>Richard Crew (rich@archytas.duckpond) wrote:
>[...]
>:  My own experience with professors of literature is that they aren't usually
>:  willing to make such efforts on behalf of students. But apparently its
>:  different when Revered Authorities are in question. Whence an elaborate
>:  paper by A. Plotnitsky in 'Postmodern Culture,' offering an unconvincing
>:  explanation of what Derrida might have meant by "The Einsteinian constant."
>
>Why did you find it unconvincing? I'll forward your reservations to 
>Arkady and ask him to respond.

http://muse.jhu.edu/journals/pmc/v007/7.2plotnitsky.html

One of these is the following (from [AP] par. 12; he's discussing the claims of "literal accuracy" made by Derrida's scientific critics):

....However, even assuming that such quotations are accurate, their literal accuracy is meaningless if the reader is not provided with the meanings of the terms involved (such as "play/game" or "the Einsteinian constant"), is deprived of the possibility of establishing them from the quotation itself, or is free to construe them on the basis of other sources--say, one's general knowledge of physics, as opposed to the meaning given to these terms by Derrida's essay or by Hyppolite's question.

As far as the possibility of establishing meaning "from the quotation itself," let us first consider what Derrida and Hyppolite have to say directly about physics in their exchange. This seems to be contained in the following quotes:

Hyppolite: They [i.e. the natural sciences] are like an image of the problems which we, in turn, put to ourselves. With Einstein, for example, we see the end of a kind of privilege of empiric evidence. And in that connection we see a constant appear, a constant which is a combination of space-time, which does not belong to any of the experimenters who live the experience, but which, in a way, dominates the whole construct, and this constant -- is this the center? But natural science has gone much further. It no longer searches for the constant. It considers that there are events, somehow improbable, which bring about for a while a structure and an invariability...

Derrida: Concerning the first part of your question, the Einsteinian constant is not a constant, not a center. It is the very concept of variablility -- it is, finally, the concept of the game. In other words, it is not the concept of something -- of a center from which an observer could master the field -- but the very concept of the game which, after all, I was trying to elaborate.

H: It is a constant in the game?

D: It is the constant of the game...

H: It is a rule of the game

D: It is a rule of the game that does not govern the game; it is a rule of the game which does not dominate the game. Now when the rule of the game is displaced by the game itself, we must find something other than the word rule.

As used by Hyppolite, the "constant" here may not mean--and does not appear to mean--a numerical constant, as virtually all the physicists who commented on it appear to assume. Instead it appears to mean the Einsteinian (or Einsteinian-Minkowskian) concept of space-time itself, since Hyppolite speaks of "a constant which is a combination of space-time" (emphasis added), or the so-called spatio-temporal interval, invariant ("constant") under Lorentz transformations of special relativity. This interval is also both "a combination of space-time" and something that "does not belong to any of the experimenters who live the experience," and can be seen as "dominat[ing] the whole construct" (i.e. the conceptual framework of relativity in this Minkowskian formulation). Indeed, it is possible that Hyppolite has in mind this latter (more elegant) interpretation, while Derrida understood the "constant" as referring to the Einsteinian concept of space-time itself. This difference is ultimately not that crucial, since both these notions are correlative (and both are correlative to the constancy of the speed of light c in a vacuum and its independence of the state of motion of the source) and both reflect key features--decentering, variability, play (in Derrida's sense), and so forth--at stake in Hyppolite's and Derrida's statements. In any event, given the text, these interpretations are more plausible than seeing the phrase as referring to a numerical constant.

[the "emphasis added" is Plotnitsky's, not mine]

He seems to be relying on an assimilation of the meanings of "constant" and "invariant," so that he can assert that the Lorentz distance, being "invariant" under the group of Lorentz transformations, is the desired "constant." Again we ask how this can be justified on the basis of the text. Hyppolite only uses the word "invariability" only once, and in a way that distinguishes it from "constant" ("science no longer searches for the constant..."; but it finds things which "bring about a structure and an invariability"). So we can't look to Hyppolite here, and Derrida doesn't use the word "invariant" at all. He says "constant" -- but -- constant in what sense? There are many senses of the words "constant" and "invariant," and even in mathematics and physics, they don't coincide. For example, a function on a space can be invariant under a group of transformations, without being a constant function; the Lorentz distance is itself an example of this. Points of a space left unchanged by a transformation are called "invariants" or "fixed points" of a transformations; they are almost never called "constant."

