What is Information Theory? 19 



page from a table of random numbers? Are you transmitting 

 information, and how would you determine how much? 



Saltzberg: Yes. You are always transmitting information when- 

 ever you convey a message, unless the noise is so great that the 

 equivocation of the system is equal to the information content of 

 the source. Your question apparently refers to tlie importance of 

 the information. A table of random numbers may be useless to 

 the receiver, but, nevertheless, statistical information has been 

 communicated . 



Shapiro: Then it is not really true, as you started out by saying, 

 that the meaning of what you transmit has nothing to do with how 

 much information is transmitted. The meaning apparently has a 

 great deal to do with how much information is transmitted. 



Saltzberg: Apparently I have caused some confusion. Seman- 

 tic meaning or the importance of a message is subjective and is 

 not part of statistical information theory. The previously used 

 example applies here. A message announcing the birth of a boy 

 conveys one bit of information to an unknowing" receiver inde- 

 pendent of whether the receiver is the father or not. Thus, whether a 

 number is taken from a table of random numbers or a table of 

 trigonometric functions has no bearing on the information received, 

 providing the receiver has no a priori knowledge of these numbers. 



Walter Abbott (Houston, Texas): The point has been made 

 that the information content of any datum is proportional to its 

 surprise value. Does this get involved in your semantic implications? 



Saltzberg: Surprise, as used in this context, does not have any 

 semantic implications. If a datum or a message identifies one of a 

 thousand possible states, then it has surprise value in the sense that 

 you would have been extremely surprised to have guessed the state 

 without receipt of the information provided by the message. If a 

 system had only two possible states, then you would not be so sur- 

 prised to guess the correct state. 



Mary A. B. Brazier (Los Angeles, California) : I believe that 

 by surprise value Dr. Abbott means an event of low probability. 



Myron F. Weiner (Dallas, Texas) : How much must be known 

 of the probabilities, or of the number of probabilities of different 

 messages, or of the number of possible different messages to be 

 conveyed before one can get some idea of what a message is, 



