Part 12

The laying bare of the experimental, logical, and formal root of the present principle of energy will perhaps contribute much to the removal of the mysticism which still clings to this principle. With respect to our formal need of a very simple, palpable, substantial conception of the processes in our environment, it remains an open question how far nature corresponds to that need, or how far we can satisfy it. In one phase of the preceding discussions it would seem as if the substantial notion of the principle of energy, like Black's material conception of heat, has its natural limits in facts, beyond which it can only be artificially adhered to.

FOOTNOTES:

[Footnote 39: Published in Vol. 5, No. I, of _The Monist_, October, 1894, being in part a re-elaboration of the treatise _Ueber die Erhaltung der Arbeit_, Prague, 1872.]

[Footnote 40: _On Matter, Living Force, and Heat_, Joule: _Scientific Papers_, London, 1884, I, p. 265.]

[Footnote 41: "Atqui hoc si sit, globorum series sive corona eundem situm cum priore habebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris, ideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese _continuum et aeternum motum efficient, quod est falsum_."]

[Footnote 42: "A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum non servato, ac delabatur in _D_; quibus positis aqua quae ipsi _A_ succedit eandem ob causam deffluet in _D_, eademque ab alia istinc expelletur, atque adeo aqua haec (cum ubique eadem ratio sit) _motum instituet perpetuum, quod absurdum fuerit_."]

[Footnote 43: "Accipio, gradus velocitatis ejusdem mobilis super diversas planorum inclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes aequales sint."]

[Footnote 44: "Voi molto probabilmente discorrete, ma oltre al veri simile voglio con una esperienza crescer tanto la probabilità, che poco gli manchi all'agguagliarsi ad una ben necessaria dimostrazione. Figuratevi questo foglio essere una parete eretta all'orizzonte, e da un chiodo fitto in essa pendere una palla di piombo d'un'oncia, o due, sospesa dal sottil filo _AB_ lungo due, o tre braccia perpendicolare all'orizzonte, e nella parete segnate una linea orizontale _DC_ segante a squadra il perpendicolo _AB_, il quale sia lontano dalla parete due dita in circa, trasferendo poi il filo _AB_ colla palla in _AC_, lasciata essa palla in libertà, la quale primieramente vedrete scendere descrivendo l'arco _CBD_, e di tanto trapassare il termine _B_, che scorrendo per l'arco _BD_ sormonterà fino quasi alla segnata parallela _CD_, restando di per vernirvi per piccolissimo intervallo, toltogli il precisamente arrivarvi dall'impedimento dell'aria, e del filo. Dal che possiamo veracemente concludere, che l'impeto acquistato nel punto _B_ dalla palla nello scendere per l'arco _CB_, fu tanto, che bastò a risospingersi per un simile arco _BD_ alla medesima altezza; fatta, e più volte reiterata cotale esperienza, voglio, che fiechiamo nella parete rasente al perpendicolo _AB_ un chiodo come in _E_, ovvero in _F_, che sporga in fuori cinque, o sei dita, e questo acciocchè il filo _AC_ tornando come prima a riportar la palla _C_ per l'arco _CB_, giunta che ella sia in _B_, inoppando il filo nel chiodo _E_, sia costretta a camminare per la circonferenza _BG_ descritta in torno al centro _E_, dal che vedremo quello, che potrà far quel medesimo impeto, che dianzi concepizo nel medesimo termine _B_, sospinse l'istesso mobile per l'arco _ED_ all'altezza dell'orizzonale _CD_. Ora, Signori, voi vedrete con gusto condursi la palla all'orizzontale nel punto _G_, e l'istesso accadere, l'intoppo si metesse più basso, come in _F_, dove la palla descriverebbe l'arco _BJ_, terminando sempre la sua salita precisamente nella linea _CD_, e quando l'intoppe del chiodo fusse tanto basso, che l'avanzo del filo sotto di lui non arivasse all'altezza di _CD_ (il che accaderebbe, quando fusse più vicino al punto _B_, che al segamento dell' _AB_ coll'orizzontale _CD_), allora il filo cavalcherebbe il chiodo, e segli avolgerebbe intorno. Questa esperienza non lascia luogo di dubitare della verità del supposto: imperocchè essendo li due archi _CB_, _DB_ equali e similmento posti, l'acquisto di momento fatto per la scesa nell'arco _CB_, è il medesimo, che il fatto per la scesa dell'arco _DB_; ma il momento acquistato in _B_ per l'arco _CB_ è potente a risospingere in su il medesimo mobile per l'arco _BD_; adunque anco il momento acquistato nella scesa _DB_ è eguale a quello, che sospigne l'istesso mobile pel medesimo arco da _B_ in _D_, sicche universal-mente ogni memento acquistato per la scesa d'un arco è eguale a quello, che può far risalire l'istesso mobile pel medesimo arco: ma i momenti tutti che fanno resalire per tutti gli archi _BD_, _BG_, _BJ_ sono eguali, poichè son fatti dal istesso medesimo momento acquistato per la scesa _CB_, come mostra l'esperienza: adunque tutti i momenti, che si acquistano per le scese negli archi _DB_, _GB_, _JB_ sono eguali."]