It's equally hard to justify the meaning of "space-time" for the "constant" simply on the basis of the text. If Hyppolite really meant "space-time" when he said "constant which is a combination of space-time," then why didn't he simply say "space-time"? His very choice of words suggests that he has something different in mind. This is probably why Plotnitsky thinks that Hyppolite is thinking of the spatio-temporal interval, while Derrida is thinking of space-time itself. But then the question arises again -- why should Derrida think this? If Hyppolite says "constant that is a combination of space-time," and Derrida hears this as "space-time," then doesn't this seem to indicate that Derrida is not listening all that closely?

One can also ask what it can mean to assert that space-time can be "constant." It can't mean "not varying with time" because time and change are internal to space-time. It can't mean "invariant under Lorentz transformations" because physical space-time doesn't really "undergo" Lorentz transformations: from the point of view of physical space-time, Lorentz transformations describe how the reference frames of various observers are related to each other. In a sense, space-time just sits there. Perhaps that's what "constant" means.

Plotnitsky tries to insist that there's no basic difference between asserting that the "constant" in question is the spatio-temporal interval, and asserting that it is space-time itself:

This difference is ultimately not that crucial, since both these notions are correlative (and both are correlative to the constancy of the speed of light c in a vacuum and its independence of the state of motion of the source) and both reflect key features--decentering, variability, play (in Derrida's sense), and so forth--at stake in Hyppolite's and Derrida's statements. In any event, given the text, these interpretations are more plausible than seeing the phrase as referring to a numerical constant.

...The Einsteinian or Einsteinian-Minkowskian concept of space-time may be seen as correlative to the assumption that the speed of light is independent of the state of motion of either the source or the observer, and, in this sense, these "two Einsteinian constants" may be seen as conceptually equivalent.

Having developed this interpretation, Plotnitsky retreats from it almost immediately ([AP] par. 18):

This alternative interpretation is not definitive, and no definitive interpretation may be possible, given the status of the text as considered earlier.

At the same time, interpretations of these statements are possible and may be necessary--for many reasons, for example, the interpretations that occasion this article. For these statements have been interpreted without any consideration of these complexities or any serious attempt to make sense of them.

To begin with, how many different interpretations can one devise of Hyppolite's phrase, "a constant which is a combination of space-time, which does not belong to any of the experimenters who live the experience, but which, in a way, dominates the whole construct"? Plotnitsky has given two related ones; related, but not (for the reasons given above) identical. And given the latitude with which he is willing to interpret the word "constant," it seems that there should be many other possibilities. If "invariant" is a possible interpretation, then why not "covariant" as well? After all, for functions, "invariant" is simply what guarantees that the function has a "real" physical or geometric meaning; the corresponding conditions for vectors and higher order tensors is covariance (I am eliding the distinction between "covariance" and "contravariance" which is significant for general relativity, but not for special relativity). But then we can find other "constants," i.e. covariant tensors, which are "combinations of space-time," which do not "belong to any of the experimenters who live the experience, but which, in a way, dominate the whole construct," for example, the electromagnetic field tensor, or the energy-momentum tensor. And then, why should we limit ourselves to what is available in special relativity? This brings in the whole menagerie of constructions of general relativity: the curvature tensor, the Ricci tensor, the scalar curvature, all of them "interpretations" of the "Einsteinian constant" which could be, in Plotnitsky's words, "possible and plausible, or at least allowable."

