Chapter 3: Space and Time
Participants: Chris Clarke leading; Margaret Masterman, R B Braithwaite, Dorothy Emmet, Jonathan Westphal, and Rupert Sheldrake participating
CC: I will first describe the source of my current interest in Whitehead’s ideas on space and time. Then I want to pick up from the remarks I was listening to from Margaret yesterday morning, and then go on to the particular ways I am thing to think about space and time at the moment.
A Whiteheadian position seems to be required by quantum mechanics. Quantum mechanics is usually presented in terms which are extremely heterogeneous. There is the "state" out there which is observed -- to some it is observed by mind, so this is explicitly heterogeneous. Most people for obvious reasons don’t like the state being observed by mind, and they say "the observer," but this is a cop out: It is more honest to call it mind. Now my previous attempts to get round this may have been another sort of cop out. I wanted there to be macroscopic forms as an essential ingredient in the theory, and these exerting an influence on what happened by providing a sort of filter into which the causation of quantum mechanics had to direct itself. But when one introduces macroscopic forms as well as the conventional forces of quantum mechanics one still has a sort of heterogeneity, though it isn’t between mind and matter. So once again there is a requirement for homogeneous thinking not based on this bifurcation of nature. The example of homogeneous thinking Whitehead develops concerns space and time; presumably he thought one could pursue the same sort of analysis in other fields. There could be generalizations of Extensive Abstraction applicable to colors and so on, but the particular example he develops concerns space and time, where proceeding from perceived events one achieves points as ideal limits of a series of approximations. I think the derivation of space and time is a primary necessity in any Whiteheadian scheme. On the one hand if you presuppose space and time, I suppose most people would find themselves led into bifurcated thinking, which is essentially the conventional position. On the other hand you have got to have space and time to make contact with any conventional science at all. One cannot make statements comparable to conventional science if you don’t have space and time. So you cannot embark on any sort of Whiteheadian scheme if you have not some idea of how you are going to get space and time out of it. The particular way he gets them is, I think, basically inconsistent with his own principles; he gets space and time by staring off with the duration and then passing to what yesterday we called the "duro." The duration is something perceived, with structure in it because of one’s focus of attention. A "duro" has a much more generalized connotation, It is shorn of its attention focus and is globalized. The duro is supposed to be a slice of the entire universe, whereas we certainly don’t perceive a slice of the whole universe: we perceive a chunk of it. The second way in which his approach is inconsistent is that duros are supposed to obey axioms which are contrived to give Special Relativity. Nothing in our experience corresponds to these axioms, and their introduction is a glaring peculiarity in his development. What is more, his derivation of space depends on them. If one had the axioms of Galilean or Newtonian physics one would not get space as Whitehead gets it. But space is so basic in our experience that there is something rather fishy about a development that has to introduce Special Relativity to get it.
RB: When you say "Special Relativity" you mean essentially Lorentz transformations?
CC: Yes. So just on a logical level I find his approach unacceptable. I also find it unacceptable scientifically because if one is approaching it from our current understanding of Relativity, the thing that corresponds to our awareness of the universe over an interval of time is not a simultaneity slab, because in General Relativity there is no such thing. It is a thickening of our past light cone. It is a perception of what we can see, and what is fairly immediately causally related to us. At the time when Whitehead was writing The Concept of Nature, and also when he was thinking about the theory of Relativity, it was still possible to adhere to a Special Relativist view of the Universe. Now with the very strong tests of the Equivalence Principle which have been done it is impossible to have this, so one has to presuppose a General Relativist view of the way space-time is, where there is no natural definition of simultaneity relative to an observer. This means I am dissatisfied with his derivation of space and time and in particular I want to reject duros. On the other hand the concept of the duration alone, while it is adequate for time and for understanding the flow of nature, cannot, as I see it, give you space. One requires more structure than is inherent just in durations. So in order to get space as well as time, I want to go back to his concept of events, as a more general category than durations, and regard events as constituents of durations, with the connotations of maximality which inhere in the idea of a duration. Durations can be decomposed into events which are contemporaneous in a particular perception of them.
