I
The Making of Numbers

There is very good reason to believe that primitive peoples
were unable to distinguish any number greater than two.
This may seem difficult to accept in the present age, for the
science of mathematics has made such rapid and tremendous
strides in many directions within comparatively recent times
that mere counting has now become, within limits, literally
child’s play.

Nevertheless it is a fact that the vocabularies of many of
these early races contained only ‘one’, ‘two’ and ‘many’ as
their counting words. To such peoples the visualizing of any
number greater than two was as difficult as it still is for us
properly to visualize numbers like a million billion. We may
talk about immense numbers with gay abandon, but their
size is so great as to make the imagination boggle at any
attempt to understand their full significance.

Fortunately few people ever need to make such an imagin-
ative attempt; yet comparatively large numbers are apt to
intrude upon the average reader’s own interests without
his becoming aware of the intrusion. It would be interest-
ing, for instance, to ascertain just how many sportsmen
who complete their football coupons week by week do so
with the realization that there are more than 536 million
different ways of selecting eight teams out of a possible
fifty.

Early counting methods undoubtedly depended upon the
use of the ten fingers (hence the derivation of the word
‘digit’), so that it has been customary for most counting to be
effected in groups of ten. Various other systems however were
evolved from varying sources and some still survive. The

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