DESIGN FOR A BRAIN 



2/13 



The tabular form has one outstanding advantage: it contains 

 the facts and nothing more. Mathematical forms are apt to 

 suggest too much: continuity that has not been demonstrated, 

 fictitious values between the moments of observation, and an 

 accuracy that may not be present. Unless specially mentioned, 

 all lines of behaviour will be assumed to be recorded primarily 

 in tabular form. 



2/13. The behaviour of a system can also be represented in. 

 phase-space. By its use simple proofs may be given of many 

 statements difficult to prove in the tabular form. 



/O 



A) 



5- 



IO 



Figure 2/13/1. 



If a system is composed of two variables, a particular state 

 will be specified by two numbers. By ordinary graphic methods, 

 the two variables can be represented by axes ; the two numbers 

 will then define a point in the plane, Thus the state in which 

 variable x has the value 5 and variable y the value 10 will be 

 represented by the point A in Figure 2/13/1. The representative 

 point of a state is the point whose co-ordinates are respectively equal 

 to the values of the variables. By S. 2/5 ' time ' is not to be one 

 of the axes. 



Suppose next that a system of two variables gave the line of 

 behaviour shown in Table 2/13/1. The successive states will be 



22 