MM: Durations have what he calls factors, and I call aspects, which enable you to discriminate.
CC: When I talk about events, I am not talking about factors. In speaking of events, he introduces "factors" which give rise to objects and so on.
DE: I don’t think you can say the factors give rise to objects: the objects are factors. Events are perceived as having qualities, patterns, and when you single these out you call them factors. You can’t have a bare perception of events and start putting objects into them.
CC: No. That’s right.
MM: I query that there is nothing spatial in durations. Dorothy wanted to say they had spread. The problem about a duration isn’t so much its relation to a particular percipient as whether it is a visual or a tactual, an auditory, an olfactory duration, or several of these. They all have different imagined universes they live in.
CC: So you think durations have enough structure to give rise to space?
DE: What they have are what Whitehead calls "events in unison of becoming" -- this is where the families of durations with parallel events come in. You are aware of these, and these produce already a spatialized notion. Whitehead would talk about "regions in an extensive continuum" -- not space in the sense of a measurable grid.
CC:The relations durations can have with each other is that of "extending over." If one restricts this simply to durations, then unless you bring in Special Relativity axioms, all you can get is some sort of time.
DE: Whitehead doesn’t think his relation of "extending over" is only extending over in time.
MM: When I look at that window, however much I focus I see two bars, not one. This is why in Richard’s example yesterday of the two clocks striking at the same time, if you heard the one you heard the other. Durations are given in sense-awareness, and what I am looking at is spreading in its nature.
DE: It has seemed to me that what Whitehead calls a duration is much more a spatial than a temporal concept. What he calls the Extensive Continuum is four-dimensional, with regions in it. You are wanting a more conventional space, Chris.
RB: He is only wanting to separate space and time.
CC: Certainly it is the case with duros that if one does not impose Special Relativity axioms, all one can get out of them is time. The relation of "extending over" as applied to duros is not sufficiently rich to give one more than some sort of time. My own feeling is that when Whitehead introduces the term "durations" he has at the back of his mind duros and is wanting to de-focus as far as possible. What we need is a duration that still preserves the focussing.
DE: Isn’t this where that note to the Principle of Natural Knowledge comes in. He says when he wrote the book he was thinking of durations too much just in terms of "extending over," and he brings in the notion of "cogredience."
CC: Cogredience is a relation between events.
DE: It is a relation where one is a percipient event.
CC: I want to make a logical leap, which I shall claim is a smaller leap than that taken by Whitehead. I was saying earlier that if one wants to do physics one has got to get space, and I didn’t want to do it the way Whitehead did. So the question is how do you do it. The scheme I have been looking at is very far from full implementation of the ideas we have been discussing. I have been looking at a set of entities with some sort of relations between them which I hope is capable of being developed more in the direction Whitehead wants to have it developed. But it is still very materialistic in Whitehead’s sense. I have a temporal succession, though not a succession of instants. It is possible to say one thing happens later than another thing, so temporal succession is presupposed, whereas Whitehead, I think, would want temporal succession to be deduced. I was thinking of my entities as analogous to events, though in view of what we have been saying I would like to push them in the direction of durations. But right now, they are very thin things with very abstract properties indeed. To go through Whitehead’s materialist trinity: my events are chained together in succession, and so far as they are, I have material entities. To some extent space arises out of relations of these material entities. But I don’t think these are essential to the scheme. It would be possible to remove material entities and temporal succession. Also it is not a relativistic scheme. The relation between my events is different from Whitehead’s. Whitehead’s is the relation of extending over. I would like a scheme in which events are related by something other than extending over -- one, for instance, of being a recapitulation or reflection of another.
RB: If you want the logic, you ought to look at Russell’s Analysis of Matter where Russell disliked Whitehead’s Extensive Abstraction for purely technical reasons. It requires an existence theorem for an infinite number of events. If you have a limiting process, you have to have an infinite number to specify a point. Russell did it by overlaps of events.
A point for Russell is the class of things which overlap, and he thinks this doesn’t need an infinite number. This is a technical matter.
