P e g ST ST :

14
Fallacies

Mathematics is an exact science. The number 2, multiplied
by the number g, will always give a result equivalent to the
number 6. That is incontrovertible fact, but there are numer-
ous pitfalls for the unwary. In all scientific laws there is the
proviso: ‘all other things being equal’. Numbers will always
behave towards each other in a fixed and certain manner
provided they are treated purely as numbers; when they are
used to represent something else, this ‘something’ may intro-
duce certain complicating extraneous factors.

In mathematics, as all who have struggled through exam-
inations will agree, everything is not always what it seems.
Thus, although it is a fact that twice times x will always be
equivalent to 2x, it does not necessarily follow that the
doubling of an excise rate on tobacco will inevitably result
in the doubling of the total revenue derived from the tax.
This is because the amount of revenue will depend upon the
amount of tobacco purchased as well as on the actual excise
rate. The raising of the rate of tax might conceivably reduce
the total revenue if it resulted in a heavy drop in tobacco
consumption.

In the same way, it must be remembered that the use of
mathematical devices for the solution of problems will give
ridiculous results, when applied to practical matters, if cer-
tain factors are ignored. If a man can plough two fields in
one day, then two men—with equal facilities and at equal
speeds—will be able to plough the same two fields in half a
day. In the circumstances quoted, the doubling of the labour
force will halve the time taken to complete the task in hand.
It does not necessarily follow however that twenty men will

I35