# Popular Science Monthly/Volume 75/August 1909/Josiah Willard Gibbs and his Relation to Modern Science IV

 JOSIAH WILLARD GIBBS AND HIS RELATION TO MODERN SCIENCE. IV

ASSISTANT LIBRARIAN, ARMY MEDICAL LIBRARY, WASHINGTON, D. C.

The naturalist Haeckel has explicitly denied the doctrine of universal increase of entropy[16] because, pointing as it does to the ultimate thermal death of different worlds, it conflicts with his monistic conception of the universe as a perpetuum mobile, consisting of infinite substance in eternal motion, without beginning and without end. Yet the cosmogony of Kant and Laplace, which Haeckel accepts, points to the same conclusion as well as to formative periods in the history of the solar and sidereal systems, in which entropy decreases, and energy, instead of dissipating; tends, after a maximum of degradation, to concentrate. Even possibilities of this kind put the second law on a lower plane of probability than the first as far as man is concerned, unless it be that the irreversible processes of nature are in reality cyclic, in which case we should have Nietzsche's "eternal return" of all things. But as Bumstead has so admirably said, "It is nearer the truth to base the doctrine of entropy upon the finite character of our perceptions than upon infinity of time."

In connection with the validity of the second law arises the important question of the extent of its application to animate nature and whether it is capable of reversal in vital processes. "The first law (conservation of energy) has been proven," says Ostwald, "with an exactness of 1: 1,000 even for physiological combustion (including mechanical and psychical work performed)." The second law, whether in the Clausius form of increase of entropy, the Kelvin form of

dissipation of available energy, or the Gibbs-Helmholtz form of decrease of free energy, is assumed by recent physiologists to be characteristic of all spontaneous or metabolic processes, but both Helmholtz[17] and Kelvin[18] have doubted whether it is either necessary or sufficient for their production, while Maxwell[19] and Boltzmann[20] have asserted, what Gibbs's statistical researches seem to prove, that it is sometimes possible for entropy to decrease, that is for small isolated temporary violations of the second law to occur in any real body. Has animal or vegetable protoplasm ever the power ascribed to Maxwell's demon of reversing the thermodynamic order of nature, and directing physicochemical forces? Such a demon, according to Lord Kelvin, might, through his superior intelligence or motor activity, render one half of a bar of metal glowing hot, while the other half remained icy cold. We have something analogous to this in certain diseases, as gangrene, aphasia, various forms of paralysis, the curious vasomotor and trophic disorders of the nervous system. Are these phenomena then of a thermodynamic nature? The animal body, Lord Kelvin thought, does not act like a thermodynamic engine, but "in a manner more nearly analogous to that of an electric motor working in virtue of energy supplied to it by a voltaic battery." Here, as Gibbs has shown in his theory of the chemical cells, the electromotive force would be identical with the free energy upon which the surface energies of the body must ultimately depend. Beyond these speculations we know nothing. Gibbs himself avowed his express disinclination to "explain the mysteries of nature," while Lord Kelvin, although affirming that physicists are bound "by the everlasting law of honor," to explain everything material upon physical principles, mystified friends and opponents alike by falling back upon a "vital principle" with "creative power" behind it as the causa causans of biological happenings. But the business of physics is with the material facts of the universe, and the invocation of creative power explains nothing and is subversive of determinism, or the relation of cause and effect in science. It may be that "man was born too late to ascertain final causes": he can only interpret the physical facts of his experience as he finds them and with the means at his disposal. An interesting attempt to explain the relation of life and mind to matter is found in the energetische Weltanschauung or energetic philosophy of Ostwald, which confessedly derives[21] from the thermodynamic argument of Gibbs, but should not be confused with the latter. Gibbs was concerned only with applying the laws of mechanics to physical chemistry. Compared with the case of nature, he says, thermodynamic systems are "of an ideal simplicity." To Ostwald, however, mind and matter are but forms of energy, which is the only thing eternal and immortal. "We can deal with measurable things, never with the unknown heart of nature," says Ostwald, yet his basic principle, energy, is to all intents and purposes identical with the eternal infinite substance of Spinoza, Goethe and Haeckel, "sive Deus, sive Natura naturans, sive Anima mundi appelletur." Matter, in Ostwald's scheme, is a group of energies in space; thought becomes a mode of energy involving evolution of heat, and "the problem of the connection between body and spirit belongs to the same series as the connection between chemical and electrical energy, which is treated in the theoiy of voltaic chains."[22] Falling in love, listening to a Beethoven symphony, identifying oneself with nature, are to Ostwald instances of dissipation of energy like any other.[23] Philosophy of this kind does not clear up the mystery of the relation of mind and matter. Descartes assumed that mind and matter exist apart as parallels, having no causal connection with each other. Spinoza held that neither can exist apart; indeed, he sometimes asserts their practical identity as different modes of the same eternal substance. But however intimately they may be associated, no scientist or philosopher has yet proven, whether.in the body of man or in the origin of the universe, that one is either the cause or the effect of the other.

