MATHEMATICAL FICTIONS.

Previous

(British Association, 1871.)

The President’s inaugural address, which was going through the press in London while being spoken in Edinburgh, has already been subject to an unusual amount of sharp criticism. For my own part I cannot help regarding it as one of the least satisfactory of all the inaugural addresses that have yet been delivered at these annual meetings. They have been of two types, the historical and the controversial; the former prevailing. In the historical addresses the President has usually made a comprehensive and instructive survey of the progress of the whole range of science during the past year, and has dwelt more particularly on some branch which from its own intrinsic merits has claimed special attention, or which his own special attainments have enabled him to treat with the greatest ability and authority. A few Presidents have, like Dr. Huxley last year, taken up a particular subject only, and have discussed it more thoroughly than they could have done had they also attempted a general historical survey.

Every President until 1871 has scrupulously kept in view his judicial position, and the fact that he is addressing, not merely a few learned men, but the whole of England, if not the whole civilized world. They have therefore clearly distinguished between the established and the debatable conclusions of science, between ascertained facts and mere hypotheses, have kept this distinction so plainly before their auditors that even the most uninitiated could scarcely confound the one with the other.

In Sir William Thomson’s address this desirable rule is recklessly violated. He tells his unsophisticated audience that Joule was able “to estimate the average velocity of the ultimate molecules or atoms” of gases, and thus determined the atomic velocity of hydrogen “at 6225 feet per second at temperature 60 degs. Fahr., and 6055 feet at the freezing point;” that “Clausius took fully into account the impacts of molecules upon one another, and the kinetic energy of relative motion of the matter constituting an individual atom;” and that “he investigated the relation between their diameters, the number in a given space, and the mean length of path from impact to impact, and so gave the foundation for estimates of the absolute dimensions of atoms.” Also that “Loschmidt, in Vienna, had shown, and not much later Stoney, independently, in England, showed how to reduce from Clausius and Maxwell’s kinetic theory of gases a superior limit to the number of atoms in a given measurable space.”

The confiding auditor follows the President through further disquisitions on the “superlatively grand question, what is the inner mechanism of an atom?” and a minute and most definite description of the “regular elastic vibrations” of “the ultimate atom of sodium,” of the manner in which “any atom of gas, when struck and left to itself, vibrates with perfect purity its fundamental note or notes,” and how, “in a highly attenuated gas, each atom is very rarely in collision with other atoms, and therefore is nearly at all times in a state of true vibration,” while “in denser gases each atom is frequently in collision;” besides, a great deal more, in all of which the existence of these atoms is coolly taken for granted, and treated as a fundamental established scientific fact.

After hearing all these oracular utterances concerning atoms, the unsophisticated listener before mentioned will be surprised to learn that no human being has ever seen an atom of any substance whatever; that there exists absolutely no direct evidence of the existence of any such atoms; that all these atoms of which Sir W. Thomson speaks so confidently and familiarly, and dogmatically, are pure fragments of the imagination.

He will be still further surprised to learn that the bare belief in the existence of ultimate atoms as a merely hypothetical probability is rejected by many of the most eminent of scientific men, and that among those who have disputed the idea of the atomic constitution of matter, is the great Faraday himself; that the question of the existence or non-existence of atoms has recently been rather keenly discussed; and that even on the question of the permissibility of admitting their hypothetical existence, scientific opinion is divided; and that such a confident assumption of their existence as forms the basis of this part of the President’s address is limited to only a small section of mutually admiring transcendental mathematicians, Sir W. Thomson being the most admired among them, as shown by the address of Professor Tait to Section A.

It would have been perfectly legitimate and most desirable that Sir W. Thomson should give the fullest and most favorable possible statement of the particular hypotheses upon which he and his friends have exercised their unquestionably great mathematical skill; but he should have stated them as what they are, and for what they are worth, and have clearly distinguished between such hypotheses and the established facts of universally admitted science. Instead of doing this, he has so mixed up the actual discoveries of indisputable facts with these mere mathematical fancies as to give them both the semblance of equally authoritative scientific acceptance, and thus, without any intention to deceive anybody, must have misled nearly all the outside public who have heard or read his address.

As these letters are mainly intended for those who are too much engaged in other pursuits to study science systematically, and as most of the readers of such letters will, as a matter of course, read the inaugural address of the President of the British Association, I have accepted the duty of correcting among my own readers the false impression which this address may create.

