When, and why
We take a tired cliché seriously.
Last week we mentioned that one of our consultants was in the process of rereading one of his old textbooks, and that he had found it was out of date in places. That is, there had been progress in the field (Physical Chemistry) since he took the class, and some updating was in order. That brought to mind the claim sometimes found in popular science news articles that “this means they’ll have to rewrite the textbooks.” The implication is that science, as taught up to now, is either wrong or at least seriously incomplete. We can’t recall seeing this cliché recently, which may mean even the journalists have found it tired; but may only mean our reading habits have changed over time. What would it actually take to “rewrite the textbooks?” Well, it depends on which subject, and what level, and why.
We think mathematics textbooks, up through the introductory college level at least, are pretty safe. Algebra, Geometry and Calculus are sufficiently well-defined and rigorously established that no surprises can be expected from them. Number theory, which is not included at a very high level in the current curriculum, sprang the last big surprise when Fermat’s Last Theorem was finally proved. However, the actual proof required math far beyond what most college students would ever see; so the rewriting would just change “Fermat’s Last Theorem has never been proved” to “After 358 years, Fermat’s Last Theorem was finally proved, but we cannot present the proof here.”
That’s not to say that present-day textbooks are identical to those of our youth. There is a great difference in presentation, in graphics and in pedagogy. And there is a subtle difference in subject matter. We find Algebra 2 students doing least-squares fits to data, and Calculus students working out approximate Riemann sums. These would have been impossibly tedious before calculators, a matter for specialists, those with a tolerance for columns of numbers unusual in the general populace. The textbooks have indeed been rewritten, but (we contend) not in the sense of the cliché.
But the advent of digital computers does lead us to a proper rewriting. As we noted, calculations in Physical Chemistry that were unsatisfying and approximate in the Old Days are now feasible and accurate. It is less that the former answers were wrong, than that they were inaccurate in detail (and known to be so); we now have better answers, and more reliable ones. And the related improvement in instrumentation has filled in great areas of ignorance.
The digital revolution has been nowhere more important than in Astronomy. The shift from the photographic plate and the analog computer to the CCD and the digital one has indeed transformed the science. Again, it’s not that the old answers were wrong, but that vast areas of ignorance have been filled in with precise detail.
We’re not going to say much about Biology, a field in which we have no particular expertise. But we have observed enough of the fireworks across the way, from the Genetics faculty alone, to conclude that they have left the Astronomy revolution in the dust.
It appears that “rewriting the textbooks” nowadays is not (for instance) the throwing out of the Artistotelian picture for the Galilean, but the colonization of new areas, hitherto inaccessible. Or is this an illusion, and we’re overdue for a upending of everything?