Assuming matter in mass to be ultimately made up of rotational, vortical or gyrostatic stresses or of energies, whether kinetic or potential, we encounter the formidable objection of Boltzmann, that it seems illogical, not to say unmechanical, to postulate motion as the primary idea with the moving thing as the derived one. Motion of what? we have a right to ask, since Ostwald disdains the ether of the physicists.[24] Matter, in the words of Sir Oliver Lodge, may be physically resolved "perhaps, into electricity, and that into some hitherto unimagined mode of motion of the ether," but no dynamic theory of the ether can resolve the ether into nothing. Assuming thought to be a mode of energy, the metaphysical argument that mind is at the bottom of motion seems more likely, in the last analysis, than that motion should be the cause of mind, for we can not conceive of a thing moving unless something moves it. Mind seems almost like an assemblage or complex of causes in itself, and is probably related to the brain as music to the violin. Destroy the violin and there will be an end of its music, but it needs other coefficients than the violin itself to get music out of it. Ostwald has himself admitted the force of Leibnitz's argument, that no mechanical explanation of cerebral action will ever account for the genesis of thought or the nature of consciousness: "Nihil in intellectu quod non prius in sensu, nisi intellectus ipse." Individual thinking may be the result of physico-chemical differences of structure or substance in the brain, but apart from the evidence of mind in the evolution and structure of the universe, different aspects of mind, as ideas, sensations and sentiments, seem to have an individual life of their own so far as man is concerned, and are "things" in the sense that, like external forces, they have profoundly influenced and determined the actions of individuals and of entire races. Human thought as a function of the human brain may disappear with man himself, but this does not annul the possibility of mind existing in manifold ways elsewhere in the universe. The electric waves of wireless telegraphy undoubtedly existed as motions in the air before man discovered and labeled them and may continue to exist and be apprehended in other spheres of thought when man is gone.