[Footnote 45: "Constat jam, quod mobile ex quiete in _A_ descendens per _AB_, gradus acquirit velocitatis juxta temporis ipsius incrementum: gradum vero in _B_ esse maximum acquisitorum, et suapte natura immutabiliter impressum, sublatis scilicet causis accelerationis novae, aut retardationis: accelerationis inquam, si adhuc super extenso plano ulterius progrederetur; retardationis vero, dum super planum acclive _BC_ fit reflexio: in horizontali autem _GH_ aequabilis motus juxta gradum velocitatis ex _A_ in _B_ acquisitae in infinitum extenderetur."]

[Footnote 46: "Si gravitas non esset, neque aër motui corporum officeret, unumquodque eorum, acceptum semel motum continuaturum velocitate aequabili, secundum lineam rectam."]

[Footnote 47: "Si pondera quotlibet, vi gravitatis suae, moveri incipiant; non posse centrum gravitatis ex ipsis compositae altius, quam ubi incipiente motu reperiebatur, ascendere.

"Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud sibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe sursum non ferri.--Et sane, si hac eadem uti scirent novorum operum machinatores, qui motum perpetuum irrito conatu moliuntur, facile suos ipsi errores deprehenderent, intelligerentque rem eam mechanica ratione haud quaquam possibilem esse."]

[Footnote 48: "Si pendulum e pluribus ponderibus compositum, atque e quiete dimissum, partem quamcunque oscillationis integrae confecerit, atque inde porro intelligantur pondera ejus singula, relicto communi vinculo, celeritates acquisitas sursum convertere, ac quousque possunt ascendere; hoc facto centrum gravitatis ex omnibus compositae, ad eandem altitudinem reversum erit, quam ante inceptam oscillationem obtinebat."]

[Footnote 49: "Notato autem hic illud staticum axioma etiam locum habere:

"Ut spatium agentis ad spatium patientis Sic potentia patientis ad potentiam agentis."]

[Footnote 50: "Cependant, comme dans cet ouvrage on ne fut d'abord attentif qu'à considérer ce beau développement de la mécanique qui semblait sortir tout entière d'une seule et même formule, on crut naturellement que la science etait faite, et qu'il ne restait plus qu'à chercher la démonstration du principe des vitesses virtuelles. Mais cette recherche ramena toutes les difficultés qu'on avait franchies par le principe même. Cette loi si générale, où se mêlent des idées vagues et étrangères de mouvements infinement petits et de perturbation d'équilibre, ne fit en quelque sorte que s'obsurcir à l'examen; et le livre de Lagrange n'offrant plus alors rien de clair que la marche des calculs, on vit bien que les nuages n'avaient paru levé sur le cours de la mécanique que parcequ'ils étaient, pour ainsi dire, rassemblés à l'origine même do cette science.

"Une démonstration générale du principe des vitesses virtuelles devait au fond revenir a établir le mécanique entière sur une autre base: car la demonstration d'une loi qui embrasse toute une science ne peut être autre chose qua la reduction de cette science à une autre loi aussi générale, mais évidente, ou du moins plus simple que la première, et qui partant la rende inutile."]

