14/4 DESIGN FOR A BRAIN 



always unambiguous. Other criteria might be confused by some 

 of the fields that ingenuity can construct. But often a simple 

 uniformity holds. Two variables may be independent over all 

 such pairs of initial states ; and sometimes all variables of one 

 set may be independent of all variables of another set : a system 

 R is independent of a system S if every variable in It is independent 

 of every variable in S, all possible pairs being considered. Some 

 region of the field is understood to be given before the test is 

 applied. 



14/4. 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 but with all other constituents equal ; he seeds 

 them with equal numbers of organisms ; and he observes how 

 the increasing numbers of organisms compare in the two tubes 

 from hour to hour. Thus he is observing the numbers of organisms 

 after two initial states that differed only in the concentrations 

 of chemical. 



To test whether an absolute system is dependent on a para- 

 meter, i.e. to test whether the parameter is ' effective ', we observe 

 the system's behaviour on two occasions when the parameter 

 has different values. Thus, to test whether a thermostat is 

 really affected by its regulator one sets the regulator at some 

 value, checks that the temperature is at its usual value, and 

 records the subsequent behaviour of the temperature ; then one 

 returns the temperature to its previous value, changes the posi- 

 tion of the regulator, and observes again. A change of behaviour 

 implies an effective regulator. (Here we have used the fact that 

 by S. 21/4 we can take a null-function into the system without 

 altering its absoluteness, for the change is only formal.) 



Finally, an example from animal behaviour. Parker tested 

 the sea-anemone to see whether the behaviour of a tentacle was 

 independent of its connection with the body. 



* When small fragments of meat are placed on the tentacles 

 of a sea-anemone, these organs wind around the bits of 

 food and, by bending in the appropriate direction, deliver 

 them to the mouth.' 



156 



