Date: Thu, 30 May 1996 12:26:52 -0500 Reply-To: CSALL@gmu.edu Sender: owner-CSALL@gmu.edu From: dkaplan@OSF1.GMU.EDU (Deborah Kaplan) To: csall@gmu.edu Subject: Math and Cultural Studies Mime-Version: 1.0 X-Sender: dkaplan@osf1.gmu.edu (Unverified) Daniele-- Sorry not to have sent this out sooner. I've been out of town for a week. Deborah Date: Tue, 21 May 1996 23:40:27 -0400 (EDT) From: "Daniele C. Struppa" To: dkaplan@turtle.gmu.edu Cc: ploust@turtle.gmu.edu Subject: Math and Cultural Studies Mime-Version: 1.0 Deborah, Philippe and I have written this comment to the Sokal's hoax. Please read it and, if you feel it is appropriate, please forward it to the CS community. Best regards Daniele ==================================================================== We have read both the article in the New York Times (Postmodern Gravity Deconstructed, Slyly; 5.18.96) and in Lingua Franca (A physicists experiments with cultural studies; May/June 1996), and we wanted to share some of our thoughts with you. There are several issues which deserve attention. We would like to address two: 1. What does the hoax really show? 2. What should we do as Cultural Studies faculty? It is certainly unethical to submit a paper whose sole purpose is to deceive. The hoax could be viewed as "entrapment" and therefore void of implications. This reaction, however, would dodge the real issue which is the fact that a major scholarly journal has accepted a paper without fulfilling its editorial responsibilities towards the readers, the present and future community of scholars. These responsibilities include a careful and critical reading of the submitted paper by competent referees. This has obviously been neglected in the case of Sokal's paper. We were not able to read Sokal's paper itself, since we could not find the relevant issue of Social Text, but even the few quotes which are given in Lingua Franca show that the content of the paper was totally unacceptable from the point of view of its mathematical soundness. So, while the hoax does not imply anything concerning the quality of scholarship in the CS community, it certainly seems to indicate that the editors of Social Text have been quite negligent. In keeping with accepted standards of behavior, we would suggest that the only recourse for an editorial board that performed so poorly is resignation. On the contrary, Andrew Ross, co-editor of Social Text, accuses Sokal of misunderstanding Derrida and Aronowitz! This defensive (but unfortunately not surprising) attitude is, in our opinion, inexcusable, and not conducive to the necessary reflective (and humble) discourse which should take place. The point is not whether Sokal understands deep CS issues. The point is that he wrote a bunch of nonsense, and the editors of Social Text did not call his bluff. No matter how serious the hoax is, no matter how unpleasant the blow to our credibility is, we have no doubt that a single instance in which a single journal has not lived up to recognized standards of scholarship, cannot carry any serious consequences for the larger CS community. However it does show how easy it is to lower our intellectual guard and to be guilty of making decisions based on ideology rather than scholarship. Skepticism and scrutiny are our strongest tools. Lacking skepticism, we are all prey to what we would like to be rather than what is. This brings us directly to question 2. We believe that the only way to deal with this hoax is to not be defensive or dismissive but to acknowledge the fact that, in all fields (scientific and non-scientific), some scholars may become negligent or arrogant so as to decide not to need external referees for papers they do not understand, and to decide the value of a paper using some sort of ideological or moral authority. When this happens, such scholars abandon their intellectual honesty, and should leave the job to those who can perform better. Any "defensive" attitude with respect to Sokal's hoax is short-sighted and intellectually indefensible. We think it would be a good idea for us to reflect collectively on the meaning of the hoax. In particular, it may be a good idea to open up the floor for a discussion of the relationships between science and CS, maybe during our next meeting. The article in Lingua Franca raises some interesting questions, such as how much scientific knowledge is necessary to be a critic of science. We should probably address those questions. While we recognize that it is necessary for science and mathematics to be scrutinized, we are also concerned that distortions and exaggerations about science and mathematics poison the discourse between scientists and non-scientists, and threaten the capability of scientists and non-scientists to interact fruitfully with each other. This is a danger to the intellectual collegiality necessary for the health of our scholarly pursuits. So, we are naturally lead to the problem of the relationship between science and CS. In the last 2 years we have attempted to verbalize and clarify what we think the relationship between CS and science and mathematics is. It is clearly not a simple task. We would like to mention some points which are important to us. First, mathematical theories and results are not subjective, nor are they "feminist", or "western", or "moral", or "amoral", or whatever. Mathematical theories and results are irrefutable and devoid of societal values. However, the kind of mathematics that is developed, and even the way it is developed has a component that is culturally determined. Let us give a few examples to clarify this. It is fairly well known that there are only five regular solids (solids with equal sides, equal regular faces, equal solid angles, inscribable in a sphere). Given the axiomatic system of Euclidean geometry, and given the rules of inference of formal logic we abide by, there is no doubt whatsoever that there are only five such solids (Tetrahedron, Octahedron, Cube, Icosahedron and Dodecahedron). It can be proved and anyone can verify the proof. This is what mathematicians refer to as an "absolute truth". It was established about 500 B.C. and it is still valid. On the other hand, there are several interesting and culturally relevant questions one may pose. Why did the Greek get interested in such solids? What was their purpose? What was their interpretation of the result we just described? You are certainly familiar with the most influential of all of Plato's dialogues, Timaeus, in which Plato uses these five solids to describe his cosmology. It is interesting to note that Plato, in the dialogue, makes a good distinction between the FACT that there are only five regular solids (whose proof he ascribes to Pythagoreans), and the "eikos mythos" that they are the constituents of the universe. In fact, the notion of "eikos mythos" (or sometimes "eikos logos") is crucial to distinguish true statements from their interpretations (which are only "eikos", i.e. only "likely"). This was in 400 B.C.. About 2000 years later Kepler finally put forth a workable model for the universe, using observations and refined mathematical tools; still, in his work, he uses once again the five Platonic solids to justify his own construction. Once again, the results of Kepler are still valid (as the Galileo mission, for example, proved last fall) but the interpretation has the theological and teleological characteristics which makes it an interesting study from the cultural point of view. A similar problem is raised by pi (3.14....). Unlike what Sokal suggested in his hoax, pi is a universal constant. Of course, we need to specify what we mean by saying that it is a universal constant: within the Euclidean axiomatic system, it can be proved that the ratio between the circumference of a circle and its diameter is always pi. There will never be a discussion about this fact, and this is probably the reason why we found so disturbing that a totally ridiculous statement, such as the one contained in Sokal's paper, could have escaped the editors! The CS question, on the other hand, is whether the Euclidean axiomatic system is the appropriate system to describe our universe and why Euclid developed that particular model instead of another (for example, he could have chosen a different set of axioms which would have described the same geometry). Is it a natural and effective model? Is it culturally determined (at least to some extent)? Why did non-Euclidean models arise only in the eighteenth century (even though some of them do not require anything beyond very classical geometry)? What was the cultural impact of the realization that other models were possible, and maybe even better paradigms to describe our universe? These are interesting questions (and, in fact, raised by many philosophers). The link between the socially and mathematically constructed world is here particularly evident. One more example: in 1968, the Soviet Academy of Sciences finally published the complete collection of Karl Marx's mathematical manuscripts. We don't know whether they have been translated into English, but one of us has read the Italian version when it first appeared in 1975. These manuscripts have been studied with great interest in the Marxist circles, and they do shed some light on the most general issue of the relationship between science and society, between mathematics and dialectic materialism, and finally on the role of the use of dialectic categories in the analysis of scientific progress. Thus, for example, Marx interprets the process of differentiation as the category of "negation of negation" (because one first takes the increment to be different from zero and then equal to zero). We believe that this kind of analysis is of cultural interest, and that it can actually lead to a better understanding of the intellectual contribution of calculus, on one hand, and of Marx's scientific interests, on the other hand. Still, the fact that the derivative of ln(x) is 1/x, has no cultural value and is an absolute truth. Many more examples along these lines can be given (and are the objects of the NCC course which we will describe at the retreat). The math department had a speaker last semester, Karen Hunger-Parshall, who gave a talk on related issues. We have also suggested a speaker for the CS colloquium series for the Fall, Joan Richards, who would also address some of these issues. The thoughts included in this message are obviously only preliminary but we hope we can develop them further with the participation of other CS faculty. Daniele and Philippe