Man's capacity for error in these matters is determined by his anthropomorphic tendencies and by the fact that his intelligence is finite. Of the possibly infinite number of attributes of eternal substance postulated by Spinoza, the human mind can apprehend only two—thought and extension, and even here thought and sensation are the fundamental facts, while "all else is an inference and is probably essentially unlike what it appears to our senses." It seems impossible to break down the fact that there is no absolute causal connection between the two primary categories of Spinoza, who has anticipated most of modern psychology. For this reason such subjects as spiritualism, phrenology, faith-healing, telepathy have remained in the limbo of pseudo-science, although each has undoubtedly a shadowy reason for existence. It is as fair as any other hypothesis, then, to assume that man, in his higher mental or psychical activities, may, under certain conditions, be "freed from the galling yoke of space and time," or, in other words, released from the thraldom of the second law. Yet such an assumption, even if made by a Kelvin, would be, in our present state of knowledge, an expression of individual personal belief, a literary or humane analogy, a leaning in the direction of the "fair humanities of old religion," but not a scientific fact. To fix our ideas for the material world we may accept the expanded statement of the second law which Ostwald gave in his Ingersoll lecture in 1906:[25] i(Every known physical fact leads to the conclusion that diffusion or a homogeneous distribution of energy is the general aim of all happenings. . . . A partial concentration may be brought in a system, but only at the expense of greater dissipation, and the sum total is always an increase in dissipation."[26] Through the labors of Joule and Kelvin, Maxwell and Boltzmann, Gibbs and Helmholtz, Carnot's simple generalization about heat engines has been elevated to the dignity of an irrevocable law of nature, a principle of scientific determinism, giving one of the most complete and satisfactory answers that man can furnish to the great question: How does any event in the material universe come to pass? In Darwin's picture of nature the quiet woods and waters, so calm and peaceful on the surface, are in reality centers of "strange and cruel life," the struggle and turmoil of creatures continually preying upon each other, even trees and plants and the tiniest particles of animate bodies taking part in a definite, never-ending war for existence. But the stern law of life, whereby the strong war down the weak, loses all moral, or human significance when seen as due, in the last analysis, to an inevitable tendency to dissipation of energy or as the resultant of a play of complex forces, which, through some principle of "least action," must inexorably flow from higher to lower potentials. As Spinoza pointed out long ago, Nature could 'not change these laws which flow from its very being, without ceasing to be itself, and the conclusion of physics and biology that Nature is never on the side of the weak becomes, as far as man is related to the material universe, identical with Spinoza's denial of final causes.

"The broad Scots tongue that flatters, scolds defies,
The thick Scots wit that fells you like a mace,"

and on the other, the overconscientious, ethical arguments of a super-sensitive spirit, obviously nettled at certain rough pleasantries which were understood but not appreciated. In 1893 Heaviside, an English vectorist, reports "confusion in the quaternionic citadel : alarms and excursions and hurling of stones and pouring of water upon the invading hosts."[29] The vectorists were denounced as a "clique" and ridiculed especially for their lack of elegance, their alleged intellectual dishonesty and the fact that their pupils were "spoon-fed" upon mathematico-physical pap. But some of the notations held up to ridicule turned out to be things like Poisson's theorem or the difficult hydrodynamic problem "given the spin in a case of liquid motion to find the motion," which Helmholtz solved with one of his strokes of genius, and which Gibbs showed could be understood and interpreted by the average student without genius by a simple application of vectorial methods. The real point at issue in the controversy, the fundamental difference in the ideals of European and American education, lies here. Both have their relative advantages and defects, but the object of one has been to bring the best to the highest development, while the other is concerned with increasing the efficiency of the average man. One has been exclusive, aiming at the survival of the fittest; the other is democratic and inclusive, and aims, in Huxley's words, to make the greatest number fit to survive. The merits of the case are well summed up in Gibbs's final statement: "The notions which we use in vector analysis are those which he who reads between the lines will meet on every page of the greatest masters of analysis, or of those who have probed deepest the secrets of nature, the only difference being that the vector analyst, having regard for the weakness of the human intellect, does as the early painters who wrote beneath their pictures "This is a tree." "This is a horse."[30] This view is in perfect accord with the recent trend of mathematical teaching, European or American, which is to emphasize the meaning and interpretation of equations and formulae rather than their demonstrations or manipulation; in short, to substitute visualizing methods, the art of thinking straight and seeing clear, for what is conventional and scholastic. A Harvard professor is said to have told his students that the demonstration of a theorem is no evidence that it is understood, but the intelligent use of it is; and the object of such teaching as Gibbs's was to enable the student to see physical phenomena with the "clarity of vision" which Tait himself thought characteristic of the truly mathematical mind, and of which a good criterion is afforded in Helmholtz's unforgetable statement about Michael Faraday: "With wonderful sagacity and intellectual precision, Faraday performed on his brain the work of a great mathematician without using a single mathematical formula."[31]