At this point one may well feel that something is definitely wrong here. Perhaps, if one is interpreting a poem or novel, then the more interpretations, the better. But here we are considering a conversation. How difficult can it really be? Hyppolite refers to a "constant which is a combination of space-time" and does not really specify it further; Derrida, instead of saying "what do you mean? which constant?" answers directly, as if he were sure he knew what Hyppolite was talking about. Perhaps he is; this would be reasonable if the constant were the most well-known physical constant in the whole theory, the speed of light. But if it really requires some serious exegesis to determine what Hyppolite is talking about, if a number of possibilities are imaginable (which is the case even if one restricts one's attention to physical constants: the speed of light, the universal gravitational constant, the cosmological constant), if it really is necessary to reassure the reader that "interpretations of these statements are possible and may be necessary" -- then Derrida's readiness to answer is puzzling. In this context, the admission that there may be "no definitive interpretation" of what is meant by the "constant" is disastrous; it's perilously close to conceding that Derrida doesn't know what Hyppolite is talking about, and doesn't particularly care.

We will have to reconsider this later, when we discuss these remarks of Derrida and Hyppolite in the context of their entire conversation. We now turn to point (2) above: the interpretation of the constant as "space-time" is consistant (or rather "congruent") not only with the theory of relativity, but with the ideas that Derrida has expounded in his lecture. The key idea here concerns the "decentered play" of a structure which does not have a "center," i.e. something acting not just to "orient, balance, and organize the structure" but to "limit what we call the freeplay of the structure (the translator here explains that "freeplay" translates jeu). Plotnitsky believes that the space-time of special or general relativity is an example of such a structure ([AP] par. 19):

The moment one accepts this interpretation, Derrida's statement begins to sound quite a bit less strange. It acquires an even greater congruence with relativity once one understands the term "play/game" as connoting, in this context (it is a more radical and richer concept overall), the impossibility within Einstein's framework of space-time of a uniquely privileged frame of reference--a center from which an observer could master the field (i.e. the whole of space-time). Even if my reading of "the Einsteinian constant" is tentative, the meaning I suggest for Derrida's term "play" [jeu] is easily supportable on the basis of his essay and related works.

One might, then, see Derrida's statement reflecting the fact that, in contrast to classical--Newtonian--physics, the space-time of special, and even more so of general, relativity disallows a Newtonian universal background with its (separate) absolute space and absolute time, or a uniquely privileged frame of reference for physical events.

Derrida sometimes speaks, via Nietzsche and Heidegger, of "the play of the world" itself, as opposed to play in the world. He posits a certain irreducible variability of the world itself and/as our construction of it, as opposed to the concept of the world as a ("flat") background of events given once and for all, such as Newton's absolute space in classical physics. From this perspective, "the Einsteinian constant," understood as the concept of Einsteinian space-time, could indeed be seen, at least metaphorically, as "the very concept of variability" and, at the limit, as the concept of play/game [jeu] developed by Derrida.

Let's start by observing that it's not true that Newtonian mechanics has a "uniquely privileged frame of reference." This is explained quite clearly in the second chapter of Einstein's "The Meaning of Relativity". First of all, there is no spatial "center of the universe" singled out by the laws of physics, or any intrinsic meaning to the words "up" or "down." The laws of physics must be the same at all spatial locations and with respect to all spatial directions; Einstein calls this the "principle of relativity with respect to direction" ([MR] p.24). Next, it is required that the laws of physics should be the same for any two observers whose relative acceleration is zero; this he calls the "principle of special relativity" ([MR] p.25) and it is valid both in Newtonian mechanics and in the theory of relativity.

The difference between classical mechanics and special relativity arises when we ask how the different reference frames are related to each other. In classical mechanics, as Einstein points out, this problem is solved with the aid of the unconscious assumption that phrases such as "simultaneous" and "in the same location" have an absolute meaning; one can then write down formulas for the relation between different reference frames that Einstein calls "Galilean transformations" ([MR] p. 26, eqn. 21). For two reference frames related by Galilean transformations, accelerations are the same, and thus Newton's laws are invariant with respect to Galilean transformations. "But," as Einstein points out ([MR] pp. 26-7),

...this attempt to found relativity of translation upon the Galilean transformations fails when applied to electromagnetic phenomena. The Maxwell-Lorentz electromagnetic equations are not co-variant with respect to the Galilean transformation... But all experiments have shown that electro-magnetic and optical phenomena, relatively to the earth as the body of reference, are not influenced by the translational velocity of the earth. The most important of thos experiments are those of Michelson and Morley, which I shall assume are known. The validity of the principle of special relativity also with respect to electro-magnetic phenomena can therefore hardly be doubted.

