of Henri Poincaré was one intense and uninterrupted meditation, that despotic and pitiless meditation which bows the shoulders and bends the head, which absorbs the vital influx of one's being and too soon uses up the body it possesses.

"Henri Poincaré was not only a great creator in the positive sciences; he was a great philosopher and a great writer. Certain of his aphorisms remind one of Pascal: 'Thought is only a flash between two long nights, but this flash is everything.' His style followed the movement of his thought; brief and arresting formulas, often paradoxical when isolated, joined by hasty explanations which discard the easy details and say only the essential. This is why superficial critics have accused him of being 'incoherent'; the truth being that without some previous scientific education, such logical movement is difficult to follow. Mice cannot keep step with a lion.

"It is likewise a lack of comprehension of his philosophy as a whole that has led certain commentators to think they found a transcendental skepticism in his critical studies of the principles of science. Must he not have had faith in science who has written 'The search for truth ought to be the aim of our activity; it is the sole aim worthy of it'? His philosophy of the rational science will live as long as his own discoveries. The totality of the mathematical sciences seemed to him like a gigantic measuring instrument, harmoniously adjusted and well adapted for the evaluation of the phenomena of the universe. There remains one trait of his character that I cannot pass over in silence; that is his admirable intellectual sincerity. He gave himself, he gave to all, so far as words permit, the whole of his thought and even the mechanism of his thought. In his last publication, appearing only a few days before his death and dealing with the problem of the stability of our universe, he excused himself for giving out such incomplete results:

'It would seem under these conditions that I ought to abstain from all publication until I had solved the problem, but after the fruitless efforts I have made for months, it appeared to me wisest to let the problem ripen while I let it alone for some years. That would have been very well if I had been sure of taking it up again some day,but at my age I could not be sure of that. Besides, the importance of the subject is too great, and the results already obtained are on the whole too considerable for me to be content to leave them altogether useless. I hope that the geometricians who will interest themselves in this problem and who will doubtless be more fortunate than I will be able to get something out of it and make use of it in finding the path they should pursue.'

"What words can be added to this scientific testament, so simple and so noble, of a life altogether consecrated, without faltering even to the last hour, to the search for truth? For the first time in half a century this unparalleled brain has found repose."

Poincaré, as we have seen, was awake to the wider aspects of science. He was interested in its effects upon human life and conduct, although he himself was engaged in one of its most remote and abstract branches. Shortly before his death he discussed a question which nowadays arouses intense interest, the question of what effect the advance and popularization of science will have on ethics. Will science in destroying superstitions, in changing utterly the traditional way of regarding the universe and man, undermine the morality which forms the foundation of our civilization? This question Poincaré answers in the negative. He believes that our moral instincts lie too deep to be affected by such a revolution in thought, but on the other hand he does not think, as some do, that science will ever be able of itself to provide the moral imperative. A few paragraphs from this essay, published posthumously in "Last Thoughts", may well serve as a conclusion to this sketch of his philosophy:

