[dupuis] presidential ADDRESS 9 



sible. Similarly, if his sea of infinitesimal depth were a plane it would 

 occupy space of two dimensions only, but as soon as flexure of any kind 

 takes place, the two dimensions rise to three, and the third dimension is 

 necessaiy in order that flexure may be possible. And the fish in this 

 latter case, although supposed to have knowledge of only two dimensions, 

 is really living and moving in space of three dimensions. 



Then reasoning from analogy, again, we see that if our three-dimen- 

 sional space is curved, there must be a four-dimensional space in order to 

 make such curvature possible, and in which the curvature takes place. 

 And hence, in the new geometry, the postulate that gives to tri-dimen- 

 sional space what has been called a curve or twist, makes the existence of 

 four-dimensional space a necessity. And if there is no space of four 

 dimensions, then the transcendental geometry is an impossible one, and 

 must take rank with the mathematical imaginaries. Also, if there be 

 space of four dimensions, why not of five, or six, or n dimensions, for it 

 is just as difiicult to conceive the first of these as to conceive the last. 



It is quite impossible to describe four-dimensional space, or to say 

 what existence in such a space would be like ; for it is absolutely incon- 

 ceivable to minds like ours. IS'evertheless, it appeal's to be very j)lastic 

 in the hands of the new geometers, for in it they find the potency and 

 explanation of many difficulties in physics and chemistry. 



It has been called into use to explain the mysterious wonder-work- 

 ing sometimes eftected by spiritual mediums, for it has been shown that 

 by the aid of space of four dimensions it is possible to tie a knot or to 

 undo one in an endless piece of rope; that it is possible to pass into or 

 out of a closed room, without going through any opening in floor or 

 ceiling or walls; that it would be possible, in fact, to turn the room 

 inside out without particularly disturbing any of its arrangements. 



It is said that a person living in four dimensions could see com- 

 pletely through us, and inspect the working of every internal organ, and 

 of eveiy part of it, as clearly as if we were made of some perfectly 

 transparent liquid or jelly, thus clearly outdoing the best feats of the 

 Eoentgen rays. The value of a four- dimensional physician to the public 

 cannot be overestimated. 



Hinton has shown that by supposing a properly disposed four- 

 dimensional object to pass through our thi-ee-dimensional space, the 

 whole phenomena of the birth, growth, life, and death of an organic 

 being can be readily and scientifically explained. 



Four-dimensional space, also, can be made to furnish a reasonable 

 cause for the impenetrability and the inertia of matter, and under certain 

 conditions for the conservation of energy. 



Ball gets rid altogether of the luminiferous ether, and even gets a 

 possible explanation of the cause of gravitation, by supposing our three- 

 dimensional space to rest on a plate or lamina of four-dimensional space. 



