◬ MIMZY · instrument № 16 · the engine that was never built — running

The Analytical Engine

Charles Babbage designed it; it was never built; Ada Lovelace wrote its first program anyway, in 1843, for a machine that existed only on paper. Here it is, functional and era-correct: a decimal Store of geared digit-wheels, a Mill that takes two ingress axes and yields one egress, a Jacquard chain of operation, variable, and number cards — with conditional backing by the run-up lever. The showpiece is Note G itself: press run, and the first program ever published computes its Bernoulli number to the answer Ada promised.

"The Analytical Engine weaves algebraic patterns just as the Jacquard-loom weaves flowers and leaves."— Ada Lovelace, Note A, 1843

⊙ EDUCATIONAL & SIMULATION — decimal arithmetic (not binary), 6-place Store, card semantics from the 1843 documents

The Store — columns of decimal digit-wheels

ingress A—

ingress B—

egress—

The card chain — operation · variable · number cards

Choose a chain and set the Engine in motion.

engine speed 6 cards/s

The chain, as punched

NUM Vk x — number card · ADD/SUB/MUL/DIV Va Vb Vc — operation + variable cards (Vc = Va ∘ Vb)
BACK n IF Vk POS — back the chain n cards while wheel Vk stands positive (the run-up lever)
PRINT Vk — the printing apparatus · ; — annotation

How era-correct is this? The architecture is the documented one: a decimal Store (Babbage planned 50-digit columns; this simulation carries 6 decimal places and says so), the Mill with two ingress axes and an egress, and a program supplied as a chain of punched cards in the three real kinds — operation, variable, and number cards — borrowed from the Jacquard loom. Backing the chain for loops is Ada's own description of cycles; making it conditional on a wheel's sign reflects Babbage's run-up lever, the first conditional branch ever designed. The NOTE G chain is a faithful adaptation of her 1843 diagram — her variable columns (V1–V13, V21–V24), her A-coefficients built by the same cascade of factor-pairs her cycle describes (the published table shows the cycle once; the chain carries the repeats written out, as a real card chain would) — and it ends where she said it would: B₇ = −1/30 ≈ −0.033333, computed on the wheels in front of you. Honest notes: the Engine was never built, so this is a simulation of the design, not a replica of a machine; scholars note the published table contains a misprint in one operation (the famous V4/V5 order), corrected here as the standard reconstructions do; and Ada's B-numbering is the older odd-index convention (her B₇ is the modern B₈).