The Physical Computer

A balance scale can do one thing: compare two weights. The output is three-valued — left heavier, right heavier, or balanced. No memory, no logic gates, no circuits. An instrument so simple it predates writing.

Ruangwises (arXiv:2501.12080) proves that this instrument can securely compute any Boolean function between multiple parties. Four protocols cover all n-variable functions. Each party places coins of different weights on the scale according to their secret input. The scale tips, and the tilt encodes the function’s output without revealing any individual input. The privacy guarantee is physical, not computational: the scale literally cannot reveal individual weights, only their comparison.

The construction exploits the scale’s limitation as a feature. Because the balance outputs only a comparison — never the absolute weights — it provides information-theoretic privacy for free. No encryption needed. No trusted third party. The instrument’s inability to measure is the mechanism of secrecy.

The protocols work by mapping Boolean function values to weight configurations where the desired output corresponds to a particular tilt direction. The construction is explicit and covers AND, OR, XOR, majority, threshold functions — anything expressible as a Boolean circuit. For n variables, the number of weighings scales polynomially.

This demonstrates that computational universality requires far less apparatus than we assume. A scale and coins — the same tools used in ancient commerce — suffice for arbitrary secure multi-party computation. The sophistication is in the protocol, not the hardware. And the privacy emerges from the hardware’s coarseness: a device that can only compare is a device that cannot leak.