There can be no scientific morality; but no more can there be immoral science. And the reason is simple; it is a reason—how shall I say it?—purely grammatical.If the premises of a syllogism are both in the indicative, the conclusion likewise will be in the indicative. For the conclusion to be put in the imperative, it would be necessary that at least one of the premises should itself be in the imperative. Now, the principles of science, the postulates of geometry, are and can be only in the indicative; still in this same mood are the experimental verities, and at the foundation of the sciences there is, there can be, nothing else. Hence, the most subtle dialectician may juggle with these principles as he will, combine them, frame them up one upon another; all he will get from them will be in the indicative. He will never obtain a proposition which shall say: do this, or don't do that; that is to say, a proposition which confirms or contradicts morality....Some therefore think that science will be destructive; they fear the ruin it will make and dread lest, where it shall have passed, society can no longer survive.Is there not in these fears a sort of internal contradiction? If it is scientifically proved that such or such a custom, regarded as indispensable to the very existence of human society, had not in reality the importance attributed to it and deceived us only by its venerable antiquity, if that be proved, admitting this proof to be possible, will the moral life of humanity be shaken? One of two things, either this custom is useful, and then a reasonable science cannot prove that it is not; or else it is useless and we should not regret it. From the moment that we place at the foundation of our syllogisms one of those generous emotions which engender morality, it is still this emotion, and consequently it is still morality which we must find at the end of our whole chain of reasonings, if this has been conducted in accordance with the rules of logic. What is in danger of perishing is the non-essential, that which was merely an accident in our moral life; the sole important thing cannot fail to be found in the conclusions since it is in the premises....Science, right or wrong, is deterministic; everywhere it penetrates it introduces determinism. So long as it is only a question of physics or even of biology, this is unimportant. The domain of conscience remains inviolate. What will happen when morality in turn shall become the object of science?Is all despair, or if some day morality should accommodate itself to determinism, could it so adapt itself without dying from the effects? So profound a metaphysical revolution would doubtless have much less influence upon morals than we think. It is of course understood that penal repression is not in question. What is called crime or punishment, would be called sickness or prophylaxis, but society would retain intact its right, which is not to punish, but simply the right of self-defense. What is more serious is that the idea of merit or demerit would have to disappear or be transformed. But we should continue to love the good man, as we love all that is beautiful; we should no longer have the right to hate the vicious man, who would then inspire only disgust; but is hate necessary? Enough that we do not cease to hate vice.Apart from that, all would go on as in the past. Instinct is stronger than all metaphysics, and even though one should have laid it bare, even if one should understand the secret of its force, its power would not thereby be weakened. Is gravitation less irresistible since Newton? The moral forces which guide us would continue to guide us.[9]

There can be no scientific morality; but no more can there be immoral science. And the reason is simple; it is a reason—how shall I say it?—purely grammatical.

If the premises of a syllogism are both in the indicative, the conclusion likewise will be in the indicative. For the conclusion to be put in the imperative, it would be necessary that at least one of the premises should itself be in the imperative. Now, the principles of science, the postulates of geometry, are and can be only in the indicative; still in this same mood are the experimental verities, and at the foundation of the sciences there is, there can be, nothing else. Hence, the most subtle dialectician may juggle with these principles as he will, combine them, frame them up one upon another; all he will get from them will be in the indicative. He will never obtain a proposition which shall say: do this, or don't do that; that is to say, a proposition which confirms or contradicts morality....

Some therefore think that science will be destructive; they fear the ruin it will make and dread lest, where it shall have passed, society can no longer survive.

Is there not in these fears a sort of internal contradiction? If it is scientifically proved that such or such a custom, regarded as indispensable to the very existence of human society, had not in reality the importance attributed to it and deceived us only by its venerable antiquity, if that be proved, admitting this proof to be possible, will the moral life of humanity be shaken? One of two things, either this custom is useful, and then a reasonable science cannot prove that it is not; or else it is useless and we should not regret it. From the moment that we place at the foundation of our syllogisms one of those generous emotions which engender morality, it is still this emotion, and consequently it is still morality which we must find at the end of our whole chain of reasonings, if this has been conducted in accordance with the rules of logic. What is in danger of perishing is the non-essential, that which was merely an accident in our moral life; the sole important thing cannot fail to be found in the conclusions since it is in the premises....

Science, right or wrong, is deterministic; everywhere it penetrates it introduces determinism. So long as it is only a question of physics or even of biology, this is unimportant. The domain of conscience remains inviolate. What will happen when morality in turn shall become the object of science?

Is all despair, or if some day morality should accommodate itself to determinism, could it so adapt itself without dying from the effects? So profound a metaphysical revolution would doubtless have much less influence upon morals than we think. It is of course understood that penal repression is not in question. What is called crime or punishment, would be called sickness or prophylaxis, but society would retain intact its right, which is not to punish, but simply the right of self-defense. What is more serious is that the idea of merit or demerit would have to disappear or be transformed. But we should continue to love the good man, as we love all that is beautiful; we should no longer have the right to hate the vicious man, who would then inspire only disgust; but is hate necessary? Enough that we do not cease to hate vice.

