Section 7 of The Concept of Nature by Alfred North Whitehead. The ensuing lecture is concerned with the theory of objects. Objects are elements in nature which do not pass. The awareness of an object as some factor not sharing in the passage of nature is what I call recognition. It is impossible to recognize an event because an event is essentially distinct from every other event. Recognition is an awareness of sameness. But to call recognition an awareness of sameness implies an intellectual act of comparison accompanied with judgment. I use recognition for the non-intellectual relation of sense awareness which connects the mind with a factor of nature without passage. On the intellectual side of the mind's experience there are comparisons of things recognized in consequent judgments of sameness or diversity. Probably sense recognition would be a better term for what I mean by recognition. I have chosen the simpler term because I think that I shall be able to avoid the use of recognition in any other meaning than that of sense recognition. I am quite willing to believe that recognition in my sense of the term is merely an ideal limit and that there is in fact no recognition without intellectual accompaniments of comparison and judgment. But recognition is that relation of the mind to nature which provides the material for the intellectual activity. An object is an ingredient in the character of some event. In fact the character of an event is nothing but the objects which are ingredient in it and the ways in which those objects make their ingression into the event. Thus the theory of objects is the theory of the comparison of events. Events are only comparable because they body forth permanences. We are comparing objects and events whenever we can say there it is again. Objects are the elements in nature which can be again. Sometimes permanences can be proved to exist which evade recognition in the sense in which I am using that term. The permanences which evade recognition appear to us as abstract properties either of events or of objects. All the same they are there for recognition although undiscriminated in our sense awareness. The demarcation of events, the splitting of nature up into parts, is affected by the objects which we recognize as their ingredients. The discrimination of nature is the recognition of objects amid passing events. It is a compound of the awareness of the passage of nature, of the consequent partition of nature, and of the definition of certain parts of nature by the modes of the ingression of objects into them. You may have noticed that I am using the term ingression to denote the general relation of objects to events. The ingression of an object into an event is the way the character of the event shapes itself in virtue of being of the object. Namely the event is what it is because the object is what it is, and when I am thinking of this modification of the event by the object I call the relation between the two the ingression of the object into the event.  Nature is such that there can be no events and no objects without the ingression of objects into events. Although there are events such that the ingredient objects evade our recognition. These are the events in empty space. Such events are only analyzed for us by the intellectual probing of science. Ingression is a relation which has various modes. There are obviously very various kinds of objects and no one kind of object can have the same sort of relations to events as objects of another kind can have. We shall have to analyze out some of the different modes of ingression which different kinds of objects have into events. But even if we stick to one and the same kind of objects an object of that kind has different modes of ingression into different events. Science and philosophy have been apt to entangle themselves in a simple-minded theory that an object is at one place at any definite time and is in no sense anywhere else. This is, in fact, the attitude of common sense thought, though it is not the attitude of language which is naively expressing the facts of experience. Every other sentence and a work of literature which is endeavoring truly to interpret the facts of experience expresses the difference in surrounding events due to the presence of some object. An object is ingredient throughout its neighborhood and its neighborhood is indefinite. Also, the modification of events by ingression is susceptible of quantitative differences. Finally, therefore, we are driven to admit that each object is, in some sense, ingredient throughout nature, though its ingression may be quantitatively irrelevant in the expression of our individual experiences. This admission is not new either in philosophy or science. It is obviously a necessary axiom for those philosophers who insist that reality is a system. In these lectures we are keeping off the profound and vexed question as to what we mean by reality. I am maintaining the humbler thesis that nature is a system. But I suppose that, in this case, the less follows from the greater, and that I may claim the support of these philosophers. The same doctrine is essentially interwoven in all modern physical speculation. As long ago as 1847, Faraday in a paper in the Philosophical Magazine remarked that his theory of tubes of force implies that, in a sense, an electric charge is everywhere. The modification of the electromagnetic field at every point of space, at each instant, owing to the past history of each electron, is another way of stating the same fact. We can, however, illustrate the doctrine by the more familiar facts of life without recourse to the abstruse speculations of theoretical physics. The waves they roll on the Cornish coast tell of a gale in mid-Atlantic, and our dinner witnesses to the ingression of the cook into the dining room. It is evident that the ingression of objects into events includes the theory of causation. I prefer to neglect this aspect of ingression because causation raises the memory of discussions based upon theories of nature, which are alien to my own. Also, I think that some new light may be thrown on the subject by viewing it in this fresh aspect. The examples which I have given of the ingression of objects into events remind us that ingression takes a peculiar form in the case of some events. In a sense, it is a more concentrated form. For example, the electron has a certain position in space in a certain shape. Perhaps it is an extremely small sphere in a certain test tube. The storm is a gale situated in mid-Atlantic with a certain latitude and longitude, and the cook is in the kitchen. I will call this special form of ingression the relation of situation. Also, by a double use of the word situation, I will call the event in which an object is situated the situation of the object. Thus, a situation is an event which is a relative in a relation of situation. Now our first impression is that at last we have come to the simple plain fact of where the object really is, and that the vaguer relation which I call ingression should not be muddled up with a relation of situation, as if including it as a particular case. It seems so obvious that any object is in such and such a position, and that it is influencing other events in a totally different sense. Namely, in a sense, an object is the character of the event which is its situation, but it only influences the character of other events. Accordingly, the relations of situation and influencing are not generally the same sort of relation, and should not be subsumed under the same term ingression. I believe that this notion is a mistake, and that it is impossible to draw a clear distinction between the two relations. For example, where was your toothache? You went to a dentist and pointed out the tooth to him. He pronounced it perfectly sound and cured you by stopping