DISCUSSION

Maxwell, Matter and Motion
Part 2 (Chapter I: Sections 13–18)

MCKEON: Last time we laid out the main lines of Clerk Maxwell’s analysis and came to a pause just at the point some of the large problems of space and time come in. We were on page 7 and had finished there section 12, on the “Origin of Vectors.” We took this to be the way in which principles enter into our topics of consideration. The next two sections deal with the ways in which you relate two systems. I will assume, since our problem is not primarily that of systematic comparison, we need not go into detail on these. It’s a very neat indication of what goes on in terms of comparison of the measurement of two countries. I hope you haven’t any problem with those three variables we’ve taken up; I assume that they’re not something that needs discussing in the short time that we have left.

Let’s go on to the concept of space. This is section 15, “On the Idea of Space,” and he says that he’s now going to go on to make a few points on the metaphysics of the subject. He violates, in other words, the present age’s prejudice against metaphysics. Is Mr. Davis here? No. Mr. Flanders, will you tell us what is the problem of the idea of space as it is treated here? And to answer the question you need two points, or at least enumerate them.

FLANDERS: He says what’s going on. Space depends on the matter contained in it.

MCKEON: Space depends on what?

FLANDERS: The materials contained in it.

MCKEON: That sounds more metaphysical than even he wants. What are the problems that he deals with? Does he ask that question? Does he answer it? I can’t find either the question or the answer in my book.

FLANDERS: Well, then he pulls out this business of the error of Descartes.

MCKEON: No. In section 15 he doesn’t say anything about whether space depends on anything in it. What does he talk about?

STUDENT: Why it causes events.

MCKEON: In the case of an event, it depends on the theory; and I really don’t understand what you said. Do you mean, if you’re measuring syrup, it will be more difficult to get your equipment all the way through it than if you’re measuring air or water? Mr. Roth?

ROTH: What he says is that any place which is a definite position is in relation to another point.

MCKEON: Well, let me, again, criticize this. Most scientists and philosophers don’t begin by saying, I’m going to enunciate a high principle which is going to determine a theory of analysis and I’ll tell you what it is. What they usually say is either, “There is this problem I’ve encountered,” or, “I’ve done this thus far and I want to do something else.” There are a number of other ways in which they would put it, depending on the method, but this is the normal procedure. But let me go on: since the operational way Clerk Maxwell does this is so obvious, he’s done something so far and we have to go on and do something else. All right, what have we done, what do we have to do, and what can’t we do?

ROTH: What we’ve done is to combine the configurations into one system and have gotten our problem.

MCKEON: We have described a method of combining configurations into one system; and our configurations, you will recall, were merely the ways of identifying the location of material parts in a system. We had both the model and the material system. We have shown a way of combining two or more into a single system. If we have done this, what would it be that he would want to go on and do?

ROTH: That we could take any given place . . .

MCKEON: Why should he want to do that? I might be a poet thinking of the place where a myth occurred or someone thinking of another kind of place. . . . Are there any other theories? As I said, the one thing that reading philosophy or reading science philosophically can do is to get you to see how the argument runs, what the line of argument is.

ROTH: In talking about previous systems, he has depended upon proofs about the vectors leading out from one point to another point and another point and thus proved that the lines out of the origin might also be configurations. I mean, he’s here clarifying it by saying that it doesn’t matter if we really add up these vectors because they’re really inaccessible to us and in any method except . . .

MCKEON: Really? So if they’re inaccessible, we don’t know anything about what’s going on.

ROTH: No, I’m saying inaccessible doesn’t prevent our making them. You know, we just can’t walk there.

STUDENT: But I think he’s going to expand what he’s done. We know only a small portion of what we can describe, but we can extend our vectors for more distance and finally get a whole. And I think that in the second part . . .

MCKEON: Why is he talking this way?

STUDENT: He wants to gain access for us from . . .

MCKEON: Does anyone have any idea why he’s talking this way? What is he—yes?

STUDENT: I mean, this is the summary of what he has done. He concludes configuration and now he’s going on, in the “Error of Descartes,” to the method.

MCKEON: He is an operationalist. An operationalist . . .

STUDENT: He’s building up the idea of space from the standpoint of vectors and points. From that standpoint it’s the relative position of bodies.

MCKEON: This may be true because the title is “On the Idea of Space,” but why does he want this treated here and why is he interested in the idea of space? Yes?

STUDENT: He’s interested in the idea of space because he . . .

MCKEON: What would the idea of space be operationally?

