Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
of a circle about O, the meeting point of the horizontal
and vertical levels, which passes through (7, 1) and (5, 5),
assert that all the triangles which are right-angled and
have a hypothenuse whose square is 50 are represented
by the points on this arc.
Thus, each individual of a class being represented by a
point, the whole class is represented by an assemblage of
points forming a figure. Accepting this representation
we can attach a definite and calculable significance to the
expression, resemblance, or similarity between two individuals
of the class represented, the difference being
measure by the length of the line between two representative
points. It is needless to multiply examples, or
to show how, corresponding to different classes of triangles,
we obtain different curves.
A representation of this kind in which an object, a
thing in space, is represented as a point, and all its properties
are left out, their effect remaining only in the
relative position which the representative point bears
to the representative points of the other objects, may be
called, after the analogy of Sir William Hamilton’s
hodograph, a “Poiograph.”
Representations thus made have the character of
natural objects; they have a determined and definite
character of their own. Any lack of completeness in them
is probably due to a failure in point of completeness
of those observations which form the ground of their
construction.
Every system of classification is a poiograph. In
Mendeléeff’s scheme of the elements, for instance, each
element is represented as a point, and the relations
between the elements are represented by the relations
between the points.
So far I have simply brought into prominence processes
and considerations with which we are all familiar. But