The Concept of Nature Part 10

In general the situation is an active conditioning event; namely the coat itself, when there is no mirror or other such contrivance to produce abnormal effects. But the example of the mirror shows us that the situation may be one of the pa.s.sive conditioning events. We are then apt to say that our senses have been cheated, because we demand as a right that the situation should be an active condition in the ingression.

This demand is not so baseless as it may seem when presented as I have put it. All we know of the characters of the events of nature is based on the a.n.a.lysis of the relations of situations to percipient events. If situations were not in general active conditions, this a.n.a.lysis would tell us nothing. Nature would be an unfathomable enigma to us and there could be no science. Accordingly the incipient discontent when a situation is found to be a pa.s.sive condition is in a sense justifiable; because if that sort of thing went on too often, the _role_ of the intellect would be ended.

Furthermore the mirror is itself the situation of other sense-objects either for the same observer with the same percipient event, or for other observers with other percipient events. Thus the fact that an event is a situation in the ingression of one set of sense-objects into nature is presumptive evidence that that event is an active condition in the ingression of other sense-objects into nature which may have other situations.

This is a fundamental principle of science which it has derived from common sense.

I now turn to perceptual objects. When we look at the coat, we do not in general say, There is a patch of Cambridge blue; what naturally occurs to us is, There is a coat. Also the judgment that what we have seen is a garment of man's attire is a detail. What we perceive is an object other than a mere sense-object. It is not a mere patch of colour, but something more; and it is that something more which we judge to be a coat. I will use the word 'coat' as the name for that crude object which is more than a patch of colour, and without any allusion to the judgments as to its usefulness as an article of attire either in the past or the future. The coat which is perceived--in this sense of the word 'coat'--is what I call a perceptual object. We have to investigate the general character of these perceptual objects.

It is a law of nature that in general the situation of a sense-object is not only the situation of that sense-object for one definite percipient event, but is the situation of a variety of sense-objects for a variety of percipient events. For example, for any one percipient event, the situation of a sense-object of sight is apt also to be the situations of sense-objects of sight, of touch, of smell, and of sound. Furthermore this concurrence in the situations of sense-objects has led to the body--_i.e._ the percipient event--so adapting itself that the perception of one sense-object in a certain situation leads to a subconscious sense-awareness of other sense-objects in the same situation. This interplay is especially the case between touch and sight. There is a certain correlation between the ingressions of sense-objects of touch and sense-objects of sight into nature, and in a slighter degree between the ingressions of other pairs of sense-objects.

I call this sort of correlation the 'conveyance' of one sense-object by another. When you see the blue flannel coat you subconsciously feel yourself wearing it or otherwise touching it. If you are a smoker, you may also subconsciously be aware of the faint aroma of tobacco. The peculiar fact, posited by this sense-awareness of the concurrence of subconscious sense-objects along with one or more dominating sense-objects in the same situation, is the sense-awareness of the perceptual object. The perceptual object is not primarily the issue of a judgment. It is a factor of nature directly posited in sense-awareness.

The element of judgment comes in when we proceed to cla.s.sify the particular perceptual object. For example, we say, That is flannel, and we think of the properties of flannel and the uses of athletes' coats.

But that all takes place after we have got hold of the perceptual object. Antic.i.p.atory judgments affect the perceptual object perceived by focussing and diverting attention.

The perceptual object is the outcome of the habit of experience.

Anything which conflicts with this habit hinders the sense-awareness of such an object. A sense-object is not the product of the a.s.sociation of intellectual ideas; it is the product of the a.s.sociation of sense-objects in the same situation. This outcome is not intellectual; it is an object of peculiar type with its own particular ingression into nature.

