re-arrangement of the bits of glass, but it is invariably symmetrical.
Now the symmetry in this case is not in the bits of glass; the colours
are there no doubt, but the symmetrical arrangement of them is not. The
symmetry is entirely due to the instrument. And if a competent enquirer
looks into the instrument and examines its construction, he will be able
to lay down with absolute certainty the laws of that symmetry which
every pattern as seen through the instrument must obey.

Just such an instrument, according to Kant, is the human mind. Space
and Time and the Perceptive Faculties are the parts of the instrument.
Everything that reaches the senses must submit to the laws of Space and
Time, that is, to the Laws of Mathematics, because Space and Time are
forms of the mind itself, and, like the kaleidoscope, arrange all things
on their way to the senses according to a pattern of their own. This
pattern is as it were super-added to the manifestations that come from
the things themselves; and if there be any manifestations of such a
nature that they could not submit to this addition, or, in other words,
could not submit to Mathematical Laws, these manifestations could not
affect our senses at all. So too our Understanding has a pattern of its
own which it imposes on all things that reach its power of perception.
What cannot be accommodated to this pattern cannot be understood at all.
Whatever things may be in themselves, their manifestations are not
within the range of our intelligence, except by passing through the
arranging process which our own mind executes upon them.

It is clear that this wonderfully ingenious speculation rests its
claims for acceptance purely on the assertion that it and it alone
explains the facts. It cannot be proved from any principle of reason. It
assumes that there is a demonstrative science of Mathematics quite
independent of experience, and that there are necessary principles of