A machine can carry out any calculation at all, however long. Punched cards tell it which operations to perform on which numbers. It keeps the numbers in a store, works on them in a mill, and chooses which cards to follow next by its own results.

The Analytical Engine needn’t stop at numbers. It works on symbols by rules, and symbols can stand for anything whose relations can be put into rules, like the notes of music. So it could compose music, or work in any field whose rules we can write down.

The Analytical Engine needn’t stop at numbers. It works on symbols by rules, and symbols can stand for anything whose relations can be put into rules, like the notes of music. So it could compose music, or work in any field whose rules we can write down.

Whatever a person can compute by following rules, a simple machine can compute, reading and writing symbols on a tape. And a single machine, given a description of any other on its tape, can do whatever that machine does: one universal machine can compute anything that can be computed at all.

Whatever a person can compute by following rules, a simple machine can compute, reading and writing symbols on a tape. And a single machine, given a description of any other on its tape, can do whatever that machine does: one universal machine can compute anything that can be computed at all.

Every physical system that can be built can be perfectly simulated by a universal computer working by finite means – but only by a quantum one. A universal quantum computer can do whatever any physical machine can do, and some things far faster than any classical computer could.