STUDENT: Space is measured distance.

MCKEON: I know, but what is it operationally? All of them will measure distances, dialecticians like the rest. . . . It will be the act of measuring space. How do we measure space? Well, we measure space first of all by stretching out our arms. All of the measurements that, without getting up, I could make on a table that I was sitting at are of this sort. Next, I can extend what I do with the table to what I can do with the room, what I can do with the campus, what I can do with the city: I can walk around. My mode of measurement would be different. You’ll remember, in lecture 7 I pointed out that Bridgman, who died only a few years ago, argued that the length of things that we measure in molar space, the length within an atom, and the length between the stars are different because we measure them. There is a third step that we go to which goes beyond anything we can walk to: this is calculation. Calculation can range all the way from things on the earth to things beyond the earth. But as we go on in this fashion beyond the most distant regions that we can walk to, this is where the inaccessible regions come in, and the inaccessible regions are not something that he invented just to take into account. This is what we can do in the way of measurement by calculation; that is, calculation will bring us to regions that we can’t walk to or regions that we can’t dig to or regions that we can’t fly to. They’ve calculated distances to the moon and to the heavenly bodies even though the space program has barely begun operating; you can’t get there. This is the only reason for it. Consequently, this leads us to the recognition that every place has a definite position relative to every other place, and this is all we’re going to mean by space. That is, space is this extension by the operational device from putting a foot rule down to walking and using a pedometer or a speedometer or anything else you wanted to use, to calculation. This is one point.

But then, secondly, there will be different ways of measuring that will be independent of each other. You can watch as you go along: there are curious interrelations between the various dimensions that Clerk Maxwell talks about and curious separations where he will want to keep them distinct. It will be possible to locate the center of the earth at a definite position relative to objects that we know, like Mandel Hall;1 but that position is inaccessible, that is, you can’t get to the center of the earth. Also, we can measure the number of cubic miles in the earth, that is, the whole content of the earth, without any hypothesis about where the center is. You don’t need to do the two; you can do either or both. Why would we be interested in making this point which we’ve raised? . . . Yes?

STUDENT: Perhaps because in relative space it’s all the same thing?

MCKEON: That, again, sounds like a dogma. Why don’t you put it the other way around. He is defending Newton’s position. Newton used a logistic method; Maxwell is substituting an operational method for it. What would be the difference between the two with respect to method on this point? . . . Why did Newton worry so much about whirling water in a pot or balls around on a string or the pendulum? Yes?

STUDENT: Well, whether space was absolute or relative would indicate what you could know . . .

MCKEON: And to have absolute space for Newton, what do you have to know?

STUDENT: You have to have a way of determining absolute motion.

MCKEON: And since it’s centripetal motion, what do you have to know?

STUDENT: The center?

MCKEON: The center of gravity of any system you are talking about. Clerk Maxwell is shrewdly seeing that he can deal with the whole universe in terms of its three-dimensional extension without any need to deal with an actual center. Ergo, this chapter on space. Let me indicate again what I meant by there being two answers to my original question. The one answer was that as an operationalist, he wanted to point out that the different meanings of measurement had to be combined into a single system; therefore, the meaning of space would be the position of any point relative to any other point—notice, any point, not a center. Secondly, he wanted to separate explicitly, therefore, the discovery of the center of the earth from the discovery of the cubic content of the earth; and he’ll do the same all the way through the système du monde, the system of the world. Once it’s stated, I hope this seems perfectly simple to you, even though you had trouble seeing it. Are there any questions about it?

All right, then, let’s go on to section 16, the “Error of Descartes.” Again, don’t get into your own method, but get into Clerk Maxwell’s. Miss Frankl? What’s this business about the error of Descartes?

FRANKL: Well, he says that . . .

MCKEON: Incidentally, in section 15 there’s a footnote on Newton which, if we had more time, we’d go into in some respects because in it he explicitly talks about space and the flux of time; and without denying them, he is turning, rather, to the relativity as regards space and time in these discussions. But tell me about the error of Descartes. And don’t tell me what he says; tell me why he brings it in at all.

FRANKL: I’m not sure, but he seems to be objecting either to Descartes’s principle or his method.

MCKEON: Well, leave out whether it’s principle or method; that’s merely a private vocabulary. Tell me what it is that he is objecting to.

FRANKL: He says that Descartes confused matter with space.

MCKEON: What other philosopher has a doctrine like this? What was Plato trying to do? What was space in Plato?

