the colour of the Needle. I call these simple objects, such as colours or sounds, sense-objects. An artist will train himself to attend more particularly to sense- objects where the ordinary person attends normally to material objects. Thus if you were walking with an artist, when you said 'There's Cleopatra's Needle,' perhaps he simultaneously exclaimed 'There's a nice bit of colour.' Yet you were both expressing your recognition of different component characters of the same event. But in science we have found out that when we know all about the adventures amid events of material physical objects and of scientific objects we have most of the relevant information which will enable us to predict the conditions under which we shall perceive sense-objects in specific situations. For ex- ample, when we know that there is a blazing fire {i.e. material and scientific objects undergoing various exciting adventures amid events) and opposite to it a mirror (which is another material object) and the positions of a man's face and eyes gazing into the mirror, we know that he can perceive the redness of the flame situated in an event behind the mirror — thus, to a large extent, the appearance of sense-objects is conditioned by the adventures of material objects. The analysis of these adventures makes us aware of another character of events, namely their characters as fields of activity which determine the subsequent events to which they will pass on the objects situated in them. We express these fields of activity in terms of gravitational, electro- magnetic, or chemical forces and attractions. But the exact expression of the nature of these fields of activity forces us intellectually to acknowledge a less obvious type of objects as situated in events. I mean molecules
Viii] Summary 171
and electrons. These objects are not recognised in
isolation. We cannot well miss Cleopatra's Needle, if
we are in its neighbourhood ; but no one has seen a single
molecule or a single electron, yet the characters of
events are only explicable to us by expressing them in
terms of these scientific objects. Undoubtedly molecules
and electrons are abstractions. But then so is Cleo-
patra's Needle. The concrete facts are the events them-
selves — I have already explained to you that to be an
abstraction does not mean that an entity is nothing. It
merely means that its existence is only one factor of a
more concrete element of nature. So an electron is
abstract because you cannot wipe out the whole structure
of events and yet retain the electron in existence. In
the same way the grin on the cat is abstract; and the
molecule is really in the event in the same sense as the
grin is really on the cat's face. Now the more ultimate
sciences such as Chemistry or Physics cannot express
their ultimate laws in terms of such vague objects as
the sun, the earth, Cleopatra's Needle, or a human
body. Such objects more properly belong to Astro-
nomy, to Geology, to Engineering, to Archaeology,
or to Biology. Chemistry and Physics only deal with
them as exhibiting statistical complexes of the effects
of their more intimate laws. In a certain sense, they
only enter into Physics and Chemistry as technological
applications. The reason is that they are too vague.
Where does Cleopatra's Needle begin and where does
it end.? Is the soot part of it.? Is it a different
object when it sheds a molecule or when its surface
enters into chemical combination with the acid of a
London fog? The definiteness and permanence of the
Needle is nothing to the possible permanent definiteness
172 THE CONCEPT OF NATURE [CH.
of a molecule as conceived by science, and the per-
manent definiteness of a molecule in its turn yields to
that of an electron. Thus science in its most ultimate
formulation of law seeks objects with the most per-
manent definite simplicity of character and expresses
its final laws in terms of them.
Again when we seek definitely to express the relations of events which arise from their spatio-temporal structure, we approximate to simpUcity by progressively diminishing the extent (both temporal and spatial) of the events considered. For example, the event which is the life of the chunk of nature which is the Needle during one minute has to the life of nature within a passing barge during the same minute a very complex spatio-temporal relation. But suppose we progressively diminish the time considered to a second, to a hun- dredth of a second, to a thousandth of a second, and so on. As we pass along such a series we approximate to an ideal simplicity of structural relations of the pairs of events successively considered, which ideal we call the spatial relations of the Needle to the barge at some instant. Even these relations are too complicated for us, and we consider smaller and smaller bits of the Needle and of the barge. Thus we finally reach the ideal of an event so restricted in its extension as to be without ex- tension in space or extension in time. Such an event is a mere spatial point-flash of instantaneous duration. I call such an ideal event an ' event-particle.' You must not think of the world as ultimately built up of event- particles. That is to put the cart before the horse. The world we know is a continuous stream of occurrence which we can discriminate into finite events forming by their overlappings and containings of each other and
viii] SUMMARY
separations a spatio-temporal structure. We can express the properties of this structure in terms of the ideal limits to routes of approximation, which I have termed event-particles. Accordingly event-particles are abstrac- tions in their relations to the more concrete events. But then by this time you will have comprehended that you cannot analyse concrete nature without abstracting. Also I repeat, the abstractions of science are entities which are truly in nature, though they have no meaning in isolation from nature.