[Footnote 51: _Traité de la lumière_, Leyden, 1690, p. 2.]

[Footnote 52: "L'on ne sçaurait douter que la lumière ne consiste dans le _mouvement_ de certaine matière. Car soit qu'on regarde sa production, on trouve qu'içy sur la terre c'est principalement le feu et la flamme qui l'engendrent, lesquels contient sans doute des corps qui sont dans un mouvement rapide, puis qu'ils dissolvent et fondent plusieurs autres corps des plus solides: soit qu'on regarde ses effets, on voit que quand la lumière est ramasseé, comme par des miroires concaves, elle a la vertu de brûler comme le feu. c-est-à-dire qu'elle desunit les parties des corps; ce qui marque assurément du _mouvement_, au moins dans la _vraye Philosophie_, dans laquelle on conçoit la cause de tous les effets naturels par des raisons de _mechanique_. Ce qu'il faut faire à mon avis, ou bien renoncer à tout espérance de jamais rien comprendre dans la Physique."]

[Footnote 53: _Sur la puissance motrice du feu_. (Paris, 1824.)]

[Footnote 54: "On objectra peut-être ici que le mouvement perpétuel, démontré impossible par les _seules actions mécaniques_, ne l'est peut-être pas lorsqu'on emploie l'influence soit de la _chaleur_, soit de l'électricité; mais pent-on concevoir les phénomènes de la chaleur et de l'électricité comme dus à autre chose qu'à des _mouvements quelconques des corps_ et comme tels ne doivent-ils pas être soumis aux lois générales de la mécanique?"]

[Footnote 55: By this is meant the temperature of a Celsius scale, the zero of which is 273° below the melting-point of ice.]

[Footnote 56: I first drew attention to this fact in my treatise _Ueber die Erhaltung der Arbeit_, Prague, 1872. Before this, Zeuner had pointed out the analogy between mechanical and thermal energy. I have given a more extensive development of this idea in a communication to the _Sitzungsberichte der Wiener_ _Akademie_, December, 1892, entitled _Geschichte und Kritik des Carnot'schen Wärmegesetzes_. Compare also the works of Popper (1884), Helm (1887), Wronsky (1888), and Ostwald (1892).]

[Footnote 57: Sir William Thomson first consciously and intentionally introduced (1848, 1851) a _mechanical_ measure of temperature similar to the electric measure of potential.]

[Footnote 58: Compare my _Analysis of the Sensations_, Jena, 1886: English translation, Chicago, 1897.]

[Footnote 59: A better terminology appears highly desirable in the place of the usual misleading one. Sir William Thomson (1852) appears to have felt this need, and it has been clearly expressed by F. Wald (1889). We should call the work which corresponds to a vanished quantity of heat its mechanical substitution-value; while that work which can be _actually_ performed in the passage of a thermal condition _A_ to a condition _B_, alone deserves the name of the _energy-value_ of this change of condition. In this way the _arbitrary_ substantial conception of the processes would be preserved and misapprehensions forestalled.]

THE ECONOMICAL NATURE OF PHYSICAL INQUIRY.[60]

When the human mind, with its limited powers, attempts to mirror in itself the rich life of the world, of which it is itself only a small part, and which it can never hope to exhaust, it has every reason for proceeding economically. Hence that tendency, expressed in the philosophy of all times, to compass by a few organic thoughts the fundamental features of reality. "Life understands not death, nor death life." So spake an old Chinese philosopher. Yet in his unceasing desire to diminish the boundaries of the incomprehensible, man has always been engaged in attempts to understand death by life and life by death.

