X-Message-Number: 8631
Date: Sat, 27 Sep 1997 10:38:27 -0400
From: "John P. Pietrzak" <>
Subject: Re: Digital Shakespeare
References: <>
John K. Clark wrote:
> John P. Pietrzak wrote:
> >(a) You give AIC as possible definiton of complexity.
>
> And then immediately pointed out it's shortcomings and said nobody
> has a good definition of complexity, but that doesn't mean the word
> is meaningless, just definitionless.
Ah, so, to prove your claim about the lack of good definitions of
complexity, you provided a bad definition of complexity. I see.
[On to the intricacies of the surprisingly complex Turing Machine]
> >What is a mark? Anything you want it to be.
>
> No. If your only option is putting down a mark or failing to do, as
> in a Turing machine, then one mark can only represent 2 things.
I'm sorry, I've obviously learned a different kind of TM than you have.
In Hopcroft & Ullman's book, a TM is a device with a tape, the tape
is divided into cells, and each cell can contain a symbol from Lambda,
the (finite, but can be greater than 2) set of allowable tape symbols
(p. 148). In fact, in order to encode a set of ones and zeros on the
tape using their formalization, you'll always need at least three
symbols in your language, since you'll need a "blank" symbol for tape
manipulation purposes.
Generally, there can be all sorts of different kinds of marks on a TM
tape.
> >I am certainly allowed to use a language containing two
> >particular marks, those being "printf" and the string I want
> >to print. I then place those two marks on the tape, and
> >have a truly trivial algorithm for the TM to execute.
>
> I'm afraid I don't see your point.
My point: one mark + one mark = two marks. Very small program. Works
with all strings.
> >Ok. Now, let me assume that you were talking about a TM
> >using a binary language,
>
> Obviously, did I really have to spell that out?
Yes, I'm afraid you did. When you start talking not about a set of
actions but rather about the written representation describing a set
of actions, we now have to start being very specific about just how
those actions are encoded. (The "add" instruction on an eight-bit
processor is encoded in exactly half the space of the "add" instruction
on a sixteen-bit processor. This means, the encoded length of an
algorithm consisting of a single addition on both processors differs
greatly (in fact, by 100%) even though they may be EXACTLY THE SAME
ALGORITHM.)
> Turing machines have no "printf" statements, they don't distinguish
> between data and instructions, not at the lowest level, and that's
> what we're debating.
Turing machines have whatever instructions you define them to have
(your FSA controlling the tape head will encode whatever instructions
you like), and they distinguish between data and instructions in
exactly the same way that a real-world general-purpose computer does:
by defining some sequences of symbols as instructions when they are in
a particular state, and some sequences of symbols as data when they are
in another state. No, the tape doesn't make the distinction, but "a
tape alone does not a Turing Machine make," or something like that.
Besides, there is nothing at all stopping me from creating a FSA which,
when it reads a "1", performs the actions of a printf statement, and
when it reads a "0", gives that printf statement the string I'm
interested in printing.
[On definitions of complexity]
> I said figuring out the trillionth digit of PI was a complex task,
> you said it was simple and as "proof" you presented a computer program
> that could do it,... eventually. You said because the program was
> short that proved the task was simple. I said your proof was flawed,
> and it is, but if AIC really was complexity then your proof would have
> been valid. But it's not so it isn't.
Ah, now I begin to understand. Determining the trillionth digit of Pi
is a time-consuming task. Personally, I don't consider the consumption
of time as being complicated, and so I didn't find your argument
convincing. Unfortunately, it seems almost impossible to convince you
that that is all I meant, and you've gone to great lengths to pigeonhole
my answer into something which deals with the number of ones and zeroes
on a magnetic tape.
[Now, we return to the question of definitions of intelligence]
> >axiom 1) You chose several examples of intelligence.
>
> Yes, I did that.
>
> >axiom 2) You did _not_ choose them randomly.
