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This is a series on the book Gödel, Escher, Bach: An eternal golden braid by Douglas Hofstadter.  

Earlier diaries are here

Today, we will examine Jumping out of the System p. 465-479.

UPDATE We've got a ways to go with GEB, but I am already thinking about the NEXT book we should read together.  So, make suggestions in the comments; I will collect them over the weeks, and then, when we are near the end of GEB, start doing polls.

From the overview:

The repeatability of Godel's argument is shown, with the implication that TNT is not only incomplete, but "essentially incomplete".  The fairly notorious argument by J.R. Lucas, to the effect that Godel's theorem says that human thought cannot in any sense be "mechanical" is analyzed and found wanting.

There are two parts to this chapter.  In the first, DH shows that an argument very like the Cantor diagonal argument can be applied to Godel's theorem and TNT, and that it can be applied as many times as you want, as in Birthday Cantatatata.  This is important, but I have little to say about  it.  At the end of this part he defines "essential incompleteness" - by the nature of formal systems, you can always add another axiom, but that doesn't get around Godel.  

On p. 470, DH likens formal systems to fissionable material.  Each can reach "critical mass" and blow up.  I don't think DH really proves that there is nothing right at the edge of this - but I think Godel does.

The second part is more interesting to me.  DH fairly well demolishes the Lucas argument given on p. 471 ... namely, that since people can Godelize, and computers cannot Godelize, people must be smarter.  But he does not go far enough; computers can clearly do things that people cannot, and some of these have something to do with what we tend to think of as 'intelligent'.  Does that mean computers are smarter than people?  Some people cannot Godelize, and, until Godel came along, no one could Godelize, so, were the people who existed before Godel only as smart as computers?  Did people become smarter after Godel?

The real problem is defining intelligence.  Since we can't even agree on what intelligence is among humans, how can we do it between humans and animals, much less humans and computers?

Originally posted to plf515 on Sun Jun 14, 2009 at 03:33 AM PDT.

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Comment Preferences

  •  Tip Jar (19+ / 0-)

    NYC meetup Monday, 6:30! NY Milkshake Company 342 E 47th St, across from the UN. RSVP to me or to sidnora.

    by plf515 on Sun Jun 14, 2009 at 03:33:05 AM PDT

  •  What next? How about (2+ / 0-)
    Recommended by:
    RunawayRose, plf515

    George Spencer-Brown's 1969 book Laws of Form?

    Or, for something shorter, less philosophically deep, easily digested but quite nourishing (and highly relevant to politics), Robin Farqharson's Theory of Voting.

  •  You (3+ / 0-)
    Recommended by:
    RunawayRose, Nova Land, plf515

    asked if computers are smarter than people?  

    Maybe smarter is the wrong choice of words.  

    Until computers can make decisions based upon illogical emotional conclusions and logic, man will still be one up on them.

    Since we humans have an emotional component our ability to view the "world" is not static which gives rise to our inventiveness. We fit Godel's theroem because we put that unknowable component into everything.  If a machine could compute the way we do wouldn't it then be a living machine?

    Have a nice weekend!

  •  I can do anything a computer can do... (4+ / 0-)
    Recommended by:
    RunawayRose, Nova Land, plf515, DBunn

    ...but it's going to take me a whole lot longer.  So if the task involves a time limit (e.g. "within my lifetime"), then computers win.

    Don't be a DON'T-DO... Be a DO-DO!

    by godwhataklutz on Sun Jun 14, 2009 at 07:47:41 AM PDT

  •  the question of people vs computer is one I've (4+ / 0-)
    Recommended by:
    RunawayRose, cfk, plf515, DBunn

    been playing with a bit in Sunday Puzzles.

    Last year I'd been posting occasional cryptoquotes -- and was surprised when someone was able to use an on-line program to solve it.  I hadn't realized there were programs available for that now (although I guess it should have been obvious that modern computers are capable of running through the combinations quickly enough, and of storing dictionaries in memory which the combinations can be checked against, which enable a computer through brute force to solve cryptograms faster than a human using familiarity with word and letter patterns.

    Soon after I had posted a cryptarithm -- and again had been surprised (though again I shouldn't have been) that people can now solve these as fast or faster with computer aid than without.  

    I have therefore begun experimenting with puzzles which are intended to be easier for a person unaided by computer to solve than a person aided by computer.

    I have an idea in mind that I think would make cryptograms virtually uncrackable by (present-day) computer programs, while still being solvable by human reasoning. I haven't tried creating and posting any of those because there's too much chance of my making a careless error in the creation so it doesn't seem a good use of time at the moment.  But the Ana-Gremlin puzzles I've been posting are a simpler (easier to create, less chance of screwing up) kind of puzzle which I believe are virtually unsolveable by the current level of anagram-solving programs but extremely easy for a human puzzler to solve.

    It seems to me that this is a never-ending contest -- that it will always be possible for people to improve computers / computer programs to be able to solve puzzles which were once unsolveable by computer, and in turn it will always be possible for humans to then come up with additional tweaks which will make puzzles unsolveable by the new level of computer / computer programs.  That's my theory, anyway.  But I could very well be wrong.

  •  A purely "mechanical" AI system cannot (1+ / 0-)
    Recommended by:
    plf515

    represent the idea of a "material universe" distinct from a Platonic, logically possible universe ("world") of the sort used by modal realists (see    ) to argue that there is in fact no distinction between PWs and incarnate, "real" ones. Indeed, there is no rigorous, logical way to state the difference! Really, try it and see...
    (More later if I have time.)

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