Among the ancient civilised peoples, nature was filled with demons and spirits having the feelings and desires of men. In all essential features, this animistic view of nature, as Tylor[61] has aptly termed it, is shared in common by the fetish-worshipper of modern Africa and the most advanced nations of antiquity. As a theory of the world it has never completely disappeared. The monotheism of the Christians never fully overcame it, no more than did that of the Jews. In the belief in witchcraft and in the superstitions of the sixteenth and seventeenth centuries, the centuries of the rise of natural science, it assumed frightful pathological dimensions. Whilst Stevinus, Kepler, and Galileo were slowly rearing the fabric of modern physical science, a cruel and relentless war was waged with firebrand and rack against the devils that glowered from every corner. To-day even, apart from all survivals of that period, apart from the traces of fetishism which still inhere in our physical concepts,[62] those very ideas still covertly lurk in the practices of modern spiritualism.

By the side of this animistic conception of the world, we meet from time to time, in different forms, from Democritus to the present day, another view, which likewise claims exclusive competency to comprehend the universe. This view may be characterised as the _physico-mechanical_ view of the world. To-day, that view holds, indisputably, the first place in the thoughts of men, and determines the ideals and the character of our times. The coming of the mind of man into the full consciousness of its powers, in the eighteenth century, was a period of genuine disillusionment. It produced the splendid precedent of a life really worthy of man, competent to overcome the old barbarism in the practical fields of life; it created the _Critique of Pure Reason_, which banished into the realm of shadows the sham-ideas of the old metaphysics; it pressed into the hands of the mechanical philosophy the reins which it now holds.

The oft-quoted words of the great Laplace,[63] which I will now give, have the ring of a jubilant toast to the scientific achievements of the eighteenth century: "A mind to which were given for a single instant all the forces of nature and the mutual positions of all its masses, if it were otherwise powerful enough to subject these problems to analysis, could grasp, with a single formula, the motions of the largest masses as well as of the smallest atoms; nothing would be uncertain for it; the future and the past would lie revealed before its eyes." In writing these words, Laplace, as we know, had also in mind the atoms of the brain. That idea has been expressed more forcibly still by some of his followers, and it is not too much to say that Laplace's ideal is substantially that of the great majority of modern scientists.

Gladly do we accord to the creator of the _Mécanique céleste_ the sense of lofty pleasure awakened in him by the great success of the Enlightenment, to which we too owe our intellectual freedom. But to-day, with minds undisturbed and before _new_ tasks, it becomes physical science to secure itself against self-deception by a careful study of its character, so that it can pursue with greater sureness its true objects. If I step, therefore, beyond the narrow precincts of my specialty in this discussion, to trespass on friendly neighboring domains, I may plead in my excuse that the subject-matter of knowledge is common to all domains of research, and that fixed, sharp lines of demarcation cannot be drawn.

The belief in occult magic powers of nature has gradually died away, but in its place a new belief has arisen, the belief in the magical power of science. Science throws her treasures, not like a capricious fairy into the laps of a favored few, but into the laps of all humanity, with a lavish extravagance that no legend ever dreamt of! Not without apparent justice, therefore, do her distant admirers impute to her the power of opening up unfathomable abysses of nature, to which the senses cannot penetrate. Yet she who came to bring light into the world, can well dispense with the darkness of mystery, and with pompous show, which she needs neither for the justification of her aims nor for the adornment of her plain achievements.

The homely beginnings of science will best reveal to us its simple, unchangeable character. Man acquires his first knowledge of nature half-consciously and automatically, from an instinctive habit of mimicking and forecasting facts in thought, of supplementing sluggish experience with the swift wings of thought, at first only for his material welfare. When he hears a noise in the underbrush he constructs there, just as the animal does, the enemy which he fears; when he sees a certain rind he forms mentally the image of the fruit which he is in search of; just as we mentally associate a certain kind of matter with a certain line in the spectrum or an electric spark with the friction of a piece of glass. A knowledge of causality in this form certainly reaches far below the level of Schopenhauer's pet dog, to whom it was ascribed. It probably exists in the whole animal world, and confirms that great thinker's statement regarding the will which created the intellect for its purposes. These primitive psychical functions are rooted in the economy of our organism not less firmly than are motion and digestion. Who would deny that we feel in them, too, the elemental power of a long practised logical and physiological activity, bequeathed to us as an heirloom from our forefathers?