another tooth. Which tooth was the situation of the toothache? Again, a man has an arm amputated and experiences sensations in the hand which he has lost. The situation of the imaginary hand is in fact merely thin air. You look into a mirror and see a fire. The flames that you see are situated behind the mirror. Again at night you watch the sky. If some of the stars had vanished from existence hours ago, you would not be any the wiser. Even the situations of the planets differ from those which science would assign to them. Anyhow, you were tempted to exclaim, the cook is in the kitchen. If you mean her mind, I will not agree with you on the point, for I am only talking of nature. Let us think only of her bodily presence. What do you mean by this notion? We can find ourselves to typical manifestations of it. You can see her, touch her, and hear her. But the examples which I have given show you that the notions of situations of what you see, what you touch, and what you hear are not so sharply separated out as to defy further questioning. You cannot cling to the idea that we have two sets of experiences of nature, one of primary qualities which belong to the objects perceived, and one of secondary qualities which are the products of our mental excitements. All we know of nature is in the same boat, to sink or swim together. The constructions of science are merely expositions of the characters of things perceived. Accordingly to affirm that the cook is a certain dance of molecules and electrons, is merely to affirm that the things about her which are perceivable have certain characters. The situations of the perceived manifestations of her bodily presence have only a very general relation to the situations of the molecules to be determined by discussion of the circumstances of perception. In discussing the relations of situation in particular and of ingression in general, the first requisite is to note that objects are of radically different types. For each type's situation and ingression have their own special meanings which are different from their meanings for other types, though connections can be pointed out. It is necessary, therefore, in discussing them to determine what types of objects are under consideration. There are, I think, an indefinite number of types of objects. Happily we need not think of them all. The idea of situation has its peculiar importance in reference to three types of objects, which I call sense objects, perceptual objects, and scientific objects. The suitability of these names for the three types is of minor importance, so long as I can succeed in explaining what I mean by them. These three types form an ascending hierarchy of which each member presupposes the type below. The base of the hierarchy is formed by the sense objects. These objects do not presuppose any other type of objects. A sense object is factor of nature posited by sense awareness, which, one, in that it is an object does not share in the passage of nature, and two, is not a relation between other factors of nature. It will, of course, be a relative in relations which also implicate other factors of nature. But it is always a relative and never the relation itself.  I am not talking of a particular patch of blue as seen during a particular second of time at a definite date. Such a patch is an event where Cambridge Blue is situated. Similarly, I am not talking of any particular concert room as filled with the note. I mean the note itself, and not the patch of volume filled by the sound for a tenth of a second. It is natural for us to think of the note in itself, but in the case of color we are apt to think of it merely as a property of the patch. No one thinks of the note as a property of the concert room. We see the blue and we hear the note. Both the blue and the note are immediately posited by the discrimination of sense awareness which relates the mind to nature. The blue is posited as a nature related to other factors of nature. In particular it is posited as in the relation of being situated in the event which is its situation. The difficulties which cluster around the relation of situation arise from the obstinate refusal of philosophers to take seriously the ultimate fact of multiple relations. By a multiple relation I mean a relation which in any concrete instance of its occurrence necessarily involves more than two Rolada. For example, when John likes Tom there are only two Rolada, John and Thomas. But when John gives that book to Thomas there are three Rolada, John, that book and Thomas. Some schools of philosophy under the influence of the Aristotelian logic in the Aristotelian philosophy endeavor to get on without admitting any relations at all except that of substance and attribute. Namely all apparent relations are to be resolvable into the concurrent existence of substances with contrasted attributes. It is fairly obvious that the Leibnizian monadology is the necessary outcome of any such philosophy. If you dislike pluralism there will only be one monad. Other schools of philosophy admit relations but obstinately refuse to contemplate relations with more than two Rolada. I do not think that this limitation is based on any set purpose or theory. It merely arises from the fact that more complicated relations are a bother to people without adequate mathematical training when they are admitted into the reasoning. I must repeat that we have nothing to do in these lectures with the ultimate character of reality. It is quite possible that in the true philosophy of reality there are only individual substances with attributes or that there are only relations with pairs of Rolada. I do not believe that such is the case but I am not concerned to argue about it now. Our theme is nature. So long as we can find ourselves to the factors posited in a sense awareness of nature it seems to me that there certainly are instances of multiple relations between these factors and that the relation of situation for sense objects is one example of such multiple relations. Consider a blue coat, a flannel coat of Cambridge blue belonging to some athlete. The coat itself is a perceptual object and its situation is not what I'm talking about. We are talking of someone's definite sense awareness of Cambridge blue as situated in some event of nature. He may be looking at the coat directly. He then sees Cambridge blue as situated practically in the same event as the coat at that instant. It is true that the blue which he sees is due to light which left the coat some inconceivably small fraction of a second before. This difference would be important if you were looking at the star whose color was Cambridge blue. The star might have ceased to exist days ago or even years ago. The situation of the blue will not then be very intimately connected with the situation in another sense of situation of any perceptual object. This disconnection of the situation of the blue and the situation of some associated perceptual object does not require a star for its exemplification. Any looking glass will suffice. Look at the coat through a looking glass. Then blue is seen as situated behind the mirror. The event which is at situation depends on the position of the observer. The sense awareness of the blue as situated in a certain event which I called the situation is thus exhibited as a sense awareness of a relation between the blue, the recipient event of the observer, the situation, and intervening events. All nature is in fact required though only certain intervening events require their characters to be of certain definite sorts. The ingression of blue into the events of nature is thus exhibited as systematically correlated. The awareness of the observer depends on the position of the recipient event in this systematic correlation. I will use the term ingression into nature for this systematic correlation