There are two kinds of perceptual objects, namely, 'delusive perceptual objects' and 'physical objects.' The situation of a delusive perceptual object is a pa.s.sive condition in the ingression of that object into nature. Also the event which is the situation will have the relation of situation to the object only for one particular percipient event. For example, an observer sees the image of the blue coat in a mirror. It is a blue coat that he sees and not a mere patch of colour. This shows that the active conditions for the conveyance of a group of subconscious sense-objects by a dominating sense-object are to be found in the percipient event. Namely we are to look for them in the investigations of medical psychologists. The ingression into nature of the delusive sense-object is conditioned by the adaptation of bodily events to the more normal occurrence, which is the ingression of the physical object.

A perceptual object is a physical object when (i) its situation is an active conditioning event for the ingression of any of its component sense-objects, and (ii) the same event can be the situation of the perceptual object for an indefinite number of possible percipient events. Physical objects are the ordinary objects which we perceive when our senses are not cheated, such as chairs, tables and trees. In a way physical objects have more insistent perceptive power than sense-objects. Attention to the fact of their occurrence in nature is the first condition for the survival of complex living organisms. The result of this high perceptive power of physical objects is the scholastic philosophy of nature which looks on the sense-objects as mere attributes of the physical objects. This scholastic point of view is directly contradicted by the wealth of sense-objects which enter into our experience as situated in events without any connexion with physical objects. For example, stray smells, sounds, colours and more subtle nameless sense-objects. There is no perception of physical objects without perception of sense-objects. But the converse does not hold: namely, there is abundant perception of sense-objects unaccompanied by any perception of physical objects. This lack of reciprocity in the relations between sense-objects and physical objects is fatal to the scholastic natural philosophy.

There is a great difference in the _roles_ of the situations of sense-objects and physical objects. The situations of a physical object are conditioned by uniqueness and continuity. The uniqueness is an ideal limit to which we approximate as we proceed in thought along an abstractive set of durations, considering smaller and smaller durations in the approach to the ideal limit of the moment of time. In other words, when the duration is small enough, the situation of the physical object within that duration is practically unique.

The identification of the same physical object as being situated in distinct events in distinct durations is effected by the condition of continuity. This condition of continuity is the condition that a continuity of pa.s.sage of events, each event being a situation of the object in its corresponding duration, can be found from the earlier to the later of the two given events. So far as the two events are practically adjacent in one specious present, this continuity of pa.s.sage may be directly perceived. Otherwise it is a matter of judgment and inference.

The situations of a sense-object are not conditioned by any such conditions either of uniqueness or of continuity. In any durations however small a sense-object may have any number of situations separated from each other. Thus two situations of a sense-object, either in the same duration or in different durations, are not necessarily connected by any continuous pa.s.sage of events which are also situations of that sense-object.

The characters of the conditioning events involved in the ingression of a sense-object into nature can be largely expressed in terms of the physical objects which are situated in those events. In one respect this is also a tautology. For the physical object is nothing else than the habitual concurrence of a certain set of sense-objects in one situation.

Accordingly when we know all about the physical object, we thereby know its component sense-objects. But a physical object is a condition for the occurrence of sense-objects other than those which are its components. For example, the atmosphere causes the events which are its situations to be active conditioning events in the transmission of sound. A mirror which is itself a physical object is an active condition for the situation of a patch of colour behind it, due to the reflection of light in it.

Thus the origin of scientific knowledge is the endeavour to express in terms of physical objects the various _roles_ of events as active conditions in the ingression of sense-objects into nature. It is in the progress of this investigation that scientific objects emerge. They embody those aspects of the character of the situations of the physical objects which are most permanent and are expressible without reference to a multiple relation including a percipient event. Their relations to each other are also characterised by a certain simplicity and uniformity. Finally the characters of the observed physical objects and sense-objects can be expressed in terms of these scientific objects. In fact the whole point of the search for scientific objects is the endeavour to obtain this simple expression of the characters of events.

These scientific objects are not themselves merely formulae for calculation; because formulae must refer to things in nature, and the scientific objects are the things in nature to which the formulae refer.