At Yale Gibbs was esteemed an ideal teacher of physics, cordial, quick, helpful, willing to devote unlimited time to assist plodders and giving his students ample opportunity to learn "what may be regarded as known, what is guessed at, what a proof is and how far it goes." Of the qualities that make for distinction of mind and character he had the impersonal gift, "le don d'être nè essentiellement impersonnel," which Renan thought highest of all, and which, fortunately for the advance of real knowledge, has been characteristic of most of the great leaders of science. He could build no wall of personal egotism between himself and the external facts, and "few could come in contact with this serene and impartial mind without feeling profoundly its influence in all his future studies of nature."[32] We know little of his life beyond the fact that he was a man of stoic fiber, who lived and worked alone. The countenance in the portraits expresses the Puritan austerity with lines that tell of mental stress and struggles with illness, but the man himself was "unassuming in manner, genial and kindly in his intercourse with his fellow men." "In the minds of those who knew him," concludes his biographer, "the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life."[33]

American contributions to physics, from Franklin to Michelson, have been characterized by originality of invention and experiment. The work of Gibbs has a place apart as that of a mathematical theorist whose ideas have found wide application in the main current of modern thought, and his true position is best described in his own often-quoted estimate of his great predecessor, Clausius. "Such work as that of Clausius," he says, "is not measured by counting titles or pages. His true monument lies not on the shelves of libraries, but in the thoughts of men and the history of more than one science."[34] The general scientific reputation of Gibbs is of this kind, while in his chosen field of activity, the austere region of physics in which Newton and Lagrange, Hamilton and Jacobi are the leaders, his is assuredly the most distinguished American name.

