12/8 TEMPORARY INDEPENDENCE 



about a system quickly and easily when the system has a suitable 

 simplicity and when it is known that the listener will interpret 

 them suitably. But always the speaker must be prepared, if the 

 system is not simple, to add supplementary details or even to go 

 back to a description of the transitions themselves ; here there is 

 always security, for here the information is complete. 



12/5. Because there are various degrees of independence, so that 

 Y may be independent of X over a small region of the field but 

 not independent if the same region is extended, it follows that 

 one system can give a variety of diagrams of immediate effects — 

 as many as there are ranges and conditions of independence 

 considered. This implication is unpleasant for us; but we cannot 

 evade the fact. (Fortunately it commonly happens that the inde- 

 pendencies in which we are interested give much the same diagram, 

 so often one diagram will represent all the significant aspects of 

 independence.) 



12/6. So far we have discussed F's independence of X. What- 

 ever this is, it in no way restricts, in general, whether X is or is 

 not independent of Y. If X is independent of Y, but Y is not 

 independent of X, then X dominates F. 



12/7. The definition given so far refers to independence between 

 two variables. It may happen that every variable in a system A 

 is independent of every variable in a system B, all possible pairs 

 being considered. We then say that system A is independent of 

 system B. 



Again, such independence does not, in general, restrict the 

 possibilities whether B is or is not independent of A; A may 

 dominate B. 



12/8. To illustrate the definition's use, and to show that its 

 answers accord with common experience, here are some examples. 

 If a bacteriologist wishes to test whether the growth of a micro- 

 organism is affected by a chemical substance, he prepares two 

 tubes of nutrient medium containing the chemical in different 

 concentrations (X) but with all other constituents equal; he seeds 

 them with equal numbers of organisms ; and he observes how the 

 numbers (Y) change as time goes on. Then he compares the two 



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