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Re: Brainstorming about STEM (was About Functions)
Posted:
Dec 16, 2011 6:07 PM
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On Thu, Dec 15, 2011 at 10:40 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>It's not "guilty until proved innocent" i.e. it's not >necessarily up to Penrose to "prove" humans do >non-computable things, so much as up
>>to those who hold the reverse, that what humans do is >always computable.
>
> Nonsense! It was *you* who made the affirmative proclamation that humans perform these feats and they were "easy" to find examples thereof, now when I call you on it you slide into this position.
>
Huh? You didn't "call me" on anything. You asked for examples and I
gave them, citing talks Penrose gave in person, me in the audience.
I'm not "sliding" to any new position.
I'm asserting the obvious: those who think they might model humans on
the basis of computational processes have so far not produced, have no
evidence, haven't a leg to stand on. I wouldn't give them the time of
day on a normal day.
>>Qualified people" means nothing here really.
>
> Since I'm arguing with one who easily confuses solving chess problems with "non-computable" feats of derring-do, I'll have to concede that point.
>
The was Sir Roger's example, which I was dutifully citing from memory.
I wasn't "confusing" anything.
If we're doing argument from authority, I think Penrose is not just a
lightweight either.
Like the pawns were all lined up and it was easy to see that a rook...
anyway Deep Blue was stumped. Not hard to come up with puzzles no
computer can solve, proved theorems they can't prove (I gave the
example of Von Staudt for V + F = E + 2).
A "chess puzzle" may be analogized to a proof.
Automation of proving is not hugely impressive (to say the least) yet
TV shows like NUMB3RS seem to suggest superpowers, on the part of both
mathematicians (e.g. the star), and the computers they work with
("computer: Earl Gray Hot" -- to quote Picard).
AI people have been engaged in conspicuous self-promotion for decades
and now we're all trying to "disprove" that they haven't already
achieved their goal. Somehow, a fool's errand became a fait accompli.
Nice hat trick.
> But I'll reiterate that granting "there are things that humans do that are a mystery and a wonder" does not lead to therefore "they are in principle non-algorithmic".
> That's right - if you are claiming the latter, you have to do more than talk a lot about the former.
>
It's a semi-clever debater's trick to put the burden of proof on the
opposition, but like I said, I see no compelling evidence to posit all
that humans do is computational in nature.
It's an hypothesis.
So far I'd say we're a very long way from proving it. I'm not about
to call it "proved" and now make it an uphill battle to prove the
contrary.
Phrenology anyone?
>>I'm not willing to concede that those without evidence >(Penrose has plenty -- lots that humans do, computers >cannot and have not
>
> Penrose does not have "plenty". He made a curious argument based on a very specific (mistaken) way of viewing Godel Incompleteness Theorem(s). Here's a flat out rebuttable that for me says it best:
> http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
>
> I'd say the situation regarding these claimed powers to transcend Turing computability in human symbolic reasoning is much more akin to claims of flying saucers and ESP - show 'em if you got 'em. Factor me some really big numbers in an instant.
>
> Joe N
I understand that's your opinion and of course you know mine.
Plus you're introducing new terms like "symbolic reasoning" whereas I
was just saying "non-computable".
Look carefully at this expression for 1/pi by Ramanujan.
There is no symbolic chain of reasoning going on for many pages to
back it up, neither in the form of a derivation nor a proof.
http://worldgame.blogspot.com/2008/02/reflective-fragment.html
(graphic, middle of the column)
We have computer programs that verify it. I've written some myself.
We have no evidence that software will ever come up with this
expression independently, except perhaps by mindless brute force.
Is that what you think Ramanujan was using?
Kirby
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