of the blue with nature. Thus the ingression of blue into any definite event is a part statement of the fact of the ingression of blue into nature. In respect to the ingression of blue into nature events may be roughly put into four classes which overlap and are not very clearly separated. These classes are one the recipient events, two the situations, three the active conditioning events, four the passive conditioning events. To understand this classification of events in the general fact of the ingression of blue into nature let us confine attention to one situation for one recipient event and to the consequent roles of the conditioning events for the ingression is thus limited. The recipient event is the relevant bodily state of the observer. The situation is where he sees the blue say behind the mirror. The active conditioning events are the events whose characters are particularly relevant for the event which is the situation to be the situation for that recipient event namely the coat, the mirror, and the state of the room has to light an atmosphere. The passive conditioning events are the events of the rest of nature. In general the situation is an active conditioning event namely the coat itself when there is no mirror or other contrivance to produce abnormal effects but the example of the mirror shows us that the situation may be one of those passive 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 the characters of the events of nature is based on the analysis of the relations of situations to recipient events. If situations were not in general active conditions this analysis 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 passive condition is in a sense justifiable because of that sort of thing went on too often the role the intellect would be ended. Furthermore the mirror is itself the situation of other sense objects either for the same observer with the same recipient event or for other observers with other recipient 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 is derived from common sense. I now turn to perceptual objects. When we look at the coat we do not in general say there was a patch of Cambridge blue. What naturally occurs to us is there as a coat. Also the judgment that what we have seen is a garment of a man's tire is a detail. What we perceive is an object other than a mere sense object. It is now a mere patch of color 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 color 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 nature 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 recipient event but is the situation of a variety of sense objects for a variety of recipient events. For example for any one recipient 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 recipient 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 interplays 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 classify 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. Anticipatory judgments affect the perceptual object perceived by focusing and directing 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 association of intellectual ideas. It is the product of the association 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 passive 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 recipient 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 mirror patch of color. 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 recipient 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 one its object is an active conditioning event for the ingression of any of its component sense objects and two the same event can be the situation of the perceptual object for an indefinite number of possible recipient events. Physical objects are the ordinary events 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 connection with physical objects. For example stray smells, sounds, colors, and more subtle nameless senses 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 and thought along an abstract 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 and distinct durations is affected by the condition of continuity. This condition of continuity is the condition that a continuity of passage 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 species present this continuity of passage 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 passage 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 in 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 as components 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 color behind due to the reflection of light in it. Thus the origin of scientific knowledge is the endeavor 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 the situations of the physical objects which are most permanent and are expressible without reference to a multiple relation including a recipient event. Their relations to each other are also characterized by a certain simplicity in 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 endeavor 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 quantitative 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 quantitative 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 entity which concerns science and which I've 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 co-gredient in the flux of their positions and the corresponding durations. This is the foundation of the denial of action at a distance namely the progress of the stream of situations of a scientific object can be determined by an analysis 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 space and throughout time. The best expression of the character 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 connection of objects with space 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-term 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 abstract of 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 abstract of element. In this sense an object may be located in a moment of time in a volume of space, 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'll proceed to explain. Also location in the timeless space of some time system is a relation derivative from location and instantaneous spaces of the same time system. Accordingly location in an instantaneous space 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 abstract of element when an abstract of 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 abstract of element is a certain group of abstract of sets and that each abstract of set is a set of events. This definition defines the location of an element in any type of abstract of 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 space of that moment. A quantity can be said to be located in an abstract of element when an abstract of set belonging to the element can be found such that the quantitative expressions of the corresponding characters of its events converge to the measure of the given quantity as a limit when we pass along the abstract of set toward its converging end. By these definitions location in elements of instantaneous spaces is defined. These elements occupy corresponding elements of timeless spaces. An object located in an element of an instantaneous space will also be said to be located at that moment in the timeless element of the timeless space 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 assume 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 source of objects e.g. electrons minimum quanta of time or 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 quantitative electric charge of its situation and the electron is standing for the ingression of an object throughout nature illustrates 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 is 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 perception of objects as distinct entities which are mere subtle ideas through 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 we could think it would anticipate and if it anticipated it would soon perceive for itself. In these lectures we have been scrutinizing the foundations of natural philosophy. We are stopping at the very point where a boundless ocean of inquiries 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 assurance with which every age prides itself that it is at last hit upon the ultimate concepts in which all that happens can be formulated? The aim of science is to seek the simplest explanation 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. End of section seven. