CONSTANCY AND INDEPENDENCE 14/6 



(He has established that the behaviour is regular, and that the 

 system of tentacle-position and food-position is approximately 

 absolute. He has described the line of behaviour following the 

 initial state : tentacle extended, food on tentacle.) 



4 If, now, a distending tentacle on a quiet and expanded 

 sea-anemone is suddenly seized at its base by forceps, cut 

 off and held in position so that its original relations to the 

 animal as a whole can be kept clearly in mind, the tentacle 

 will still be found to respond to food brought in contact 

 with it and will eventually turn toward that side which was 

 originally toward the mouth.' 



(He has now described the line of behaviour that follows an initial 

 state identical with the first except that the null-function ' con- 

 nection with the body ' has a different value. He observed that 

 the two behaviours of the variable ' tentacle-position ' are identi- 

 cal.) He draws the deduction that the tentacle-system is, in this 

 aspect, independent of the body-system : 



4 Thus the tentacle has within itself a complete neuro- 

 muscular mechanism for its own responses.' 



The definition, then, agrees with what is usually accepted. 

 Though clumsy in simple cases, it has the advantage in complex 

 cases of providing a clear and precise foundation. By its use 

 the independencies within a system can be proved by primary 

 operations only. 



14/5. In an absolute system it is not generally possible to 

 assign the dependencies and independencies arbitrarily. For if 

 x is dependent on y, and y is dependent on z, then x must neces- 

 sarily be dependent on z. This is evident, for when s's initial 

 state is changed, i/'s behaviour is changed ; and these changed 

 values of y, acting in an absolute system, will cause x , s behaviour 

 to change. So the observer will find that a change in z 9 s initial 

 state is followed by a change in as's behaviour. (A formal proof 

 is given in S. 24/11.) 



14/6. We can now see that the method for testing an imme- 

 diate effect, described in S. 4/12, is simply a test for independence 

 applied when all the variables but two are held constant. The 

 relation can be illustrated by an example. Suppose three real 

 machines are linked so that their diagram of immediate effects is 



% — > y — > x. 

 157 



