12/11 TEMPORARY INDEPENDENCE 





A C 



Figure 12/10/2. 



The question has not only theoretical but practical importance. 

 Many experiments require that one system be shielded from effects 

 coming from others. Thus, a system using magnets may have to 

 be shielded from the effects of the earth's magnetism ; or a thermal 

 system may have to be shielded from the effects of changes in 

 the atmospheric temperature; or the pressure which drives blood 

 through the kidneys may have to be kept independent of changes 

 in the pulse-rate. 



A first suggestion might be that the three variables B should 

 be removed. But this conceptual removal corresponds to no 

 physical reality: the earth's magnetic field, the atmospheric 

 temperature, the pulse-rate cannot be 4 removed '. In fact the 

 answer is capable of proof (S. 22/14): that A and C should be 

 independent and state-determined it is necessary and sufficient that 

 the variables B should be null-functions. In other words, A and C 

 must be separated by a wall of constancies. 



It also follows that if the variables B can be sometimes fluctu- 

 ating and sometimes constant (i.e. if they behave as part-functions), 

 then A and C can be sometimes functionally joined and sometimes 

 independent, according to B's behaviour. 



12/11. Here are some illustrations to show that the theorem 

 accords with common experience. 



(a) If A (of Figure 12/10/1) is a system in which heat-changes 

 are being studied, B the temperatures of the parts of the con- 

 tainer, and C the temperatures of the surroundings, then for A 

 to be isolated from C and state-determined, it is necessary and 

 sufficient for the .B's to be kept constant, (b) Two electrical 

 systems joined by an insulator are independent, if varying slowly, 

 because electrically the insulator is unvarying, (c) The centres 

 in the spinal cord are often made independent of the activities in 

 the brain by a transection of the cord; but a break in physical 

 continuity is not necessary: a segment may be poisoned, or 



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