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org. Recorded by Julian Jamison. The Concept of Nature by Alfred North Whitehead. Section 8. Summary. There is a general agreement that Einstein's investigations have one fundamental merit, irrespective of any criticisms which we may feel inclined to pass 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. Space 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 assimilate and to criticize 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. 1. Yesterday a man was run over on the Chelsea embankment. 2. Cleopatra's needle is on the Charing Cross embankment. And 3. 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 assigned 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 passing 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 passing events. In this complex, we discern definite mutual relations between component events, which we may call their relative positions. In these positions, we express partly in terms of space 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 the 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 chairing cross embankment. At first sight, we should hardly call this an event. It seems to lack the element of time or transitoryness. 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. It admits the structure of events which form the medium within which the daily life of Londoners is passed. 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 assigned circumstances, 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 characterized. 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 space 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 space and as time. And under some circumstances we adopt one way and under other circumstances we adopt another way. Thus there is no paradox in holding that what we mean by space under one set of circumstances is not what we mean by space under another set of circumstances. And equally, what we mean by time under one set of circumstances is not what we mean by time under another set of circumstances. By saying that space 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 is no spatial facts or temporal facts apart from physical nature. Namely, that space and time are merely ways of expressing certain truths about the relations between events. Also, that under different circumstances there are different sets of truths about the universe which are naturally presented to us as statements about space. In such a case, what a being under one set of circumstances means by space will be different from that meant by a being under the other set of circumstances. Accordingly, when we are comparing two observations made under different circumstances, we have to ask do the two observers mean the same thing by space 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 neighborhood of the Sun have been solved by reference to this purely relative significance of space 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, Hello, there's the needle. In other words, you recognize it. You cannot recognize an event because when it is gone, it is gone. You may observe another event of analogous character but the actual chunk of the life of nature is inseparable from its unique occurrence. But a character of an event can be recognized. We all know that if we go to the embankment near Charing Cross we shall observe an event having the character which we recognize as Cleopatra's needle. Things which we thus recognize 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 color 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 color, such as the color of the needle. I call these simple objects such as colors 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 is Cleopatra's needle, perhaps he simultaneously exclaimed there is a nice bit of color. 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 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, 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 recognized in isolation. We cannot well miss Cleopatra's needle if we are in its neighborhood, 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 entity is nothing. It means merely 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 and 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 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. As 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 hundredth 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 extension 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 separations a spatiotemporal structure. We can express the properties of this structure in terms of the ideal limits to roots 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 analyze 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 spatiotemporal 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 spacetime 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 spacetime 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 conceiving 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 space 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 exposition to 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 spacetime 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 we'll 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 spacetime 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 spacetime manifold. These measurements have appeared to be very simple to the land surveyor and raise in his mind no philosophical difficulties. But suppose there are beings on Mars sufficiently advanced in scientific invention to be able to watch and detail the operations of this survey on earth. Suppose that they construe the operations of their English land surveyors in reference to the space natural to a being on Mars. Namely a martiocentric space 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 fashion affect 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. I have discussed this example in order to make you realize that in thinking of the possibilities of measurement in the spacetime 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 measurements respectively of independent types such as measurements 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. 