The character of the spatio-temporal structure of events can be fully expressed in terms of relations between these more abstract event -particles. The ad- vantage of dealing with event-particles is that though they are abstract and complex in respect to the finite events which we directly observe, they are simpler than finite events in respect to their mutual relations. Accordingly they express for us the demands of an ideal accuracy, and of an ideal simplicity in the exposition of relations. These event-particles are the ultimate elements of the four-dimensional space-time manifold which the theory of relativity presupposes. You will have observed that each event-particle is as much an instant of time as it is a point of space. I have called it an instantaneous point-flash. Thus in the structure of this space-time manifold space is not finally discriminated from time, and the possibility remains open for diverse modes of discrimination according to the diverse circumstances of observers. It is this possibility which makes the fundamental distinction between the new way of con- ceiving the universe and the old way. The secret of understanding relativity is to understand this. It is of no use rushing in with picturesque paradoxes, such as
174 THE CONCEPT OF NA'iURii [CU.
' Space caught bending,' if you have not mastered this fundamental conception which underUes the whole theory. When I say that it underlies the whole theory, I mean that in my opinion it ought to underlie it, though I may confess some doubts as to how far all expositions of the theory have really understood its implications and its premises.
Our measurements when they are expressed in terms of an ideal accuracy are measurements which express properties of the space-time manifold. Now there are measurements of different sorts. You can measure lengths, or angles, or areas, or volumes, or times. There are also other sorts of measures such as measurements of intensity of illumination, but I will disregard these for the moment and will confine attention to those measurements which particularly interest us as being measurements of space or of time. It is easy to see that four such measurements of the proper characters are necessary to determine the position of an event-particle in the space-time manifold in its relation to the rest of the manifold. For example, in a rectangular field you start from one corner at a given time, you measure a definite distance along one side, you then strike out into the field at right angles, and then measure a definite distance parallel to the other pair of sides, you then rise vertically a definite height and take the time. At the point and at the time which you thus reach there is occurring a definite instantaneous point-flash of nature. In other words, your four measurements have deter- mined a definite event-particle belonging to the four- dimension space-time manifold. These measurements have appeared to be very simple to the land-surveyor and raise in his mind no philosophic difficulties. But
viii] SUMMARY
suppose there are beings on Mars sufficiently advanced in scientific invention to be able to watch in detail the operations of this survey on earth. Suppose that they construe the operations of the English land-surveyors in reference to the space natural to a being on Mars, namely a Martio-centric space in which that planet is fixed. The earth is moving relatively to Mars and is rotating. To the beings on Mars the operations, con- strued in this fashion, effect measurements of the greatest complication. Furthermore, according to the relati- vistic doctrine, the operation of time-measurement on earth will not correspond quite exactly to any time- measurement on Mars.
I have discussed this example in order to make you
realise that in thinking of the possibilities of measure-
ment in the space-time manifold, we must not confine
ourselves merely to those minor variations which might
seem natural to human beings on the earth. Let us
make therefore the general statement that four measure-
ments, respectively of independent types (such as mea-
surements of lengths in three directions and a time),
can be found such that a definite event-particle is
determined by them in its relations to other parts of
the manifold.
176 THE CONCEPT OF NATURE [CH.
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-measure- ment. Then we should naturally say that (pi, p^, p^) determined a point in space and that the event-particle happened at that point at the time ^4. 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 (pi, p^, p^) of the space in the ^-system is merely the collection of event-particles {pi, p^, pz^ [pj)? where ^4 is varied and (Pi, p2, ps) 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.
vni] SUMMARY