Such primitive acts of knowledge constitute to-day the solidest foundation of scientific thought. Our instinctive knowledge, as we shall briefly call it, by virtue of the conviction that we have consciously and intentionally contributed nothing to its formation, confronts us with an authority and logical power which consciously acquired knowledge even from familiar sources and of easily tested fallibility can never possess. All so-called axioms are such instinctive knowledge. Not consciously gained knowledge alone, but powerful intellectual instinct, joined with vast conceptive powers, constitute the great inquirer. The greatest advances of science have always consisted in some successful formulation, in clear, abstract, and communicable terms, of what was instinctively known long before, and of thus making it the permanent property of humanity. By Newton's principle of the equality of pressure and counterpressure, whose truth all before him had felt, but which no predecessor had abstractly formulated, mechanics was placed by a single stroke on a higher level. Our statement might also be historically justified by examples from the scientific labors of Stevinus, S. Carnot, Faraday, J. R. Mayer, and others.

All this, however, is merely the soil from which science starts. The first real beginnings of science appear in society, particularly in the manual arts, where the necessity for the communication of experience arises. Here, where some new discovery is to be described and related, the compulsion is first felt of clearly defining in consciousness the important and essential features of that discovery, as many writers can testify. The aim of instruction is simply the saving of experience; the labor of one man is made to take the place of that of another.

The most wonderful economy of communication is found in language. Words are comparable to type, which spare the repetition of written signs and thus serve a multitude of purposes; or to the few sounds of which our numberless different words are composed. Language, with its helpmate, conceptual thought, by fixing the essential and rejecting the unessential, constructs its rigid pictures of the fluid world on the plan of a mosaic, at a sacrifice of exactness and fidelity but with a saving of tools and labor. Like a piano-player with previously prepared sounds, a speaker excites in his listener thoughts previously prepared, but fitting many cases, which respond to the speaker's summons with alacrity and little effort.

The principles which a prominent political economist, E. Hermann,[64] has formulated for the economy of the industrial arts, are also applicable to the ideas of common life and of science. The economy of language is augmented, of course, in the terminology of science. With respect to the economy of written intercourse there is scarcely a doubt that science itself will realise that grand old dream of the philosophers of a Universal Real Character. That time is not far distant. Our numeral characters, the symbols of mathematical analysis, chemical symbols, and musical notes, which might easily be supplemented by a system of color-signs, together with some phonetic alphabets now in use, are all beginnings in this direction. The logical extension of what we have, joined with a use of the ideas which the Chinese ideography furnishes us, will render the special invention and promulgation of a Universal Character wholly superfluous.

The communication of scientific knowledge always involves description, that is, a mimetic reproduction of facts in thought, the object of which is to replace and save the trouble of new experience. Again, to save the labor of instruction and of acquisition, concise, abridged description is sought. This is really all that natural laws are. Knowing the value of the acceleration of gravity, and Galileo's laws of descent, we possess simple and compendious directions for reproducing in thought all possible motions of falling bodies. A formula of this kind is a complete substitute for a full table of motions of descent, because by means of the formula the data of such a table can be easily constructed at a moment's notice without the least burdening of the memory.

No human mind could comprehend all the individual cases of refraction. But knowing the index of refraction for the two media presented, and the familiar law of the sines, we can easily reproduce or fill out in thought every conceivable case of refraction. The advantage here consists in the disburdening of the memory; an end immensely furthered by the written preservation of the natural constants. More than this comprehensive and condensed report about facts is not contained in a natural law of this sort. In reality, the law always contains less than the fact itself, because it does not reproduce the fact as a whole but only in that aspect of it which is important for us, the rest being either intentionally or from necessity omitted. Natural laws may be likened to intellectual type of a higher order, partly movable, partly stereotyped, which last on new editions of experience may become downright impediments.

When we look over a province of facts for the first time, it appears to us diversified, irregular, confused, full of contradictions. We first succeed in grasping only single facts, unrelated with the others. The province, as we are wont to say, is not _clear_. By and by we discover the simple, permanent elements of the mosaic, out of which we can mentally construct the whole province. When we have reached a point where we can discover everywhere the same facts, we no longer feel lost in this province; we comprehend it without effort; it is _explained_ for us.