4/23 AN INTRODUCTION TO CYBERNETICS 



In general, therefore, changes that are self-locking are usually of 

 high importance in determining the eventual state of the system. 



4/23. Properties that breed. It should be noticed that in the 

 previous section we considered, in each example, two different 

 systems. For though each example was based on only one material 

 entity, it was used to provide two sets of variables, and these sets 

 form, by S. 3/11, two systems. The first was the obvious set, very 

 large in number, provided by the parts; the second was the system 

 with one variable: ''number of parts showing the property". The 

 examples showed cases in which this variable could not diminish 

 with time. In other words it behaved according to the trans- 

 formation (if the number is n)\ 



n > n. 



This transformation is one of the many that may be found when 

 the changes of the second system (number of parts showing the 

 property) is considered. It often happens that the existence of the 

 property at some place in the system affects the probability that it 

 will exist, one time-interval later, at another place. Thus, if the 

 basic system consists of a trail of gunpowder along a hne 12 inches 

 long, the existence of the property "being on fire" now at the fourth 

 inch makes it highly probable that, at an interval later, the same 

 property will hold at the third and fifth inches. Again, if a car has 

 an attractive appearance, its being sold to one house is likely to 

 increase its chance of being sold to adjacent houses. And if a 

 species is short of food, the existence of one member decreases the 

 chance of the continued, later existence of another member. 



Sometimes these effects are of great complexity; sometimes how- 

 ever the change of the variable "number having the property" can 

 be expressed sufficiently well by the simple transformation n' = kn, 

 where k is positive and independent of n. 



When this is so, the history of the system is often acutely dependent 

 on the value of k, particularly in its relation to + 1 . The equation 

 has as solution, if t measures the number of time-intervals that have 

 elapsed since ? = 0, and if /7o was the initial value: 



n = n^e^^'^''^ 



Three cases are distinguishable. 



(1)^<1. In this case the number showing the property falls 

 steadily, and the density of parts having the property decreases. It 



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