FRANKL: Space was all possible . . .

MCKEON: Space was room, room and potentiality.

FRANKL: Yes, space was potentiality.

MCKEON: What was space for Newton? . . . Space was void. What is space for Clerk Maxwell?

FRANKL: Measured distance.

MCKEON: Measured distance. What is wrong with thinking that space is void? . . . What’s wrong with space as void? . . .

STUDENT: It’s impossible to conceive of?

MCKEON: There’s no trouble conceiving of the void; the void is as real as the thing, according to Democritus.

STUDENT: But not according to Clerk Maxwell.

MCKEON: No. The reason why void is wrong is that if there were a void, you’d have to know the center, which is what Newton said, too; but the previous section knocked that idea on its head. We now go on to the next possibility, namely, that space is potentiality. We’re going to knock that on its head, too. What do you think, are there any scientists today who think that space is dense, that there isn’t any void?

STUDENT: The atomists?

MCKEON: What?

STUDENT: The atomists?

MCKEON: The atomists think there is a void. Are there any atomists any more? . . . No. There aren’t any atomists in quantum mechanics; there aren’t any atomists in relativity physics. Do any of you know why there is empty

space between us and Mars, a void? Yes?

STUDENT: There are people who have conceived of the space as being empty?

MCKEON: Well, let me ask this question. In designing my trip to Mars, could I draw a straight line as a possible path for the trip? And in this case it would be easier than in other cases since there aren’t many gravitational centers that I’d be passing through. But even in the case of that trip . . .

STUDENT: No.

MCKEON: No, I couldn’t. How would I have to travel?

STUDENT: In an ellipse.

MCKEON: Why?

STUDENT: Well, the nature of the phase of the earth and Mars is that it’s preventing you from making a straight path.

MCKEON: That’s right: because of concentrations of matter. And when you get metaphysical about why this is or what the nature of the force is, there are a variety of answers here. You cannot travel in a straight line in empty astronomical space anymore. That was abolished by 1917.

Incidentally, the vortices of Descartes were probably right in this case. He thought that space was full, that it was made up of a lot of little eddies rotating relative to each other. One of the reasons he gave the idea up—I mentioned this in lecture 1—was that if anyone showed that light took time to travel, he would be wrong because then light wouldn’t travel in a straight line and, obviously, light travels in a straight line. Because light since 1917 no longer travels in a straight line, he wouldn’t have had to give up his theory of vortices. This is known today in science as progress in a straight line, building only on truth and not on error. Bear in mind, Clerk Maxwell is writing before we found this out; but he helped prepare for this knowledge that we’ve come to, so it’s not a bit surprising that this sounds contemporary although he didn’t know it yet.

All right, let’s go on. What is it (a) that Descartes had in mind, and what is it (b) that Clerk Maxwell is objecting to? How could anyone mistake matter for space? Didn’t Descartes know the difference between what is on top of the table resting on it and what’s on top of the table where our books come down on it?

STUDENT: Would it be that the character of the space would depend on the matter for Descartes because the characteristics of the space determine the matter?

MCKEON: No. There are two steps you would need to make. That is, what Descartes was arguing was not that space was matter but that matter was three-dimensional. It would obviously be the case that you could have parts of three-dimensional extension in which there was a greater concentration than in others. That’s what makes motion possible. If you have a plenum, which is a fitting name for this, the way in which a body moves is in the less dense and not in the more dense concentration. Therefore, you would have two kinds of problems. One would be the problem of motion, where bodies move in space where there aren’t any concentrations; the other would be the problem of the way in which bodies themselves change, including the way in which the atoms are changed into each other. This would be merely a change of qualities of the three dimensions. Remember, Descartes’s example is a piece of gold,2 a piece of gold which you put first in the form of a sphere, then in the form of a square, then in any of a number of forms—you even melt it. If someone points at it and says, “What is it? What is the gold?,” you can’t say that it’s any of the shapes that it took. What you can say is that the matter of the gold is the three-dimensional extension which it contains and that the various qualities added were added to it. It is in this sense that space is potentiality; that is to say, it is the possibility of any change that it determines. It is empty because it doesn’t have any of the qualities that are acquired. All right?

This is the answer to half of the question, Miss Frankl. Having gotten this, with, as I say, a little excursion into the perfectly good scientific tradition today, what is it Clerk Maxwell is objecting to? . . . Miss Marovski? . . .³

Again, I hope that the way in which you have to take a man of Clerk Maxwell’s importance is to find not what he’s going to believe and what he says the other fellow’s wrong about but, rather, what it is, if he’s working with a definition of matter and if he says someone else is wrong, that he thinks is essential in the definition of matter and whether it is in the other fellow’s position. Now, if Clerk Maxwell is as good as I’m saying he is, you have a difference over what space is.

