[DUPUis] PRESIDENTIAL ADDRESS IS 



these. So that if space possesses all or any of these, it is difficult to see 

 how we are to distinguish between space and matter. For we are com- 

 pelled to call that matter which possesses the attributes of matter, and 

 just to the extent to which space possesses these attributes, to that extent 

 it is akin to matter. It appears then that this new space, being to some 

 extent, at least, akin to matter is best described as some new form of ether. 

 For although very little is known of the luminiferous ether which the 

 physicist has been compelled to create for the purpose of explaining 

 phenomena, yet it is assumed to have some properties which are more or 

 less physical, and which are not very different from those attributed to 

 the new space. 



But it is hard to see what we arc to gain by substituting for the 

 luminiferous ether something very like it, but which we agree to call 

 space. 



Of course the new geometer may say that his space has reference to 

 the possibility of describing geometrical figures, while the luminiferous 

 ether has no such reference. This is quite correct. But, after all. the 

 power of restricting the forms of geometrical figures is only a new 

 property added to the ether, and does not therefore transform the ether 

 into space. And the only way out of the dilemma is for the new geometer 

 to deprive his space of all physical properties whatever. 



But this would destroy the new geometry, because a space without 

 physical properties cannot have a bend in it, or have curvature ; it cannot 

 exert an influence, or offer a resistance ; it cannot suffer displacement, or 

 propagate wave motion, or be thrown in vortex whirls. 



The fact is that space is the antithesis of matter, and instead of being 

 endowed with phj^sical properties, is the negation of all such proi^erties. 

 When we, in thought, extract from any material thing ever}' property 

 except that of extension, we ai'rive, as nearly as we can get, to the idea 

 of space. And even the extension does not belong to space or form any 

 part of it, but to the material thing which exists in space. So that space 

 is merely the possibility of the existence of material or of conceptual 

 entities. As such it is not subject to any tests or any hy^DOtheses, and 

 instead of geometry being determined by the conditions of space, space 

 is determined by the conditions Of geometry. 



To say that we can imagine elliptic space on the surface of a great 

 sphere, or hyperbolic space on the surface of an extended hyperboloid, is 

 of no account whatever ; for space in the absolute is unimaginable and 

 unthinkable, and all that we imagine is something which can exist in 

 space. When we try to imagine a point in space what we really imagine 

 is that point in its relation to ourselves, through some geometrical figure, 

 usually the straight line, which in this case resolves itself into the idea of 

 distance, and possibly of dii'cction. 



Then, that geometry which is thinkable and consistent carries within 

 itself the idea of a thinkable and consistent space ; and a geometry which 