1. Nature, 1877–8, XVII., 280.
2. "It can never be proved from the equations of motions alone, that the minimum function H must always decrease. It can only be deduced from the laws of probability, that if the initial state is not specially arranged for a certain purpose, but haphazard governs freely the probability that H decreases is always greater than it increases." Boltzmann, Nature, 1894-5, LI., 414.
3. Tr. Connect. Acad., III., 229.
4. "Almost all these trees are extremely low, and have branches very nearly horizontal. Here H has nearly the minimum value. Only very few trees are higher, and have branches inclined to the axis of abscissa?, and the improbability of such a tree increases enormously with its height." Boltzmann, Nature, 1894-5, LI., 581.
5. Neither the theory of Gases nor any other physical theory can be quite a congruent account of facts, and I can not hope with Mr. Burbury that Mr. Bryan will be able to deduce all the phenomena of spectroscopy from the electromagnetic theory of light. Certainly, therefore, Hertz is right when he says: 'The rigour of science requires that we distinguish well the undraped figure of Nature itself from the gay-coloured vesture with which we clothe it at our pleasure.' But I think the predilection for nudity would be carried too far if we were to forego every hypothesis. Only we must not demand too much from hypotheses." Boltzmann, Ibid., 413.
6. The principal opponent of the Maxwell-Boltzmann partition of energies was Lord Kelvin in his "Nineteenth Century Clouds over the Dynamical Theory of Heat and Light." When asked what he had against it, he replied point-blank: "I don't think there is a single thing about it that is right" (Science, Jan. 3 r 1908, p. 6).
7. "Yale Bicentennial Publications," 1903. Translated into German by Ernst Zermelo, Leipzig, 1905.
8. Phil. Mag., 1904, 6. s., VIII., 44.
9. Ibid., 45.
10. Tr. Connect. Acad., III., 108.
11. Proc. Am. Ass. Adv. Sc., 1886, Salem, 1887, XXXV., 62.
12. Let us read Bacon again, and agree with him that we understand only what we have observed." S. P. Langley, Science, 1902, XV., p. 927.
13. Physical chemistry is not yet a quantitative science; it is a pseudo-quantitative science. There are all the outward signs of a quantitative science. We have formulas and tables; we make use of thermodynamics and the differential calculus; but this is for the most part a vain show. Long before we reach the point where the formula is to be tested experimentally we slip in a simplifying assumption: that the concentration of one component may be considered as a constant; that the heat of dilution is zero; that the solute may be treated in all cases as though it. were an indifferent gas; that the concentration of the dissociated portion of a salt may be substituted for the total concentration; etc., etc. The result is that our calculations apply at best only to limiting or ideal cases, where an error in deducing the formula may be masked by errors in observation. Helmholtz did not do this, but Helmholtz is considered old-fashioned." W. D. Bancroft, J. Phys. Chem., 1899, III., 604.
14. H. A. Rowland, Am. J. Sc., 1899, 4. s. . VIII., 409.
15. Bumstead, Am. J. Sc., 1903, 4. s M XLI., 199.
16. Haeckel, "The Riddle of The Universe," New York, 1900, 246-248.
17. Helmholtz, J. f. Math., v. 100, 137. Auerback, "Kanon der Physik.," 414.
18. Kelvin, "Pop. Lect.," II., 190, 463, 404. See, also, the discussion in Science, 1903, N. S., XVIII., 138-146.
19. Maxwell, Nature, 1877-8, XVII., 280.
20. Der grosse Meister, dem auch diese Zeilen huldigen möchten, hat einst den Gedanken ausgesprochen, dass es in der Welt vielleicht Stellen giebt, wo die Entropie nicht wächst, sondern zunimmt," O. Chwolson. Boltzmann, Festschr.," 1904, 33.
21. "Wir wollen daher den Versuch wagen, eine Weltansicht ohne die Benutzung des Begriffs der Materie ausschliesslich aus energetischem Material aufzubauen. . . In der für die neuere Chemie grundlegenden Abhandlung von. Willard Gibbs ist sogar dies Postulat praktisch in weitestem Umfange durchgeführt worden, allerdings ohne dass es ausdrücklich aufgestellt worden wäre." W. Ostwald, "Vorles. über Naturphilosophie," 165.
22. Monist, 1907.
23. W. Ostwald, "Individuality and Immortality," 44-46.
24. "What the atom of each element is, whether it is a movement or a thing, or a vortex, or a point having inertia, all these questions are surrounded by profound darkness. I dare not use any less pedantic word than entity to designate the ether, for it would be an exaggeration of our knowledge to speak of it as a body, or even a substance," Lord Salisbury, "Rep. Brit. Ass. Adv. Sc," 1894, 8.
25. W. Ostwald, "Individuality and Immortality," Boston, 1906, 42.
26. As a fundamental formula for all material happenings, analogous to the "world-formula" of Laplace, J G. Vogt proposes the following (Polit. Anthrop. Rev., Leipzig, 1907-8, VI., 573): If Pe represent the positive or dissipation potential (emissives Potential) and Pr the negative or concentrational potential (rezeptives Potential) of any given set of forces, then ${\displaystyle Pe+Pr=0}$ or ${\displaystyle \int _{n}d\ Pe+\int _{o}^{n}d\ Pr=0}$. This is, however, only another restatement of Newton's Third Law of Motion, that action and reaction are equal and in opposite directions.
27. "I have the highest admiration for the notion of a quaternion; but. . . as I consider the full moon far more beautiful than any moonlit view, so I regard the notion of a quaternion as far more beautiful than any of its applications. . . . I compare a quaternion formula to a pocket-map—a capital thing to put in one's pocket, but which for use must be unfolded: The formula, to be understood, must be translated into coordinates," Arthur Cayley, Proc. Roy. Soc. Edinb., 1892-5, XX., 271. At the Southport meeting of the British Association in 1903, Professor Larmor, while admitting the extreme usefulness of the different methods of vector analysis, argued that their slow progress in physics was due to the lack of uniformity in definitions and notations, requiring that each system must be mastered separately before it can be applied. To which Professor Boltzmann not inaptly replied that the confusion might have been avoided, if Hamilton had adopted the notations of Grassmann in the first instance.
28. Nature, 1891-3, passim.
29. Ibid., 1892-3, XLVII., 534.
30. Ibid., 464.