Indexing the archive…
Your Universe of Digital Possibilities
Slide a heavy block into a light one against a wall and count the clacks: mass ratio 1 gives 3, a hundred gives 31, a million gives 3141 — the collisions are computing π (Galperin, 2003). No circle is anywhere in the apparatus; it hides in phase space, where energy conservation bends the state onto a circle and every collision advances it by the same angle. The dumbest experiment on the rack is an algorithm.
Two conservation laws — momentum and energy — pin the outcome of a head-on elastic collision completely: no fitting, no friction, no choice. Huygens settled the rule in 1669; every clack in this instrument is this one line, applied exactly.
Rescale each velocity by the square root of its mass and energy conservation draws a circle; momentum conservation draws a line. Every collision is then a reflection — the messy clatter of blocks becomes a polygon of equal chords inscribed in one circle.
Each clack turns the state around the circle by the same angle 2θ, so the total count is how many fit in a half-turn: π/θ. Set the mass ratio to 100^(d−1) and θ ≈ 10^(1−d) radians — and the count spells the first d digits of π.
Brown (2019) showed the blocks arequantum search: their phase point turns by 2θ per clack exactly as Grover’s state turns by 2θ per query, and both stop after ⌊π/θ⌋-ish steps. The Search’s speedup, clacking on a desk.
This is the rack’s bluntest case of dynamics running a computation. The apparatus is The Arrow’s gas cut down to two particles — and with so few degrees of freedom, mechanics stops being heat and becomes arithmetic. With The Billiard it forms the Elias pair: unfold these collisions and they area billiard in a wedge of angle θ, the bounce count a geometry fact. And the hidden circle is the reveal — the same phase-space geometry that turns Grover’s search in The Search, discovered clacking in wood.