132 HABIT AND INTELLIGENCE. [ch. xxxvi. 



a rapid inference. The conce^dion of plane surfaces and straight 

 lines, or rather the possibility of those conceptions, comes not 

 through sight, but through touch. 



Parallel straight lines never meet ; but two parallel great 

 circles cannot be drawn on the sjahere. Any two great circles 

 which must necessarily intersect each other in two points (thus the 

 when ^T)ro- ^^I'i'^i^^ lines on a globe intersect at the two poles). Now, as 

 cluced. straight lines are represented to the eye by arcs of great circles, 

 it follows that straight lines as seen by the eye are lines which 

 would meet and intersect if they were produced. 

 Reid's All this was stated long ago by Eeid, in his " Geometry of 



o/v'isibles ^i^i^^^s," and has often been stated since. But it has been stated 

 in that form of needless jjaradox, ■which tends to obscure truth 

 at once to those who are urging it and to those whom they 

 address. It has been said that if we had no geometrical con- 

 ceptions except what came to us through the sense of sight, it 

 would appear to us that parallel straight lines could, and if 

 produced must, enclose a space. Now, the accurate way of 

 making this statement is, that if we had no geometrical concep- 

 tions except what we acquired through the sense of sight, we 

 should have no concejDtion of straight lines at all, but of great 

 circles instead. 



These remarks will show us what to think of the following 

 puzzle — for it is really no better — from " Essays by a Bar- 

 rister : " — 

 A Bar- " It would also be possible to put the case of a world in 



nsters -yvhich two lines would be universally supposed to include a 

 space. Imagine a man who had never had any experience ot 

 straight lines through the medium of any sense whatever, sud- 

 denly placed ujDon a railway stretching out on a perfectly 

 straight line to an indefinite distance in each direction. He 

 would see the rails, which would be the first straight lines he 

 had ever seen, apparently meeting, or at least tending to meet, 

 at each horizon ; and he would thus infer, in the absence of all 

 other experience, that they actually did enclose a space when 

 produced far enough." 



The answer to this is, that what he would see would not be 

 two straight lines, but arcs of two great circles, each of the arcs 

 being nearly, if not quite, a semicii'cle ; and, I supjiose, he would 

 have no reason to infer anything else. 