MAROVSKI: Well, he says here that Descartes states what the primary property is of matter, but I don’t understand why Maxwell thinks he didn’t understand his own words.

MCKEON: Well, he refers back to what Descartes said, and Descartes had a good “First Law of Nature”: “That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest” [10]. What is the name of this process?

STUDENT: I don’t know.

MCKEON: It’s inertia, isn’t it? Clerk Maxwell is saying, It’s funny about this fellow Descartes: he knew that matter had inertia; this is the primary characteristic of matter. He stated it in his law, but he never fully understood it. Why would this give us the means by which to deal with the process?⁴ . . .

STUDENT: Well, if space is potentiality, the meaning of inertia changes. It implies that the space denies the force of inertia because the capacity of the matter does not lead to change. In other words, space is a condition of change, whereas . . .

MCKEON: Space is a condition of change in both of them, one as potentiality, the other as a measured distance which we identify with a material system.

STUDENT: He seems, though, to be separating the inertia from the body and motion so that it is in space. In other words, space . . .

MCKEON: No, no. Inertia is the tendency of a body with respect to motion or rest. That’s Descartes, too. Consequently, you don’t move it in time or space or the mass. . . .

Let me indicate again the way to go about this. If we have an operational method, then what we mean by any of our concepts will have to be measured. We can measure the inertia of a body; we can’t measure the potentiality of space. Consequently, we would look for the characteristics of matter in something measurable which persists in motion or rest, whatever the state of the body was. Descartes is using a different method, the logistic method; therefore, what he is says is nearer to what Newton thought applicable. Descartes was talking about potentialities and their realization. Consequently, although he can deal with inertia, he takes inertia as a posterior, not a primary, characteristic of matter. Many of the changes that occur within a system depend on what it is that you take as first. Descartes wants to deal with many kinds of motion that the entitative approach of Clerk Maxwell will not bring in as primary; consequently, we’re over on interpretation. This would constitute the difference here. What he will want to account for, then, is the way in which any change occurs, and it is particular. This is the reason why I brought in the transmutation of elements above, particularly questions of generation, which Clerk Maxwell isn’t interested in at all. He’s interested only in local motion.

But leave all that out as irrelevant to our discussion. All I’ve said thus far that’s important is that Clerk Maxwell is looking for a measurable characteristic. Inertia is here in both of its varieties; but Maxwell thinks Descartes did not understand fully the words “so far as in it lies,” quantum in se est, which is an essential characteristic. Therefore, this means for Clerk Maxwell that what we look at, instead, is what we would say about bodies in relations. What Descartes had said was that if you took a flask and emptied it of everything, its sides would go together; in other words, if you took all matter out, there would be nothing left. Incidentally, if he said that today, would he be wrong? For centuries we’ve said that Boyle demonstrated he’s obviously wrong: it’s just air. Well, let me ask you, What’s the relation between photons and a proton or an electron? . . . They can transmute into the other; therefore, it is out of whatever matter they have in common. Just an atom, then, would have a comparable relation. Can you have light in a flask without a photon?

STUDENT: No.

MCKEON: Remember Boyle’s vacuum pump? When it exhausts the jar, does it go dark?

STUDENT: No.

MCKEON: Obviously, there are photons in it. With a sufficiently expensive experiment, those photons can lead into material particles in the ordinary sense. Again, Descartes doesn’t know any of these things; but if we are dealing with the broad lines of the argument, he’s not wrong in the terms in which it is brought up today. In any case, these are the two points about Descartes’s error. First, the argument for the plenum makes it necessary to say that there are no empty spaces. Clerk Maxwell picks the example which seems to him most absurd to show that there are empty spaces. Second, in place of the potentiality notion of space, therefore, you put in the measured-distance notion of space; and then matter, instead of being space, is inertia. Matter and space are what we’re talking about. Descartes identifies the two, according to Clerk Maxwell. Maxwell gives you the art by which you can tell if they’re one or separate because it’s based on this point of inertia.

All right, let’s go on to section 17, “On the Idea of Time.” Mr. Henderson, do you want to tell me about time? Just tell me in broad terms. Again, I would suspect that there are two points you could make.

