4/19 AN INTRODUCTION TO CYBERNETICS 



random" are possible. Thus he might, if there are n boxes, label 

 6« cards with numbers from 1 to 6/?, label the terminals similarly, 

 shuffle the cards and then draw two cards to nominate the two 

 terminals that shall be joined with the first wire. A second pair of 

 cards will name the terminals joined by the second wire; and so on. 

 A decision would have to be made whether the first two drawn cards 

 were to be replaced or not before the next shuffling and drawing. The 

 decision is important, for replacement allows some terminals to 

 have no wire and others to have several, while non-replacement 

 forces every terminal to have one wire and one only. This dis- 

 tinction would probably be significant in the characteristics of the 

 network, and would therefore require specification. Again, the 

 method just mentioned has the property of allowing output to be 

 joined to output. If this were undesirable a new method would 

 have to be defined; such might be: "Label the inputs 1 to 3« and also 

 the outputs 1 to 3« ; label 3« cards with numbers 1 to 3// ; join a wire to 

 input 1 and draw a card to find which output to connect it to; go on 

 similarly through inputs 2, . , ,, 3«". Here again replacement of the 

 card means that one output may go to several inputs, or to none; 

 non-replacement would give one output to each input. 



Enough has probably been said to show how essential an accurate 

 definition of the mode of sampling can be. Sometimes, as when the 

 experimenter takes a sample of oxygen to study the gas laws in it, 

 he need not specify how he obtained the sample, for almost all 

 samples will have similar properties (though even here the possibility 

 of exact definition may be important, as Rayleigh and Ramsay 

 found when some specimens of nitrogen gave persistently different 

 atomic weights from others). 



This "statistical" method of specifying a system — by specification 

 of distributions with samphng methods — should not be thought of as 

 essentially different from other methods. It includes the case of 

 the system that is exactly specified, for the exact specification is 

 simply one in which each distribution has shrunk till its scatter is 

 zero, and in which, therefore, "sampling" leads to one inevitable 

 result. What is new about the statistical system is that the specifica- 

 tion allows a number of machines, not identical, to qualify for 

 inclusion. The statistical "machine" should therefore be thought 

 of as a set of machines rather than as one machine. For this 

 chapter, however, this aspect will be ignored (it is taken up fully in 

 Chapter 7). 



It will now be seen, therefore, that it is, in a sense, possible for an 

 observer to specify a system that is too large for him to specify! 

 The method is simple in principle : he must specify broadly, and must 



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