The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919Whitehead, Alfred North
Philosophy
The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919
Whitehead, Alfred North
Knowledge, Theory of; Nature; Science -- Philosophy
If (p₁, p₂, p₃, p₄) be a set of measurements of this system, then the
event-particle which is thus determined will be said to have p₁, p₂, p₃,
p₄ as its co-ordinates in this system of measurement. Suppose that we
name it the p-system of measurement. Then in the same p-system by
properly varying (p₁, p₂, p₃, p₄) every event-particle that has been, or
will be, or instantaneously is now, can be indicated. Furthermore,
according to any system of measurement that is natural to us, three of
the co-ordinates will be measurements of space and one will be a
measurement of time. Let us always take the last co-ordinate to
represent the time-measurement. Then we should naturally say that (p₁,
p₂, p₃) determined a point in space and that the event-particle happened
at that point at the time p₄. But we must not make the mistake of
thinking that there is a space in addition to the space-time manifold.
That manifold is all that there is for the determination of the meaning
of space and time. We have got to determine the meaning of a space-point
in terms of the event-particles of the four-dimensional manifold. There
is only one way to do this. Note that if we vary the time and take times
with the same three space co-ordinates, then the event-particles, thus
indicated, are all at the same point. But seeing that there is nothing
else except the event-particles, this can only mean that the point (p₁,
p₂, p₃) of the space in the p-system is merely the collection of
event-particles (p₁, p₂, p₃, [p₄]), where p₄ is varied and (p₁, p₂, p₃)
is kept fixed. It is rather disconcerting to find that a point in space
is not a simple entity; but it is a conclusion which follows immediately
from the relative theory of space.
Furthermore the inhabitant of Mars determines event-particles by another
system of measurements. Call his system the q-system. According to him
(q₁, q₂, q₃, q₄) determines an event-particle, and (q₁, q₂, q₃)
determines a point and q₄ a time. But the collection of event-particles
which he thinks of as a point is entirely different from any such
collection which the man on earth thinks of as a point. Thus the q-space
for the man on Mars is quite different from the p-space for the
land-surveyor on earth.
Public-domain text, read in full here on John Shaqi.
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