THE GEOMETRY OF MOTION 195 



^ 2. — Conceptual Analysis of a Case of Perceptual Motion. 



Point- Motion 



We shall, I think, best obtain clear ideas of motion by 

 examining some familiar case of physical change of 

 position and endeavouring to analyse it into simple types 

 which may be easily discussed by the aid of geometrical 

 ijdeals. Let us take, for instance, the case of a man 

 ascending a staircase which may have several landings and 

 turns in its course. The changes in our sense-impressions 

 during the man's ascent are of an extremely complex 

 character, and we see at once how difficult, if not 

 impossible, it would be to describe all that we perceive. 

 Not only the position of the man on the staircase changes, 

 but his hands and his legs are perpetually varying their 

 position with regard to his trunk, while his trunk itself 

 turns and oscillates, bends and alters its shape. For 

 simplification let us, in the first place, fix our attention on 

 some small element of his person ; let us follow with our 

 eye, for example, the top button of his waistcoat. Now 

 the first observation that we make is that this button 

 takes up a series of positions which are perfectly con- 

 tinuous from the start to the finish of the ascent. There 

 can be no break in this series of positions anywhere 

 throughout the whole extent of the staircase ; for, if there 

 were any, the button must, in accurate language, have 

 ceased to be a permanent group of sense-impressions, and 

 to be distinguished from other groups under the mode 

 space. In ordinary parlance, it must " have left our space 

 and come back to it again " — a phenomenon totally con- 

 trary to the experience of the normal human perceptive 

 faculty. If we cut the button off the waistcoat, we could 

 still conceive it to move up the staircase in precisely the 

 same manner as when the man wore it, — carried up, 

 let us suppose, by an invisible spirit hand. It will be 

 obvious that this motion of the button, if fully known to 

 us, would tell us a good deal about the motion of the 

 man. It would not describe, of course, how he moved his 

 legs and arms about, but it would indicate very fairly 