One can summarize the situation as follows. There is a principle of relativity in both Newtonian mechanics and in Einstein's theory; neither theory has a "privileged reference frame." The difference arises from the fact that "space" and "time" are absolutely meaningful in the Newtonian picture, and this leads to the form of the Galilean transformations. But this theory is not consistent with Maxwell's equations, so the hypothesis of an "absolute space" (i.e. the assumption that spatial distances are intrinsically meaningful) and "absolute time" is replaced by the weaker hypothesis of an "absolute space-time" (c.f. [MR] p. 55), in which different reference frames are related by Lorentz transformations.

It's true that many physicists in the classical period -- Newton included -- assumed it was absolutely meaningful to assert that an object was "at rest" or "in motion." Serious doubts about this assumption, however, surface as early as the first decade of the 18th century (Leibniz, in the Leibniz-Clarke correspondence). But the historical record is not at issue here: the point is that theory itself does not require such an assumption. Newtonian mechanics functions in the same way, and makes the same predictions, with or without the assumption that "rest" has an absolute meaning.

One might then ask whether Newtonian mechanics could itself be described as a "decentered structure." This is certainly a possibility, at least if the lack of a "privileged frame of reference" is, in this setting, equivalent to the lack of a center in Derrida's sense. But it's not clear that Derrida's essay really allows this. Decentered play only emerges subsequent to an event, a "rupture" that Derrida evokes at the beginning of "Structure, Sign, and Play," which he locates approximately during the decades surrounding the turn of the century, evoking the names of Nietzsche, Freud, and Heidegger. This is not the heyday of classical mechanics! For chronological reasons, if no other, Newtonian mechanics must be viewed as a "classical" theory (in the sense of Derrida's essay).

Another question -- the reverse of the preceding -- is whether the theory of relativity might have a "center" after all: for Plotnitsky has not shown that in this context, "center" must mean "privileged frame of reference." Indeed, a number of things might well serve as an "organizing principle of the structure" which "would limit what we might call the play of the structure." One thinks, for example, of the representation theory of the Lorentz group, which classifies the various invariant and covariant quantities for the action of the group, and thus the mathematical constructions which are to be allowed as "physically meaningful." It could therefore be seen as limiting the "play" of the structure, in the sense that it establishes what can be meaningful in the theory and what cannot.

But none of these questions can be answered unless one confronts what Derrida has to say about the decentered play of a structure; it is only after having examined this that one can answer the question of whether the multiplicity of reference frames in Special Relativity is an aspect of "the game," of decentered play. Plotnitsky does not really do this. Here, for example, is how Derrida introduces this notion [SSP] p. 249:

From then on [i.e. after the "rupture"] it was probably necessary to begin to think that there was no center, that the center could not be thought in the form of a being-present, that the center had no natural locus, that it was not a fixed locus but a function, a sort of non-locus in which an infinite number of sign-substitutions came into play. This moment was that in which language invaded the universal problematic; that in which, in the absence of a center or origin, everything became discourse -- provided we can agree on this word -- that is to say, when everything became a system where the central signified, the original or transcendental signified, is never absolutely present outside a system of differences.

This field is in fact that of freeplay, that is to say, a field of infinite substitutions in the closure of a finite ensemble. This field permits these infinite substitutions only because it is finite...

In fact, what Derrida even meant by "center" was unclear to at least one auditor -- Hyppolite himself. To see this, one has to go back to the exchange between Derrida and Hyppolite, and reconsider it in its entirety. This would seem essential to placing the remark about the "Einsteinian constant" in its proper context, the importance of which is emphasized by Plotnitsky. Hyppolite is in fact the first to speak after Derrida's lecture:

Hyppolite: I should simply like to ask Derrida, whose presentation and discussion I have admired, for some explanation of what is, no doubt, the technical point of departure of the presentation. That is, a question of the concept of the center of structure, or what a center might mean.

