The Information Density of Old Textbooks

There’s a YouTube short making the rounds about how textbooks seem to have been dumbed down:

The upshot seems to be that the venerated classic textbooks of yesteryear — e.g. Thomas’ Calculus and Analytic Geometry; 2nd ed. (~1958) — got to the heart of the matter much more directly than do the bloated, ridiculously-expensive textbooks of the present moment e.g. Stewart’s Calculus. The elder tome covered the derivative about page 24; the latter finally gets there on page 144.

Being a connoisseur of textbooks, and having even bought several ancient ones for my own personal library, I fully agree, and I note that the essential difference is that the authors of older textbooks expected their starter ideas, their directional notions, their dashed and incomplete lines to be finished as part of the reading of the book by the student.

They left the dehydrated granules of knowledge with an eye-dropper of water. They expected the rest of the bulk to be rehydrated by the sweat of the eager learner’s brow.

In an age where attention is fought for against phones; in an age where any resistance or friction summons desk-side genies of the LLM companies, these books are a rebellious, challenging throwback. And they might be a way to get learning back in the classroom. If you have to complete the connect-the-dots (even with the help of an LLM), you’re still connecting the dots and participating instead of consuming. And that may make all the difference in terms of synthesis and retention.

Three examples after the jump.

Philosophy in 1998

In fall 1998 I returned from a year of study abroad to continue my progress on my degree in philosophy. I had been greatly interested in symbolic logic the Fall before my departure, so on my return it seemed sensible enough to sign up for Philosophy 344K, “Intermediate Symbolic Logic.”

The catalog copy reads:

…A second-semester course in symbolic logic: formal syntax and semantics, basic metatheory (soundness, completeness, compactness, and the Loewenheim-Skolem theorem), and further topics in logic. Three lecture hours a week for one semester. Prerequisite: Philosophy 313, 313K, or 313Q.

The source book for this course — Herbert Enderton’s A Mathematical Introduction to Logic, first edition, 1972 — to my joy and my pocketbook’s joy, when I went to purchase it at the university co-op, was shockingly thin — no more than two hundred fifty pages, quarto size. I had never seen a textbook so small or so thin. Little did I know that little books are to be treated as little venomous serpents: to be approached only with great caution and great respect.

Opening that book was like opening a book into a universe I had never visited. The psis and existential qualifiers I knew had been replaced with a whole additional symbology of the arcane. Despite my sincerest efforts, the book (and the course) came to best me. I switched to German Idealism and have no regrets.

Logic in 1996

My introductory symbolic logic text, written by Irving Copi in 1954, worked similarly, but had entrance ramps to each chapter. On the other hand, I did have the brilliant Tracy Lupher as TA who helped me understand how to unpack Copi’s compressed lesson payloads.

The contents were small, intense exercises, there was a quick reference to the fundamental operations of logic on the anterior and posterior covers, but otherwise the student was expected to hydrate the desiccated dust of expertise with the sweat of his own brow (or bitter tears, sometimes both) to render it into something that looks like a modern textbook.

Latin in 2009

I saw the same thing in my beloved Latin grammar, Allen and Greenough’s, first published in 1903. Stems and paradigms are given, but the exhaustive enumeration of every conjugation of every verb, every declension of every noun, is not. The student is assumed to find the paradigm and, by their own hand, their own ink, their own paper; they’re expected to extend the lessons themselves into the fully worked-out, hydrated textbook a modern student is simply handed.

The Modern Textbook

The modern textbook, as the short points out, hands you the graphs, the graphing-calculator exercises, the real-life high-speed photography of birds or plane wings — all of it already yoked to the beautifully inset formula draped atop the problem set.

McGraw-Hill or any of the publishers on Fifth avenue are justifying the bonkers bat-shit insane prices of these textbooks by providing all this watery fat around the essential core of the topics. They’re doing that to suggest value-add synergies and job-ready multi-disciplinary learning modalities. They’re selling hype.

These elder textbooks were thin. I suppose economics must have had a hand in the matter as well paper was expensive, so textbooks were built to be as dense as the printer could make them, leaving the reader to do the work of expanding a compressed lesson into full understanding. In this way, the high expectations blunted the high cost of the book in exchange for the student’s co-operation in the act of filling out the book — that is, learning. A few answers could be given, sure but the bulk of the material that the student learned from was co-created. Their notes, their copy books, their graph papers of botched parabolas were as essential to the elder textbook as is the modern textbook’s special insets for using your graphing calculator or writing the algorithm in Java.

But the elder books trusted us to grow, to learn to feel the force flowing through us as we grew to trust our lightsabers. The modern textbook is the trusty ol’ blaster.

Conclusion

I suppose the young commentator, in the new medium — the YouTube short — is noticing what I noticed about 12 years ago: The student isn’t asked to conjure the enrichment of the textbook themselves. In a world where we’re comfortable mowing Oregons of trees to create year-incompatible new editions of textbooks teaching transcendental truths (pi ain’t changed ever..), not serving students multiple demonstrations of problem solving at multiple tiers of difficulty is unthinkable — verily I say, unsellable. I suspect this has some pedagogical impact, and it isn’t limited to math or philosophy. I do wonder about the effect of that change — whether it enforces a kind of learned helplessness in students, taught to be governed by the tyranny of low expectations.

Perhaps the direction forward can and will be slimmer volumes, distributed electronically where learners’ LLM token budgets are used to hydrate the guild master’s lines into more fully-realized exemplars that the learners can take as foundation for their own studies. This seems better than the back-breaking textbooks of today and who knows — the kids might learn something.

• pedagogy
• philosophy
• nostalgia
• logic
• latin

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