A scientific object such as a definite electron is a systematic correlation of the characters of all events throughout all nature. It is an aspect of the systematic character of nature. The electron is not merely where its charge is. The charge is the quant.i.tative character of certain events due to the ingression of the electron into nature. The electron is its whole field of force. Namely the electron is the systematic way in which all events are modified as the expression of its ingression. The situation of an electron in any small duration may be defined as that event which has the quant.i.tative character which is the charge of the electron. We may if we please term the mere charge the electron. But then another name is required for the scientific object which is the full ent.i.ty which concerns science, and which I have called the electron.

According to this conception of scientific objects, the rival theories of action at a distance and action by transmission through a medium are both incomplete expressions of the true process of nature. The stream of events which form the continuous series of situations of the electron is entirely self-determined, both as regards having the intrinsic character of being the series of situations of that electron and as regards the time-systems with which its various members are cogredient, and the flux of their positions in their corresponding durations. This is the foundation of the denial of action at a distance; namely the progress of the stream of the situations of a scientific object can be determined by an a.n.a.lysis of the stream itself.

On the other hand the ingression of every electron into nature modifies to some extent the character of every event. Thus the character of the stream of events which we are considering bears marks of the existence of every other electron throughout the universe. If we like to think of the electrons as being merely what I call their charges, then the charges act at a distance. But this action consists in the modification of the situation of the other electron under consideration. This conception of a charge acting at a distance is a wholly artificial one.

The conception which most fully expresses the character of nature is that of each event as modified by the ingression of each electron into nature. The ether is the expression of this systematic modification of events throughout s.p.a.ce and throughout time. The best expression of the character of this modification is for physicists to find out. My theory has nothing to do with that and is ready to accept any outcome of physical research.

The connexion of objects with s.p.a.ce requires elucidation. Objects are situated in events. The relation of situation is a different relation for each type of object, and in the case of sense-objects it cannot be expressed as a two-termed relation. It would perhaps be better to use a different word for these different types of the relation of situation.

It has not however been necessary to do so for our purposes in these lectures. It must be understood however that, when situation is spoken of, some one definite type is under discussion, and it may happen that the argument may not apply to situation of another type. In all cases however I use situation to express a relation between objects and events and not between objects and abstractive elements. There is a derivative relation between objects and spatial elements which I call the relation of location; and when this relation holds, I say that the object is located in the abstractive element. In this sense, an object may be located in a moment of time, in a volume of s.p.a.ce, an area, a line, or a point. There will be a peculiar type of location corresponding to each type of situation; and location is in each case derivative from the corresponding relation of situation in a way which I will proceed to explain.

Also location in the timeless s.p.a.ce of some time-system is a relation derivative from location in instantaneous s.p.a.ces of the same time-system. Accordingly location in an instantaneous s.p.a.ce is the primary idea which we have to explain. Great confusion has been occasioned in natural philosophy by the neglect to distinguish between the different types of objects, the different types of situation, the different types of location, and the difference between location and situation. It is impossible to reason accurately in the vague concerning objects and their positions without keeping these distinctions in view.

An object is located in an abstractive element, when an abstractive set belonging to that element can be found such that each event belonging to that set is a situation of the object. It will be remembered that an abstractive element is a certain group of abstractive sets, and that each abstractive set is a set of events. This definition defines the location of an element in any type of abstractive element. In this sense we can talk of the existence of an object at an instant, meaning thereby its location in some definite moment. It may also be located in some spatial element of the instantaneous s.p.a.ce of that moment.

A quant.i.ty can be said to be located in an abstractive element when an abstractive set belonging to the element can be found such that the quant.i.tative expressions of the corresponding characters of its events converge to the measure of the given quant.i.ty as a limit when we pa.s.s along the abstractive set towards its converging end.

By these definitions location in elements of instantaneous s.p.a.ces is defined. These elements occupy corresponding elements of timeless s.p.a.ces. An object located in an element of an instantaneous s.p.a.ce will also be said to be located at that moment in the timeless element of the timeless s.p.a.ce which is occupied by that instantaneous element.

