by Alan Sokal
Obviously, setting up a frame of reference involves making a number of arbitrary choices: for example, where to locate the origin of spatial coordinates (here 0th Avenue and 0th Street at ground level), how to orient the spatial axes (here east-west, north-south, up-down), and where the locate the origin of time (here midnight on 1 January, year 0). But this arbitrariness is relatively trivial, in the sense that if we make any other choice of origins and orientations, there are quite simple formulae for translating from the former coordinates to the latter.
A more interesting situation arises when we consider two frames of reference in relative motion. For example, one frame of reference might be attached to the Earth, while another is attached to a car moving at 100 metres per second eastwards relative to the Earth. Much of the history of modern physics since Galileo concerns the question of whether the laws of physics take the same form with respect to each of these two frames of reference, and what equations are to be used for translating from the former coordinates (x,y,z,t) to the latter (x′,y′,z′,t′). In particular, Einstein’s theory of relativity deals precisely with these two questions.152
In pedagogical presentations of the theory of relativity, a frame of reference is often equated loosely with an ‘observer’. More precisely, a frame of reference can be identified with a set of observers, one placed at each point in space, all at rest with respect to one another, and all equipped with suitably synchronized clocks. But it is crucial to note that these ‘observers’ need not be humans: a frame of reference can perfectly well be constructed entirely out of machines (as is nowadays done routinely in high-energy-physics experiments). Indeed, a frame of reference need not be ‘constructed’ at all: it makes perfect sense to imagine the frame of reference attached to a moving proton in a high-energy collision.153
Returning to Latour’s text, we may distinguish three errors in his analysis. First of all, he appears to think that relativity is concerned with the relative location (rather than the relative motion) of different frames of reference, at least in the following excerpts (italics added by us):
I will use the following diagram in which the two (or more) frames of reference mark different positions in space and time ...
(Latour 1988, p. 6)
[N]o matter how far away I delegate the observers, they all send back superimposable reports ...
(ibid. p. 14)
[E]ither we maintain absolute space and time and the laws of nature become different in different places ...
(ibid. p. 24)
[P]rovided the two relativities [special and general] are accepted, more frames of reference with less privilege can be accessed, reduced, accumulated and combined, observers can be delegated to a few more places in the infinitely large (the cosmos) and the infinitely small (electrons), and the readings they send will be understandable. His [Einstein’s] book could well be titled: ‘New Instructions for Bringing Back Long-Distance Scientific Travellers’.
(ibid. pp. 22–3)
This error can perhaps be attributed to a lack of precision in Latour’s style. A second error – which is in our opinion more serious, and is indirectly related to the first – comes from an apparent confusion between the concept of ‘frame of reference’ in physics and that of ‘actor’ in semiotics:
How can one decide whether an observation made in a train about the behaviour of a falling stone can be made to coincide with the observation made of the same falling stone from the embankment? If there are only one, or even two, frames of reference, no solution can be found ... Einstein’s solution is to consider three actors: one in the train, one on the embankment and a third one, the author [enunciator] or one of its representants, who tries to superimpose the coded observations sent back by the two others.
(ibid. pp. 10–11, italics in the original)
In reality, Einstein never considers three frames of reference. The Lorentz transformations154 allow one to establish a correspondence between the coordinates of an event in two frames of reference, without ever having to use a third one. Latour seems to think that this third frame is of crucial importance from a physical point of view, since he writes, in an endnote:
Most of the difficulties related to the ancient history of the inertia principle are related to the existence of two frames only; the solution is always to add a third frame that collects the information sent by the two others.
(ibid. p. 43)
Not only does Einstein never mention a third frame of reference, but in Galilean or Newtonian mechanics, to which Latour is probably alluding when he mentions ‘the ancient history of the inertia principle’, this third frame does not appear either.155
In the same spirit, Latour lays great stress on the role of human observers, which he analyses in sociological terms, evoking Einstein’s purported
obsession with transporting information through transformations without deformation; his passion for the precise superimposition of readings; his panic at the idea that observers sent away might betray, might retain privileges, and send reports that could not be used to expand our knowledge; his desire to discipline the delegated observers and to turn them into dependent pieces of apparatus that do nothing but watch the coincidence of hands and notches ...
(ibid. p. 22, italics in the original)
But, for Einstein, the ‘observers’ are a pedagogical fiction and can perfectly well be replaced by apparatus; there is absolutely no need to ‘discipline’ them. Latour also writes:
The ability of the delegated observers to send superimposable reports is made possible by their utter dependence and even stupidity. The only thing required of them is to watch the hands of their clocks closely and obstinately ... That is the price to pay for the freedom and credibility of the enunciator.