Apart from that, all would go on as in the past. Instinct is stronger than all metaphysics, and even though one should have laid it bare, even if one should understand the secret of its force, its power would not thereby be weakened. Is gravitation less irresistible since Newton? The moral forces which guide us would continue to guide us.[9]

A complete analytical bibliography of Poincaré's writings up to 1909 will be found in Ernest Lebon's "Henri Poincaré" (Paris: Gaultier-Villars), which contains the biographical address of M. Frédéric Masson on his admission to the French Academy and other eulogies. The list comprises 436 articles and books classified as follows: Mathematical analysis, 146; analytical and celestial mechanics, 85; mathematic physics, 78; scientific philosophy, 51; necrology, 17; miscellaneous, 59; an astonishing output for thirty years' work, considering the amount and difficulty of the labor involved in some of the contributions.

The mathematical works of Poincaré are too difficult for the layman and indeed for many professional mathematicians. But there are five volumes of general interest published by Flammarion, Paris: "La Science et l'Hypothèse", "La Valeur de la Science", "Science et Méthode", "Savants et Ecrivains", and "Dernières Pensées." The first of these has had a wide popularity, having been translated into English, German, Spanish, Hungarian, and Japanese. The English translation of "Science and Hypothesis", by Professor George Bruce Halsted (New York: Science Press), which appeared in 1905, is introduced by an interesting criticism of Poincaré's philosophy by Professor Josiah Royce, of Harvard. Two years later "The Value of Science" was published in this country (Science Press). "Science et Méthode", though it contains some matter of more general interest than the others, particularly his account of the rôle played by unconscious mind in mathematical invention and his explanation of the newer conceptions of physics, has not yet appeared in English. The fourth volume, "Savants et Ecrivains", is an evidence of Poincaré's good will rather than his literary talents, as it consists of perfunctory addresses on deceased Academicians, the most extensive being that on Sully-Prudhomme, whose chair he holds. The fifth, published after his death, contains the essay on "Science and Morality" from which I have quoted, as well as interesting discussions of recent science and philosophy. The volume entitled "Foundations of Science" (published by the Science Press, New York) contains "Science and Hypothesis", "Value of Science", and "Science and Method" with the introduction by Professor Royce.

From either of the two volumes, "Science and Hypothesis" or "The Value of Science", one can get an idea of Poincaré's philosophy, which is of importance because it is not merely the philosophy of an individual but the point of view of most men of science nowadays, though rarely so definitely recognized or clearly expressed. Both books consist of a somewhat heterogeneous collection of studies on the method and logic of the mathematical and physical sciences, containing much that the general reader will have to skip because of its use of unfamiliar terms, but it will not be safe for him to skip any whole pages without looking them over carefully, for he is likely to find brilliant and suggestive sentences embedded in the most unpromising material.

Separate articles by Poincaré, forming chapters from the above-mentioned volumes, are accessible in American periodicals. "The Future of Mathematics" inMonist, Vol. XX, pp. 76-92; also in the 1909 Smithsonian Report, which is in every public library. "The Choice of Facts" inMonist, Vol. XIX, pp. 231-239. "The Principles of Mathematical Physics" in the report of the St. Louis Congress of Arts and Sciences, Vol. I, pp. 604-624, and inMonist, Vol. XV, pp. 1-24. "The Bolyai Prize" (Report on the Work of Hilbert) inScience, May 19 and 26, 1911. "Mathematical Creations" inMonist, Vol. XX, pp. 321-335. "The Value of Science" was first published complete in thePopular Science Monthly, September, 1906, and later; "Relativity of Space", "The New Logics", and "Chance" in theMonist, 1913.

For biographical details besides the references already given in footnotes, see Nordmann's article on Poincaré in Smithsonian Report, 1912; Darbou's eulogy inLe Temps, December 15, 1913; and articles inRevue du Mois, February 10, 1913;La Revue de Paris, February 15, 1913;The Nation,September 12, 1912.

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