When I take, for example, the structure of certain algebraic constructions [the translator supplies the word "ensembles" here], where is the center? Is the center the knowledge of general rules which, after a fashion, allow us to understand the interplay of the elements? Or is the center certain elements whihc enjoy a particular privilege within the ensemble?

With the last part of your remarks, I can say that I agree fully -- but you were asking a question.

I was wondering myself if I know where I am going. So I would answer you by saying, first, that I am trying, precisely, to put myself at a point so that I do not know where I am going. And, as to this loss of the center, I refuse to approach an idea of the "non-center" which would no longer be the tragedy of the loss of the center -- this sadnes is classical. And I don't mean to say that I thought of approaching an ide by which this loss of the center would be an affirmation.

As to what you said about the nature and situation of man in the products of nature [i.e. the last part of Hyppolite's question], I think that we have already discussed this together. I will assume entirely with you this partiality which you expressed -- with the exception of your [choice of] words, and here the words are more than mere words, as always.

That is to say, I cannot accept your precise formulation, although I am not prepared to offer a precise alternative. So, it being understood that I do not know where I am going, that the words which we are using do not satisfy me, with these reservations in mind, I am entirely in agreement with you.

In what concerns algebra, then, I think it is an example in which a group of significant figures, if you wish, or of signs, is deprived of a center. But we can consider algebra from two points of view. Either as the example or analogue of this absolutely de-centered game of which I have spoken; or we can try to consider algebra as a limited field of ideal objects, products in the Husserlian sense, beginning from a history, from a Lebenswelt, from a subject, etc., which constituted, created its ideal objects, and consequently we should always be able to make substitutions, by reactiviating in it the origin -- that of which the significants, seemingly lost, are the derivations. I think it is in this way that algebra was thought of classically. One could, perhaps, think of it otherwise as an image of the game. Or else one thinks of algebra as a field of ideal objects, produced by the activity of what we call a subject, or man, or history, and thus, we recover the possiblility of algebra in the field of classical thought; or else we consider it as a disquieting mirror of a world which is algebraic through and through.

Hyppolite: What is a structure then? If I can't take the example of algebra anymore, how will you define a structure for me? -- to see where the center is.

Derrida: The concept of structure itself -- I say in passing -- is no longer satisfactory to describe that game. How to define a structure? Structure should be centered. But this center can be either thought, as it was classically, like a creator or being or a fixed and natural place; or also as a deficiency, let's say; or something which makes possible "free play;" in the sense in wich one speaks of the "jeu dans la machine," of the "jeu des pieces," and which recieves -- and this is what we call history -- a series of determinations, of signifiers, which have no signifieds finally, which cannot become signifiers except as they begin from this deficiency. So, I think that what I have said can be understood as a criticism of structuralism, certainly.

What is one to make of the whole exchange? Derrida's discussion of "center" in [SSP] is abstract and metaphorical throughout. In the whole first half of the essay there are, quite simply, no examples. In the second half he isolates some contrasting tendencies in a few texts of Levi-Strauss which one gathers are meant to illustrate the constrast between classical "centered" structure and decentered play (e.g. the nature/culture opposition, the discussion of "totalization") and the impossibility of choosing between them. But it is left to the reader to work out the details of how his "defintions" of center and freeplay are put into effect, and one has no guidance as to how to do this by oneself in different situations. The result is a confusing variety of possibilities, as we have seen above. So it is not surprising that Derrida rebuffs Hyppolite's repeated attempts to press him for clarifications.

One is tempted to conclude that tendency to relentless intellectualism characteristic of certain strains of modern French thought is alive and well. In any case, one is not left with the impression, as Plotinitsky would have it, that "these concepts, such as 'play,' are thought through in Derrida in the most rigorous way" ([AP] par. 22).

Richard Crew
November 1997

References

[MR] Albert Einstein, The Meaning of Relativity, 5th ed. Princeton Univ. Press 1956.

[SSP] Jacques Derrida, "Structure, Sign, and Play," in The Languages of Criticism, ed. Richard Mackesy & Eugenio Donato, The Johns Hopkins Press 1970. This essay, without the accompanying discussion, is reprinted (in the original French) in Ecriture et Difference.