192 Henry Quastler 



for a great variety of addresses and the contradictory demand to keep each 

 address simple. For any kind of system, there will be an optimum number of 

 different hormones; the actual number will depend on the relative strength 

 of the two competing needs. By Dancoflf's principle, we expect that the actual 

 number will not be too far from the optimum number. 



We can add another line of considerations on the number of possible addresses. 

 In order to fulfill its function, the hormone molecule has to enter into some 

 kind of relation with the target organ ; most likely, it has to form a complex. 

 Now, the total surface area of any molecule that can enter into a specific 

 complexing process is rather limited, and so is the number of molecular con- 

 figurations available to living organisms; hence, a limited space accommodates 

 only a limited number of significantly different configurations — and this limits 

 the number of different hormones possible (and, incidentally, the number of 

 distinct antigens and antibodies, enzymes and co-enzymes). 



The example illustrates the concern with the whole system which is charac- 

 teristic of many applications of infomiation theory. It also illustrates a rather 

 profound difference between the information theorist and many of his scientific 

 colleagues. The information theorist will remain fairly cool at the news that 

 another enzyme, or hormone, or vitamin has been isolated ; his basic question 

 is: 'How many more are there to be discovered?' 



II. LIMITATIONS 



Information theory could not possibly apply to a wide variety of situations 

 if it were sensitive to every detail in every situation. Like thermodynamics 

 (to which information theory is related) it has a vast domain of application, 

 and like in thermodynamics, the vastness of the domain is paid for by a limited 

 scope of every single application (16). The following four limitations deserve 

 emphasis : (i) information measures refer to ensembles and not to single instances, 

 (ii) they are relative and not absolute, (iii) informational capabilities are often 

 not fully utilized, (iv) information measures are related to other aspects of 

 systems such as utilities and mechanisms but the relations are not simple. 

 None of these observations is particularly profound, but each one has been 

 overlooked by competent investigators. 



1 . Information Measures are Functions of Ensembles 



Information measures are not defined for particular historical occurrences 

 or existing individual things; rather, they are defined for whole ensembles of 

 events that could happen, or things that could be. The information measures 

 are descriptive of the operations by which a particular item is selected from the 

 set of possible items, and are associated with the whole set and not with any 

 particular item that happened to be selected in a particular instance. 



Ensembles are specified by their elements, by the classification to which 

 these elements are subjected, and by the probability measures associated with 

 the diverse classes. If these specifications are known, then the information 

 functions can be derived — but not vice versa. For example: if it is known 

 that a certain chemical system contains certain enzymes and certain substrates, 

 if the probabilities of the various coUisions and the probabilities of all possible 