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 coordinates 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 coordinates will be measurements of space and one will be a measurement of time. Let us always take the last coordinate 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 spacetime manifold. That manifold is all that there is for the determination of the meaning of space and time. We've 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 coordinates 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, bracket 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 called 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. So far in speaking of space we've been talking of the timeless space of physical science namely of our concept of eternal space in which the world adventures. But the space which we see as we look about is instantaneous space. Thus if our natural perceptions are adjustable to the P system of measurements we see instantaneously all the event particles at some definite time P4 and observe a succession of such spaces as time moves on. The timeless space is achieved by stringing together all these instantaneous spaces. The points of an instantaneous space are event particles and the points of an eternal space are strings of event particles occurring in succession. But the man on Mars will never perceive the same instantaneous spaces as the man on Earth. This system of instantaneous spaces will cut across the Earthman system. For the Earthman there is one instantaneous space which is the instantaneous present. There are the past spaces and the future spaces. But the present space of the man on Mars cuts across the present space of the man on Earth. So that of the event particles which the Earthman thinks of as happening now in the present the man on Mars thinks that some are already past and are ancient history that others are in the future and others are in the immediate present. This breakdown in the neat conception of a past, a present, and a future is a serious paradox. I call two event particles which on some or other system of measurement are in the same instantaneous space co-present event particles. Then it is possible that A and B may be co-present and that A and C may be co-present but that B and C may not be co-present. For example, at some inconceivable distance from us there are events co-present with us now and also co-present with the birth of Queen Victoria. If A and B are co-present there will be some systems in which A precedes B and some in which B precedes A. Also, there can be no velocity quick enough to carry a material particle from A to B or from B to A. These different measure systems with their divergences of time reckoning are puzzling and to some extent affront our common sense. It is not the usual way in which we think of the universe. We think of one necessary time system and one necessary space. According to the new theory there are an indefinite number of discordant time series and an indefinite number of distinct spaces. Any correlated pair, a time system and a space system will do in which to fit our description of the universe. We find that under given conditions our measurements are necessarily made in some one pair which together form our natural measure system. The difficulty as to discordant time systems is partly solved by distinguishing between what I call the creative advance of nature which is not properly serial at all and any one time series. We habitually muddle together this creative advance which we experience and know as the perpetual transition of nature into novelty with the single time series which we naturally employ for measurement. The various time series each measure some aspect of the creative advance and the whole bundle of them express all the properties of this advance which are measurable. The reason why we have not previously noted this difference of time series is the very small difference of properties between any two such series. Any observable phenomena due to this cause depend on the square of the ratio of any velocity entering into the observation to the velocity of light. Now light takes about 50 minutes to get around the Earth's orbit and the Earth takes rather more than 17,531 half hours to do the same. Hence all the effects due to this motion are the order of the ratio of 1 to the square of 10,000. Accordingly an Earth man and a Sun man have only neglected effects whose quantitative magnitudes all contain the factor 1 over 10 to the 8th. Evidently such effects can only be noted by means of the most refined observations. They have been observed however. Suppose we compare two observations on the velocity of light made with the same apparatus as we turn it through a right angle. The velocity of the Earth relative to the Sun is in one direction. The velocity of light relatively to the ether should be the same in all directions. Hence if space when we take the ether as at rest means the same thing as space when we take the Earth as at rest we ought to find that the velocity of light relatively to the Earth varies according to the direction from which it comes. These observations on Earth constitute the basic principle of the famous experiments designed to detect the motion of the Earth through the ether. You all know that quite unexpectedly they gave a null result. This is completely explained by the fact that the space system and the time system which we are using are in certain minute ways different from the space and the time relatively to the Sun or relatively to any other body with respect to which it is moving. All this discussion as to the nature of time and space has lifted above our horizon a great difficulty which affects the formulation of all the ultimate laws of physics. For example, the laws of the electromagnetic field and the law of gravitation. Let us take the law of gravitation as an example. Its formulation is as follows. Two material bodies attract each other of the force proportional to the product of their masses and inversely proportional to the square of their distances. In this statement the bodies are supposed to be small enough to be treated as material particles in relation to their distances and we need not bother further about that minor point. The difficulty to which I want to draw your attention is this. In the formulation of the law one definite time and one definite space are presupposed. The two masses are assumed to be in simultaneous positions. But what is simultaneous in one time system may not be simultaneous in another time system. So according to our new views the law is in this respect not formulated so as to have any exact meaning. Furthermore an analogous difficulty arises over the question of distance. The distance between two instantaneous positions i.e. between two event particles is different in different space systems. What space is to be chosen? Thus again the law lacks precise formulation if relativity is accepted. Our problem is to seek a fresh interpretation of the law of gravity in which these difficulties are evaded. In the first place we must avoid the abstractions of space and time in the formulation of our fundamental ideas and must recur to the ultimate facts of nature namely to events. Also in order to find the ideal simplicity of expressions of the relations between events we restrict ourselves to event particles. Thus the life of a material particle is its adventure amid a track of event particles strung out as a continuous series or path in the four-dimensional space-time manifold. These event particles are the various situations of the material particle. We usually express this fact by adopting our natural space-time system and by talking of the path in space of the material particle as it exists at successive instance of time. We have to ask ourselves what are the laws of nature which lead the material particle to adopt just this path among event particles and no other? Think of the path as a whole. What characteristic has that path got which would not be shared by any other slightly varied path? We are asking for more than a law of gravity. We want laws of motion and a general idea of the way to formulate the effects of physical forces. In order to answer our question we put the idea of the attracting masses in the background and concentrate attention on the field of activity of the events in the neighborhood of the path. In so doing we are acting in conformity with the whole trend of scientific thought during the last hundred years which has more and more concentrated attention on the field of force as the immediate agent in directing motion to the exclusion of the consideration of the immediate mutual influence between two distant bodies. We have got to find a way of expressing the field of activity of events in the neighborhood of some definite event particle E of the four-dimensional manifold. I bring in a fundamental physical idea which I call the impetus to