Hinton - The Fourth Dimension.pdf

THE FIRST CHAPTER IN THE HISTORY OF FOUR SPACE 31
on the diagonal is equal to the sum of the squares on
the sides. This property of matter is one of the first
great discoveries of applied mathematics. We shall prove
afterwards that it is not a property of space. For this
present it is enough to remark that the positions in
which the points are arranged is entirely experimental.
It is by means of equal pieces of some material, or the
same piece of material moved from one place to another,
that the points are arranged.
Pythagoras next enquired what the relation must be
so that a square drawn slanting-wise should be equal to
one straight-wise. He found that a square whose side is
five can be placed either rectangularly along the lines
of points, or in a slanting position. And this square is
equivalent to two squares of sides 4 and 3.
Here he came upon a numerical relation embodied in
a property of matter. Numbers immanent in the objects
produced the equality so satisfactory for intellectual apprehension.
And he found that numbers when immanent
in sound—when the strings of a musical instrument
were given certain definite proportions of length—were
no less captivating to the ear than the equality of squares
was to the reason. What wonder then that he ascribed
an active power to number.
We must remember that, sharing like ourselves the
search for the permanent in changing phenomena, the
Greeks had not that conception of the permanent in
matter that we have. To them material things were not
permanent. In fire solid things would vanish; absolutely
disappear. Rock and earth had a more stable existence,
but they too grew and decayed. The permanence of
matter, the conservation of energy, were unknown to
them. And that distinction which we draw so readily
between the fleeting and permanent causes of sensation,
between a sound and a material object, for instance, had