which is absolutely true for infinitely short waves. Einstein's principle, thus partially verified, stated in my language is that a ray of light always follows a path such that the integral impetus along it is zero. This involves that every element of impetus along it is zero.
In conclusion, I must apologise. In the first place
I have considerably toned down the various exciting
peculiarities of the original theory and have reduced it
to a greater conformity with the older physics. I do not
allow that physical phenomena are due to oddities of
space. Also I have added to the dullness of the lecture
by my respect for the audience. You would have enjoyed
a more popular lecture with illustrations of delightful
paradoxes. But I know also that you are serious
students who are here because you really want to know
how the new theories may affect your scientific re-
searches.
Chapter Ix
The Ultimate Physical Concepts
The second chapter of this book lays down the first
principle to be guarded in framing our physical concept.
We must avoid vicious bifurcation Nature is nothing
else than the deliverance of sense-awareness. We have
no principles whatever to tell us what could stimulate
mind towards sense-awareness. Our sole task is to
exhibit in one system the characters and inter-relations
of all that is observed. Our attitude towards nature is
purely * behaviouristic,' so far as concerns the formulation
of physical concepts.
Our knowledge of nature is an experience of activity (or passage). The things previously observed are active entities, the 'events.' They are chunks in the life of nature. These events have to each other relations which in our knowledge differentiate themselves into space- relations and time-relations. But this differentiation between space and time, though inherent in nature, is comparatively superficial ; and space and time are each partial expressions of one fundamental relation between events which is neither spatial nor temporal. This relation I call ' extension.' The relation of ' extending over' is the relation of 'including,' either in a spatial or in a temporal sense, or in both. But the mere 'inclu- sion' is, more fundamental than either alternative and does not require any spatio-temporal differentiation. In respect to extension two events are mutually related so that either (i) one includes the other, or (ii) one over- laps the other without complete inclusion, or (iii) they
l86 THE CONCEPT OF NATURE L^h.
are entirely separate. But great care is required in the
definition of spatial and temporal elements from this
basis in order to avoid tacit limitations really depend-
ing on undefined relations and properties.
Such fallacies can be avoided by taking account of
two elements in our experience, namely, (i) our ob-
servational 'present,' and (ii) our 'percipient event.'
Our observational ' present ' is what I call a ' duration.' It is the whole of nature apprehended in our immediate observation. It has therefore the nature of an event, but possesses a peculiar completeness which marks out such durations as a special type of events inherent in nature. A duration is not instantaneous. It is all that there is of nature with certain temporal limitations. In contradistinction to other events a duration will be called infinite and the other events are finite^. In our knowledge of a duration we distinguish (i) certain included events which are particularly discriminated as to their peculiar individualities, and (ii) the remaining included events which are only known as necessarily in being by reason of their relations to the discriminated events and to the whole duration. The duration as a whole is signified 2 by that quality of relatedness (in respect to extension) possessed by the part which is immediately under observation; namely, by the fact that there is essentially a beyond to whatever is observed. I mean by this that every event is known as being related to other events which it does not include. This fact, that every event is known as possessing the quality of exclusion, shows that exclusion is as positive a relation as inclusion. There are of course no merely negative
^ Cf. note on 'significance,' pp. 197, igS. ^ Cf. Ch. in, pp. 51 et seq.
Ix] the Ultimate Physical Concepts 187
relations in nature, and exclusion is not the mere
negative of inclusion, though the two relations are
contraries. Both relations are concerned solely with
events, and exclusion is capable of logical definition in
terms of inclusion.
Perhaps the most obvious exhibition of significance
is to be found in our knowledge of the geometrical
character of events inside an opaque material object.
For example we know that an opaque sphere has a
centre. This knowledge has nothing to do with the
material; the sphere may be a solid uniform billiard
ball or a hollow lawn-tennis ball. Such knowledge is
essentially the product of significance, since the general
character of the external discriminated events has in-
formed us that there are events within the sphere and
has also informed us of their geometrical structure.
Some criticisms on 'The Principles of Natural Knowledge' show that difficulty has been found in apprehending durations as real stratifications of nature. I think that this hesitation arises from the unconscious influence of the vicious principle of bifurcation, so deeply embedded in modern philosophical thought. We observe nature as extended in an immediate present which is simultaneous but not instantaneous, and there- fore the whole which is immediately discerned or signified as an inter-related system forms a stratification of nature which is a physical fact. This conclusion immediately follows unless we admit bifurcation in the form of the principle of psychic additions, here rejected.
