DESIGN FOR A BRAIN 21/14 



These observations give the functions of S. 19/7. Differentiation 

 of these (as in the Corollary of S. 19/9) will give the canonical 

 representation, and thus those of the parts, to which the other 

 variables now come as parameters. Thus we can also work from 

 an empirical knowledge of the whole to a deduced knowledge of 

 the parts and their joining. 



21/14. It is now becoming clear why the state-determined 

 system, and its associated canonical representation, is so central 

 in the theory of mechanism. If a set of variables is state-deter- 

 mined, and we elicit its canonical representation by primary 

 operations, then our knowledge of that system is complete. It is 

 certainly not a complete knowledge of the real ' machine ' that 

 provides the system, for this is probably inexhaustible; but it is 

 complete knowledge of the system abstracted — complete in the 

 sense that as our predictions are now single-valued and verified, 

 they have reached (a local) finality. If a tipster names a single 

 horse for each race, and if his horses always win, then though he 

 may be an ignorant man in other respects we would have to admit 

 that his knowledge in this one respect was complete. 



The state-determined system must therefore hold a key place 

 in the theory of mechanism, by the strategy of S. 2/17. Because 

 knowledge in this form is complete and maximal, all the other 

 branches of the theory, which treat of what happens in other 

 cases, must be obtainable from this central case as variations 

 on the question: what if my knowledge is incomplete in the 

 following way . . . ? 



So we arrive at the systems that actually occur so commonly 

 in the biological world — systems whose variables are not all 

 accessible to direct observation, systems that must be observed 

 in some way that cannot distinguish all states, systems that can 

 be observed only at certain intervals of time, and so on. 



21/15. Identical with the state-determined system is the ' noise- 

 less transducer ' defined by Shannon. This he defines as one that, 

 having states a and an input x, will, if in state a„ and given input 

 x n , change to a new state a n+1 that is a function only of x n and a n : 



«n+i = g(*n> a«)- 



Though expressed in a superficially different form, this equation 



270 