CC: I think in a full-bodied system one would want both a relation of overlap or extending over and probably also a relation of resonance or recapitulation between durations which did not extend over each other. I was looking at systems with some external relation other than extending over. I then looked at whether it was possible to get space out of entities with some sort of relation like this. One of my motivations in this was the quantum mechanical. I took the simplest system, where my events were two-state systems with only two possibilities. I was representing them quantum mechanically in the usual quantum formalism for possibilities. The relation between any two events was the natural quantum relation between their possibilities. Between any two events it is possible to say whether two aspects are similar or dissimilar. I was also allowing this relation to be stronger or weaker on a continuous scale. I was then looking at the possibility of chaining these recapitulatory relationships together -- if you had a relation of A to B to C to D, I could automatically set up a relation of A to D.
DE: It is transitive.
CC: The relation itself is not transitive, but given a set of relations, one could define further relations by chaining them together. The dynamics of the situation was that there was an evolution whose effect was to make the relation transitive, so that it became the average of the relations you got by chaining them together. I was looking at two systems in this way. One was a large number of elements I was simulating on a computer. The other was the continuum analogue of this, where you have a very large number of entities and treat them statistically. In both cases the entities do evolve to a three-dimensional structure, in the sense that you get a three-dimensional distance geometry out of them. As far as it has gone, I am satisfied that it is possible to get space out of this network of relationships, and you don’t need duros or Special Relativity axioms. It is sufficient to have any sort of relationship which at a minimum has the sort of quantum mechanical relation I was indicating in it, to give space as I have tried to get it. So what I have got out of this is that I want to take this relation and thicken it up. There is a structure there whereby one can get space, and I see no reason why one shouldn’t get space-time if one drops the assumption there is a fixed temporal succession.
MM: So you don’t get a conventional Newtonian space and time?
CC: In the way I have been doing it, with temporal succession in, you get space rather than space-time. What I have been doing on the computer is represent these things in a large number of dimensions and then I have a scheme by which you can look on them on a screen from any angle. If you look on them as they develop, they squash down to a three-dimensional slice.
CC: It is not completely reliable -- they do a lot of the time, but they sometimes seem to screw themselves up. It depends rather critically on the number of dimensions you work in. If you work in a high enough number they form a nicely balanced two and three-dimensional slice. If you work in too few they screw themselves up and fold over.
DE: To ask an ignorant question, what makes this happen? Is there a sort of averaging out?
CC: Yes. I am putting points in the dimension I am working in at distances that reflect their similarity. So two whose relation is very dissimilar are a long way away, and it is an averaging out of the chaining together of the relations which causes these relations to evolve.
RS: "Evolve" means become more similar, does it?
CC: There is a temporal succession. You set the thing up and average Out at one time, and that is what it looks like at a later time.
MM: So you have got time in as well as similarity.
CC: It needn’t be there. I can do something with it. That’s all I want to say.
RS: Good heavens. That is a real cliff hanger.
CC: I think the development of getting space and time is now separate from the development of seeing how this relates to morphic resonance. The main thing we want to work at here is thickening up these concepts. At present all I am trying to do is to get space and time from concepts that seem roughly along the right lines. But I am miles away from seeing how you could get both morphic resonance and Schroedinger’s equation.
MM: If we get rich durations, aren’t we going to get morphic conformation and moiphic resonance and morphic jumping long before we get space and time?
CC: Precisely. They are going to be different developments, and space-time an extremely lengthy abstract development and morphic resonance an immediate thing, whereas on the conventional way of looking at it, it is the opposite way round.
MM: We are turning the whole thing on its head, so what needs accounting for is how G. E. Moore’s common sense ever got going at all.
DE: Do you mean by G. F. Moore’s common sense Newtonian space and time?
CC: The hypothesis we are thinking about is about what is going on among elementary particles, which we don’t know anything much about. What we see is the end result, which is of the same nature as the process itself. The way we get our ideas of space could be through Extensive Abstraction and so on -- I don’t actually think it is.
DE: I have heard you say Special Relativity was now only thought to be a local theory.