It is not every object which can be located in a moment. An object which can be located in every moment of some duration will be called a 'uniform' object throughout that duration. Ordinary physical objects appear to us to be uniform objects, and we habitually a.s.sume that scientific objects such as electrons are uniform. But some sense-objects certainly are not uniform. A tune is an example of a non-uniform object.

We have perceived it as a whole in a certain duration; but the tune as a tune is not at any moment of that duration though one of the individual notes may be located there.

It is possible therefore that for the existence of certain sorts of objects, _e.g._ electrons, minimum quanta of time are requisite. Some such postulate is apparently indicated by the modern quantum theory and it is perfectly consistent with the doctrine of objects maintained in these lectures.

Also the instance of the distinction between the electron as the mere quant.i.tative electric charge of its situation and the electron as standing for the ingression of an object throughout nature ill.u.s.trates the indefinite number of types of objects which exist in nature. We can intellectually distinguish even subtler and subtler types of objects.

Here I reckon subtlety as meaning seclusion from the immediate apprehension of sense-awareness. Evolution in the complexity of life means an increase in the types of objects directly sensed. Delicacy of sense-apprehension means perceptions of objects as distinct ent.i.ties which are mere subtle ideas to cruder sensibilities. The phrasing of music is a mere abstract subtlety to the unmusical; it is a direct sense-apprehension to the initiated. For example, if we could imagine some lowly type of organic being thinking and aware of our thoughts, it would wonder at the abstract subtleties in which we indulge as we think of stones and bricks and drops of water and plants. It only knows of vague undifferentiated feelings in nature. It would consider us as given over to the play of excessively abstract intellects. But then if it could think, it would antic.i.p.ate; and if it antic.i.p.ated, it would soon perceive for itself.

In these lectures we have been scrutinising the foundations of natural philosophy. We are stopping at the very point where a boundless ocean of enquiries opens out for our questioning.

I agree that the view of Nature which I have maintained in these lectures is not a simple one. Nature appears as a complex system whose factors are dimly discerned by us. But, as I ask you, Is not this the very truth? Should we not distrust the jaunty a.s.surance with which every age prides itself that it at last has. .h.i.t upon the ultimate concepts in which all that happens can be formulated? The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, Seek simplicity and distrust it.

CHAPTER VIII

SUMMARY

There is a general agreement that Einstein's investigations have one fundamental merit irrespective of any criticisms which we may feel inclined to pa.s.s on them. They have made us think. But when we have admitted so far, we are most of us faced with a distressing perplexity.

What is it that we ought to think about? The purport of my lecture this afternoon will be to meet this difficulty and, so far as I am able, to set in a clear light the changes in the background of our scientific thought which are necessitated by any acceptance, however qualified, of Einstein's main positions. I remember that I am lecturing to the members of a chemical society who are not for the most part versed in advanced mathematics. The first point that I would urge upon you is that what immediately concerns you is not so much the detailed deductions of the new theory as this general change in the background of scientific conceptions which will follow from its acceptance. Of course, the detailed deductions are important, because unless our colleagues the astronomers and the physicists find these predictions to be verified we can neglect the theory altogether. But we may now take it as granted that in many striking particulars these deductions have been found to be in agreement with observation. Accordingly the theory has to be taken seriously and we are anxious to know what will be the consequences of its final acceptance. Furthermore during the last few weeks the scientific journals and the lay press have been filled with articles as to the nature of the crucial experiments which have been made and as to some of the more striking expressions of the outcome of the new theory.

's.p.a.ce caught bending' appeared on the news-sheet of a well-known evening paper. This rendering is a terse but not inapt translation of Einstein's own way of interpreting his results. I should say at once that I am a heretic as to this explanation and that I shall expound to you another explanation based upon some work of my own, an explanation which seems to me to be more in accordance with our scientific ideas and with the whole body of facts which have to be explained. We have to remember that a new theory must take account of the old well-attested facts of science just as much as of the very latest experimental results which have led to its production.

