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MatPlus.Net Forum Internet and Computing Azlan Iqbal on beauty
 
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(21) Posted by Kevin Begley [Friday, Jan 18, 2013 08:43]; edited by Kevin Begley [13-01-18]

Siegfried is right -- humans regularly fail to identify beautiful art, according to the most reliable measurement (a statistical analysis of what essentially amounts to a Turing Test).

Gödel's work is highly interesting; but, so is the law of entropy.
It is a poor extrapolation to suggest that either have any relevance here.
I wish there were some law to explain why errors are routinely extrapolated from these two concepts -- I suspect an inverse relationship with understanding (probably owing to our yet primitive semantic vocabulary).

There are inherent limitations for what can be formally proven, in mathematics, yes -- so what?
This doesn't prevent a computer from smashing Grandmasters in the game of chess.
The same will eventually be true of judging/composing chess problems (by whatever means you want to measure success).

There is nothing transcendental about it.
A formal mathematical proof is not required for an algorithm to function/fail (for computers and humans, similarly); and, even it were required, you offer no reason to suspect that this must fall within the set of true statements which can not be formally proven.

What justifies dropping Gödel's name?
Why are you always trying to rely on the Incompleteness Theorem, to prove Zeno's paradox?
 
   
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(22) Posted by Ian Shanahan [Saturday, Jan 19, 2013 06:17]; edited by Ian Shanahan [13-01-19]

@Kevin. "Gödel's work is highly interesting; but, so is the law of entropy.
It is a poor extrapolation to suggest that either have any relevance here."

RUBBISH! Godel's metamathematics and computers are intimately connected. Just inform yourself about the work of Gregory Chaitin, for a start! That nobody can claim, for example, to have written the shortest possible program to accomplish a given task - this being formally undecidable - Chaitin proved to be a direct result of Godel's Theorems. Ergo, computers can't do aesthetics (which is beyond the magisterium of science), even if the latter were based on logic. About 10 years ago, Stephen Hawking invoked Godel to explain why physicists will never find a Theory of Everything. You grossly underestimate the ramifications of Godel's work - which applies to anything algorithmic and/or information-theoretic. Indeed, since mathematics underpins ALL science, and Godel is at the core of (meta)mathematics, ANYTHING to do with science falls under the aegis of Godel's Theorems!

http://www.cs.auckland.ac.nz/~chaitin/georgia.html
 
   
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(23) Posted by Neal Turner [Saturday, Jan 19, 2013 09:58]

I agree with Kevin(!).
The theoretical stuff isn't particularly relevent - it's only necessary that a program could pass a Turing Test in the domain of chess aesthetics.
This reminds me of a comment by one of the Deep Blue designers after it had beaten Kasparov:
'Everybody thought that Chess was an Artificial Intelligence problem, but it turned out to be just a programming problem.'
 
 
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(24) Posted by seetharaman kalyan [Saturday, Jan 19, 2013 13:52]

@Siegfried
That was an amazing report in the Washington Post. Thanks.
 
 
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(25) Posted by Kevin Begley [Saturday, Jan 19, 2013 15:37]; edited by Kevin Begley [13-01-19]

@Ian,

Rubbish? No, hogwash!

Sorry, my friend, but this is not the first time you misplayed the Gödel card.
You once claimed that a Fairy Codex could never completely describe the rules for a sanctioned set of fairy elements, because Gödel's Incompleteness Theorem would not allow this.
You never managed to explain why Gödel would necessarily apply to a Fairy Codex, whereas the orthodox FIDE Codex (and indeed even the rulebook for Tic-Tac-Toe!) can enjoy a functional immunity.

This time, you're using Gödel to argue another Zeno-like proposition: specifically, that no forward progress is possible for computerized chess problem judging.
You are repeating the same error -- you can't explain how a human (using a biological neural computer, called a "brain") manages to enjoy a functional immunity.

Ian's Theorem: Nothing can be completely, mathematically proven.
Formal Proof: According to Ian's Theorem, it is impossible to disprove Ian's Theorem.

Conclusion: Your understanding of Gödel must be Incomplete!
hint: Gödel only says that some things which may be true can not be mathematically proven.

To the degree that an orthodox codex can function, so could a fairy codex.
Computers will eventually function as well (likely better) than human judges.
 
   
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(26) Posted by Neal Turner [Saturday, Jan 19, 2013 17:10]; edited by Neal Turner [13-01-19]

It seems the theorists have always been invoking Gödel to assert that this, that or the other can't be done with computers - meanwhile the programmers have just got on with the job of doing it!

Even if there are theoretic limits to the power of computing, how can it be known that an artificial intelligence on a par with human intelligence is within or beyond these limits?
 