express this physical field. The event particle E is related to any neighboring event particle P by an element of impetus. The assemblage of all the elements of impetus relating E to the assemblage of event particles in the neighborhood of E expresses the character of the field of activity in the neighborhood of E. Where I differ from Einstein is that he conceives this quantity which I call the impetus as merely expressing the characters of the space and time to be adopted and thus ends by talking of the gravitational field expressing a curvature in the space-time manifold. I cannot attach any clear conception to his interpretation of space and time. My formulae differ slightly from his though they agree in those instances where his results have been verified. I need hardly say that in this particular of the formulation of the law of gravitation I have drawn on the general method or procedure which constitutes his great discovery. Einstein showed how to express the characters of the assemblage of elements of impetus of the field surrounding an event particle E in terms of ten quantities which I will call j sub one one j sub one two equals j sub two one j sub two two j sub two three equals j sub three two etc. It will be noted that there are four spatiotemporal measurements relating E to its neighbor P and that there are ten pairs of such measurements if we are allowed to take any one measurement twice over to make one such pair. The ten j's depend merely on the position of E in the four-dimensional manifold and the element of impetus between E and P can be expressed in terms of the ten j's and the ten pairs of the four spatiotemporal measurements relating E and P. The numerical values of the j's will depend on the system of measurement adopted but are so adjusted to each particular system that the same value is obtained for the element of impetus between E and P whatever be the system of measurement adopted. This fact is expressed by saying that the ten j's form a tensor. It is not going too far to say that the announcement that physicists would have in future to study the theory of tensors created a veritable panic among them when the verification of Einstein's predictions was first announced. The ten j's at any event particle E can be expressed in terms of two functions which I call the potential and the associate potential at E. The potential is practically what is meant by the ordinary gravitation potential when we express ourselves in terms of the Euclidean space in reference to which the attracting mass is at rest. The associate potential is defined by the modification of substituting the direct distance for the inverse distance in the definition of the potential and its calculation can easily be made to depend on that of the old-fashioned potential. Thus the calculation of the j's the coefficients of impetus as I will call them does not involve anything very revolutionary in the mathematical knowledge of physicists. We now return to the path of the attracted particle. We add up all the elements of impetus in the whole path and obtain thereby what I call the integral impetus. The characteristic of the actual path as compared with neighboring alternative paths is that in the actual paths the integral impetus would neither gain nor lose if the particle wobbled out of it into a small extremely near alternative path. Mathematicians would express this by saying that the integral impetus is stationary for an infinitesimal displacement. In this statement of the law of motion I have neglected the existence of other forces but that would lead me too far afield. The electromagnetic theory has to be modified to allow for the presence of a gravitational field. Thus Einstein's investigations led to the first discovery of any relation between gravity and other physical phenomena. In the form in which I have put this modification we deduce Einstein's fundamental principle as to the motion of light along its rays as a first approximation 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 apologize. 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 researches. End of section eight. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org. Recording by Psuke Berea. The concept of nature by Alfred North Whitehead. Section nine 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 interrelations of all that is observed. Our attitude towards nature is purely behavioristic 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 inclusion is more fundamental than either alternative and does not require any spatiotemporal differentiation. In respect to extension two events are mutually related so that either one one includes the other or two one overlaps the other without complete inclusion or three they 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 depending on undefined relations and properties. Such fallacies can be avoided by taking account of two elements in our experience namely one our observational present and two our recipient 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 contra distinction to other events a duration will be called infinite and other events are finite. In our knowledge of a duration we distinguish one certain included events which are particularly discriminated as to their peculiar individualities and two the remaining included events which are only known as necessarily in being by reason of the relations to the discriminated events and to the whole duration. The duration as a whole is signified 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 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 center. This knowledge has nothing to do with the material. This 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 informed us that there are events within this sphere and 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 principles 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 therefore the whole which is immediately discerned or signified as an interrelated 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 within the present duration. The theory of perception as evolved by medical psychology is based on significance. 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 peculiar relation 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 in the case of images seen behind a mirror may have a very little to do with the actual course of the ray. In the course of evolution those animals have survived whose sense awareness is concentrated 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 Co-Gredients. The notion of arrest is derivative from that of Co-Gredients and the notion of motion is derivative from that of inclusion within a duration without Co-Gredients in it. In fact motion is a relation of varying character between an observed event and an observed duration and Co-Gredients 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 Percipient Event is a Co-Gredient with the duration. Our knowledge of the peculiar characters of different events depends upon our power of comparison. I call the exercise of this factor in our 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 recognize without abstraction. Perception involves apprehension of the event and recognition of the factors of its character. The things recognized 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 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 characters of all events and with the property that these modifications 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 paragraph is nothing else than another way of expressing the unresolved 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 one one includes the other or two they overlap so as to include a third duration common to both or three are entirely separate. The excluded case is that of two durations overlapping so is 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 