y 



64 THEORETICAL BIOLOGY 



unperceived ; as, for instance, when one direction-sign falls 

 on several moment-signs. The movement then remains below 

 the threshold, because the content of one moment-sign is not 

 appreciably distinguishable from that of its predecessor ; for 

 the observer, this means that nothing changes. 



It is only when, in a series of moments, several direction- 

 signs coincide with one moment, that their content is differen- 

 tiated and movement is perceived. 



The rule that a movement is perceptible only when its 

 gradient is neither too steep nor too level, is rendered in- 

 telligible through the introduction of threshold ; moreover, 

 this concept makes it more clearly defined. Movement must 

 be slow enough for all the direction-signs to occur within 

 three moment-signs, and yet it must be fast enough for at 

 least two direction-signs to occur within each moment-sign. 

 If these conditions are unfulfilled, then no movement is 

 initiated ; everything is stationary. 



CALCULATION OF THE RULE OF MOTION 



In order to make susceptible of calculation the relations 

 between these fundamental qualities of space and time, it is 

 necessary to consider them as world-factors. So long as we 

 consider local signs, moment-signs and direction-signs as mere 

 qualities of our mind, they remain three non-comparable 

 magnitudes. But each of these elementary magnitudes has 

 its task to perform in the world, and then it comes into correla- 

 tion with the other magnitudes, which can be expressed in 

 numbers. 



For all three qualities, the task prescribed is the same. 

 Each serves as the smallest receptacle or the smallest frame 

 for other qualities which, only by being so enclosed, become 

 part of the cosmic system. Local, moment- and direction- 

 signs renounce all claim to being " content," and endow the 



