Before Alan Sokal and Francis Wheen, there was…George Steiner

3 May

Between verbal languages, however remote in setting and habits of syntax, there is always the possibility of equivalence, even if actual translation can only attain rough and approximate results. The Chinese ideogram can be transposed into English by paraphrase or lexical definition. But there are no dictionaries to relate the vocabulary and grammar of higher mathematics to those of verbal speech. One cannot “translate” the conventions and notations governing the operations of Lie groups or the properties of n-dimensional manifolds into any words or grammar outside mathematics. One cannot even paraphrase. A paraphrase of a good poem may turn out to be bad prose; but there is a discernible continuity between shadow and substance. The paraphrase of a complex theorem in topology can only be a grossly inadequate approximation or a transposal into another branch or “dialect” of the particular mathematical language. Many of the spaces, relations, and events that advanced mathematics deals with have no necessary correlation with sense-data; they are “realities” occurring within closed axiomatic systems. You can speak about them meaningfully and normatively only in the speech of mathematics. And that speech, beyond a fairly rudimentary plane, is not and cannot be verbal. (I have watched topologists, knowing no syllable of each other’s language, working effectively together at a blackboard in the silent speech common to their craft.)…It is arrogant, if not irresponsible, to invoke such basic notions in our present model of the universe as quanta, the indeterminacy principle, the relativity constant or the lack of parity in so-called weak interactions of atomic particles, if one cannot do so in the language appropriate to them – that is to say, in mathematical terms. Without it, such words are phantasms to deck out the pretence of philosophers of journalists. Because physics has had to borrow them from the vulgate, some of these words seem to retain a generalized meaning; they give a semblance of metaphor. But this is an illusion. When a critics seeks to apply the indeterminacy principle to his discussion of action painting or of the use of improvisation in certain contemporary music, he is not relating two spheres of expereience; he is merely talking nonsense.

–From George Steiner, Language and Silence (London: Faber & Faber, 1967), pp. 33-34

A quick disclaimer: I personally much prefer Steiner’s gracious delivery of points not dissimilar to those made by Wheen and Sokal (and let us not forget Jean Bricmont), as their approach can tend more toward tilting at windmills. I would also argue against the implication that the Chinese language is composed of “ideograms”, but that’s another story.

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