CC: Yes, if you are thinking of the universe as a whole in the way Whitehead does in his duros, it is now not consistent to use Special Relativity. It is a local theory which can be applied anywhere.
DE: You also said it didn’t answer to anything in our experience.
CC: Our experience is Newtonian.
MM: It is touch that gives you space.
CC: It is action -- movement. This is why I was expressing doubts as to whether Extensive Abstraction actually corresponds to the way we get our intuitive idea of space.
MM: If you go about with your eyes shut, you get a very atomic view of space, not at all like anything you see. I don’t think Whitehead faces how different senses give you totally different durational worlds.
RS: On my view all senses give possible actions. Visual sense gives possible actions involving movement towards things distributed around us. Auditory sensations to some extent give that; olfactory a different kind of potential response, and you have a whole set of sensory potential action fields which have different properties depending on which sense. An amoebae which doesn’t have eyes has a rather limited set of fields, in response to contact. When you have organisms with eyes, they have more extended fields of potential action. Bats have a field that comes from the specialization of the auditory sense. Electric fish which swim about in muddy rivers have electric fields, and through these get a sense of where things are around them. These fields give senses of objects near by to which they can act or react. I think this is how it is built up. The only things in these fields which influence us are things on which we could potentially act. Organisms on the whole don’t respond to things they can’t act on. Birds respond to things that mean something to them -- they hear the song of other birds, or alarm cries, and there are a lot of other things to which they are indifferent. They soon habituate to the general background.
JW: To what potential actions is color sense a response?
RS: A robin responds to the color red, and so does a stickleback, because this is a sign of another male in the mating season. Outside the mating season it doesn’t respond much to that color. You have what the ethologists call fixed action patterns that are inherited, in this case those which give in-built responses to certain colors. I think the color responses are inherited in these cases. In our own case I think we have such sophisticated potential actions we no longer have these simple instinctive reactions. We then start abstracting and talking about colors just by themselves. I think butterflies when they respond to other butterflies of the same pattern, or animals when they run away from something striped respond in a fairly simple way to particular patterns of color. These fixed action patterns are what I call motor fields. They can be in response to different sensory things -- smells or colors. Gypsy moths respond to the smell of the female and fly towards it.
MM They respond to a whole pattern, and it can be a multi-sensory pattern.
RS It needn’t be.
MM: No, but it can be.
JW: The message from Whitehead seems to be that in thinking about perception you have to start from more basic things -- what you call fixed action patterns -- and then go on to the more sophisticated and abstract.
MM: The more bare (in the sense of raw) it is, the more comes into you at once, and you then can abstract one aspect. Then it is not so bare, but is simpler.
JW: With children I believe that all the color terms came in a bunch very suddenly, none being used properly; and secondly, they are associated with liking. The child can call the color "red" because he is interested in it.
MM: "I like a banana and it is yellow."
JW: It is not a mastery of color terminology by itself.
RS: In other words, there are potential actions. Like and dislike involve potential actions towards things. So the point of the ethological account is that there is always an association with potential action. Only things involving potential action are noticed. Animals notice novelties in their environment because anything new could be a threat. You usually get avoidance responses to anything new. Then if it doesn’t do anything, they rapidly habituate and cease to respond. So, so long as the background doesn’t change it doesn’t provoke response. Changes trigger off action patterns.
CC: Of the things given us, dominant are patterns which arise from our vision, which are linked with space -- concepts like nearness. But there are other things given to us as well which we can interpret by non-standard space.
MM: If your olfactory sense is your main one, or if you live in a marsh, half in water, half out, you will get "half in, half out of water," but not much else.
CC: If there is anything in the idea of trying to start with what you are mainly given and working from there, you would hope that whatever you started from, whether you were an electric fish or what, you would finish up with the same things, but in different orders.
MM: I don’t think you end up with the same things, you end up with lots of local universes. We can’t yet ask the electric fish, but maybe one day we shall be able to.
CC: You have a lot of local universes based on potential actions of organisms, and they overlap. After all, we can see and catch an electric fish and it gets involved in our set of actions. Animals respond to other animals though they have different perceptual universes, so they overlap.