 
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(27) Posted by Nikola Predrag [Saturday, Jan 19, 2013 17:46]

This is very funny! We are already able to create computers and we already know so much about a human brain that - we are about to create one soon? After all, it is "only" ->a biological neural computer, called a "brain"<-
 
   
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(28) Posted by Hauke Reddmann [Saturday, Jan 19, 2013 19:53]

Just for the record, I (I'm an amateur mathematician after all)
should give a more precise formulation of Gödels theorem:

Any formal system S [that is capable at least of doing arithmetic
with + and *! This is relevant!] will allow true statements
that can be formulated but not proven inside this system
[This is relevant either!] A particular such statement is
"S is selfconsistent".

Chaitins corollary: Any computer program P which is Turing-complete
will allow an input that makes P throw a bluescreen. (Loosely
formulated. Consider the original source for technicalities.)

Reddmanns Addition: That aesthetics is computable function is merely
hinted at by Iqbals paper, and neither proven by Ian nor disproven
by Kevin.

Hauke
 
   
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(29) Posted by Ian Shanahan [Sunday, Jan 20, 2013 01:52]; edited by Ian Shanahan [13-01-20]

"You are repeating the same error -- you can't explain how a human (using a biological neural computer, called a "brain") manages to enjoy a functional immunity."

Read "The Emperor's New Mind" by Roger Penrose.

I have studied metamathematics as an undergraduate, and I'm certainly not overreaching with it.

http://en.wikipedia.org/wiki/The_Emperor's_New_Mind
 
   
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(30) Posted by Ian Shanahan [Sunday, Jan 20, 2013 01:57]

@Neal. "I agree with Kevin(!).
The theoretical stuff isn't particularly relevent - it's only necessary that a program could pass a Turing Test in the domain of chess aesthetics".

But who programmed the computer with the (subjective) aesthetic yardsticks? Not another computer, but a human being who did not use algorithms to decide upon those yardsticks! The "theoretical stuff" is NEVER irrelevant! (OK, I'm showing my background in pure maths *wink*.)
 
   
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(31) Posted by Hauke Reddmann [Sunday, Jan 20, 2013 18:29]

Additionally, I suggest to read the opinion of God (i.e. Douglas Hofstadter :-) on the matter, namely the scene in GEB with Turtles magic flute allegedly proving math statements, but Achilles calling the bluff by demanding a "proof" of Goldbach.
The metapher of course indicates DH doesn't believe in magic flutes, or, by analogy,
that human reasoning is something fundamentally different from computer reasoning.

At the present time, I fear we mostly do assertions based more on personal ideology
than on solid proof. May I suggest we repeat this discussion in say, 50 years?
I think given my families longevity I still compose with 102 :-)

Hauke

P.S. Wouldn't this well-known Monty Python scenario not be cool?
I: "Wenn ist das Nunstück git und Slotermeyer? Ja! Beiherhund das Oder die Flipperwaldt gersput!"
Unnice person (It's not a MPF member :-) : <tilt> <falls into catatony by endless brain loop>
 
   
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(32) Posted by Neal Turner [Sunday, Jan 20, 2013 19:00]

@Ian
"That nobody can claim, for example, to have written the shortest possible program to accomplish a given task - this being formally undecidable - Chaitin proved to be a direct result of Godel's Theorems. Ergo, computers can't do aesthetics..."

How exactly does the 'Ergo' connect those two sentences?
 
   
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(33) Posted by Ian Shanahan [Monday, Jan 21, 2013 00:31]; edited by Ian Shanahan [13-01-21]

The "Ergo" is there because attempting to write a computer program that engages with a subjective, non-algorithmic activity like aesthetics is surely an infinitely taller order than merely writing the shortest possible program! Godel shows that the 'easier' task here, though achievable, is impossible to determine. The 'harder' task, which necessarily transcends logic, must therefore be beyond the reach of technology that is limited to algorithmic processes. (Maybe not for quantum computers?)
 
   
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(34) Posted by Neal Turner [Monday, Jan 21, 2013 13:20]; edited by Neal Turner [13-01-21]

I think a good analogy is with Grammar.
A native speaker, on hearing something in his own language, 'knows' when it's in the correct form.
Most likely he won't be able to explain in technical terms the reasons for his conclusion, but he'll just say that it 'sounds' right.
What's going on in his brain is certainly subjective and almost certainly non-algorithmic, but now we do have computers that can do a decent job with natural language using objective and algorithmic methods.

