Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
Does this mean that space and all that it means is due
to a condition of the observer?
If a universal law in one case means nothing affecting
the objects themselves, but only a condition of observation,
is this true in every case? There is shown us in
astronomy a vera causa for the assertion of a universal.
Is the same cause to be traced everywhere?
Such is a first approximation to the doctrine of Kant’s
critique.
It is the apprehension of a relation into which, on the
one side and the other, perfectly definite constituents
enter—the human observer and the stars—and a transference
of this relation to a region in which the constitutents
on either side are perfectly unknown.
If spatiality is due to a condition of the observer, the
observer cannot be this bodily self of ours—the body, like
the objects around it, are equally in space.
This conception Kant applied, not only to the intuitions
of sense, but to the concepts of reason—wherever a universal
statement is made there is afforded to him an opportunity
for the application of his principle. He constructed a
system in which one hardly knows which the most to
admire, the architectonic skill, or the reticence with regard
to things in themselves, and the observer in himself.
His system can be compared to a garden, somewhat
formal perhaps, but with the charm of a quality more
than intellectual, a besonnenheit, an exquisite moderation
over all. And from the ground he so carefully prepared
with that buried in obscurity, which it is fitting should
be obscure, science blossoms and the tree of real knowledge
grows.
The critique is a storehouse of ideas of profound interest.
The one of which I have given a partial statement leads,
as we shall see on studying it in detail, to a theory of
mathematics suggestive of enquiries in many directions.