Search Ideas

Reality is a multiverse, as Everett’s theory says, and single-particle interference shows it. Photons sent through slits one at a time stop reaching some places when more slits are open, so something coming through the other slits interferes with them: shadow photons, which are the photons of other universes. Every kind of particle has such counterparts, and they make up a huge number of universes like ours.

Quantum errors can be corrected faster than they arise, as long as each step errs less often than a certain threshold. Nest codes inside codes, and a quantum computation can run as long as needed, as accurately as wanted.

Error correction can’t save a quantum computer in practice. It needs many more qubits and steps, each of which errs too, and the large entangled states it relies on are extremely fragile, so it would add errors faster than it removes them.

A quantum computer could factor numbers hundreds of digits long in hours, by finding how often the remainders of a number’s powers repeat. That would break the codes that protect most of the internet’s secrets, which rely on factoring being too hard.

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.

A classical computer can’t simulate quantum physics efficiently: the numbers it needs double with every particle added, so a few hundred particles would take more numbers than there are atoms in the universe. To simulate nature, build a computer of quantum parts that behaves as nature does.

A computer can run by the laws of quantum mechanics alone. A Turing machine can be built of quantum parts that carry it through its steps one after another, as an isolated system, without losing energy.

Guinea pigs breathing air from a tuberculosis ward caught the disease. With ultraviolet light killing the germs in the same air, they didn’t. It’s the germs in the air that spread disease, not the air itself.

Germs cause infectious diseases, and they pass from one person to the next by touch, in water or food, and through the air, on droplets so small that they float. Tuberculosis spreads that way.

Then the test needs tightening: put the competitors in a telepathy-proof room.

That confuses rules of conduct, which we can know and act on, with laws of behavior, the laws of nature that govern our bodies. We can be sure there are no complete rules of conduct, but never that there are no complete laws of behavior: we can never say we’ve searched enough. Even a small program of mine on the Manchester computer can’t be predicted from its replies.

A discrete-state machine is different from a continuous one, but in the imitation game, the interrogator can’t take advantage of the difference. A digital computer couldn’t predict exactly what a continuous machine, like a differential analyzer, would answer, but it could give the right sort of answer.

No support is usually offered for these claims. They generalize from the machines people have seen, which are ugly, each built for a narrow purpose, and able to do little else. Many of those limits come from their tiny memories, and computers’ memories are growing.

Then the only way to be sure that a machine thinks is to be the machine, and the only way to know that a man thinks is to be that man. That’s solipsism. Instead of arguing over it, we have the polite convention that everyone thinks. And if a machine could defend its sonnet’s wording under questioning as well as a person can, I don’t think anyone would call that an easy contrivance.

That the human mind has no such limits has only been stated, without any sort of proof. We give wrong answers too often ourselves to be pleased at the machines’ fallibility. And there may be people cleverer than any given machine, but then there may be other machines cleverer again.

That’s a hope, not an argument, and it isn’t substantial enough to require refutation. Consolation would be more appropriate.

That restricts the omnipotence of the Almighty. Couldn’t He confer a soul on an elephant, or on a machine, if He saw fit? Besides, theological arguments have often failed before: in Galileo’s time, Bible verses were held to refute Copernicus.

Machines take me by surprise with great frequency. To think that nothing new can come from following given rules is to assume that as soon as we know a fact, all its consequences spring to mind at once. They don’t: working them out is real work.

A machine can be made to learn. Instead of programming it to act like an adult mind, program it like a child’s, and educate it. Its teachers won’t know quite what is going on inside it, so it won’t only do what we know how to order it to do.

Machines will be able to think. The question “Can machines think?” is too meaningless to deserve discussion as it stands. Ask instead whether a machine can play the imitation game, passing for a person in typed conversation. In about fifty years, computers will play it so well that an average interrogator won’t have more than a 70 percent chance of telling them apart after five minutes of questioning, and one will be able to speak of machines thinking without expecting to be contradicted.

No machine can decide, for every statement of logic, whether it can be proved. If one could, it could decide whether any machine ever prints a 0, and a machine that asked it that about itself could be made to do the opposite.

Some problems can’t be solved by any effective calculation: I’ve found one in elementary number theory. So no mechanical procedure can decide, for every statement of logic, whether it can be proved.

General relativity can’t be the whole truth about gravity. Together with quantum theory, it implies that gravity can’t be measured precisely in tiny regions of space. So the smooth spacetime of general relativity must break down there.

Truth for a language rich enough for arithmetic can be defined only in a richer language, never within the language itself. So no one system of symbols and rules can even say which of its own statements are true: there’s no universal criterion of truth.

In any consistent system of rules strong enough for arithmetic, there are true statements that the rules can neither prove nor disprove. So no one system can answer every question of mathematics.