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, nonexistent, durations of zero temporal thickness indicated by roots 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. One, its extrinsic character which is its character as a definite root of convergence among events. Two, its intrinsic character which is the peculiar quality of nature in its neighborhood namely the character of the physical field in the neighborhood. And three, 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 duration 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 prime, M double prime, etc. in which it also lies. The differentiation of M into a geometry of event particles instantaneous points expresses 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 in the same time system intersecting M. Similarly, the order of parallel planes and of event particles on straight lines arises from the time order of these intersecting moments. The explanation is not given here. It is sufficient now merely to mention the sources from which the whole geometry receives its physical explanation. The correlation of the various momentary spaces of one time system is achieved by the relation of co-gradients. Evidently, motion in an instantaneous space is unmeaning. Motion expresses a comparison between position in one instantaneous space with positions in other instantaneous spaces of the same time system. Co-gradients yields the simplest outcome of such comparison, namely rest. Motion and rest are immediately observed facts. They are relative in the sense that they depend on the time system which is fundamental for the observation. A string of event particles whose successive occupation means rest in the given time system forms a timeless point in the timeless space of that time system. In this way, each time system possesses its own permanent timeless space peculiar to it alone, and each such space is composed of timeless points which belong to that time system and to no other. The paradoxes of relativity arise from neglecting the fact that different assumptions as to rest involve the expression of the facts of physical science in terms of radically different spaces and times in which points and moments have different meanings. The source of order has already been indicated and that of congruence is now found. It depends on motion. From co-gradients, perpendicularity arises and from perpendicularity in conjunction with the reciprocal symmetry between the relations of any two time systems, congruence both in time and space is completely defined. The resulting formulae are those for the electromagnetic theory of relativity or as it is now termed the restricted theory. But there is this vital difference. The critical velocity C which occurs in these formulae has now no connection whatever with light or with any other fact of the physical field in distinction from the extensional structure of events. It simply marks the fact that our congruence determination embraces both times and spaces in one universal system and therefore if two arbitrary units are chosen one for all spaces and one for all times the ratio will be a velocity which is a fundamental property of nature expressing the fact that times and spaces are really comparable. The physical properties of nature are expressed in terms of material objects electrons, etc. The physical character of an event arises from the fact that it belongs to the field of the whole complex of such objects. From another point of view we can say that these objects are nothing else than our way of expressing the mutual correlation of the physical characters of events. The spatiotemporal measurableness of nature arises from one the relation of extension between events and two the stratified character of nature arising from each of the alternative time systems and three rest in motion as exhibited in the relations of finite events two time systems. None of these sources of measurement depend on the physical characters of finite events as exhibited by the situated objects. They are completely signified for events whose physical characters are unknown. Thus the spatiotemporal measurements are independent of the objectival physical characters. Furthermore, the character of our knowledge of a whole duration which is essentially derived from the significance of the part within the immediate field of discrimination constructs it for us as a uniform whole independent so far as its extension is concerned of the unobserved characters of remote events. Namely, there is a definite whole of nature simultaneously now present whatever may be the character of its remote events. This consideration reinforces the previous conclusion. This conclusion leads to the assertion of the essential uniformity of the momentary spaces of the various time systems and thence to the uniformity of the timeless spaces of which there is one to each time system. The analysis of the general character of observed nature set forth above affords explanations of various fundamental observational facts. Alpha, it explains the differentiation of the one quality of extension into time and space. Beta, it gives a meaning to the observed facts of geometrical and temporal position of geometrical and temporal order and of geometrical straightness and plainness. Gamma, it selects one definite system of congruence embracing both space and time and thus explains the concordance as to measurement which is in practice attained. Delta, it explains consistently with the theory of relativity the observed phenomena of rotation, e.g. Foucault's pendulum, the equatorial bulge of the earth, the fixed senses of rotation of cyclones and anticyclones and the gyro compass. It does this by its admission of definite stratifications of nature which are disclosed by the very character of our knowledge of it. Epsilon, its explanations of motion are more fundamental than those expressed in Delta for it explains what is meant by motion itself. The observed motion of an extended object is the relation of its various situations to the stratification of nature expressed by the time system fundamental to the observation. This motion expresses a real relation of the object to the rest of nature. The quantitative expression of this relation will vary according to the time system selected for its expression. This theory accords no peculiar character to light beyond that accorded to other physical phenomenon such as sound. There is no ground for such a differentiation. Some objects we know by sight only and other objects we know by sound only and other objects we observe neither by light nor by sound but by touch or smell or otherwise. The velocity of light varies according to its medium and so does that of sound. Light moves and curves paths under certain conditions and so does sound. Both light and sound are waves of disturbance in the physical characters of events and as has been stated above the actual course of the light is of no more importance for the perception than is the actual course of the sound. To base the whole philosophy of nature upon light is a baseless assumption. The Michelson-Morley and analogous experiment show that within the limits of our inexactitude of observation the velocity of light is an approximation to the critical velocity C which expresses the relation between our space and time units. It is provable that the assumption as to light by which these experiments and the influence of the gravitational field on the light rays are explained as deducible as an approximation from the equations of the electromagnetic field. This completely disposes of any necessity for differentiating light from other physical phenomenon as possessing any peculiar fundamental character. It is to be observed that the measurement of extended nature by means of extended objects is meaningless apart from some observed fact of simultaneity, inherent in