SPACE 655 



same object produce on it much brighter impressions, but in the 

 whole of the limited framework the point which occupies the centre 

 will not appear identical with a point near one of the edges. Closer 

 analysis no doubt would show us that this continuity of visual space 

 and its two dimensions are but an illusion. It would make visual 

 space even more different than before from geometrical space, but we 

 may treat this remark as incidental. 



However, sight enables us to appreciate distance, and therefore to 

 perceive a third dimension. But every one knows that this perception 

 of the third dimension reduces to a sense of the effort of accommoda- 

 tion which must be made, and to a sense of the convergence of the 

 two eyes, that must take place in order to perceive an object distinctly. 

 These are muscular sensations quite different from the visual sensa- 

 tions which have given us the concept of the two first dimensions. 

 The third dimension will therefore not appear to us as playing the 

 same role as the two others. What may be called complete visual space 

 is not therefore an isotropic space. It has, it is true, exactly three 

 dimensions; which means that the elements of our visual sensations 

 (those at least which concur in forming the concept of extension) 

 will be completely defined if we know three of them ; or, in mathemat- 

 ical language, they will be functions of three independent variables. 

 But let us look at the matter a little closer. The third dimension is 

 revealed to us in two different ways: by the effort of accommodation, 

 and by the convergence of the eyes. No doubt these two indications 

 are always in harmony; there is between them a constant relation; or, 

 in mathematical language, the two variables which measure these two 

 muscular sensations do not appear to us as independent. Or, again, 

 to avoid an appeal to mathematical ideas which are already rather too 

 refined, we may go back to the language of the preceding chapter and 

 enunciate the same fact as follows : If two sensations of conver- 

 gence A and B are indistinguishable, the two sensations of accom- 

 modation A' and B' which accompany them respectively will also be 

 indistinguishable. But that is, so to speak, an experimental fact. Noth- 

 ing prevents us a priori from assuming the contrary, and if the con- 

 trary takes place, if these two muscular sensations both vary inde- 

 pendently, we must take into account one more independent variable, 

 and complete visual space will appear to us as a physical continuum 

 of four dimensions. And so in this there is also a fact of external 

 experiment. Nothing prevents us from assuming that a being with 

 a mind like ours, with the same sense-organs as ourselves, may be 

 placed in a world in which light would only reach him after being 

 passed through refracting media of complicated form. The two indi- 

 cations which enable us to appreciate distances would cease to be con- 

 nected by a constant relation. A being educating his senses in such a 