(ibid. p. 19)
In the foregoing passages, as well as in the remainder of his paper, Latour makes a third mistake: he emphasizes the alleged role of the ‘enunciator’ (author) in relativity theory. But this idea is based on a fundamental confusion between Einstein’s pedagogy and the theory of relativity itself. Einstein describes how the space-time coordinates of an event may be transformed from any reference frame to any other by means of the Lorentz transformations. No reference frame plays any privileged role here; nor does the author (Einstein) exist at all – much less constitute a ‘reference frame’ – within the physical situation he is describing. In a certain sense, the sociological bias of Latour has led him to misunderstand one of the fundamental tenets of relativity, namely that no inertial reference frame is privileged over any other.
Finally, Latour draws an eminently sensible distinction between ‘relativism’ and ‘relativity’: in the former, points of view are subjective and irreconcilable; in the latter, space-time coordinates can be transformed unambiguously between reference frames (ibid. pp. 13–14). But he then claims that the ‘enunciator’ plays a central role in relativity theory, which he renders in sociological and even economic terms:
[I]t is only when the enunciator’s gain is taken into account that the difference between relativism and relativity reveals its deeper meaning. ... It is the enunciator that has the privilege of accumulating all the descriptions of all the scenes he has delegated observers to. The above dilemma boils down to a struggle for the control of privileges, for the disciplining of docile bodies, as Foucault would have said.
(ibid. p. 15, italics in the original)
And even more starkly:
[T]hese fights against privileges in economics or in physics are literally, and not metaphorically, the same.156 ... Who is going to benefit from sending all these delegated observers to the embankment, trains, rays of light, sun, nearby stars, accelerated lifts, the confines of cosmos? If relativism is right, each one of them will benefit as much as any other. If relativity is right, only one of them (that is, the enunciator, Einstein or some other physicist) will be able to accumulate in one place (his laboratory, his office) the documents, reports and measurements sent back by all his delegates.
> (ibid. p. 23, italics in the original)
This last error is rather important, since the sociological conclusions Latour wants to draw from his analysis of the theory of relativity are based on the privileged role he attributes to the ‘enunciator’, which is in turn related to his notion of ‘centres of calculation’.157
In conclusion, Latour confuses the pedagogy of relativity with the ‘technical content’ of the theory itself. His analysis of Einstein’s semi-popular book could, at best, elucidate Einstein’s pedagogical and rhetorical strategies – an interesting project, to be sure, albeit a rather more modest one than showing that relativity theory is itself ‘social through and through’. But, even to analyse the pedagogy fruitfully, one needs to understand the underlying theory in order to disentangle the rhetorical strategies from the physics content in Einstein’s text. Latour’s analysis is fatally flawed by his inadequate understanding of the theory Einstein is trying to explain.
Let us note that Latour rejects contemptuously the comments of scientists about his work:
First, the opinions of scientists about science studies are not of much importance. Scientists are the informants for our investigations of science, not our judges. The vision we develop of science does not have to resemble what scientists think about science ...
(Latour 1995, p. 6)
One may agree with the last statement. But what should one think of an ‘investigator’ who misunderstands so badly what his ‘informants’ tell him?
Latour concludes his analysis of the theory of relativity by asking modestly:
Did we teach Einstein anything? ... My claim would be that, without the enunciator’s position (hidden in Einstein’s account), and without the notion of centres of calculation, Einstein’s own technical argument is ununderstandable ...
(Latour 1988, p. 35)
Postscript
Almost simultaneously with the publication of our book in France, the American journal Physics Today carried a essay by physicist N. David Mermin proposing a sympathetic reading of Latour’s article on relativity and taking issue, at least implicitly, with our own rather more critical analysis.158 Basically, Mermin says that criticisms of Latour’s misunderstandings of relativity miss the point, which, according to his ‘uniquely qualified daughter Liz, who has been in cultural studies for some years’, is as follows:
Latour wants to suggest translating the formal properties of Einstein’s argument into social science, in order to see both what social scientists can learn about ‘society’ and how they use the term, and what hard scientists can learn about their own assumptions. He is trying to explain relativity only insofar as he wants to come up with a formal (‘semiotic’) reading of it that can be transferred to society. He’s looking for a model for understanding social reality that will help social scientists deal with their debates – which have to do with the position and significance of the observer, with the relation between ‘content’ of a social activity and ‘context’ (to use his terms), and with the kinds of conclusions and rules that can be extracted through observation.
(Mermin 1997b, p. 13)
This is half true. Latour, in his introduction, sets forth two goals:
[O]ur purpose ... is the following: in what ways can we, by reformulating the concept of society, see Einstein’s work as explicitly social? A related question is: how can we learn from Einstein how to study society?
(Latour 1988, p. 5, italics in the original; see pp. 35–6 for similar statements)
For brevity, we have refrained from analyzing the extent to which Latour achieves either of these goals, and have confined ourselves to pointing out the fundamental misconceptions about relativity that undermine both of his projects. But since Mermin has raised the question, let us address it: Has Latour learned anything from his analysis of relativity that can be ‘transferred to society’?
