March 12, 1885] 



NA TURE 



43i 



SCIENTIFIC ROMANCES ' 



•//>ff Romances. No. I. " What is the Fourth 

 Dimension?" By C. H. Hinton, B.A. (London: W. 

 Swan Sonnenschein, 1884.) 



THE subject discussed in this short but carefully 

 worked out pamphlet of 32 pages, seems to be 

 coming to the front once more. Helmholtz, in his classi- 

 cal paper on " The Origin and Meaning of Geometrical 

 Axioms" {Mind, Xo. 3, July 1S76), clearly states our 

 ion with regard to its representation: "As all our 

 means of sense-perception extend only to space of three 

 dimensions, and a fourth is not merely a modification of 

 what we have, but something perfectly new, we find our- 

 selves, by reason of our bodily organisation, quite unable 

 to represent a fourth dimension.'' 



In this article, as also in the excellent paper on 

 " Measurement," contributed by Dr. Ball to the " Ency- 

 clopaedia Britannica" (vol. xv.), many references are 

 given to writers who have touched upon this point, but 

 our present author has made a contribution to the subject 

 which is independent of these writers, and puts it clearly 

 before his readers. There are many backward glances 

 to the inferior spaces, and here and there we find slight 

 points of contact between our author and him of " Flat- 

 land," which show that the two were thinking of the same 

 matter, possibly at the same time. 



" By supposing away certain limitations of the funda- 

 mental conditions of existence as we know it, a state of 

 being can be conceived with powers far transcending our 

 own. When this is made clear it will not be out of place 

 to investigate what relations would subsist between our 

 mode of existence and that which will be seen to be a 

 possible one." From a simple illustration it is shown 

 that in our space there are three independent directions, 

 and only three (as Helmholtz says, by the motion of a 

 surface, a surface or a solid is described, but by the 

 movement of a solid a solid and nothing else is 

 described). Why should there be this limitation ? He 

 then discusses the cases of the inferior beings, which we 

 put thus : it would be as surprising for a Flat'lander to be 

 lifted out of his closed pentagonal house and put outside 

 as it would be to an ordinary human being " if he were 

 suddenly to find himself outside a room in which he had 

 been, without having passed through the window, doors, 

 chimney, or any opening in the walls, ceiling, or 

 floor." 



The upshot of the first chapter is that beings can be 

 conceived as living in a more limited space than 

 ours. 



A straight line by a movement at right angles to itself 

 begets a square, but the Linelander can only conceive of 

 movement in its straight line. The square in the same 

 way can be made to move so as to beget a cube, yet the 

 Flatlander has no idea of movement perpendicular to its 

 plane. Now proceed similarly with the cube : " We must 

 suppose the whole figure as it exists to be moved in some 

 direction entirely different from any direction within it, 

 and not made up of any combination of the directions in 

 it. What is this? It is the fourth direction." 



Arguing from the analogy we know, we arrive at the 



1 For some remarks on the subject of this article, by Mr. G. F. Rodwell, 

 we refer the reader to Nature, vol. viii. pp. 8, 9. 



following results : The line has 2 points, the- square 4 

 (angular) points, the cube S points, the foursquare (Mr. 

 Hinton's name for the fourth dimension figure) 16 points ; 

 in the respective cases the lines are 1, 4, 12, and 

 2 X 12 + 8, i.e. 3: ; the plane surfaces are o, 1,6, and 

 2x6+12, i.e. 24. We get then the foursquare with 16 

 points, 32 lines, 24 surfaces, and bounded by 8 cubes ; to 

 us, if it were resting in " space," it would look like a cube. 

 Of course there are other details. We pass on to Chapter 

 III., in which are discussed the relations which beings in 

 four dimensions would have with us. To us, of course, 

 they would have the appearances of beings in space (as 

 to a Flatlander a sphere appears to be a circle). " Why, 

 then, should not the four dimensional beings be ourselves, 

 and our successive states the passing of them through the 

 three-dimensional space to which our consciousness is^ 

 confined?" This is discussed in some detail and illus- 

 trated by means of threads. We confess to not quite 

 following our author in his conclusion : " It is needless to 

 say that all the considerations that have been brought 

 forward in regard to the possibility of the production of 

 a system satisfying the conditions of materiality by the 

 passing of threads through a fluid plane, holds (sic) good 

 with regard to a four-dimensional existence passing 

 through a three-dimensional space. Each part of the 

 ampler existence which passed through our space would 

 seem perfectly limited to us. We should have no indica- 

 tion of the permanence of its existence. Were such a 

 thought adopted, we should have to imagine some stu- 

 pendous whole, wherein all that has ever come into being 

 or will come, co-exists, which, passing slowly on, leaves 

 in this flickering consciousness of ours, limited to a 

 narrow space and a single moment, a tumultuous record of 

 changes and vicissitudes that are but to us (sic). Change 

 and movement seem as if they were all that existed. But 

 the appearance of them would be due merely to the 

 momentary passing through our consciousness of ever- 

 existing realities." 



The concluding chapter leads up from the inferior 

 dimensions, and shews how, in four dimensions, the 

 "box trick" might be effected. Some interesting illus- 

 trations from liquids and gases follow, and then, on the 

 hyp' 'thesis of there being a fourth dimension, two possible 

 alternatives arc discussed. " If we are in three dimen- 

 sions only, while there are really four dimensions, then 

 we must be relatively to those beings who exist in four 

 dimensions as lines and planes are in relation to us. 

 That is, we must be mere abstractions. In this case we 

 must exist only in the mind of the being that conceives 

 us, and our experience must be merely the thoughts of 

 his mind- a result which has apparently been arrived at, 

 on independent grounds, by an idealist philosopher. 

 The ether alternative is that we have a four-dimensional 

 existence. In this case our proportions in it must be 

 infinitely minute, or we should be conscious of them. If 

 such be the case, it would probably be in the ultimate 

 particles of matter that we should discover the fourth 

 dimension, for in the ultimate particles the sizes in the 

 three dimensions are very minute, and the magnitudes in 

 all four dimensions would be comparable." 



We have aid enough to show that the "Romance " is 

 a curious one, and not without interest to many of ou r 

 readers, to whom we commend it. 



