At different times and for different reasons, famous, thoughtful people have said that the world is going to hell in a bucket. St. Augustine said it: The barbarians are at the gates, and we have allowed ourselves to be barbarized. Jules Verne, creator and avatar of sci-fi, said it in his last book, La Mission Barsac, when he allowed that not all inventions are beneficial. In 1900, historian Henry Adams, sitting in Washington across the street from the White House, said it. Dreaming of the mediaeval Virgin, he blamed our Descent to Avernus on her replacement by the dynamo. One or two generations later, our love affairs with the car and the TV have been cited as prime devils in our civilization of machinery. Mihai Nadin, a very verbal man and basically a semioticist, now a professor at the University of Wuppertal, worries about the kind of human product about to be produced by the recent rapid transition in the various modes of human communication. The "civilization of illiteracy" of his title refers to the replacement of books as the primary means of non-oral communication by all the stuff that's now around: fax, CD-ROM, videos, Web sites, icons for international travelers, talking automobiles, virtual reality, etc. "If you give someone a hammer, every problem looks like a nail" (page 283); Nadin's hammer is the decline and fall of the book. In a civilization that stresses speed and economy, Rudolf Flesch's 1955 book.
Why Johnny Can't Read would have to be replaced by "Why Teaching Johnny to Read Is No Longer Cost-Effective." Nadin is right to worry, of course. His many examples of what is now happening, running over practically the whole gamut of human experience, and his linguistic and semiotic interpretations, are in turn informative and eyebrow-raising, sometimes banal, sometimes funny, and not infrequently conjectural. Although he writes with considerable nostalgia about the civilization of literacy of which he is a product, he knows that it was not altogether peaches and cream. He knows about Mein Kampf and the horrendous damage it did (although he hardly talks about it). He knows about Das Kapital and its impossibly abstracted reconstruction of human nature. He quotes with approval Marshall McLuhan's view of our Western "alphabetic cultures" as having "uniformized, fragmented, and sequentialized the world, generating an excessive rationalism, nationalism and individualism." He notes the power and the efficiency of our new modes characterized by "the change from a literacy-oriented culture to a visually-oriented culture." And he suggests that our policy makers and our educators had better get off the old literacy kick and help retool our institutional thought to accommodate to the new realities, virtual or otherwise. Fairly free of professional jargon (though you may have to decide on every other page just what "human self-constitution" means and how the European-sounding "praxis" differs from "practice"), the many descriptions of what is going on at present can be read with the same ease and perverse enjoyment one experiences in reading popular books of the "USA Today" variety. Although formatted traditionally, this book strangely exhibits one of the sins of multimedia that its author decries, i.e., information overload. One book? Well, it's really five books, acknowledged as such by Nadin in his table of contents. It adds up to 880 pages of text and annotated bibliography, embracing language, logic, history, the visual, sexuality, religion, education, science and philosophy, politics, the economics of merchandising, the relation between Japanese and Western alphabets as reflected in the cooking of their respective cultures, and much, much more. I found that I couldn't embrace it all; I confess that I feel about this book the way Sydney Smith felt about a large woman-that one couldn't embrace her, one could only circumnavigate her. Nadin's fellow semioticist Umberto Eco wrote (in How to Travel with a Salmon), "The whole information industry runs the risk of no longer communicating anything because they tell too much." One wonders what strange compulsion led Nadin to take up his hammer and drive in every single nail.
From illiteracy to illiteracy in three generations, it would seem then, given that so-called universal literacy is scarcely a hundred years old. (My father and mother never read a book.) And literacy, in the narrow meaning of the word, may very well be headed right back to where it came from: a skill limited to a small, and hopefully happy, class of scholars and intellectuals. About which Nadin remarks, implicitly and sadly: Requiescat in pace.
What does all this have to do with mathematics? While the book does not pay much attention to mathematics as such, it does note that mathematics has developed its own super-unambiguous languages and that the computer derives in considerable measure from mathematical impulses, potentialities, and stringencies. So I should like to take off from Nadin and ask what mathematics might look like in an age of illiteracy. Start with communication. We have become our own typesetters and may shortly become our own publishers and jobbers. (Oh well, Tycho Brahe in 1597 lugged his own heavy printing press from Copenhagen to Prague when he took a job there.) We have become matheNETicians. Teachers? Built-in HELP statements, so it is said, can impart plug-and-chug mathematics far more efficiently than any human can. Journals? Who needs them now? One industrial researcher I know (prudently?) begins each task at his terminal, inquiring what is known about the mathematics relevant to his problem. When the mathematical data spot he interrogates (or visits, depending on the metaphor you prefer) finishes spewing out its raw, unassimilated information overload, my friend chokes and wonders whether he can afford to take the time to assess this material or should simply plow ahead on his own as best he can. These are some indications of how we now go about our business. But what really interests me is how, internally, conceptually, methodologically, mathematics might change in a civilization of illiteracy. We already have some important indications. Chaos theory has battened on-would hardly be possible without-computation. In fact, any decent scientific numerical calculation is a theorem that could hardly be derived and validated by other means. Computer proofs in geometry, via, for example, Grûbner bases, are all over the place. Despite these and other important developments, the answer to the question might be: No change, fundamentally. The production of new mathematics has always been in the hands of a very tiny and methodologically conservative elite. The tie-in between the old and the new remains substantial, the latter chewing on the rump of the former as nourishment. And to understand a new phenomenon still means to have an explanation along old symbolically deductive lines. But even elites are not islands unto themselves. Are really fundamental changes ahead for mathematics? Let me pick up on Nadin's "change to a visually-oriented culture." For some years I have been commenting on the fact that for two centuries mathematics has had harsh words to say about visual evidence. The French mathematicians around the time of Lagrange got rid of visual arguments in favor of the purely verbal-logical (analytic) arguments that they thought more secure. Proof in an increasingly logical and supposedly rigorous sense became the name of the game. Referring to the assertion that the left lobe of the brain is verbally and the right lobe visually oriented, I have characterized this kind of mathematics as "half-brained" and expressed the hope that perhaps we might redress the balance by acknowledging openly the existence of "visual theorems" whose theorematic content need not-in fact, could not-be expressed verbally (see, for example, Spirals: From Theodorus to Chaos, pages 225-228). In a totally different and somewhat frightening direction, we have today's mathematical concern with hermeticisms, apocalypses of various sorts: final theories of everything, secret messages hidden in the Bible, everything under the sun implied by Gûdel's Incompleteness Theorem. The marriage of literacy and rationality seems to be ending in divorce, as rationality shacks up with fanaticisms. Are these changes part of the breakdown of a literate civilization or merely the age-old and temporary concern that accompanies the arrival of a new millennium? We have today's ethno-mathematicians to thank for reminding us that different cultures, primitive and advanced, have had different takes on what mathematics is and how it should be pursued and valued. (Ancient Oriental mathematics, for example, was carried on in a proof-free manner. Indian mathematics expressed itself in verse.) Will a civilization of illiteracy compel a major paradigm shift in mathematics? Extrapolating from Nadin, one might conclude that such a shift might arrive sooner than I thought and perhaps more rapidly than is good for us.