Hinton - The Fourth Dimension.pdf
Hinton - The Fourth Dimension.pdf Hinton - The Fourth Dimension.pdf
118 THE FOURTH DIMENSION being, those that do survive will possess such and such characteristics. This is the necessary beginning for ascertaining what kinds of organisms do come into existence. And so Kant’s hypothesis of a random consciousness is the necessary beginning for the rational investigation of consciousness as it is. His assumption supplies, as it were, the space in which we can observe the phenomena. It gives the general laws constitutive of any experience. If, on the assumption of absolute randomness in the constituents, such and such would be characteristic of the experience, then, whatever the constituents, these characteristics must be universally valid. We will now proceed to examine more carefully the poiograph, constructed for the purpose of exhibiting an illustration of Kant’s theory of apperception. In order to show the derivation order out of non-order it has been necessary to assume a principle of duality— we have had the axes and the posits on the axes—there are two sets of elements, each non-ordered, and it is in the reciprocal relation of them that the order, the definite system, originates. Is there anything in our experience of the nature of a duality? There certainly are objects in our experience which have order and those which are incapable of order. The two roots of a quadratic equation have no order. No one can tell which comes first. If a body rises vertically and then goes at right angles to its former course, no one can assign any priority to the direction of the north or to the east. There is no priority in directions of turning. We associate turnings with no order, progressions in a line with order. But in the axes and points we have assumed above there is no such distinction. It is the same, whether we assume an order among the turnings, and no order among the points on the axes, or, vice versa, an order in
APPLICATION TO KANT’S THEORY OF EXPERIENCE 119 the points and no order in the turnings. A being with an infinite number of axes mutually at right angles, with a definite sequence between them and no sequence between the points on the axes, would be in a condition formally indistinguishable from that of a creature who, according to an assumption more natural to us, had on each axis an infinite number of ordered points and no order of priority among the axes. A being in such a constituted world would not be able to tell which was turning and which was length along an axis, in order to distinguish between them. Thus to take a pertinent illustration, we may be in a world of an infinite number of dimensions, with three arbitrary points on each—three points whose order is indifferent, or in a world of three axes of arbitrary sequence with in infinite number of ordered points on each. We can’t tell which is which, to distinguish it from the other. Thus it appears the mode of illustration which we have used is not an artificial one. There really exists in nature a duality of the kind which is necessary to explain the origin of order out of no order—the duality, namely, of dimension and position. Let us use the term group for that system of points which remains unchanged, whatever arbitrary change of its constituents takes place. We notice that a group involves a duality, is inconceivable without a duality. Thus, according to Kant, the primary element of experience is the group, and the theory of groups would be the most fundamental branch of science. Owing to an expression in the critique the authority of Kant is sometimes adduced against the assumption of more than three dimensions to space. It seems to me, however, that the whole tendency of his theory lies in the opposite direction, and points to a perfect duality between dimension and position in a dimension.
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APPLICATION TO KANT’S THEORY OF EXPERIENCE 119<br />
the points and no order in the turnings. A being with<br />
an infinite number of axes mutually at right angles,<br />
with a definite sequence between them and no sequence<br />
between the points on the axes, would be in a condition<br />
formally indistinguishable from that of a creature who,<br />
according to an assumption more natural to us, had on<br />
each axis an infinite number of ordered points and no<br />
order of priority among the axes. A being in such<br />
a constituted world would not be able to tell which<br />
was turning and which was length along an axis, in<br />
order to distinguish between them. Thus to take a pertinent<br />
illustration, we may be in a world of an infinite<br />
number of dimensions, with three arbitrary points on<br />
each—three points whose order is indifferent, or in a<br />
world of three axes of arbitrary sequence with in infinite<br />
number of ordered points on each. We can’t tell which<br />
is which, to distinguish it from the other.<br />
Thus it appears the mode of illustration which we<br />
have used is not an artificial one. <strong>The</strong>re really exists<br />
in nature a duality of the kind which is necessary to<br />
explain the origin of order out of no order—the duality,<br />
namely, of dimension and position. Let us use the term<br />
group for that system of points which remains unchanged,<br />
whatever arbitrary change of its constituents takes place.<br />
We notice that a group involves a duality, is inconceivable<br />
without a duality.<br />
Thus, according to Kant, the primary element of experience<br />
is the group, and the theory of groups would be<br />
the most fundamental branch of science. Owing to an<br />
expression in the critique the authority of Kant is sometimes<br />
adduced against the assumption of more than three<br />
dimensions to space. It seems to me, however, that the<br />
whole tendency of his theory lies in the opposite direction,<br />
and points to a perfect duality between dimension and<br />
position in a dimension.
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