From Brass to Billions

Thread 1 The Machine

Two paths to take:

• Toward real LLMs: map each station to its production counterpart — subword tokenisation; embeddings as learned vectors; attention (the 2017 invention the cabinet can only pantomime); dozens of stacked layers; a softmax over the whole vocabulary; temperature sampling; autoregression with a KV-cache. Training is optimisation: predict, measure error, nudge billions of parameters by gradient descent, repeat at vast scale — code written by no one.
• Toward theory: the cabinet is a finite lookup table, computationally shallow; Babbage's Analytical Engine design, with branching and loops, was general-purpose — in principle Turing-complete a century early. The inversion: the Victorian paper machine is computationally stronger than our working brass one.

Thread 2 The Mathematics

Give the full formulas (the About page derives them): interpolated estimation P(w|a,b) ∝ λ₃P₃ + λ₂P₂ + λ₁P₁ with λ = 0.72 / 0.21 / 0.07; temperature q ∝ P^(1/T); inverse-CDF sampling. Two extensions worthy of seniors:

And the Markov property's failure: a three-word memory cannot close a quotation mark opened ten words ago, cannot keep a subject and its distant verb in agreement — and that inadequacy is precisely the problem attention was invented to solve. The math narrative has an arc: counting → conditioning → smoothing → its limits → the modern solution.

Thread 3 The True History

Seniors can handle historiography. How much of Note G is Lovelace and how much Babbage remains genuinely contested — the Bernoulli program was worked out in correspondence with him; the visionary prose of the Notes is hers; both hagiography and dismissal are errors, and weighing evidence about a 180-year-old collaboration is itself the lesson. Add the sobering thread: the engines' direct influence on modern computing was slight — Turing and von Neumann built on logic, not on Babbage's drawings, and the line from brass to silicon is more prophecy rediscovered than unbroken inheritance (Howard Aiken of the Harvard Mark I being the notable exception who invoked Babbage directly). The 1991 Difference Engine No. 2 build is worth presenting as experimental archaeology: a hypothesis about the past, tested in five tonnes of bronze and iron, confirmed.

Thread 4 Can a Machine Think?

A four-stop seminar arc, with the cabinet as the shared intuition pump:

1. Lovelace (1843): the objection above — mechanism without origination.
2. Turing (1950): answers "Lady Lovelace's Objection" by name — the surprise reply and the learning-machines reply; his reduction of "can machines think?" to the imitation game.
3. Searle (1980): the Chinese Room — flawless symbol manipulation without understanding. Note that everyone agrees about the cabinet: it manipulates symbols and understands nothing. The dispute is whether scale changes the verdict.
4. The present: "stochastic parrots" versus emergent-capability arguments — is a large model still the cabinet, only bigger, or does quantity become quality?

Close with authorship: when the engine mints a sentence no one has ever written, who wrote it — Babbage's ghost, the 79 sentences' authors, the dice, no one? The question is live in copyright law and AI policy right now; your students will vote on it in earnest within the decade.

Thread 5 At the Cabinet

• Read the source, then rebuild it. The whole engine is one commented HTML file. Implement the trigram model in ~30 lines of Python; reproduce the gauges' numbers exactly; then improve it (4-grams? different λ?) and report what changed.
• Entropy lab. Compute H from the gauges at five temperatures; plot H(T); connect the curve to the frost/fever behaviour observed in actual outputs.
• Cabinet vs. frontier. Same prompt to the ILM and to a modern LLM; catalogue the differences and explain each mechanistically (vocabulary size, context length, learned representations), not magically.
• Seminar paper. 1,500 words on the Lovelace objection today, citing Note G, Turing 1950, Searle 1980, and one contemporary source — with the cabinet as the running example.