Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
If the order and the law we see is due to the conditions
of conscious experience, we must conceive nature as
spontaneous, free, subject to no predication that we can
devise, but, however apprehended, subject to our logic.
And our logic is simply spatiality in the general sense
—that resultant of a selection of the permanent from the
unpermanent, the ordered from the unordered, by the
means of the group and its underlying duality.
We can predicate nothing about nature, only about the
way in which we can apprehend nature. All that we can
say is that all that which experience gives us will be considered
as spatial, subject to our logic. Thus, in exploring
the facts of geometry from the simplest logical relations
to the properties of space of any number of dimensions,
we are merely observing ourselves, becoming aware of
the conditions under which we must perceive. Do any
phenomena present themselves incapable of explanation
under the assumption of the space we are dealing with,
then we must habituate ourselves to the conception of a
higher space, in order that our logic may be equal to the
task before us.
We gain a repetition of the thought that came before,
experimentally suggested. If the laws of the intellectual
comprehension of nature are those derived from considering
her as absolute chance, subject to no law save
that derived from a process of selection, then, perhaps, the
order of nature requires different faculties from the intellectual
to apprehend it. The source and origin of
ideas may have to be sought elsewhere than in reasoning.
The total outcome of the critique is to leave the
ordinary man just where he is, justified in his practical
attitude towards nature, liberated from the fetters of his
own mental representations.
The truth of a picture lies in its total effect. It is vain
to seek information about the landscape from an examina-