Basically I think it's wrong to suggest that Aesthetics is a subjective, non-algorithmic activity.
In our own field of problem chess the criteria for judging a problem are well-defined and generally accepted, making it pretty much objective.
If it's non-algorithmic it's only because nobody has yet come up with an adequate algorithm!
I reckon Professor Iqbal and his team have made a good choice to use Chess composition as their medium for exploring Aesthetics - although maybe they made it more difficult for themselves looking at endgames rather than problems - helpmates would have been my choice.
 
   
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(35) Posted by Ian Shanahan [Tuesday, Jan 22, 2013 05:21]; edited by Ian Shanahan [13-01-22]

@Neal"... but now we do have computers that can do a decent job with natural language using objective and algorithmic methods."

If the methods are algorithmic, then they are subject to Godelian limitations! Language is not, because it evolves in non-logical ways.

"Basically I think it's wrong to suggest that Aesthetics is a subjective, non-algorithmic activity."

Of course it's subjective and non-algorithmic! Aesthetic judgement is based upon knowledge of the field (which varies from person to person) and each individual's subjective biases (such as, for example, personal preferences for one attribute of a problem to another - e.g. favouring strategic elements over formal patterns, or favouring cross-checks to self-blocks): choosing the yardsticks and their various weightings is ineluctably a _subjective_ act, although once chosen, an algorithm can provide a rating (as in the case of MOE). But that rating is still subjective!

"In our own field of problem chess the criteria for judging a problem are well-defined and generally accepted, making it pretty much objective."

Really? I think not! You only have to read the other recent thread here on whether or not obtrusive force is a flaw - and if so, to what degree? Even when the _criteria_ are widely accepted, their relative importance is not! One only has to encounter ongoing discussions and criticisms of awards to see that judges' and pundits' opinions vary from problemist to problemist. I would say there are very few iron-clad criteria that are universally adopted, such as positional legality. Most other things are mere conventions that change with the prevailing fashions.

"If it's non-algorithmic it's only because nobody has yet come up with an adequate algorithm!"

No - they are qualitatively completely different, for all of the reasons given above. Moreover, an algorithm cannot judge a problem against its historical precursors (which would demand access to a database containing every problem ever composed). Anticipation devalues the aesthetic merit of a problem, regardless of its contents.
 
   
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(36) Posted by Sergiy Didukh [Tuesday, Jan 22, 2013 07:13]

I think that aesthetics is algorithmic. Computers can't yet assess chess problems like Ian because he is unable to write down the whole set of criteria he uses in the judging process. But I hope that I'll grasp the algorithms my own brain works with and there will be computers judging studies like Didukh. And they will do the job in seconds. Isn't that amazing?! Of course, it's not that easy even for me to comprehend my algorithms of chess beauty because they are probably much more sophisticated than Ian's, but since Ian has refused to give a hand to the programmers working in this field, I must explore my complex mental activities alone :-).
 
   
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(37) Posted by Neal Turner [Tuesday, Jan 22, 2013 14:31]; edited by Neal Turner [13-01-22]

What is the big deal about Gödel anyway!?
After all in mathematics these Gödel statemants are very obscure self-referential objects - does anyone in the applied mathematics community actually use them for anything?
I thought not.

We're all aware of computer projects which, for a variety of reasons, have been late or cancelled or underperforming, but one reason I've never heard voiced is that they got stuck in a Gödelian cul-de-sac.

I've never heard the theorists stating that banking systems, airline reservation systems, computer games etc are doomed to fail because of Gödelian limitations, why to single out AI projects?

These are after all just computer programs!
Show me the Gödelian piece of code which is spoiling my program and I'll reprogram it just as I would any other bug.

Telling me my program won't work because of Gödelian limitations is like going down to the building site and telling the guys that Quantum Uncertainty means they can never build the house that they're working on.
 
   
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(38) Posted by Hauke Reddmann [Tuesday, Jan 22, 2013 15:16]

Sidenotes...
@Ian: No, to my best knowledge a quantum computer doesn't differ in
it's limitations from a normal one. It's just faster.
@Neal: "Obscure" maybe, but yes, there are statements in, eh, what
was it, Ramsey theory I think, that are fairly natural (from a
mathematicians view) and undecidable for Gödel reason. Never, EVER
underestimate those wacky mathematicians' fantasy :-)

Hauke
 
   
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(39) Posted by Ian Shanahan [Wednesday, Jan 23, 2013 03:47]; edited by Ian Shanahan [13-01-23]

"Of course, it's not that easy even for me to comprehend my algorithms of chess beauty because they are probably much more sophisticated than Ian's ...".

What pretentious, self-aggrandizing twaddle!

@Hauke. Well said! Neal needs to learn more about metamathematics!
 
 
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MatPlus.Net Forum Internet and Computing Azlan Iqbal on beauty