Is the Mandelbrot Set Real?

John K Clark (
Fri, 5 Sep 1997 20:51:33 -0700 (PDT)


On Wed, 03 Sep 1997 Hara Ra <> Wrote:

>Please provide a summary of the various current interpetations of
> "complexity".

You like the Algorithmic Information Content (AIC) definition of complexity,
that's the length of the smallest computer program that can produce the
message string in question. Besides having the considerable disadvantage of
not being able to know what the damn thing is, it also tells me that figuring
out the trillionth digit of PI should be simple, but that's certainly not
what I mean by the word "simple", not even close.

Another possible definition is a measure of how long a program must run to
produce its result, not how big the program is. Yet another is a measure of
how much working memory the machine would need to produce the result, not the
size of the initial program or the time it takes to run it. The trouble is
that by all these definitions the random gibberish produced by a monkey is
more complex than a Shakespeare play. Could these things really be measuring
simplicity not complixity? :>)

I think the problem is that complexity like intelligence is best explained by
example not by definition.

>>1) Exactly what is this property you call "physical" and how can I
>>test to see if an object has it?

>Each element of the object can be one for one mappped into the

You're saying that the Real numbers are not real, I hesitate to even mention
the imaginary numbers. I'm reminded of the infamous 19'th century
mathematician who opposed all these newfangled ideas and said "God created
the integers, all others are man's invention".

>and the number of integers required is less than the number of
>integers required to count the number of particles in the Universe.
>The Universe is presumed to contain a finite number of particles,
>appproximately 10^80.

Nothing special about 10^80, if the Bekenstein bound is true then the total
amount of information the universe contains can be unlimited in 2 ways:

1) if it's open and so keeps getting bigger, although in this case the time
required to access the information would keep getting longer too, so you
couldn't have subjective immortality.

2) The other way is if The Universe gets more energy without limit and thus
heavier through gravitational collapse and an Omega point is formed, this
way the information retrieval time would keep getting reduced forever.

John K Clark

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