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Your Universe of Digital Possibilities
A small wheel resting on a spinning disk turns at a speed set by how far it sits from the centre — so its shaft adds up the radius against the disk: an integral. James Thomson put the principle to work in 1876 (with a ball between disk and cylinder); his brother, Lord Kelvin, saw that integrators feeding each other could solve a differential equation; Vannevar Bush made it work at MIT in 1931, with wheels on disks like these. Wire the shafts, run the machine, and watch a pen draw the answer — and the auditor price every creep of every wheel.
A wheel resting on a turning disk at distance y from its centre is dragged round at y times the disk’s speed, so its shaft turns by the running integral of y against the disk’s rotation x. The radius is the integrand, the disk is the variable, the wheel is the answer.
Feed the second integrator’s output back, reversed, into the first one’s lead screw, and the shafts can only turn in the ratio the equation allows: y and v trace a circle. The machine does not compute the solution — the solution is the only motion it has.
The fourth Heron machine turns the planimeter’s wheel into a component. Thomson’s integrator keeps the running sum that Amsler’s wheel only reported at the end; couple two outputs back into two inputs and the shafts can only move in ways that obey y″ = −ω²y. The equation is not computed — it is the only motion the wiring allows, and the pen draws it. What the auditor finds is the price of friction: creep, phase lag and an opening circle, fixed by an amplifier. The planimeter’s wheel is in The Planimeter; the feedback that made engines self-correcting — and sometimes hunt — is The Governor, and the harmonic analyzer Kelvin built from the same integrators to predict tides belongs beside The Spectrum.