Where Are We ?
BY F. W. BAIN.
MATHEMATICS, a " Mesopotamian " word, meaning nothing but quantitative-calculation, is, like machinery, a good servant, but a bad master. And a recent controversy in The Times, set going by Mr. Stephen Coleridge, is a symptom of the uneasiness widely felt, yet shrinking from expression, by the man in the street. The world of non-mathematical laymen, which, like Carlyle's Black African, looks at mathematics with " upturned awe-struck eye," is beginning to kick a little at the things which mathematical pundits are blandly requiring them to swallow on their knees, as it were, before authority hidden in the clouds, enigmatic and oracular, unintelligible, incomprehensible. Thus, on Monday, Sir James Jeans headed his last pon- tifical utterance, New Wine in old Bottles; thereby begging the question, which is simply—are these " novelties " wine at all, and not rather a dubious and muddy liquid unworthy of any bottles, old or new ? We submit, with respect, a far better heading, New Lamps for old Ones : an exchange notoriously not always for the better. God forbid that we should here impiously revive the old controversy as to whether mathematical calcula- tion deserves to be regarded as thinking at all. But we may perhaps profitably remember a morsel of the wisdom of Aristotle, that the discussion of the basic ideas of mathematics is the proper business, not of the mathe- matician, but of the philosopher : a great truth, of which very few mathematical disputants seem to be aware.
Space, for example. The Einsteins, Eddingtons, Jeans and company, limited or unlimited, present us (we refrain from introducing " space-time," which, Mr. Bertrand Russell tells' us is the most important of all the novelties that Einstein has introduced) present us with a space that curves, bends, and otherwise possesses figure. Mr. Stephen Coleridge objects, and with reason. The German word for space—Raum—is more expressive of the nonsensical absurdity than ours. Nothing can curve, or bend in any direction, unless it has room in which to do it. That room is space, infinite space, the possibility of movement, or figure, in any or all directions. Far be it from us to suggest that Einstein and company, by bestowing so generously a figure on space—nay, even more generously, presenting it with time as an extra dimension—are only thereby betraying the most lamentable incapacity to grasp elementary philosophical ideas. As if, forsoOth that were possible. We modestly confine ourselves to pointing out, what is undeniable, that their space is not space, and their time is not time. Like the ideas of the orthodox economists, now happily buried, these their ideas arc, so to say, only Platonic ideas, unreal figments, non- existent entities, a mathematical phantasmagoria. We must realize this, without allowing ourselves to be brow- beaten by visionary skeletons, or seared, as we may well be, by that truly Mesopotamian absolute—relafirify.
There, said the immortal Panurge, did I wait for thee ! And we have been waiting for something more or less resembling the Einstein incarnation, ever since the
eighties " of last century, when we were a Junior Student of Christ Church, that very House which is now, by a strange coincidence, the home of Einstein himself : where among other things, we studied attentively that masterly and indirectly prophetic volume of analysis and criticism—The Concepts and Theories of Modern Physics, by J. B. Stallo. Once you start juggling with transcendental geometry and its kin, anything may happen : strange entities, ethers, times, spaces, dimensions innumerable, dance about like ghosts in a dim vacuum of thought, recalling vaguely the " horrific question " raised by Rabelais, so much enjoyed by Michelet : Could the Chimera, buzzing in the Void, devour the Second In- tentions? But critical reason, sooner or later, takes her revenge on the calculator who ignores her. The relativity that is not rooted in reality is rotten at the core : and the game of " explaining the Universe "—a large order— by postulating self-contradictory figments is just as idle in science as it is in theology : a mere waste of time : not Einstein's time, but ours, the time of the world, ancient or modern. When space bends, and time becomes a dimension of space, thinking disappears, and a lunatic asylum would be recommended by the faculty.
The cure is in Aristotle, that wonderful legislator of thought, who anticipated and provided against all these delusions beforehand, two thousand years ago, by prefixing to his immortal analysis of science in general and the various sciences in particular something more necessary still, a preliminary investigation of the back- ground of Nature, her warp and woof, time and space, infinity and causation, necessity and chance, motion and change, which modern science and philosophy despised and rejected only to go wildly astray. Hence come scientific men, like Huxley, professing a philosophy that makes science impossible, or like Darwin, vainly endeavouring to explain organic Nature by accidental infinitesimal variation : hence come the Rants, advocating a theory of knowledge which cuts its own throat, or the Hegels, confusing Being with Thinking, and contraries with contradictions : hence come the calculators, noticed by Aristotle in his own day, who mistake calculation for philosophy, the instrument for the brain. But we may safely leave Aristotle to look after himself, and say, with Macrobius, hinc profecti, hue revertuntur. The world will return to him, all in good time, when it is tired of floundering about in the bogs of philosophical absurdity into which it has fallen by following a succession of Wills o' the Wisp, who arc notable for nothing so much as a total lack of Aristotle's most characteristic and invaluable quality, critical common sense. And common sense is emphatically the true Catholic Church of humanity outside which there is no salvation, so that we may say to every philosopher who flouts it, with rugged old Piers Plowman :
" But holychirehe and holde better togideres,
The moste myschief on molde is mountyng wel Caste."
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