Read The Nature of Mathematics Online

54 THE NATURE OF MATHEMATICS 

accurate description of things in the world around us, of 
which we become conscious through our senses. 

Among these things, let us consider, say, a particular 
person's face, and a billiard ball. The appearance to the eye 
of the ball is obviously much easier to describe than that of 
the face. We can call up the image a very accurate one 
of a billiard ball in the mind of a person who has never seen 
it by merely giving the colour and radius. And, unless we 
are engaged in microscopical investigations, this description 
is usually enough. The description of a face is a harder 
matter: unless we are skilful modellers, we cannot do this 
even approximately ; and even a good picture does not attempt 
literal accuracy but only conveys a correct impression often 
better than a model, say in wax, does. 

Our ideal in natural science is to build up a working model 
of the universe out of the sort of ideas that all people carry 
about with them everywhere "in their heads, 1 ' as we say, and 
to which ideas we appeal when we try to teach mathematics. 
These ideas are those of number, order, the numerical measures 
of times and distances, and so on. One reason why we strive 
after this ideal is a very practical one. If we have a working 
model of, say, the solar system, we can tell, in a few minutes, 
what our position with respect to the other planets will be at 
all sorts of far future times, and can thus predict certain 
/uture events. Everybody can see how useful this is ; perhaps 
those persons who see it most clearly are those sailors who 
use the Nautical Almanac. We cannot make the earth 
tarry in its revolution round its axis in order to give us a 
longer day for finishing some important piece of work ; but, 
by finding out the unchanging laws concealed in the phenomena 
of the motions of earth, sun, and stars, the mathematician can 
construct the model just spoken of. And the mathematician 
is completely master of his model; he can repeat the occur- 
rences in his universe as often as he likes; something like 
Joshua, he can make his " sun " stand still, or hasten, in 
order that he may publish the Nautical Almanac several 
years ahead of time. Indeed, the "world" with which we 
have to deal in theoretical or mathematical mechanics is but 
a mathematical scheme, the function of which it is to imitate, 
by logical consequences of the properties assigned to it by