Chapter 



INCESSANT TRANSMISSION 



9/1. The present chapter will continue the theme of the previous, 

 and will study variety and its transmission, but will be concerned 

 rather with the special case of the transmission that is sustained for 

 an indefinitely long time. This is the case of the sciatic nerve, or the 

 telephone cable, that goes on incessantly carrying messages, unlike 

 the transmissions of the previous chapter, which were studied for 

 only a few steps in time. 



Incessant transmission has been specially studied by Shannon, and 

 this chapter will, in fact, be devoted chiefly to introducing his 

 Mathematical Theory of Communication, with special emphasis on 

 how it is related to the other topics in this Introduction. 



What is given in this chapter is, however, a series of notes, 

 intended to supplement Shannon's masterly work, rather than a 

 description that is complete in itself. Shannon's book must be 

 regarded as the primary source, and should be consulted first. I 

 assume that the reader has it available. 



9/2. The non-determinate transformation. If the transmission is to 

 go on for an indefinitely long time, the variety must be sustained, 

 and therefore not like the case studied in S.8/11, in which T's 

 transmission of variety stopped after the first step. Now any 

 determinate system of finite size cannot have a trajectory that is 

 infinitely long (S.4/5). We must therefore now consider a more 

 comprehensive form of machine and transformation — the non- 

 determinate. 



So far all our transformations have been single-valued, and have 

 thus represented the machine that is determinate. An extension 

 was hinted at in S.2/10, and we can now explore the possibility of 

 an operand having more than one transform. Some supplementary 

 restriction, however, is required, so as to keep the possibilities within 

 bounds and subject to some law. It must not become completely 

 chaotic. A case that has been found to have many applications is 

 that in which each operand state, instead of being transformed to a 



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