E of the even integers.
O of the odd ones.
F of the fractions having integers for their terms.
No two of these have a single element in common, yet the three
together constitute one manifold M, that is exactly equal in wealth
of elements to _each_ of its infinite components.
Again, there is the apparent opposition between the Omniscience of
God and the freedom of man. The antithesis disappears if we realise
that from the point of view of Infinites the dignity and power of
Omniscience remain the same, even if some part of experience is not
yet drawn into the sphere of Omniscience.[28]
Here we have the present conceived of as a moving plane separating
the unknown from the known. The “past” can be said to be known,
though its content changes every instant. This is the real answer
to W. James’s cry that he could accept an Absolute if it had even
the fragment of an “other.” There can be this “other,” and yet the
Absolute still remains an Absolute.
The doctrine of _Omnipresence_ follows from the argument of the
Continuum (which is the aggregate of all real numbers). Thus the
number of points in space of infinite dimension is no greater than
the number of points in any part of space as known to us. The whole
is incarnate in every part, because to each part, in however small an
atom, corresponds a point in the universal whole, and the number of
points in a space of infinite dimensions is equal to the number of
points in a straight line however small.
And this is true not merely of points but also of forces. “The
Universe is dynamic, charged throughout with innumerable modes of
motion. Each point, however, of any moving thing--an ion of gas, a
vibrating fibre of brain--is represented by a corresponding point
in S (a small typical atom), and so within the tiny sphere--indeed,
in every room, however small--the whole dynamics of the universe
is depicted completely and co-enacted by motion of points and
transformation of point configurations. There in miniature proceed at
once the countless play and interplay of every kind of motion, small
and large, simple and complex, the quivering dance of the molecule,
the wave and swing of universal æther.”[29]