[Bobboau]

I think so.

I am not claiming Turing equivalence.

[Phantom Hoover]

No: the proof is trivial. Turing-completeness requires infinite storage capacity and running time; if you're going to argue the human brain has either... well, I don't really know what to say.

[Scourge of Ages]

[The E]

No: the proof is trivial. Turing-completeness requires infinite storage capacity and running time; if you're going to argue the human brain has either... well, I don't really know what to say.

If you're using the pedantic version of testing for Turing completeness, that is. Then, no machine ever built will be Turing-complete, ever; That's not a useful basis for discussing this.

Now, personally, while I am pretty sure the brain can model a Turing machine, that's not what it's made for (or, for that matter, something it is particularly good at).

[Kopachris]

Some say his brain is Turing-complete

[Bobboau]

No: the proof is trivial. Turing-completeness requires infinite storage capacity and running time; if you're going to argue the human brain has either... well, I don't really know what to say.

the brain is capable of acquiring an effectively unlimited amount of external storage from which to offload data storage onto, you may say that this doesn't count, but I think that the ability to augment it's own capabilities should entitle it to the fruits of that augmentation. in addition human brains are capable of transferring their state of operation on a given problem from one to another, allowing an effectivly infinite amount of  time to work on a given problem.

however, I believe the infinites are not requirements of a Turing machine, rather this is a quality of a Turing Oracle, if given these resources the machine would have certain additional qualities, qualities that I think the human brain would have if given those resources.

Now, personally, while I am pretty sure the brain can model a Turing machine, that's not what it's made for (or, for that matter, something it is particularly good at).

If it is capable of modeling a Turing Machine, then it is capable of performing all of the operations of a Turing Machine. If it is capable of performing the operations of a Turing machine it is a Turing complete by definition.

[General Battuta]

imo, yes

[Phantom Hoover]

No: the proof is trivial. Turing-completeness requires infinite storage capacity and running time; if you're going to argue the human brain has either... well, I don't really know what to say.

If you're using the pedantic version of testing for Turing completeness, that is. Then, no machine ever built will be Turing-complete, ever; That's not a useful basis for discussing this.

'pedantic', as in the only meaning of Turing completeness that makes sense. You know what a Turing machine is, formally? A bog-standard finite-state machine, with an infinite tape for storage. Generally when one speaks about some computational system being 'Turing complete' one means that it has no 'specified' limit to its memory; but the human brain isn't defined as an abstract system, it's a physical entity which can't really be extended past what it already is.

[Bobboau]

so the human brain cannot interact via its connected peripherals with the physical world and construct or acquire external storage that it can then offload any extra data?

[Phantom Hoover]

Sure, give a human an interface to an infinite tape (and eternal life) and they can very easily emulate a Turing machine. But so can a finite state machine, or any number of other very simple computational systems. That's not saying much.

however, I believe the infinites are not requirements of a Turing machine, rather this is a quality of a Turing Oracle, if given these resources the machine would have certain additional qualities, qualities that I think the human brain would have if given those resources.

The term 'Turing oracle' refers very specifically to a hypothetical machine which could solve the halting problem for an arbitrary Turing machine, not to a TM with infinite tape or running time or whatever.

[Bobboau]

ok, fine, but this is irrelevant, The question is not is the human brain a Turing Machine, but is it Turing Complete?
yes I did stumble over the difference there myself.

[Phantom Hoover]

And as I said at the start of the thread, it's very definitely not Turing complete. Not all Turing machines can be emulated by the human brain.

[AdmiralRalwood]

Not all Turing machines can be emulated by the human brain.

Oh really? Provide an example.

[Phantom Hoover]

Just pick a Turing machine which has... hmm, I think as many distinct states in its control machine as there are atoms in the universe should do it.

[Nuke]

a brain is essentially a neural network which is fundamentally a completely different device from a computer. its a comparison i like to avoid (really, how many 32-bit flops can you do a second? its probibly not a whole number). turing complete just means it has memory. its true that there is in fact no such thing as a true turing machine, it is an ideal concept that can never be fully attained. memories will always be finite, even yours. human memory is a very fuzzy concept, given the nature of nerual networks. if the brain was a turing machine: you would only store a fraction of write operations, read operations would only return useful information sometimes, and when you do shifts you sometimes give random integers. needless to say your brain wont be passing memtest86 any time soon.

[Polpolion]

turing complete just means it has memory.

Tape-capable memory, specifically. For example if all you have is a stack you really just have a pushdown automaton, which are not as capable as turing machines. Anyway, I think you guys are all completely missing the point of turing completeness. Languages can be turing complete, things cannot.

[Nuke]

memory performs the same job regardless of dimensionality. whether it be a serial eeprom, dram (and its damn columns and rows), and sram (linear address space), or some block based format like flash, then you got potential for 3 dimentional storage in a holographic medium. we might even eventually use storage in more than 4 dimensions if certain quantum theories are found to be accurate. a turing machine is more or less a though experiment to describe the basic functionality of a memory system. sure there are some rudimentary memory systems (tape, delay lines, etc) that take the concept literally, but pretty much all of those are slow dead ends. multidimensional systems are actually preferable because they greatly shorten distance signals must travel. the only way to get better latency is make the memory really dense.

[AdmiralRalwood]

Just pick a Turing machine which has... hmm, I think as many distinct states in its control machine as there are atoms in the universe should do it.

So nothing is Turing-complete, rendering the word meaningless. What a useful definition.

[Phantom Hoover]

Duh, it's a mathematical ideal, not a physical classification. You might as well call the idea of a square meaningless because you can never have a shape with perfectly straight sides.

[pecenipicek]

The term 'Turing oracle' refers very specifically to a hypothetical machine which could solve the halting problem for an arbitrary Turing machine, not to a TM with infinite tape or running time or whatever.

Dont our brains solve that particular bit of logic with going "maybe" and rolling with it?


[/half-joke]