Our 'percipient event' is that event included in our
observational present which we distinguish as being in
some peculiar way our standpoint for perception. It is
roughly speaking that event which is our bodily life
i88 THE CONCEPT OF NATURE [ch.
within the present duration. The theory of perception as evolved by medical psychology is based on signifi- cance. The distant situation of a perceived object is merely known to us as signified by our bodily state, i.e. by our percipient event. In fact perception requires sense-awareness of the significations of our percipient event together with sense-awareness of a peculiar re- lation (situation) between certain objects and the events thus signified. Our percipient event is saved by being the whole of nature by this fact of its significations. This is the meaning of calling the percipient event our standpoint for perception. The course of a ray of light is only derivatively connected with perception. What we do perceive are objects as related to events signified by the bodily states excited by the ray. These signified events (as is the case of images seen behind a mirror) may have very little to do with the actual course of the ray. In the course of evolution those animals have survived whose sense-awareness is con- centrated on those significations of their bodily states which are on the average important for their welfare. The whole world of events is signified, but there are some which exact the death penalty for inattention.
The percipient event is always here and now in the associated present duration. It has, what may be called, an absolute position in that duration. Thus one definite duration is associated with a definite percipient event, and we are thus aware of a peculiar relation which finite events can bear to durations. I call this relation ' cogredience,' The notion of rest is derivative from that of cogredience, and the notion of motion is derivative from that of inclusion within a duration without cogre- dience with it. In fact motion is a relation (of varying
Ix] the Ultimate Physical Concepts 189
character) between an observed event and an observed
duration, and cogredience is the most simple character
or subspecies of motion. To sum up, a duration and a
percipient event are essentially involved in the general
character of each observation of nature, and the per-
cipient event is cogredient with the duration.
Our knowledge of the pecuhar characters of different events depends upon our power of comparison. I call the exercise of this factorinour knowledge 'recognition,' and the requisite sense-awareness of the comparable characters I call 'sense-recognition.' Recognition and abstraction essentially involve each other. Each of them exhibits an entity for knowledge which is less than the concrete fact, but is a real factor in that fact. The most concrete fact capable of separate discrimination is the event. We cannot abstract without recognition, and we cannot recognise without abstraction. Perception involves apprehension of the event and recognition of the factors of its character.
The things recognised are what I call 'objects.' In this general sense of the term the relation of extension is itself an object. In practice however I restrict the term to those objects which can in some sense or other be said to have a situation in an event ; namely, in the phrase ' There it is again ' I restrict the ' there ' to be the indication of a special event which is the situation of the object. Even so, there are different types of objects, and statements which are true of objects of one type are not in general true of objects of other types. The objects with which we are here concerned in the formulation of physical laws are material objects, such as bits of matter, molecules and electrons. An object of one of these types has relations to events other than those
I90 THE CONCEPT OF N ATI DTTE [CH,
belonging to the stream of its situations. The fact of its situations within this stream has impressed on all other events certain modifications of their characters. In truth the object in its completeness may be conceived as a specific set of correlated modifications of the charac- ters of all events, with the property that these modifica- tions attain to a certain focal property for those events which belong to the stream of its situations. The total assemblage of the modifications of the characters of events due to the existence of an object in a stream of situations is what I call the 'physical field' due to the object. But the object cannot really be separated from its field. The object is in fact nothing else than the systematically adjusted set of modifications of the field. The conventional limitation of the object to the focal stream of events in which it is said to be ' situated ' is convenient for some purposes, but it obscures the ultimate fact of nature. From this point of view the antithesis between action at a distance and action by transmission is meaningless. The doctrine of this para- graph is nothing else than another way of expressing the unresolvable multiple relation of an object to events.
A complete time-system is formed by any one family of parallel durations. Two durations are parallel if either (i) one includes the other, or (ii) they overlap so as to include a third duration common to both, or (iii) are entirely separate. The excluded case is that of two durations overlapping so as to include in common an aggregate of finite events but including in common no other complete duration. The recognition of the fact of an indefinite number of families of parallel durations is what differentiates the concept of nature here put forward from the older orthodox concept of
Ix] the Ultimate Physical Concepts 191
the essentially unique time-systems. Its divergence from Einstein's concept of nature will be briefly indicated later.
The instantaneous spaces of a given time-system are the ideal (non-existent) durations of zero temporal thickness indicated by routes of approximation along series formed by durations of the associated family. Each such instantaneous space represents the ideal of nature at an instant and is also a moment of time. Each time-system thus possesses an aggregate of moments belonging to it alone. Each event-particle lies in one and only one moment of a given time-system. An event- particle has three characters^: (i) its extrinsic character which is its character as a definite route of convergence among events, (ii) its intrinsic character which is the peculiar quality of nature in its neighbourhood, namely, the character of the physical field in the neighbourhood, and (iii) its position.
The position of an event-particle arises from the
aggregate of moments (no two of the same family) in
which it lies. We fix our attention on one of these
moments which is approximated to by the short dura-
tion of our immediate experience, and we express
position as the position in this moment. But the event-
particle receives its position in moment M in virtue of
the whole aggregate of other moments M' , M" , etc.,
in which it also lies. The diflFerentiation of M into a
geometry of event-particles (instantaneous points) ex-
presses the differentiation of M by its intersections with
moments of alien time-systems. In this way planes and
straight lines and event-particles themselves find their
being. Also the parallelism of planes and straight lines
arises from the parallelism of the moments of one and
^ Cf. pp. 82 et seq.