At a purely logical level, the answer is no: relativity theory in physics has no implications whatsoever for sociology. (Suppose that tomorrow an experiment at CERN were to demonstrate that the relation between an electron’s velocity and its energy is slightly different from that predicted by Einstein. This finding would cause a revolution in physics; but why on earth should it oblige sociologists to alter their theories of human behaviour?) Clearly, the connection between relativity and sociology is, at best, one of analogy. Perhaps, by understanding the roles of ‘observers’ and ‘frames of reference’ in relativity theory, Latour can shed light on sociological relativism and related issues. But the question is who is speaking and to whom. Let’s assume, for the sake of the argument, that the sociological notions used by Latour can be defined as precisely as the concepts of relativity theory and that someone familiar with both theories can establish some formal analogy between the two. This analogy might help in explaining relativity theory to a sociologist familiar with Latour’s sociology, or in explaining his sociology to a physicist, but what is the point of using the analogy with relativity to explain Latour’s sociology to other sociologists? After all, even granting Latour a complete mastery of the theory of relativity,159 his sociologist colleagues cannot be presumed to possess such knowledge. Typically, their understanding of relativity (unless they happen to have studied physics) will be based on analogies with sociological concepts. Why doesn’t Latour explain whatever new sociological notions he wants to introduce by making direct reference to his readers’ sociological background?
7
INTERMEZZO: CHAOS THEORY AND
‘POSTMODERN SCIENCE’
The day will come when, by study pursued through several ages, the things now concealed will appear with evidence; and posterity will be astonished that truths so clear had escaped us.
(Seneca on the motion of comets, cited by Laplace, 1902 [1825], p. 6)
One encounters frequently, in postmodernist writings, the claim that more-or-less recent scientific developments have not only modified our view of the world but have also brought about profound philosophical and epistemological shifts – in short, that the very nature of science has changed.160 The examples cited most frequently in support of this thesis are quantum mechanics, Gödel’s theorem and chaos theory. But one also finds the arrow of time, self-organization, fractal geometry, the Big Bang and assorted other theories.
We think that these ideas are based mostly on confusions, which are, however, much subtler than those of Lacan, Irigaray or Deleuze. Several books would be needed to disentangle all the misunderstandings and to do justice to the kernels of truth which sometimes lie at their core. In this chapter we shall sketch such a critique, limiting ourselves to two examples: ‘postmodern science’ according to Lyotard, and chaos theory.161
A by-now-classic formulation of the idea of a profound conceptual revolution can be found in Jean-François Lyotard’s The Postmodern Condition, in a chapter devoted to ‘postmodern science as the search for instabilities’.162 Here Lyotard examines some aspects of twentieth-century science that indicate, in his view, a transition towards a new ‘postmodern’ science. Let us examine some of the examples he puts forward to support this interpretation.
After a fleeting allusion to Gödel’s theorem, Lyotard addresses the limits of predictability in atomic and quantum physics. On the one hand, he observes that it is impossible, in practice, to know the positions of all the molecules in a gas, as there are vastly too many of them.163 But this fact is well known, and it has served as the basis for statistical physics since at least the last decades of the nineteenth century. On the other hand, while apparently discussing indeterminism in quantum mechanics, Lyotard uses as an illustration a perfectly classical (non-quantum) example: the density of a gas (the ratio mass/volume). Quoting from a passage in French physicist Jean Perrin’s semi-popular book on atomic physics,164 Lyotard observes that the density of a gas depends upon the scale at which the gas is observed: for example, if one considers a region whose size is comparable to that of a molecule, the density within that region may vary from zero to a very high value,
depending on whether a molecule happens to be in that region or not. But this observation is banal: the density, being a macroscopic quantity, is meaningful only when a large number of molecules are involved. Nevertheless, the conceptual conclusions Lyotard draws are rather radical:
Knowledge about the density of air thus resolves into a multiplicity of absolutely incompatible statements; they can only be made compatible if they are relativized in relation to a scale chosen by the speaker.
(Lyotard 1984, p. 57)
There is a subjectivist tone in this remark, which is not justified by the case at hand. Clearly, the truth or falsity of any statement depends on the meaning of the words used. And when the meaning of those words (like density) depends on the scale, the truth or falsity of the statement will depend on the scale as well. The ‘multiplicity of statements’ on the density of the air, when expressed carefully (i.e., specifying clearly the scale to which the statement refers), are perfectly compatible.
Later in the chapter, Lyotard mentions fractal geometry, which deals with ‘irregular’ objects such as snowflakes and coastlines. These objects have, in a certain technical sense, a geometrical dimension that is not a whole number.165 In a similar vein, Lyotard invokes catastrophe theory, a branch of mathematics which is devoted, roughly speaking, to classifying the cusps of certain surfaces (and similar objects). These two mathematical theories are certainly interesting, and they have had some applications in the natural sciences, notably in physics.166 Like all scientific advances, they have provided new tools and focused attention on new problems. But they have in no way called into question traditional scientific epistemology.
The bottom line is that Lyotard provides no argument to support his philosophical conclusions: