DIMENSIONS IN PHYSICS.

Press, 1 February 1930, Page 7

DIMENSIONS IN PHYSICS.

THAT PROBLEM OF THE FIFTH

We have scarcely accustomed ourselves to talk of four-dimensional space, and now Professor Richardson, the latest Englishman to be awarded the Nobel Prize, threatens us with a. space that has five dimens : ons. Modern phvsies make us feel ill at ease. We wonder where we stand. What ought we to think about it »ll! Writes Montague Slater, in the London "Daily Telegraph.'' But on reflection we find (as tin Frenchwoman remarked of the man who walked several miles without his head) that "in a case like that it is the first steps that count." Space as we know it has length, breadth, and height. Once that eoncaption is put aside by physicists, whether in favour of four, Ave, or seven dimensional space, we move into an unfamiliar world. We have stepped through the looking-glass, and as the Bed Qiwen might have said, eutered a valley compared to which yo.u might call any other valley a mountain. And*in passing it might be well to notice that it is not by accident that the theories of modern physicists remind us of the adventures of Alice. Carroll was not a mathematician for nothing. Id?as, conceptions, laws of nature, ean be, and ofte- arc, dissociated from anything we ean visualise. The joko in the Red Queen's remark is simply in this—that it expresses in words that seem perfectly sensible an idea which our imaginations cannot grasp—a mountain which is like a vall*»y. That is, I take it, precisely what the modern physicist is doing. Our minds are made in such a way that in no circumstances can we imagine anything in more or less than threo dimensions. We cannot picture a line or a plane. The nearest we ean get i-=, say, a piece of wire infinitely fine, and a piece of paper equally thin. But once we fulfil the terms of tho definitions and give our wir«? no breadth and our paper no thickness, wo aro forced to say that they cannot exist. These are facts which schoolboys aro familiar with. But they are also principles on which Kant basod his critique of pur* reason. Threedimensional space—or what we call >olidity—is the shape of our mental images of things. Nothing we can do can alter it. But long before Einstein we talked as though we could think in terms of other than three dimensions. For instance, art critics wiJI say of a drawing that it is two-dimensional, flat. Perhaps the fascination of drawing is that it wems to be playing tricks with space—making a hole in a solid wall. But it is better to tread carefully here or we shall find ourselves involved in a controversy that has divided studios into warring camps. Vet to have peeped into that odd space "behind the picture,'' and to see that there is no need to go in for five dimensions to find a mystery or two, will serve our turn. A picture never is "flat," or we should s're nothing but a blank; vet we know what wo mean when we call it "flat." (By the by, what do we meant) If only we consider what we wew doing when we studied Euclid at school

we ur*-> less awed by the exploit* of physicists in 11 dimensional geometry. We began by thinking of one-diiueii-sional space," which is unimaginable, but which wo could represent to our selves by drawing n lin-. We w.-nr ,m to work out proposition* about two dimensional space (also unimaginable i, cutting it up into triangles which wo represented by figure*. Few of us go t». the point of attacking 1 hree dimensional geometry. Wo rested among the parallelograms and mad" no attack on the parallelepiped. Physicists are in a higher form, and do not even represent their unimjjginabilities ♦» themselves b.v figures, but are content with /ilgebraie symbols. " One draws reluctantly to Hie conclusion that most of us will linv« to be eon tent to remain in the lower form. Whether physicists find it more cm venient to ut*e. the algebraic formula which imply (our diineiiHioiiK, or thus* which imply fivp, may disturb the sleep of mathematicians, but not of the rest of us —unless we encourage nightmare" and try to imagine what five dimensions mean. Hume, the sceptic, has a delightful passage in which he says, having proved to his own satisfaction tlml there is no such thing »s causality, he leaves his study and has dinn«r, and a game of backgammon. As soon a« lie I.as cloned the study door (he says), his scepticism melts away, and ho can account for dinner only on the assumption that effects follow causes. Life and backgammon are possible on no other term-.. I suspect it is not altogether different with five dimen 810118.