MM: But you can’t presuppose the Newtonian overlap is the ultimate overlap.
CC: I never said so. What I said was when there was an overlap, and you can make comparisons. For instance, between our perceptions and those of some hypothetically intelligent dog, we would describe the smell relation as secondary to the space relation, but the intelligent dog may well have the smell relation as primary and the space one as derivative. But, being who we are, I think we ought to start from there.
DE: We mustn’t, though, be imperialistic about it.
CC: One plays with different descriptions when one is doing a scientific description. We postulate entities like electrons whose relationships make a totally different universe, and if one does that there is a peculiar concept of space that bears no relation to our intuitive one.
MM: Rupert has been needing a crude three-dimensional space for actions, not a relativistic one.
RS: For me, what is primary are organisms and their fields of potential actions. I think we experience these ourselves, and, as well, this is primary in nature. So if we want to build up a world with space and time, I don’t see why you have to start to get them early on -- why we can’t start from organisms and their in-built action patterns which are inherited from actions or memories in the past. These are fundamental facts from which we start.
CC: I agree, but if one is talking about how things go on, you seem to have a conflict between two ways of looking at it: one is starting from organisms and working down and the other is starting from space-time and working up. This I am worried about. If you get space-time out of the organism, then there shouldn’t be a conflict. Can one see on the horizon any way of starting off from wholes? But without taking the Special Relativistic course Whitehead does, how can one finish up getting space-time?
DE: Could we just be reminded of your objections to how Whitehead does it?
CC: In order to get space, he puts in axioms which are essentially Special Relativity axioms for incidence relations about intersections of limits of durations. These are axioms of a geometrical nature.
RS: My view is that fields associated with organisms give things tendencies to develop in particular directions, and the universe is made up of vast numbers of overlapping organisms, and that these are in conflict with each other through their overlapping. Out of these conflicts you get energetic processes of change. One kind of change is this moving change; the other is inner change as organisms develop. The mechanistic view tries to explain all kinds of change in terms of the relative movement of things; but there is also, especially in living organisms, an inner kind of change which is goal-directed. Some kinds of change due to movement can be studied in isolation, and then you get a physics model trying to explain everything in terms of that, but I am suggesting that inner change is primary.
CC: But if you work on those lines, how do you get mass x acceleration force? You can only do this if you look on these fields as they arise from fairly large scale organisms. You have got to apply these same criteria across the whole board.
DE: You, Rupert, are taking a rather extreme "philosophy of organism" view.
RS: Yes -- I think changes arise ultimately from inner teleological change -- even gravitational change.
RB: You think gravitation is to be explained in a goal directed manner?
RS: Yes, I do.
DE: Teleological in terms of the goals of what?
RB: You know, Dorothy -- "Every body finds its own place" (Aristotle).
RS: I can’t answer about gravitation. I can answer about electro-magnetism. In my view this arises from the striving of partly completed atoms and molecules to complete their forms by capturing electrons. The atom takes on an electric charge only when it is incomplete. When it has the right number of electrons it becomes electrically neutral, and one can consider electro-magnetic fields arising from the morphogenetic fields of atoms and molecules.
CC: This will only give the thinnest fragment of electro-magnetism. Electro-magnetism has quantitative laws. On your principles the nature of things is to describe things like atoms interacting. But how do you get quantitative laws Out of your morphic resonance? If at the sub-microscopic level you have simple entities, you need to have not only vague appetitions but some hope of getting to the Lorentz force law, which is the particular mathematical law known to determine the motions of electrically charged particles.
RB: How are you going to get the relation of perpendicularity? What is Rupert’s spatial pattern, and what is the notion of dimensions in it?
RS: I don’t see why you shouldn’t start with organisms as three-dimensional.
RB: What is meant by three-dimensional? If you just say you have a three-dimensional space, I think Chris is right.
RS: Why can’t you start with forms of things?
RB: What is a form? If it has geometrical characteristics you have got to give it a geometry, and then you instantly start on transformation theory and the mathematics of it.
DE: Is a form meant to be a spatial distribution?
