Is There Anything Beyond Quantum Computing? • Hacker News Board

Re: Is There Anything Beyond Quantum Computing?

#41

Post by DennisP » Sat, Apr 12, 2014, 3:11 PM UTC

saalweachter wrote: post #40

Hah. So Roger Penrose, not content with the now-seemingly-attainable quantum computing, speculates there is an even more magical quantum gravity computing, which brains just happen to use, that makes them special, that Turing machines can't compute? The man just really hates the idea of AI, doesn't he?

That's nothing new for Penrose, he wrote about it in Emperor's New Mind. His whole argument is based on noncomputability, and he points out in the book that ordinary quantum computers can't do the noncomputable.

And of course if he were right and we did figure out the physics of it, there'd be nothing to prevent us from building hardware that uses the same physics.

Re: Is There Anything Beyond Quantum Computing?

#42

Post by wfo » Sun, Apr 13, 2014, 7:38 PM UTC

sp332 wrote: post #30

adamtj wrote: post #29

Earlier quoted context omitted.

Actually, no. I just recently read about this. 1 + omega == omega http://en.wikipedia.org/wiki/Ordinal_number

Weird! Thanks for the link!

Actually you are both right -- omega and omega + 1 (or omega^2) have the same 'number' of elements (there is a one to one correspondence) but the correspondence will not be (can not be) order-preserving. Ordinals are a natural extension of the natural numbers. If you take the natural numbers and add a new element that's bigger than all of them then you get a new structure (called omega + 1) which has the same size as the normal natural numbers, but has one new element which is order-distinguishable from all our normal numbers. Some ordinals, which correspond to a jump in 'size' (like 2^omega) are special and called cardinal numbers.

Re: Is There Anything Beyond Quantum Computing?

#43

Post by noselasd » Sun, Apr 13, 2014, 8:11 PM UTC

rhth54656 wrote: post #17

But the more you accelerate the spaceship, the more energy you need, with the energy diverging to infinity as your speed approaches that of light. At some point, your spaceship will become so energetic that it, too, will collapse into to a black hole. That is simply wrong. It is called relativity for a reason. An object might be traveling arbitrarily fast, but in its reference frame it is not moving. That pretty much…

Only the black hole part. As speed increases, mass increases too - and mass is energy. (Which is also why we can't have (anywhere) near speed light space travel, there's not enough energy anywhere to maintain accelerating the increasing mass)

Re: Is There Anything Beyond Quantum Computing?

#44

Post by 3rd3 » Tue, Apr 22, 2014, 5:11 PM UTC

3rd3 wrote: post #39

klodolph wrote: post #38

Earlier quoted context omitted.

No. The line of thinking is, "Well, if we had real numbers, we could compute uncomputable functions." No shit. Most real numbers are not computable. If you start with something not computable, you end up with something not computable. The big problem is that there is no way you will get more than several digits of precision on anything. The next problem is that there's zero evidence that anything in the universe is c…

How I understood it, and please correct me if i am wrong, is that a machine than can caluclate numbers with infinite precision in constant time has certainly a time benefit, but not necessarily a broader class of computable functions compared to a Turing machine. I interpreted z3phyr’s reference to Wikipedia as a hint to that idea. But I agree that the most convincing arguments are against the existence of such a mac…

Oops, sorry for this comment. ("don't drink and internet")