86 POPULAR SCIENCE MONTHLY 



Does this form exist, or, if you choose, can we represent to our- 

 selves space of more than three dimensions? And first what does this 

 question mean? In the true sense of the word, it is clear that we can 

 not represent to ourselves space of four, nor space of three, dimensions ; 

 we can not first represent them to ourselves empty, and no more can we 

 represent to ourselves an object either in space of four, or in space 

 of three, dimensions : ( 1 ) Because these spaces are both infinite and we 

 can not represent to ourselves a figure in space, that is, the part in the 

 whole, without representing the whole, and that is impossible, because 

 it is infinite; (2) because these spaces are both mathematical continua 

 and we can represent to ourselves only the physical continuum; (3) 

 because these spaces are both homogeneous, and the frames in which 

 we enclose our sensations, being limited, can not be homogeneous. 



Thus the question put can only be understood in another manner; 

 is it possible to imagine that, the results of the experiences related above 

 having been different, we might have been led to attribute to space more 

 than three dimensions; to imagine, for instance, that the sensation of 

 accommodation might not be constantly in accord with the sensation of 

 convergence of the eyes; or indeed that the experiences of which we 

 have spoken in paragraph 2 and of which we express the result by 

 saying ' that touch does not operate at a distance,' might have led us 

 to an inverse conclusion. 



And then evidently yes that is possible. From the moment one 

 imagines an experience, one imagines just by that the two contrary 

 results it may give. That is possible, but that is difficult, because we 

 have to overcome a multitude of associations of ideas, which are the 

 fruit of a long personal experience and of the still longer experience of 

 the race. Is it these associations (or at least those of them that we have 

 inherited from our ancestors), which constitute this a priori form of 

 which it is said that we have pure intuition ? Then I do not see why 

 one should declare it refractory to analysis and should deny me the 

 right of investigating its origin. 



When it is said that our sensations are ' extended ' only one thing 

 can be meant, that is that they are always associated with the idea of 

 certain muscular sensations, corresponding to the movements which 

 enable us to reach the object which causes them, which enable us, in 

 other words, to defend ourselves against it. And it is just because this 

 association is useful for the defense of the organism, that it is so old 

 in the history of the species and that it seems to us indestructible. 

 Nevertheless, it is only an association and we can conceive that it may 

 be broken; so that we may not say that sensation can not enter con- 

 sciousness without entering in space, but that in fact it does not enter 

 consciousness without entering in space, which means, without being 

 entangled in this association. 



JSTo more can I understand one's saying that the idea of time is log- 