CC: If not, and the forms are first given you, you have not got spatial structure.
CC: If you are given forms and not space, how are you going to get space out of them?
RS: You have to presuppose you have a multiplicity of forms interacting with each other. One of the ways they interact is through space.
JW: Why not say they interact by eating each other?
RS: By eating each other is one way.
RB: If you have got these forms, you have got to specify what their relations are. If you say the primary one is eating, I take that to he a spatial relation. Eating is something inside something else.
RS: I don’t see why one has got to build up everything a priori -- space for instance.
RB: My trouble with you is as with Steiner -- you have a fine metaphysics and then put in all the things which are inconsistent with it. You don’t reject physics, you use it when you want to. You should produce another physics.
CC: As a pragmatic device you have to refer to existing physics. But it shouldn’t be essential. Obviously in explaining your form and how it works in biology you presuppose physics. But it shouldn’t be a necessary part of the system that you are given both space and forms.
RB: Then please do it. You should define the relations, and get the notion of dimensions -- Whitehead and Russell tried to do it with regard to events. If you want to know, I would take your word "eating." Eating is a relation -- is it transitive? Yes. What sort of series does it illustrate? Is it completely ordered or partially ordered? You have got to have a topology to get dimensions. I think you might get a topology out of eating, but do it.
JW: You might get "nearer than" out of eating. You could see how with some organism its experience of space arose out of this.
MM: Sticking its tongue out and chewing.
JW: The primary thing is trying to kill the thing with your paw.
MM: Lots more have tongues than paws.
DE: I see a difference between what Whitehead is trying to do and what Rupert is trying to do. I don’t know if I am misrepresenting Rupert by saying he is taking a lot of normal science, and space and time, and pushing in what he calls formative causation. Whitehead is seeing that if you are having a radical view, starting from events and flying to get space-time, with his insistence on sense-awareness and durations for the strong notion of an event, this is going to affect everything all along the line.
RS: I agree, he is trying to do something more fundamental. But if one is going to start by doing something more fundamental, I think his notion of organism is likely to be more helpful than what are to me these extremely confused notions about events.
RB: For me this isn’t helpful till you say something definite about the organisms. Eating is quite an idea.
JW: "Distant" is derived from "it got away.
RB: You could get partial orderings, and then dimensions out of partial orderings.
RS: Organisms act more on things nearer to them.
RB: You could impose a metric on these simple orderings and get numbers. But you haven’t yet got dimensions, only one set of numbers.
CC: Rupert, you are thinking of eating not just as a relationship, but a quantitative ability of A to eat B as having real structure.
RS: The thing about eating is that an organism feels hungry; you have a motor field for hunger, and the organism searches for food. The actions will depend on the distance. If it is very near it pounces. Then it starts putting the food in its mouth, and it is assimilated into its body. I think the capture of molecules from solution by a growing crystal is rather like this and so is the capture of an electron by an ion. It involves a similar kind of appetite and its potential action on the electron depends on its distance from it, and it can engulf it in its orbital.
CC: I think this is fine; if you have a probability that A will succeed in eating B, you have a sort of metric, and then you have to explain how, in the space thus defined, if protons and electrons want to eat each other they obey the Lorentz force law.
RB: Yes, yes, yes.
CC: I am demanding it should be possible to see how this would be done.
RS: You might have to bring in other electrons in competition. But I’m not bothered about the Lorentz force law. It is not something I think about
RB: Then you are not producing a physical system. Or you could say this is an explanatory notion not in terms of physics at all. But then you would have to say something about the relation between the two explanations. This is a trouble I have over explanation by motivation as reasons for doing one thing rather than another. You consider crystals as organisms. It is very difficult to remove them from the realm of physics. Structures come in because the number of crystalline forms is limited.
JW: I like to say electrons want something.
RB: Then we aren’t responsible for Hiroshima. It was these wicked little electrons. No, No. We can’t get out of it like that. Perhaps you could keep a pack of electrons.
JW: Well-trained electrons.
RB: You starve them and they tear your opponents to pieces.
JW: You whip them up.
RB: That’s right.