The two types of straight routes will be called rectilinear routes and stations. Rectilinear routes are
104 THE CONCEPT OF NATURE Lch.
momental routes and stations are vagrant routes. Rectilinear routes are routes which in a sense lie in rects. Any two event-particles on a rect define the set of event-particles which lie between them on that rect. Let the satisfaction of the condition o- by an abstractive set mean that the two given event-particles and the event-particles lying between them on the rect all lie in every event belonging to the abstractive set. The group of CT -primes, where a has this meaning, form an abstractive element. Such abstractive elements are recti- linear routes. They are the segments of instantaneous straight lines which are the ideals of exact perception. Our actual perception, however exact, will be the per- ception of a small event sufficiently far down one of the abstractive sets of the abstractive element.
A station is a vagrant route and no moment can inter-
sect any station in more than one event-particle. Thus
a station carries with it a comparison of the positions
in their respective moments of the event-particles
covered by it. Rects arise from the intersection of
moments. But as yet no properties of events have been
mentioned by which any analogous vagrant loci can
be found out.
The general problem for our investigation is to
determine a method of comparison of position in one
instantaneous space with positions in other instantaneous
spaces. We may limit ourselves to the spaces of the
parallel moments of one time-system. How are positions
in these various spaces to be compared ? In other words,
What do we mean by motion.? It is the fundamental
question to be asked of any theory of relative space,
and like many other fundamental questions it is apt to
be left unanswered. It is not an answer to reply, that
v] ' SPACE AND MOTION 105
we all know what we mean by motion. Of course we
do, so far as sense-awareness is concerned. I am asking
that your theory of space should provide nature with
something to be observed. You have not settled the
question by bringing forward a theory according to
which there is nothing to be observed, and by then
reiterating that nevertheless we do observe this non-
existent fact. Unless motion is something as a fact in
nature, kinetic energy and momentum and all that
depends on these physical concepts evaporate from our
list of physical realities. Even in this revolutionary age
my conservatism resolutely opposes the identification
of momentum and moonshine.
Accordingly I assume it as an axiom, that motion
is a physical fact. It is something that we perceive as
in nature. Motion presupposes rest. Until theory arose
to vitiate immediate intuition, that is to say to vitiate
the uncriticised judgments which immediately arise
from sense-awareness, no one doubted that in motion
you leave behind that which is at rest. Abraham in his
wanderings left his birthplace where it had ever been.
A theory of motion and a theory of rest are the same
thing viewed from different aspects with altered em-
phasis.
Now you cannot have a theory of rest without in some sense admitting a theory of absolute position. It is usually assumed that relative space implies that there is no absolute position. This is, according to my creed, a mistake. The assumption arises from the failure to make another distinction; namely, that there may be alternative definitions of absolute position. This possi- bility enters with the admission of alternative time- systems. Thus the series of spaces in the parallel
io6 THE CONCEPT OF NATURE L^h.
moments of one temporal series may have their own definition of absolute position correlating sets of event- particles in these successive spaces, so that each set consists of event-particles, one from each space, all with the property of possessing the same absolute position in that series of spaces. Such a set of event- particles will form a point in the timeless space of that time-system. Thus a point is really an absolute position in the timeless space of a given time-system.
But there are alternative time-systems, and each
time-system has its own peculiar group of points — that
is to say, its own peculiar definition of absolute position.
This is exactly the theory which I will elaborate.
In looking to nature for evidence of absolute position
it is of no use to recur to the four-dimensional manifold
of event-particles. This manifold has been obtained by
the extension of thought beyond the immediacy of
observation. We shall find nothing in it except what we
have put there to represent the ideas in thought which
arise from our direct sense-awareness of nature. To
find evidence of the properties which are to be found
in the manifold of event-particles we must always
recur to the observation of relations between events.
Our problem is to determine those relations between
events which issue in the property of absolute position
in a timeless space. This is in fact the problem of the
determination of the very meaning of the timeless
spaces of physical science,.
In reviewing the factors of nature as immediately
disclosed in sense-awareness, we should note the
fundamental character of the percept of 'being here.'
We discern an event merely as a factor in a determinate
complex in which each factor has its own peculiar share.
v] SPACE AND MOTION 107
There are two factors which are always ingredient in
this complex, one is the duration which is represented
in thought by the concept of all nature that is present
now, and the other is the peculiar locus standi for mind
involved in the sense-awareness. This locus standi in
nature is what is represented in thought by the concept
of * here,' namely of an ' event here.'
