Computational Limits Quotes

Chess is far too complex to be definitively solved with any technology we can conceive of today. However, our looked-down-upon cousin, checkers, or draughts, suffered this fate quite recently thanks to the work of Jonathan Schaeffer at the University of Alberta and his unbeatable program Chinook.

Might we... be doing something with our brains that cannot be described in computational terms at all? How do our feelings of conscious awareness - of happiness, pain, love, aesthetic sensibility, will, understanding, etc. - fit into such a computational picture?

Some things, like the orbits of the planets, can be calculated far into the future. But that's atypical. In most contexts, there is a limit. Even the most fine-grained computation can only forecast British weather a few days ahead. There are limits to what can ever be learned about the future, however powerful computers become.

You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.

Man-made computers are limited in their performance by finite processing speed and memory. So, too, the cosmic computer is limited in power by its age and the finite speed of light.

One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.

A little-known truth: Every aspect of the world is fundamentally unpredictable. Computer scientists have long since proved this.

[With quantum computers] you can calculate how many bits are in the universe, how much energy it takes to flip them, how much energy exists, and use that to rule out lots of things about the universe's history. Anything that takes more bit flips couldn't have happened.

Computers are very powerful tools, but in the simulated world of the computer, everything has to be calculated.

If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.

Yeah, computers are going to take over the programming business because they have become so fast recently that they can solve the Halting Problem in five seconds flat.

There is no physical law precluding particles from being organised in ways that perform even more advanced computations than the arrangements of particles in human brains.

Electronic calculators can solve problems which the man who made them cannot solve; but no government-subsidized commission of engineers and physicists could create a worm.

If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.