Comic Discussion > QUESTIONABLE CONTENT
WCDT: 18-22 Oct 2010 (1776-1780)
peterh:
--- Quote from: Skewbrow on 23 Oct 2010, 01:34 ---Of course, those results do use a precise definition of an algorithm (something that can be carried out by a Turing machine).
--- End quote ---
I think... no, wait. I *feel* that this somehow points to a pitfall in our reasoning.
Maybe there was a reason why Edsger Dijkstra painted "Touring Machine" on the side of his camper van - which he used when he went on a lateral thinking session.
Then again, maybe he was just being facetious. But he might have been onto something.
Near Lurker:
--- Quote from: Skewbrow on 23 Oct 2010, 12:49 ---:-) Mathematicians/theoretical computer scientists use the word "Turing machine" because it has a precise definition, whereas the word "computer" has not. This is obviously necessary in order to say something precise about the capabilities of a device. I used it here so that eventual interested folks (if any?) can use it as a buzzword when searching for more information (and in order not to say something untrue). However, I'm under the impression that all current computers could (in theory) be emulated by a Turing machine, so the concept is not without practical merit. For any real work a Turing machine would be awfully clumsy, because the computers have useful add-ons like user interfaces and dedicated circuitry for frequently occuring tasks, but the range of tractable problems is the same (if the computer had access to unlimited amounts of memory).
--- End quote ---
The big difference between a real computer and a Turing machine is that a Turing machine is stuck with the input it starts with, whereas a real computer can take new input between steps. What a computer actually does with this input can be described with a Turing machine, but - and here's the catch - there's no reason at all the human brain can't be considered the same way. After all, the Turing machine was originally intended to model the human brain. The human brain may act randomly, but why can't a computer act randomly? Sure, pseudorandom numbers are just that, but if you ask a human to give you a random sequence, you'll get much worse than the worst professional pseudorandom number generator. The actions of the human brain seem more random because they rely on environmental input, as a computer well might. The physical growth of the human brain is no different from a computer modifying itself based on external seeds.
--- Quote from: peterh on 23 Oct 2010, 15:12 ---
--- Quote from: Skewbrow on 23 Oct 2010, 01:34 ---Of course, those results do use a precise definition of an algorithm (something that can be carried out by a Turing machine).
--- End quote ---
I think... no, wait. I *feel* that this somehow points to a pitfall in our reasoning.
Maybe there was a reason why Edsger Dijkstra painted "Touring Machine" on the side of his camper van - which he used when he went on a lateral thinking session.
Then again, maybe he was just being facetious. But he might have been onto something.
--- End quote ---
It's long since been shown mathematically that a Turing machine can be constructed for anything expressible in Church's lambda-calculus, which is effectively the definition of a precise description of an algorithm. "Lateral thinking" is just randomized approximation by another name.
jwhouk:
:? :-o
TL;DR.
:wink:
Skewbrow:
--- Quote from: Carl-E on 23 Oct 2010, 14:32 ---
--- Quote from: Skewbrow on 23 Oct 2010, 01:34 ---My math PhD is in rather different area...
--- End quote ---
Wait, how many mathemeticians are on this board?
And Skewbrow, what's your field? Mine's Knot Theory (classical dimensions), Indiana University, '95.
--- End quote ---
My PhD was in representation theory of algebraic groups. Notre Dame, '90. Since then I have drifted to applications of algebra into telecommunications problems: mostly coding theory.
Sorry, can't say I would know much about knot theory. I spent the few months after graduation (and before my student visa expired) at MSRI (also accompanied by my wife and unborn son). Jones had just won the Fields medal, so when he was giving a talk at Berkeley, all of the MSRI gang showed up, of course. It was a memorable moment, when the head of the department introduced Jones as "our latest Fields medalist".
peterh:
--- Quote from: Near Lurker on 23 Oct 2010, 17:52 ---It's long since been shown mathematically that a Turing machine can be constructed for anything expressible in Church's lambda-calculus, which is effectively the definition of a precise description of an algorithm. "Lateral thinking" is just randomized approximation by another name.
--- End quote ---
The difference being that the human brain has come up with quite a bit more interesting results using lateral thinking than any machine has managed to using random approximation.
I'll have to do some thinking and reading on this, but the difference may well lie in the direction of valuing seemingly random results.
How do we get a machine to actually like a result, or find it interesting?
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