25 : 3/ Information Theory and Biology 467 



The twofold redundancy in English greatly reduces the error rate 

 due to noise, such as blurred printing, bad spelling, poor lighting, and 

 so on. The error rate is reduced because there are a large number of 

 possible messages excluded. The number of 1,000 symbol messages M r , 

 if all random arrangements of letters were possible, would be 



M r = 10 1400 messages 



If one includes all influences up to eight symbols away, the number of 

 messages M 8 is reduced to 



M 8 = 10 700 



A 1,000 symbol message is about a typed page. The number M Q is 

 certainly astronomical in size, but it is microscopic compared to M r . 



Similar redundancies may exist in many biological processes. It 

 seems likely that the endocrine systems of mammals have more inter- 

 acting glands than are necessary. This redundancy makes possible the 

 action of extreme feedback (homeostatic) mechanisms. It also appears 

 to be a reasonable guess that the pigment myoglobin is not necessary. 

 Its presence in the muscles is a redundancy tending to further smooth 

 out oxygen variations. 



The most striking example of redundancy occurs in the higher plants. 

 Some are so-called "polyploids," in which, instead of having pairs of 

 chromosomes, all the body cells have sets of four or even eight homol- 

 ogous chromosomes. Each member of each set controls the same 

 characteristics. This redundancy should markedly reduce the error rate 

 during cell multiplication. (At any rate, this possibility exists whether 

 or not the plant uses it!) 



3. Information and Sensory Perception 



The senses provide the link between the central nervous system and the 

 outside world. All information reaching the central nervous system 

 comes through the senses. It seems appropriate therefore that the 

 language of information theory can be used to describe what man 

 perceives. Consider first the theory of hearing. 



A. Hearing 



All the examples in the previous section dealt with discrete phenomena. 

 Sound is continuous both in amplitude and in time. (As mentioned in 

 Chapter 1, the representation in time may be replaced by a correspond- 

 ing one in frequency.) Any discussion of the information content of 

 sound must include some method of handling continuous variables. 



