Hypercomputation: Computing more than the Turing machine (2002)

Re:Hypercomputation: Computing more than the Turing machine ... by eighthnate on Monday September 11, 2017 @02:20PM (#15220794)

That's the accepted theory for sure. It's what every CS student learns.

But never say never. "Reality/logic/math" can be a lot stranger than you think.

There used to be a time when we thought that infinity ( aka countable infinity ) was the largest number. Turns how there are bigger infinities.

And of course quantum mechanics. The duality of light ( both a wave and a particle ).

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Re:Hypercomputation: Computing more than the Turing machine ... by trishankkarthik on Monday September 11, 2017 @02:30PM (#15220867)

But never say never. "Reality/logic/math" can be a lot stranger than you think.

I understand it's a Black Swan kind of problem, but I don't think we live in that reality. Please show me a contradiction. The ramifications would be stupendous, to say the least.

There used to be a time when we thought that infinity ( aka countable infinity ) was the largest number. Turns how there are bigger infinities.

Yes, and we know how to build Turing machines that use countable infinity. Please show me a machine that actually uses bigger infinities. Please hypercompute the digits of a real number that cannot be computed by a Turing machine.

And of course quantum mechanics. The duality of light ( both a wave and a particle ).

Universal quantum computers are faster than classical computers, but they are no more powerful (they are not known to be able to hypercompute).

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Re:Hypercomputation: Computing more than the Turing machine ... by eighthnate on Monday September 11, 2017 @02:36PM (#15220928)

Why are you getting defensive? I agree with you more or less. All I said was reality can be stranger than we initially believed possible and showed you examples in other fields ( math, physics ) where "reality" got turned upside down.

Computer science is a fairly new field. It's within the realm of possibility that reality can be turned upside too. I'm not said it is or will be, but it can. Okay?

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Re:Hypercomputation: Computing more than the Turing machine ... by trishankkarthik on Monday September 11, 2017 @02:43PM (#15221009)

I'm not getting defensive, my friend. I was merely challenging you to think through the logical implications of hypercomputation. What many people miss is this: hypercomputation leads to living paradoxes. They might then have to bend over backwards to explain why these paradoxes are not possible, but that leaves the question of why some things are hypercomputable, and some are not.

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Re:Hypercomputation: Computing more than the Turing machine ... by eighthnate on Monday September 11, 2017 @02:52PM (#15221110)

I wasn't even talking about hypercomputation specifically. I was talking more in generalities about computer science and things we hold to be "reality/absolutes".

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