Chapter 



THE DETERMINATE MACHINE 



3/1. Having now established a clear set of ideas about transforma- 

 tions, we can turn to their first application : the establishment of an 

 exact parallelism between the properties of transformations, as 

 developed here, and the properties of machines and dynamic systems, 

 as found in the real world. 



About the best definition of "machine" there could of course be 

 much dispute. A determinate machine is defined as that which 

 behaves in the same way as does a closed single-valued trans- 

 formation. The justification is simply that the definition works — ■ 

 that it gives us what we want, and nowhere runs grossly counter 

 to what we feel intuitively to be reasonable. The real justification 

 does not consist of what is said in this section, but of what follows 

 in the remainder of the book, and, perhaps, in further developments. 



It should be noticed that the definition refers to a way of behaving, 

 not to a material thing. We are concerned in this book with those 

 aspects of systems that are determinate — that follow regular and 

 reproducible courses. It is the determinateness that we shall study, 

 not the material substance. (The matter has been referred to before 

 in Chapter 1.) 



Throughout Part I, we shall consider determinate machines, and 

 the transformations to be related to them will all be single-valued. 

 Not until S.9/2 shall we consider the more general type that is 

 determinate only in a statistical sense. 



As a second restriction, this Chapter will deal only with the 

 machine in isolation — the machine to which nothing actively is 

 being done. 



As a simple and typical example of a determinate machine, 

 consider a heavy iron frame that contains a number of heavy beads 

 joined to each other and to the frame by springs. If the circum- 

 stances are constant, and the beads are repeatedly forced to some 

 defined position and then released, the beads' movements will on 

 each occasion be the same, i.e. follow the same path. The whole 



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