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GROWTH OF MATHEMATICAL SCIENCE 11 

new point of view from which to consider the question, " What 
is the use of mathematics ? " To condemn even those branches 
of mathematics because their results cannot obviously be applied 
to some practical purpose is short-sighted. 

The formation of science is peculiar to human beings among 
animals. The lower animals sometimes, but rarely, make 
isolated discoveries, but never seem to reflect on these in- 
ventions in themselves with a view to rational classification 
in the interests either of the intellect, or of the indirect 
furtherance of practical ends. Perhaps the greatest difference 
between man and the lower animals is that men are capable of 
taking circuitous paths for the attainment of their ends, while 
the lower animals have their minds so filled up with their 
needs that they try to seize the object they want or remove 
that which annoys them in a direct way. Thus, monkeys 
often vainly snatch at things they want, while even savage 
men use catapults or snares or the consciously observed pro- 
perties of flung stones. 

The communication of knowledge is the first occasion that 
compels distinct reflection, as everybody can still observe in 
himself. Further, that which the old members of a guild 
mechanically pursue strikes a new member as strange, and 
thus an impulse is given to fresh reflection and investigation. 

When we wish to bring to the knowledge of a person any 
phenomena or processes of nature, we have the choice of two 
methods : we may allow the person to observe matters for 
himself, when instruction comes to an end; or, we may 
describe to him the phenomena in some way, so as to save him 
the trouble of personally making anew each experiment. To 
describe an event like the falling of a stone to the earth 
in the most comprehensive and compact manner requires that 
we should discover what is constant and what is variable in 
the processes of nature ; that we should discover the same law 
in the moulding of a tear and in the motions of the planets. 
This is the very essence of nearly all science, and we will 
return again to this point later on. 

We have thus some idea of what is known as " the econo- 
mical function of science." This sounds as if science were 
governed by the same laws as the management of a business ;