This is the concept of a definite factor in nature. This factor is an event in nature which is the focus in nature for that act of awareness, and the other events are perceived as referred to it. This event is part of the associated duration. I call it the 'percipient event.' This event is not the mind, that is to say, not the per- cipient. It is that in nature from which the mind perceives. The complete foothold of the mind in nature is represented by the pair of events, namely, the present duration which marks the ' when ' of awareness and the percipient event which marks the * where ' of awareness and the 'how' of awareness. This percipient event is roughly speaking the bodily life of the incarnate mind. But this identification is only a rough one. For the functions of the body shade off into those of other events in nature ; so that for some purposes the percipient event is to be reckoned as merely part of the bodily life and for other purposes it may even be reckoned as more than the bodily life. In many respects the demarcation is purely arbitrary, depending upon where in a sliding scale you choose to draw the line.
I have already in my previous lecture on Time dis- cussed the association of mind with nature. The difficulty of the discussion lies in the liability of constant factors to be overlooked. We never note them by contrast with their absences. The purpose of a discussion of such
io8 THE CONCEPT OF NATURE [CH.
factors may be described as being to make obvious
things lo(^ odd. We cannot envisage them unless we
manage to invest them with some of the freshness which
is due to strangeness.
It is because of this habit of letting constant factors slip from consciousness that we constantly fall into the error of thinking of the sense-awareness of a particular factor in nature as being a two-termed relation between the mind and the factor. For example, I perceive a green leaf. Language in this statement suppresses all reference to any factors other than the percipient mind and the green leaf and the relation of sense-awareness. It discards the obvious inevitable factors which are essential elements in the perception, I am here, the leaf is there ; and the event here and the event which is the life of the leaf there are both embedded in a totality of nature which is now, and within this totality there are other discriminated factors which it is irrelevant to mention. Thus language habitually sets before the mind a misleading abstract of the indefinite complexity of the fact of sense-awareness.
What I now want to discuss is the special relation of
the percipient event which is 'here' to the duration
which is ' now.' This relation is a fact in nature, namely
the mind is aware of nature as being with these two
factors in this relation.
Within the short present duration the ' here ' of the percipient event has a definite meaning of some sort. This meaning of 'here' is the content of the special relation of the percipient event to its associated duration. I will call this relation 'cogredience.' Accordingly I ask for a description of the character of the relation of cogredience. The present snaps into a past and a present
v] SPACE AND MOTION 109
when the 'here' of cogredience loses its single deter- minate meaning. There has been a passage of nature from the ' here ' of perception within the past duration to the different * here ' of perception within the present duration. But the two 'heres' of sense-awareness within neighbouring durations may be indistinguishable. In this case there has been a passage from the past to the present, but a more retentive perceptive force might have retained the passing nature as one complete present instead of letting the earlier duration slip into the past. Namely, the sense of rest helps the integration of dura- tions into a prolonged present, and the sense of motion differentiates nature into a succession of shortened durations. As we look out of a railway carriage in an express train, the present is past before reflexion can seize it. We live in snippits too quick for thought. On the other hand the immediate present is prolonged according as nature presents itself to us in an aspect of unbroken rest. Any change in nature provides ground for a differentiation among durations so as to shorten the present. But there is a great distinction between self-change in nature and change in external nature. Self-change in nature is change in the quality of the standpoint of the percipient event. It is the break up of the 'here' which necessitates the break up of the present duration. Change in external nature is com- patible with a prolongation of the present of contem- plation rooted in a given standpoint. What I want to bring out is that the preservation of a peculiar relation to a duration is a necessary condition for the function of that duration as a present duration for sense-aware- ness. This peculiar relation is the relation of cogredi- ence between the percipient event and the duration.
no THE CONCEPT OF NATURE [ch.
Cogredience is the preservation of unbroken quality of
standpoint within the duration. It is the continuance
of identity of station within the whole of nature which
is the terminus of sense-awareness. The duration may
comprise change within itself, but cannot — so far as it
is one present duration — comprise change in the quality
of its peculiar relation to the contained percipient event.
In other words, perception is always 'here,' and a
duration can only be posited as present for sense-aware-
ness on condition that it affords one unbroken meaning
of 'here' in its relation to the percipient event. It is
only in the past that you can have been ' there ' with a
standpoint distinct from your present 'here.'
Events there and events here are facts of nature, and the qualities of being ' there ' and ' here ' are not merely qualities of awareness as a relation between nature and mind. The quality of determinate station in the duration which belongs to an event which is ' here ' in one deter- minate sense of 'here' is the same kind of quality of station which belongs to an event which is 'there' in one determinate sense of 'there.' Thus cogredience has nothing to do with any biological character of the event which is related by it to the associated duration. This biological character is apparently a further condition for the peculiar connexion of a percipient event with the percipience of mind ; but it has nothing to do with the relation of the percipient event to the duration which is the present whole of nature posited as the disclosure of the percipience.
Given the requisite biological character, the event in
its character of a percipient event selects that duration
with which the operative past of the event is practi-
cally cogredient within the limits of the exactitude of