To put ourselves in the position to a.s.similate and to criticise any change in ultimate scientific conceptions we must begin at the beginning. So you must bear with me if I commence by making some simple and obvious reflections. Let us consider three statements, (i) 'Yesterday a man was run over on the Chelsea Embankment,' (ii) 'Cleopatra's Needle is on the Charing Cross Embankment,' and (iii) 'There are dark lines in the Solar Spectrum.' The first statement about the accident to the man is about what we may term an 'occurrence,' a 'happening,' or an 'event.' I will use the term 'event' because it is the shortest. In order to specify an observed event, the place, the time, and character of the event are necessary. In specifying the place and the time you are really stating the relation of the a.s.signed event to the general structure of other observed events. For example, the man was run over between your tea and your dinner and adjacently to a pa.s.sing barge in the river and the traffic in the Strand. The point which I want to make is this: Nature is known to us in our experience as a complex of pa.s.sing events. In this complex we discern definite mutual relations between component events, which we may call their relative positions, and these positions we express partly in terms of s.p.a.ce and partly in terms of time. Also in addition to its mere relative position to other events, each particular event has its own peculiar character.

In other words, nature is a structure of events and each event has its position in this structure and its own peculiar character or quality.

Let us now examine the other two statements in the light of this general principle as to the meaning of nature. Take the second statement, 'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight we should hardly call this an event. It seems to lack the element of time or transitoriness. But does it? If an angel had made the remark some hundreds of millions of years ago, the earth was not in existence, twenty millions of years ago there was no Thames, eighty years ago there was no Thames Embankment, and when I was a small boy Cleopatra's Needle was not there. And now that it is there, we none of us expect it to be eternal. The static timeless element in the relation of Cleopatra's Needle to the Embankment is a pure illusion generated by the fact that for purposes of daily intercourse its emphasis is needless. What it comes to is this: Amidst the structure of events which form the medium within which the daily life of Londoners is pa.s.sed we know how to identify a certain stream of events which maintain permanence of character, namely the character of being the situations of Cleopatra's Needle. Day by day and hour by hour we can find a certain chunk in the transitory life of nature and of that chunk we say, 'There is Cleopatra's Needle.' If we define the Needle in a sufficiently abstract manner we can say that it never changes. But a physicist who looks on that part of the life of nature as a dance of electrons, will tell you that daily it has lost some molecules and gained others, and even the plain man can see that it gets dirtier and is occasionally washed. Thus the question of change in the Needle is a mere matter of definition. The more abstract your definition, the more permanent the Needle. But whether your Needle change or be permanent, all you mean by stating that it is situated on the Charing Cross Embankment, is that amid the structure of events you know of a certain continuous limited stream of events, such that any chunk of that stream, during any hour, or any day, or any second, has the character of being the situation of Cleopatra's Needle.

Finally, we come to the third statement, 'There are dark lines in the Solar Spectrum.' This is a law of nature. But what does that mean? It means merely this. If any event has the character of being an exhibition of the solar spectrum under certain a.s.signed circ.u.mstances, it will also have the character of exhibiting dark lines in that spectrum.

This long discussion brings us to the final conclusion that the concrete facts of nature are events exhibiting a certain structure in their mutual relations and certain characters of their own. The aim of science is to express the relations between their characters in terms of the mutual structural relations between the events thus characterised. The mutual structural relations between events are both spatial and temporal. If you think of them as merely spatial you are omitting the temporal element, and if you think of them as merely temporal you are omitting the spatial element. Thus when you think of s.p.a.ce alone, or of time alone, you are dealing in abstractions, namely, you are leaving out an essential element in the life of nature as known to you in the experience of your senses. Furthermore there are different ways of making these abstractions which we think of as s.p.a.ce and as time; and under some circ.u.mstances we adopt one way and under other circ.u.mstances we adopt another way. Thus there is no paradox in holding that what we mean by s.p.a.ce under one set of circ.u.mstances is not what we mean by s.p.a.ce under another set of circ.u.mstances. And equally what we mean by time under one set of circ.u.mstances is not what we mean by time under another set of circ.u.mstances. By saying that s.p.a.ce and time are abstractions, I do not mean that they do not express for us real facts about nature. What I mean is that there are no spatial facts or temporal facts apart from physical nature, namely that s.p.a.ce and time are merely ways of expressing certain truths about the relations between events.

