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10 THE FASCINATION OF NUMBERS

system based upon groups of twenty (instead of groups of
ten) presumably required the use of the calculator’s toes
as well as of his fingers, and we may consider ourselves
fortunate that this physical process is no longer required
of us!

The Roman system of numbering suggests that at one time
counting was effected on one hand only, for this system
divided numbers into groups of five. If we study the first five
Roman numbers, it is not difficult to relate them to pictures
of the human hand. If the right hand is held face upwards
one can easily visualize each of the fingers as a vertical stroke
of a Roman number, whilst the angle at which the thumb
departs from the vertical provides the form of the letter V,
the Roman symbol for the number &.

But whatever the size of the actual groups used, it is
this fundamental system of grouping which enables us to

.deal adequately with the larger numbers. Without the
aid of the grouping system each different number would
require an entirely different figurate name instead of|
as at present, having a composite name derived from the
groups of which it is composed. In other words, a totally
different symbol would be required for each different
number.

Every number is made up from a group of digits and it is
the relative positioning of those digits—each to the other—
which gives the identity of that number. Just as the order of
musical notes decides the nature of a piece of music, so does
the order and placing of digits decide the nature of a number.
If the order of the digits is changed then an entirely different
number will emerge. This is because a digit has a different
meaning in different positions—a fact which is essential in
a system which uses only ten symbols and yet succeeds in
using those symbols to express any conceivable number.
Each number is built up to a definite pattern so that a
sequence of digits in one particular order can represent only
one particular number.

The number 1234, for instance, is made up of one thou-