Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

TRANSFORMATION 177
abolished; motion, as a change of place during a flow of
time, is gone; in the new world, where (if the term be used)
has a new meaning-it has absorbed both the old where
and the old when. Where is the particle p? Where,
that is, in the new world? At the point (x, y, z, t). Where
is the particle p'? At (x', y', z', t'). The particles p and
p' are never the same; there are relations, but no transformations; no history in ordinary sense-no past-no
future; child, youth, man coexist as phases of one individual; the same is true of morning, noon, night and so on:
all is static-as a " painted ship on a painted ocean."
You see what has happened here and how. By suppressing the fluxional character of time along with its
implicates,-motion, transformation, change,-and by
regarding time as simply a cosmic dimension to be joined
with the familiar dimensions of space, the Dynamics of
our spatially 3-dimensional world has been made to
appear as a Statics of a 4-dimensional world. I need not
say that this way of handling time, however beautiful
and helpful, is, like Newton's way (of which it is the
antithesis), not ultimately satisfactory. I should add that
Minkowski was far from regarding it as a final solution.
And so science and philosophy are still confronted and
to-day confronted afresh by the age-old problem of Time.
No one has been able to tell satisfactorily what is meant,
or should be meant, by when. From time immemorial,
human beings have talked of " instants," but no one has
discovered what an instant is. It is important to observe
that the time problem is not solitary; it is but one of a
class of kindred problems or is perhaps an aspect or à
fragment of a larger problem embracing them all. Fot
what is meant, or should be meant, by where? By here?
By there? By a point? And we talk of matter as of time