Sermo Interruptus

(originally a 3-part post)

A student wrote, on the course evaluation for my class on evidence and inference, “Regurgitation is not learning. That is what we have ChatGPT for” – referring to all the things I expect students to know for (and yes, be able to regurgitate on) the final exam. This seems to equate knowing how to find a fact with knowing the fact itself, as if the former could substitute for the latter. It’s a signature mistake of our (AI) age. Knowing something means having it reside in consciousness, or so close at hand that it can appear in consciousness unbidden. Knowing where one can go for information is different: accessing that information requires conscious effort, and the less one knows about a topic to start with, the harder it will be to learn it, even with AI help, and many people won’t bother.

I think, in a way, we’ve created this problem for ourselves, in emphasizing critical thinking as the goal of education, especially in the social sciences and humanities. The idea, obviously, is that even when a course’s content drains away, or is gleefully evacuated from the airlock, something will be left behind: the ability to spot faulty reasoning, unstated assumptions, etc. I hope that’s true, and I do a lot to cultivate this (albeit not through the mechanism of the final exam), but it devalues the contents of consciousness. David Chalmers famously said that the “hard problem” of consciousness is that there are subjective experiences, or the feeling of being “inside.” Things we know are on the inside with us, and consciousness is enriched by that, and impoverished inasmuch as we empty our minds of everything except how to engineer a good AI prompt. (Meditators might disagree, but few actually aim for a lifetime of emptiness.)

Here’s something I want my students to memorize: Euclid’s proof for the infinite number of prime numbers. A prime number is any number that can only be divided by itself and one without remainder. Nine is not a prime number because it can be divided by three, which is prime. Eleven is prime. Prime  numbers are important to cryptography and if aliens ever communicate with us there’s a good chance they’ll use prime numbers to do so.

As few of my students are likely to get a phone call from aliens and encryption is handled for us by computers, why do students need to know this proof? The reason is that it’s simple and easy to learn, and plants in their minds an extremely important insight, that a non-trivial truth can be decisively proven, for all time and throughout the universe. To know that such a truth exists and could be found online is different than seeing it from the inside, which affords you the personal experience of certainty, of knowing that you know, and leaves no doubt that when mathematicians say “prove” they mean much more than “pretty firmly demonstrate,” which is colloquial. It’s a worthy addition to a well-furnished consciousness, especially as it’s a representative of a large number of such proofs, some of them vastly more complicated.

Another thing I require my students to know is the cosmic distance ladder, and specifically stellar parallax and spectroscopic parallax. These are the methods used to infer the distance to faraway stars, building on prior knowledge, particularly the distance from the Earth to the sun, trigonometry, the way that light diffuses through three-dimensional space, and the well-established relationship between a star’s light output and its color.

My students are in in the School of Arts & Letters, which means they’ve mostly forsworn math and science careers, so it is undoubtedly nervy of me to require that they learn this. What’s the point? Discoveries that presuppose and build on earlier discoveries are ubiquitous in all of the empirical disciplines, central to knowing how we know almost anything that we can’t deduce or witness directly. That includes basically all knowledge that relies upon instrumentation, like telescopes, particle accelerators, and fMRIs. But why do students have to learn the details? The reason is that there’s a large chasm between being willing to affirm that some techniques of discovery build upon earlier discoveries and seeing exactly how this happens in a particular instance. That is, there’s a difference between knowing something is true in the sense of having been told it and being willing to assert it on an exam, and knowing it is true because you’ve directly encountered and discerned the logical connections. Of course, students can try to simply memorize the words that express the details, but that’s not a very good workaround, because brute memorization is hard, because without genuine understanding you can’t judge whether you’ve chosen the right words, and because this amounts to an end run around the actual learning that is surely one goal of higher education.