>
> I like to think that my putting various things in a category and
> putting a label on it called "intelligence" was not random and they
> all have something in common, but I'm human, I make mistakes, I could
> be wrong.
Hmm. I'm beginning to smell a rat here. I've spent, what, several
weeks now discussing intelligence with you, and now it turns out that
you may not even be able to tell if the things you label as
"intelligent" have any interrelationship between each other beyond that
of random chance? Why are you wasting my time, then?
> >thm 3) (from 1 & 2) You must have used something other
> >than random choice.
>
> Yes, if it's not random then it must have been something else.
>
> >axiom 4) In my world, "not random" == "follows rules" =>
>"has definition".
>
> No! In formal logic you can say "if A and B then C" but our brains do
> not work on formal logic, they use rules of thumb like "if A and B
> then usually something close to C".
Fascinating. If your brain was only using a rule of thumb to come up
with that statement, you may have been wrong. I'm beginning to be
unsure that I can believe anything you say.
> >thm 5) (from 3 & 4) You used a definition of
> >intelligence.
>
> No. I had no definition, I put them in the same category labeled
> "intelligence" only because I've found from experience they often, but
> not always, work well together.
Ah, good. Then that means you could have used the name "stupidity" for
that category and it would have worked just as well. "Intelligence"
doesn't actually MEAN anything, it's just the arbitrary name of an
arbitrary category.
> >axiom 6) You did not use a definition of intelligence.
>
> Axioms 1, 3 and 6 are very correct.
> Axiom 2 is mostly correct.
> Axioms 4 and 5 are dead wrong.
Ok, I'm getting it. Your arguments, therefore, are based upon the brain
using rules which are not completely defined over their range of
application. I still have a problem with my axiom 4, though: if you
*really* aren't using random chance to locate examples of intelligence,
there *MUST* be something other than random chance guiding you, no? (If
you _are_ using random chance, we have nothing further to discuss.)
[Here comes the fun part]
> >(John develops nasty grin on face) Ok, guy, tell me, what
> >is a stochastic rule of thumb?
>
> Let me give a concrete example, "if I flip a coin 1000 times then
^^^^^^^^^^^^^^^^^^
> usually I will see heads about 500 times" or "if I flip a coin 1000
> times I am unlikely to find heads exactly 500 times". Yes, a
> mathematician could calculate more precisely and replace vague words
> like "usually" and "about" and "unlikely" but this is certainly not
^^^^^^^^^^^^^
> how our brains work, we don't make such calculations in everyday life,
> most people don't know how and in fact nobody knew how to do it until
> a few hundred years ago, but people must have had something close to
^^^^^^^^^^^^^
> my to my rule of thumb in their mind for many thousands of years
Does not compute. :) (You must have known this was coming, didn't you.)
If your brain is ruled by vague and fuzzy rules of thumb, how can you
give a "concrete" example? How can a mathematician ever replace vague
words with non-vague ones? How can you be certain about how our brains
work, or in fact, certain about anything at all? Your belief in
vagueness appears to have extreme clarity here...
> >How do you know when you are properly following a rule
> >stochastically and when you aren't?
>
> Only one way, experimentally. See if it's useful, see if it works.
Well, good for you. Unfortunately, as far as I can tell, although you
can perform experiments, you can't ever tell what the experiment is
really about, because you really can't understand the concept
"stochastic" with certainty. This is my problem with your approach: if
you really are what you say you are, then you can _never_ know that you
really are what you say you are.
> >What is beautiful?
>
> I can point to things that are beautiful, I can't tell you what
> beauty is.
This would be a problem then, since I can't see your hand or the thing
you're pointing it at. I guess it doesn't really matter, since you
would only be pointing to objects chosen at random anyway.
> >What if I didn't know what Sweden was? How would you
> >explain it to me?
>
> I'd point to a place on a map and say "Sweden".
Ah, so Sweden is a colored area on a piece of paper! Great, I always
wanted to know what it was. Thanks!
John
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