THE DETERMINATE MACHINE 3/5 



concerned with them. It should be noticed that we are now 

 beginning to consider the relation, most important in machinery, 

 that exists between the whole and the parts. Thus, it often happens 

 that the state of the whole is given by a list of the states taken, at 

 that moment, by each of the parts. 



Such a quantity is a vector, which is defined as a compound entity, 

 having a definite number of components. It is conveniently written 

 thus: (fli, a^, . . ., a„), which means that the first component has the 

 particular value a^, the second the value 02, and so on. 



A vector is essentially a sort of variable, but more complex than 

 the ordinary numerical variable met with in elementary mathematics. 

 It is a natural generalisation of "variable", and is of extreme 

 importance, especially in the subjects considered in this book. 

 The reader is advised to make himself as familiar as possible with 

 it, applying it incessantly in his everyday life, until it has become as 

 ordinary and well understood as the idea of a variable. It is not 

 too much to say that his famiharity with vectors will largely deter- 

 mine his success with the rest of the book. 



Here are some well-known examples. 



(1) A ship's "position" at any moment cannot be described by a 

 single number; two numbers are necessary: its latitude and its 

 longitude. "Position" is thus a vector with two components. 

 One ship's position might, for instance, be given by the vector 

 (58°N, 17'W). In 24 hours, this position might undergo the 

 transition (58"N, 17°W)^ (59°N, 20°W). 



(2) "The weather at Kew" cannot be specified by a single number, 

 but can be specified to any desired completeness by our taking 

 sufficient components. An approximation would be the vector: 

 (height of barometer, temperature, cloudiness, humidity), and a 

 particular state might be (998 mbars, 56-2°F, 8, 72%). A weather 

 prophet is accurate if he can predict correctly what state this present 

 state will change to. 



(3) Most of the administrative "forms" that have to be filled in 

 are really intended to define some vector. Thus the form that the 

 motorist has to fill in: 



Age of car : . , 

 Horse-power: 

 Colour: , 



is merely a vector written vertically. 

 Two vectors are considered equal only if each component of the 



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