The Domain of Information Theory in Biology 191 



Because of the relative nature of information measures, it will always 

 be up to the ingenuity of the biologist to find ensembles which result in useful 

 measures. In many cases, even the estimation of a limit is of interest: as in 

 Ehret's demonstration that a few bits could be sufficient to specify the 

 nature of cytoplasmic structures (11), or the result easily derived from 

 D'Arcy Thompson's work (12) that apparently considerable differences in 

 fonn could be coded in, say, a few nucleic acid residues. 



The relativism of information measures is a basic difficulty in estimation ; 

 besides, the biologist will encounter a number of technical difficulties arising 

 from the fact that 'message sets' and 'selection rules' are not perfectly known. 

 A number of approximation methods for such situations have been worked 

 out (13). 



The relative nature of information measures and the technical difficulties 

 of their estimation, cast some doubts on the usefulness of actual information 

 measures in biology. Only experience will show whether these doubts are 

 justified or not. Measures will be valuable if they lead to the discovery of 

 invariants. In psychology, some invariants seem to be crystaUizing out of 

 a number of measurements: there seem to be invariant upper limits for the 

 channel capacity for single activities; for the range of classes distinguishable 

 in a single act, etc. (14). In biology, independent estimates of information 

 transfer associated with three elementary biological functions (allelic, anti- 

 genic, enzymatic specificity) have yielded closely similar values (15). Much 

 more material will be needed before we can draw definite conclusions. 



The analysis which underlies the estimation of information measures 

 presents certain novel features. Consider, for instance, the informational 

 analysis of a honnonal control system. The traditional approach consists 

 in isolating one hormonal function and one hormone after the other. In 

 principle, this quest never ends — although physiologists might hope that some 

 day they will run out of undiscovered hormones. The information theorist 

 attacks the problem from the opposite end. He will argue that each hormone 

 molecule constitutes a message from a control organ to a target organ, a 

 message which is diffusely broadcast through the blood stream. In general 

 each message must contain two parts, an address and an order. Actually, 

 one or the other part can be omitted. We can imagine a hormonal control 

 system in wliich only the addresses are specified — the 'order' may be completely 

 determined in the target organ, and be executed automatically upon receipt of 

 the only kind of hormone molecule with the proper address; or, the address 

 may be unspecific, but the order such that only the right target organ can 

 execute it. One would expect that the natural systems be somewhere between 

 these two extremes. For the sake of simplicity we will consider a system in 

 which only addresses are specified — the foiTnal results have complete generality. 

 Thus, each hormone will be represented only by the address of the target 

 organ. In the interest of detailed and accurate control, it is desirable to have 

 a maximum number of different addresses. Any duplication of addresses 

 will lead to concomitant responses in other organs. On the other hand, the 

 'reading' of every single address involves distinguishing it from all other 

 addresses; the greater the variety of addresses, the greater the labor in every 

 single act of recognition. A compromise is indicated between the demand 



