468 Information Theory and Biology /25 : 3 



Such theories have been developed. They show that for amplitudes 

 with no noise level, or messages of infinite length in either frequency or 

 time, the average information per message is infinite. However, all 

 sounds have a noise limit provided by molecular thermal motions, a 

 finite time of duration, and a finite frequency span, the latter two being 

 limited by the ear. 



If speech is analyzed in terms of the physical noise level and the fre- 

 quency response of the human ear, one may easily arrive at tremendous 

 values for the information per second. Although these values represent 

 the information which can be detected by a microphone or other physical 

 detector, they have no meaning for human hearing. The information 

 received is limited by the ear itself. 



Frequency wise, humans hear about 10 octaves from 20 cps to 20 kc. 

 Few people can distinguish more than 12 tones per octave. This says 

 there are essentially 120 distinguishable pure tones. If each is equally 

 probable, all the p/s are the same. One may write 



1 

 Pi = 



120 

 and the average information associated with a tone H f is 



120 |20 



H f = - 2 A log a A = J20 log2 12 ° = 7 bits/tone 



Similarly, from the threshold of hearing to the threshold of pain, man 

 can distinguish about 250 steps. Again, one may assume all steps 

 equally probable and find the average information associated with the 

 sound pressure level 



H L = log 2 250 = 8 bits/impulse 



For a pure tone, then, man's auditory apparatus can receive about 

 15 bits of information. For a complex tone, this must be increased to 

 about 20. Human auditory systems can distinguish about 10 tones 

 per second. Therefore, the rate H' of receipt of useful information by the 

 ear is 



H' = 200 bits/second 



This represents the ability of the ear to code information as neural 

 impulses. The limiting factor is most clearly the ear itself. Much 

 more information can be coded from a microphone onto magnetic tape. 

 Although 200 bits/second may reach the brain, it in no way follows 

 that these are recorded or used by the brain. When a person is asleep 

 or daydreaming, most auditory information is lost. When we con- 

 centrate on reading, we deliberately discard most auditory information. 



