CURRENT LITERATURE
FOURFOLD GEOMETRY : BEING THE ELEMENT.. ARY GEOMETRY OF THE FOUR DIMENSIONAL WORLD. By David Beveridge Mair. (Methuen. 8s. 6d. net.) —It is hard for mankind, having been conscious for so long of three dimensions only, suddenly • to wake up to four dimensional geometry and try. to think consistently in its terms: :The words themselves- must be invented. Language, on the whole, 'has been-applicable to a world-conception in which space and time were radically separate categories : it was only in mysticism that the two were taken up into a unity. Mr. Mair has written a valiant geometry. His phrases will continually Surprise = thoee whose geometrical knowledge has been confined to three dimensions. Often these new terms sound extremely simple it would not occur .tn.most of us that we were dealing with highly technical language If we caught Sight suddenly of the sentence : " This operator has a •blickhand stroke."
There are advantages in these simple terms ; they strike the mind with forde and' are easily remembered. Arid they " relieve .the _extremely difficult task.of txying insome. fashion . to visualize the lour-dimensional world-. •A quotation from the short chapter on " Enclosures " will show that there h actually almost a poetic pleasure to be gained from Mr Mair's expositions :— " A onefold is a line, and two points in it separate the 84.04 between them from the rest of the onefold. Thus if we stars from a point of the stretch and travel in either direction along the onefold we come up against one of the points. The stretch is thus enclosed by a barrier consisting of the two points. ll the line lies in a twofold and we are allowed free movement io the twofold, we can by stepping off the stretch come to any point of the line we please without meeting the barrier."
The knowledge of classical geometry necessary to the reader is not great ; he will • need, however, a constant alertness and a great power of concentration. Mr. Mair is charting regions which have as yet scarcely been explored and a good deal of his work is entirely new. He writes with an impeccable authority upon the- Einstein theory of relativity : the book is therefore invaluable to those who would be " among the well-informed." But, beyond that, its study- gives an intellectual delight comparable only with those to be gained from music; poetry, and art at the purest. We hope that Mr. Mair will presently write as condensed and illuminating an account of the geometry of spaces in which straight lines are replaced by geodesics. .
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