HENDERSON: One point would be the distinction between absolute time and relative time, namely, that relative time could be determined, whereas absolute time is ultimately apart because it’s not like clock time.

MCKEON: Those are Newton’s pair, absolute and relative time. I would have thought that the first point to make was that time has its foundation in the “sequence in our states of consciousness” [11]—the first sentence. You remember, that was something which we found in Plato, if you want to take the world soul as the state of consciousness; and I told you that in Augustine it’s our consciousness of sequence which gives us our idea of time. So that the first point would be that we begin with our states of consciousness, which are in sequences; and by means of this—again, operationalist—we find it possible to arrange a system of chronology. He even goes through a list of great men who made the system of chronology possible. In other words, our first argument went from consciousness to the inclusive chronology.

Then he comes over to Newton. What does he say about Newton?

HENDERSON: That we need it for duration also and . . .

MCKEON: He distinguishes, as you said, between relative and absolute time. What’s he do with them?

HENDERSON: He more or less reduces everything into relative time. The absolute time is almost meaningless, whereas . . .

MCKEON: He reduces it to Mean Solar Time. It’s a little more significant than that.

HENDERSON: Not really, I think. It seems that absolutely it may merely be a better approximation of its own approximation.

MCKEON: With Mean Solar Time you can run all our clocks together. This is the operational method.

HENDERSON: Yes, but this Mean Solar Time, hasn’t it been more or less disproven by the atomic clocks.

MCKEON: The atomic clock is merely another way of getting the pulse. We said that Clerk Maxwell, like his predecessors, was entitative in interpretation; therefore, he was looking for a natural clock. That’s the reason why days, months, and years are here: they’re natural clocks. The earth turning around, the moon revolving around the earth, the earth revolving around the sun, that’s a natural clock. The atomic clocks or sodium clocks or any of the other varieties are merely quantum jumps which can be set up so that you can get the pulse off them electrically. They give you a regularity which is more precise than these earlier ones, but they are continuations in the line of the entitative analysis. There are a lot of problems about the atomic clock; for example, we don’t know what the relation of the atomic clock is to the size of the atom. It’s entirely possible that you can treat them all as variations, just as you get variations in the solar basis of the year. Consequently, if we have our problem of time set down, the debate is between two extremes—I’m answering our question now. One is the extreme of trying to get an absolute time, which would be duration. Newton’s way of getting it was to assume it as an even flow underlying all of the natural clocks that we get. Clerk Maxwell does that more directly by going to these natural clocks in his list after he gets the relative time. But if you have the natural clocks, since they are inaccurate, the way in which operationally you remove the inconvenience is to set up a mean among them; and this is what we will do if we get a series of atomic clocks. They’re not quite accurate, but we’ll set up an atomic mean similar to the solar mean. Yes?

STUDENT: Could you say that this sort of mean of the differences in your relative clocks representing the absolute pulse is the operational method joined to an entitative interpretation?

MCKEON: It comes from the combination of the two, yes. But you see, this is the case whenever you fly through the various time zones in an airplane. You’re never measuring your time accurately because the time belts are likewise averages that are set up. This average hits us in Chicago in a curious way since we’re near the edge of it: all you need do is go over to Indiana and you lose an hour. You’re dealing with an average. In other words, it’s not a question of accuracy; rather, it’s a question of how you measure time, and this is the only way we can. If you have a series of natural clocks that don’t quite keep the same time—you’ll recognize this as the regular case—you pick the ones that are the most reliable and get the average that would be related to the one set of diversities. You don’t average between the solar and the lunar; you average, rather, with respect to the solar.

STUDENT: The thing with the logistic method is that they will not accept an arbitrary clock, one that would seem, you know, reasonable rather than . . .

MCKEON: No. In the logistic method, you would specify your time units, and then you would indicate the extent of the application with this timepiece.

STUDENT: Well, that depends on the accuracy. In other words, you take an atomic clock or a radioactive element . . .

MCKEON: Since all you’re doing is making comparative measures, if you keep to the same kind, one of two things will happen: either the timepiece that you picked is running down or it isn’t. Consequently, all you need to do is find out which it is.

STUDENT: But does it matter?

MCKEON: No, that is, so long as you keep your requisite standard relative to the same chronometer.

STUDENT: Doesn’t that mean it’s an interpretation which is fixed?

