MATHEMATICAL FICTIONS.

(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_.

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