As a set-off to the authoritative utterances of Sir W. Thomson on the subject of atoms, I quote the following from an Italian philosopher, who, during the present year, is holding in Italy a position very similar to that of the annual President of our British Association.

Professor Cannizzaro has been elected by a society of Italian chemists to act as this year’s director of a Chronicle of the Progress of Chemical Science in Italy and abroad. In this capacity he has published an inaugural treatise on the history of modern chemical theory, in the course of which he thus speaks of the over-confident atomic theorists: “They often speak on molecular subjects with as much dogmatic assurance as though they had actually realized the ingenious fiction of Laplace—had constructed a microscope by which they could detect the molecules, and observe the number, forms, and arrangements of their constituent atoms, and even determine the direction and intensity of their mutual actions. Many of these things, offered at what they are worth—that is, as hypotheses more or less probable, or as simple artifices of the intellect—may serve, and really have served, to collocate facts and incite to further investigations which, one day or other, may lead to a true chemical theory; but, when perverted by being stated as truths already demonstrated, they falsify the intellectual education of the students of inductive science, and bring reproach on the modern progress of chemistry.”

I translate the above from the first page of the first number of the “Gazetta Chimica Italiana,” published at Palermo in January last. Had these words been written in Edinburgh on the evening of the 2d of August, in direct application to Sir William Thomson’s address, they could not have described more pointedly and truly the prevailing vice of this production. If space permitted, I could go further back and quote the words of Lord Bacon, from the great text-book of inductive philosophy, wherein he denounces the worship of all such intellectual idols as our modern mathematical dreamers have created, and which they so fervently adore.

An able writer in the Daily News of last Friday is very severe upon the biological portion of the President’s address, which contains a really original hypothesis. Sir W. Thomson having stated that he is “ready to adopt as an article of scientific faith, true through all space and through all time, that life proceeds from life, and from nothing but life,” asks the question, “How then did life originate on the earth?” and tells us that “if a probable solution consistent with the ordinary course of nature can be found, we must not invoke an abnormal act of creative power.”

He assumes, with that perfect confidence in mathematical hypotheses which is characteristic of the school of theorists which he leads, that “tracing the physical history of the earth backwards, on strictly dynamical principles, we are brought to a red-hot melted globe, on which no life could exist;” and then, to account for the beginning of life on our earth as it cooled down, he creates another imaginary world, which he brings in collision with a second similar creation, and thereby shatters it to fragments. He further imagines that one of these imaginary broken-up worlds was already stocked with the sort of life which he says can only proceed from life, and that from such a world thus stocked and thus smashed “many great and small fragments carrying seed and living plants and animals would undoubtedly be scattered through space;” and that, “if at the present instant no such life existed upon this earth, one such stone falling upon it might, by what we blindly call natural causes, lead to its becoming covered with vegetation.”

The conclusion of this paragraph is instructively characteristic of the philosophy of Sir William Thomson and his admirers. He says that “the hypothesis that life originated on this earth through moss-grown fragments of another world may seem wild and visionary; all I maintain is that it is not unscientific.”

I have italicized the phrases which, put together, express the philosophy of this school of modern manufacturers of mathematical hypotheses. It matters not to them how “wild and visionary,” how utterly gratuitous any assumption may be, it is not unscientific provided it can be invested in formulÆ, and worked out mathematically. These transcendental mathematicians are struggling to carry philosophy back to the era of Duns Scotus, when the greatest triumph of learning was to sophisticate so profoundly an obvious absurdity that no ordinary intellect could refute it.

Fortunately for the progress of humanity, there are other learned men who firmly maintain that the business of science is the discovery and teaching of simple sober truth.

The writer of the Daily News article above referred to very charitably suggests that Sir W. Thomson may be “poking fun at some of his colleagues,” and compares the moss-grown meteorite hypothesis with the Hindoo parable which explains the stability of the earth by stating that it stands on the back of a monster tortoise, that the tortoise rests upon the back of a gigantic elephant, which stands upon the shell of a still bigger tortoise, resting on the back of another still more gigantic elephant, and so on. Sir W. Thomson, of course, requires to smash two more worlds in order to provide a moss-grown fragment for starting the life upon the world which was broken up for our benefit, and so on backwards ad infinitum.


                                                                                                                                                                                                                                                                                                           

Clyx.com


Top of Page
Top of Page