MCKEON: Well, I did bring it in by assuming that we’ve had entitative all along here. It would have to be an entitative interpretation. Here, again, the operational method can use arbitrary chronometers, arbitrary relations; and it is relative to a frame of reference that indicates the extent to which you make that application. There are, of course, differences of measure when you move from one frame of reference to another. But this is more metaphysical.

What about section 18, “Absolute Space,” the final treatment of absolute space and time? Mr. Henderson, can you build on what we have done in section 17? . . . Well, let me ask you what is on my mind. We began with the idea of space, brought in the error of Descartes, then jumped over to the idea of time, in the course of which we dealt with absolute time, and now we go back to space. Why is it that we didn’t bring in the absolute space before we brought in the idea of time?

HENDERSON: I’d like to bring in the notion of motion. If you have motion directly involved, then space is that in which motion occurs.

MCKEON: Well, what would be the characteristic of absolute space, then?

HENDERSON: He mentions the idea of it, I suppose, “as remaining always similar to itself and immovable” [12].

MCKEON: And this would come from what we have been doing in our treatment of configuration. That is to say, one aspect of space is, with respect to configuration, that it is empty, always similar to itself; and the other has to do with the fact that the configuration which we’re talking about is not itself moving. And what’s his reply to this?

HENDERSON: We can’t know it without something moving.

MCKEON: No, I meant give me the rest of the paragraph with respect to his conclusion. If this is our definition of space, what can we say about it?

HENDERSON: Our knowledge of space and time is relative.

MCKEON: All right. Well, now, how does this differ from what Newton was saying? Is he abandoning Newton? . . . He says, Just as in the case of time we cannot talk about time because it’s relative to events, so in the case of space we can’t talk about space except in terms of place occupied by material bodies.

HENDERSON: This is the physical predicament which we’ve been working on.

MCKEON: Well, I know, but tell me more about Newton and Clerk Maxwell. I mean, he obviously thinks this is important since he brings it in and does go contrary to Newton. He obviously thinks, in another sense, it doesn’t make any difference; therefore, he doesn’t push it too far, thinking that he’s following Newton.

HENDERSON: If space is thought of as an extension, then it’s a refutation of what Newton is more concerned by virtue of his particular method.

MCKEON: I would think a refutation would be one that if the man says that absolute space is necessary for the system, this is false, it’s not necessary . . .

STUDENT: Doesn’t he bring in something between motion and our knowing?

MCKEON: This is the system of physics; we’re going to have a maximum physical knowledge. According to Newton you can’t have physical knowledge without absolute time and space; according to Clerk Maxwell you can. I thought this was a contradiction, but he says it isn’t. Either tell me why it isn’t a contradiction or tell me why it is that Clerk Maxwell now tells me what he does.

HENDERSON: Well, with reference to the existence of relative space, I think that you need to have an absolute space also in order to plot relative space according to what you’re going to do with it.

MCKEON: No, no. We’ve already answered it in this respect. The method of Newton, which affects the concept of space, is logistic; therefore, in dealing with anything that takes place in space, which includes all motion, we’ve got to be able to know what the center is. Ergo, you need an absolute space. If you couldn’t talk about the motion of the body as such, it wouldn’t be any good talking about the relative motion. Since we have a center, we can talk about absolute space. Notice the two characteristics Maxwell brings in. With respect to “similar to itself,” Clerk Maxwell is going to answer that: it all turns on the other characteristic, “immovable.” What does Newton say about the center of the solar system? He says it is either at rest or it moves in a straight line. It’s not necessarily movable, but it would make no difference, provided it is not rotating or accelerating. If it is accelerating, then, this would be detectable in absolute motion. Consequently, the immovable is a requirement more than Newton needs. For the operational method, on the other hand, you don’t need any center. You can take any center successively as the means of measurement. Therefore, all you need to be able to say is that our measurements would be with respect to such and such a point. We don’t need any space in an absolute sense, according to Maxwell; the operation takes care of it. The argument is in these terms, and you don’t need to underline it. You could say, Well, maybe in the seventeenth century it was fashionable to talk about absolutes, but we won’t bring it up unduly. In Newtonian physics, if you want to, you can deal with it.

Well, our time is more than up. We have two more meetings. Next time I will lecture about the whole job we’ve been doing. Then, in our last discussion we can do one of two things. Either you can decide to spend more time on Clerk Maxwell, since I thought we’d get further into Maxwell this time; or, if you have questions that you want raised, we can talk about the whole project of the course. So you can do either one or the other. How many would want to go on and finish Clerk Maxwell? . . . How many would want to ask questions? . . . O.K., we’ll ask questions.