142 hiformation Storage and Neural Control 



where utility is understood to have a hedonistic value in either 

 1) reducing" the community's uncertainty about nature, or 2) per- 

 mitting purchase of a measure of certainty. In the latter connection, 

 energy will be identified as a universal currency. We begin with 

 a result from communication theory. 



SHANNON'S THEOREM 10 



Consider, following Shannon (10), a discrete communication 

 channel fed by an information source. If H{x) is the input entropy 

 and H{y) tnat of the output, H{x,j) is the joint entropy of input 

 and output, and H{y\x) and H{x\y) are conditional entropies, then 



[1] H{x,y) = H{x) + H{,j\x) = H{y) + H{x\ij). 



For such a system SJiannon proved his Theorem 10: If a correction 

 channel has a capacity H{x\y), correction data can be encoded in 

 such a manner that all but an arbitrarily small fraction of errors 

 induced by noise can be corrected. This is not possible if the 

 channel capacity is less than //(.vjj), which represents the amount 

 of information which must be supplied to correct the message. 



This theorem has been exploited by Ashby (11, 12) as the basis 

 for a cybernetic theory of biological homeostasis. Roughly, the 

 organism is regarded as bomJDarded by information from an 

 environment which tends to drive the organism into states outside 

 the limits which permit survival. To achieve stability, therefore, 

 it becomes necessary in light of Shannon's theorem for the organism 

 to provide information to a "regulator" (analogue of correction 

 channel) in amounts at least as great as the disturbances. Ashby 

 calls this the law of requisite variety. It implies that an organism 

 must continually be concerned with having sufficient information 

 available (accumulated against the gradient imposed by the 

 second law of thermodynamics) to meet particular environmental 

 threats. The compatibility of this theory with the Schrodinger- 

 Brillouin thesis is evident. Also apparent is the fact that its basic 

 applicability is unaltered by a conversion from the scale of organism 

 to that of ecological community: both units metabolize, both are 

 subject to the same "heat death" and, consequently, both have 

 similar problems of homeostasis. 