Also that under different circ.u.mstances there are different sets of truths about the universe which are naturally presented to us as statements about s.p.a.ce. In such a case what a being under the one set of circ.u.mstances means by s.p.a.ce will be different from that meant by a being under the other set of circ.u.mstances. Accordingly when we are comparing two observations made under different circ.u.mstances we have to ask 'Do the two observers mean the same thing by s.p.a.ce and the same thing by time?' The modern theory of relativity has arisen because certain perplexities as to the concordance of certain delicate observations such as the motion of the earth through the ether, the perihelion of mercury, and the positions of the stars in the neighbourhood of the sun, have been solved by reference to this purely relative significance of s.p.a.ce and time.

I want now to recall your attention to Cleopatra's Needle, which I have not yet done with. As you are walking along the Embankment you suddenly look up and say, 'Hullo, there's the Needle.' In other words, you recognise it. You cannot recognise an event; because when it is gone, it is gone. You may observe another event of a.n.a.logous character, but the actual chunk of the life of nature is inseparable from its unique occurrence. But a character of an event can be recognised. We all know that if we go to the Embankment near Charing Cross we shall observe an event having the character which we recognise as Cleopatra's Needle.

Things which we thus recognise I call objects. An object is situated in those events or in that stream of events of which it expresses the character. There are many sorts of objects. For example, the colour green is an object according to the above definition. It is the purpose of science to trace the laws which govern the appearance of objects in the various events in which they are found to be situated. For this purpose we can mainly concentrate on two types of objects, which I will call material physical objects and scientific objects. A material physical object is an ordinary bit of matter, Cleopatra's Needle for example. This is a much more complicated type of object than a mere colour, such as 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 example, 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 a.n.a.lysis 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 pa.s.s on the objects situated in them. We express these fields of activity in terms of gravitational, electromagnetic, 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 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 Cleopatra's Needle. The concrete facts are the events themselves--I have already explained to you that to be an abstraction does not mean that an ent.i.ty 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 Astronomy, 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 of a molecule as conceived by science, and the permanent 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 permanent 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 simplicity by progressively diminis.h.i.+ng 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 pa.s.sing barge during the same minute a very complex spatio-temporal relation. But suppose we progressively diminish the time considered to a second, to a hundredth of a second, to a thousandth of a second, and so on. As we pa.s.s 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 extension in s.p.a.ce 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 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 abstractions in their relations to the more concrete events. But then by this time you will have comprehended that you cannot a.n.a.lyse concrete nature without abstracting. Also I repeat, the abstractions of science are ent.i.ties 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 advantage 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 s.p.a.ce-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 s.p.a.ce. I have called it an instantaneous point-flash. Thus in the structure of this s.p.a.ce-time manifold s.p.a.ce is not finally discriminated from time, and the possibility remains open for diverse modes of discrimination according to the diverse circ.u.mstances of observers. It is this possibility which makes the fundamental distinction between the new way of conceiving the universe and the old way. The secret of understanding relativity is to understand this. It is of no use rus.h.i.+ng in with picturesque paradoxes, such as 's.p.a.ce caught bending,' if you have not mastered this fundamental conception which underlies 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 s.p.a.ce-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 s.p.a.ce 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 s.p.a.ce-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 determined a definite event-particle belonging to the four-dimension s.p.a.ce-time manifold. These measurements have appeared to be very simple to the land-surveyor and raise in his mind no philosophic difficulties.

But 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 s.p.a.ce natural to a being on Mars, namely a Martio-centric s.p.a.ce in which that planet is fixed. The earth is moving relatively to Mars and is rotating. To the beings on Mars the operations, construed in this fas.h.i.+on, effect measurements of the greatest complication. Furthermore, according to the relativistic doctrine, the operation of time-measurement on earth will not correspond quite exactly to any time-measurement on Mars.