nature, and not merely a play of thought. Otherwise, there is no meaning to the concept of one presentation of your extended measuring rod A B. Why not A B prime? Where B prime is the end B five minutes later. Measurement presupposes for its possibility nature as a simultaneity and an observed object present then and present now. In other words, measurement of extended nature requires some inherent character in nature affording a rule of presentation of events. Furthermore, congruence cannot be defined by the permanence of the measuring rod. The permanence is itself meaningless apart from some immediate judgment of self congruence. Otherwise, how is an elastic string differentiated from a rigid measuring rod? Each remains the same self-identical object. Why is one a possible measuring rod and the other not so? The meaning of congruence lies beyond the self-identity of the object. In other words, measurement presupposes the measurable, and the theory of the measurable is the theory of congruence. Furthermore, the admission of stratifications of nature bears on the formulation of the laws of nature. It has been laid down that these laws are to be expressed in differential equations which, as expressed in any general system of measurement, should bear no reference to any other particular measure system. This requirement is purely arbitrary. For a measure system measures something inherent in nature, otherwise it has no connection with nature at all, and that something which is measured by a particular measure system may have a special relation to the phenomenon whose law is being formulated. For example, the gravitational field due to a material object at rest in a certain time system may be expected to exhibit in its formulation particular reference to spatial and temporal quantities of that time system. The field can of course be expressed in any measure systems, but the particular reference will remain as the simple physical explanation. Note, on the Greek concept of a point, the preceding pages had been passed for press before I had the pleasure of seeing Sir T. L. Heath's Euclid in Greek. In the original Euclid's first definition is Semeon esten umeros uzen. I have quoted it on page 86 in the expanded form taught to me in childhood without parts and without magnitude. I should have consulted Heath's English edition, a classic from the moments of its issue, before committing myself to a statement about Euclid. This is however a trivial correction not affecting sense and not worth a note. I wish here to draw attention to Heath's own note to this definition in his Euclid in Greek. He summarizes Greek thought on the nature of a point from the Pythagoreans through Plato and Aristotle to Euclid. My analysis of the requisite character of a point on pages 89 and 90 is in complete agreement with the outcome of the Greek discussion. Note, on significance and infinite events. The theory of significance has been expanded and made more definite in the present volume. It had already been introduced in the principles of natural knowledge. CF sub articles 3.3 to 3.8 and 16.1, 16.2, 19.4 and articles 20 and 21. In reading over the proofs of the present volume, I came to the conclusion that in light of this development, my limitations of infinite events to durations is untenable. This limitation is stated in article 33 of the principles and at the beginning of the chapter 4 on this book. There is not only a significance of the discerned events embracing the whole present duration, but there is a significance of a co-gradient event involving its extension through a whole time system backwards and forwards. In other words, the essential beyond in nature is a definite beyond in time as well as in space. CF This follows from my whole thesis as to the assimilation of time and space and their origin and extension. It also has the same basis in the analysis of the character of our knowledge of nature. It follows from this admission that it is possible to define point tracks, i.e. the points of timeless spaces as abstractive elements. This is a great improvement as restoring the balance between moments and points. I still hold, however, to the statement in sub-article 35.4 of the principles that the intersection of a pair of non-parallel durations does not present itself to us as one event. This correction does not affect any of the subsequent reasoning in the two books. I may take this opportunity of pointing out that the stationary events of article 57 of the principles are merely co-gradient events God had from an abstract mathematical point of view. End of Chapter 9 The Ultimate Physical Concepts End of The Concept of Nature by Alfred North Whitehead


Hello and welcome to this presentation of the STM32 Random Number Generator. The features of this peripheral, which is widely used to provide random numbers, will be covered in this presentation. The Random Number Generator, or RNG, integrated inside STM32 products provides random numbers which are used when producing an unpredictable result is desirable. Applications can benefit from the RNG to increase the randomness of numbers or to decrease the possibility of guessing certain values. The RNG peripheral is based on continuous analog noise that provides a random 32-bit value which will be explained in detail later on. The RNG is able to generate 4 32-bit random numbers at a minimum frequency of 216 system clock cycles. Rule of thumb is the lower the RNG clock, the better the entropy for the sampled random source. The data-ready flag is set in the status register when a set of new random data is ready and validated. The RNG performs a basic verification of randomness on the provided data. For example, if more than 64 consecutive bits have the same value, 0 or 1, or there are more than 32 consecutive alternating 0s and 1s, a seed error current status flag is set. A clock error current status flag is set if the RNG clock is less than HCLK clock divided by 32. This check can be disabled, especially when the RNG clock is initialized low for maximum entropy. An interrupt source can also be enabled to indicate an abnormal seed sequence or frequency error. This simplified block diagram of the RNG shows its basic functional and control modules. The random number generator is based on an analog circuit made of several ring oscillators whose outputs are sampled, then XOR'd to generate the seeds that feed a digital post-processing block that is able to produce 4 32-bit random numbers per round of computation. The sampling of analog seeds is clocked by a dedicated RNG clock signal so that the quality of the random number is independent of the HCLK frequency. Contents of the post-processing block are transferred into the data register through a 4-word FIFO. The data ready flag or DRDY is triggered as soon as the FIFO is full and is automatically reset when no more data can be read back from the RNG. In parallel, an error management block verifies the correct seed behavior and the frequency of the RNG source clock. Status bits are set and an interrupt is triggered if an abnormal sequence is detected in the seed or if the RNG frequency is too low. The RNG frequency error check must be disabled if the RNG clock is fixed below HBCLK32 for example for quality reasons. The RNG can be used for a wide range of applications including cryptography, games and statistical sampling. For example, all the security of cryptography algorithms are connected to the impossibility of guessing the key. So the key has to be a random number, otherwise the attacker can guess it. This is a list of peripherals related to the random number generator. Please refer to these trainings for more information if needed. For more details, please refer to application note AN4232 about using the NIST statistical test suite to validate the random numbers generated by a selection of STM32 MCUs.