X-Message-Number: 8607
Date: Wed, 17 Sep 1997 21:50:16 -0700 (PDT)
From: John K Clark <>
Subject: Digital Shakespeare
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On Tue, 16 Sep 1997 "John P. Pietrzak" <> Wrote:
>If I may, allow me to quote from an earlier message of yours (Cryonet
>#8550): "[...] the Algorithmic Information Content (AIC) of a message
>string is the length of the smallest computer program that can produce
>the string, and that's just another way of asking how much the string
>can be compressed."
OK.
>Now, may I ask, what does string compressability have to do with
>algorithm complexity?
I don't know and never said I did, I was talking about a possible definition
so naturally I can't use the word "complexity" in a definition of complexity
and I did not. I said that if complexity is nothing but AIC (and I don't
think it is) then complexity is "the smallest computer program that can
produce the string". "Smallest" is an objective and universal measure, easy
to understand, if there is an objective and universal measure of "algorithm
complexity" nobody has found it yet and it sure isn't easy to understand.
>Suppose I take two strings of the same length, one of which is very
>uncompressible, the other being very compressible, if the algorithm
>to print out the uncompressible string consists of a single
>(gigantic) printf() statement, does that mean that _algorithm_ is
>more complex than the compression algorithm for the second string,
>which is smaller but contains more statements?
I don't know what you mean by "smaller but contains more statements" a
Turing machine makes no distinction between data and instructions, it's all
just marks on a tape. If the string is random then the length of the smallest
computer program that can produce the string is the string itself. If the
string is not random, even if it's infinitely long like PI, then length of
the smallest computer program that can produce the string is not only finite
it's downright small. Does this mean that random gibberish is more complex
than PI? Yes is you believe that complexity is just AIC. I don't.
>You are equating the cost of obtaining an answer to a problem with
>the complexity of an algorithm solving that problem. I am saying
>they are different; related, perhaps, but not equal.
Then we agree on this, all I wanted from you was that word "related". I did
not equate the cost of obtaining an answer with complexity, it's part of it
and so is AIC, but there must be more.
>In fact, _you_ don't know why you chose them; if you did,
>you'd have some sort of definition of intelligence.
>>Me:
>>Utter and complete nonsense.
>Nonsense in that you _do_ know why you chose them?
No. I chose them, I think, because they seems to work pretty well together
most of the time, but feel free to disagree because it has nothing to do with
my comment. What is utter and complete nonsense is the idea that if I did
know why I picked them then there must be a definition of intelligence.
I think it very likely that we don't know of such a definition because one
does not exist or at least can not be written down on a paper smaller than
the galaxy.
>there are rules, axioms, DEFINITIONS of things like intelligence
>stuffed somewhere down inside the brain. Just because people like
>you and me cannot determine exactly what they are, the simple fact
>that we DON'T choose randomly means that there must be some reason
>for _why_ we choose as we do!
Yes there are reasons for most of what we do, but this is not geometry, there
are no axioms and it's certainly not based on definitions, they're
stochastic rules of thumb.
Problem P1 that you want to solve seems a little similar to other problems
you already solved and put in mental category A, try using what worked for
them. If that doesn't pan out give category B a try, in some ways it's a
little like problem P1. No luck, OK try Z, it's unlikely to work but it's so
easy test you might as well give it a shot. Well I knew that wouldn't work,
I remember one time when C worked beautify when I really didn't think it
would, try something like that. Damn, you know at times like this it often
helps to give A a second look because it really does seem a lot like problem
P1, try more variations on that theme, sometimes that works. But not this
time, Problem P1 is really hard and I think you're wasting too much time on
it, if you can't knock it down go around it, find some other way to do what
you want to do. Solving Problem P2 would probably serve your purposes just as
well and might be easier than P1, so forget about P1 and work on P2 for a bit.
>Give me knowledge without definitions.
Most people like most things that are beautiful.
Most people like some things that are not beautiful.
A similar problem may have a similar solution Intelligent people usually
solve problems better that stupid people.
It's often unwise to judge the value of something by its size.
Insulting a person usually makes him dislike you.
If you want to make a lot of money it's often helpful if your employees
remain conscious when on the job.
If you travel to Sweden the first person you see when you get off the
airplane is unlikely to be an albino sumo wrestler playing the bagpipes.
I #8601 Andre Robatino <> On Tue, 16 Sep 97 Wrote:
>>Me:
>>any set of measurements you make does not correspond to a UNIQUE
>>quantum wave function.
>One can determine it uniquely up to a phase factor.
I'm not sure how much we really disagree in all this, except in our opinion
of the importance of the phase factor. It seems pretty important to me,
after all, Schrodinger's equation defines a wave in phase space and the
number of dimensions is 3 times the number of particles it works with,
hence the computational complexity of making such calculations for even a
small number of things. When 2 particles collide so does their quantum wave
function and when they separate so does the amplitude of their quantum wave
function, but their phases do not separate, they remain entangled and produce
interference effects even if the particles move a billion light years away.
Unfortunately we can not know the signs of the phase factors because of the
nature of complex numbers, measurement just won't tell us. Yes, human beings
can and do adopt an arbitrary phase convention that is consistent with
experiment, but there is nothing unique about it, other conventions would
work just as well. This arbitrary quality is why I maintain that the quantum
wave function is a calculating device, like longitude and latitude.
John K Clark
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