Even if the Koch Snowflake is restricted to those 3 angles, you don't have
to be restricted to the Snowflake itself -- by expanding, contracting or
transforming the space of interest, you can get somewhere more interesting
(anywhere you want, maybe?). For example, if you take the natural numbers,
you can expand to the naturals, rationals, reals, etc., contract to the
primes, transform to... err... something else.
My feeling being that basically you can always abstract away through some
kind of equivalence principle whenever the information available to you
doesn't explicitly forbid it.
I think it's time for someone to tear my ideas apart; after all, they're all
really just based on consideration of some themes from Greg Egan's books I
read about 8 years ago....
2008/8/21 Tom Caylor <daddycaylor.domain.name.hidden>
>
> I see that fractals also came up in the other current thread.
>
> I can see the believableness of your conjecture (Turing-completeness
> of the Mandelbrot set), but I see this (if true) as intuitive
> (heuristic, "circumstantial") evidence that reality is more than what
> can be computed. (My belief in the intuition's base outside of
> computation is an example of where I'm coming from.) There are
> undecidable properties of fractals (iterative function systems, IFS),
> and it has been conjectured that all non-trivial properties of IFS's
> are undecidable. With the Mandelbrot set it is so geometrically
> complex (the pun here is appropriate since this set involves the
> complex numbers) that it is easy to believe that you could find your
> mother-in-law of even a super-model in there somewhere. But take
> another fractal like the Koch Snowflake, which also has undecidable
> properties. Yet is it entirely made of line segments which are at
> only three angles. I can't believe that reality could be restricted
> to this kind of complexity.
>
> Have you heard of fractal Turing machines, which incorporate real
> numbers? Perhaps this is something to be explored in the Everything
> discussion.
>
> Tom
>
> On Aug 13, 2:23 am, Bruno Marchal <marc....domain.name.hidden> wrote:
> > Hi Tom,
> >
> >
> >
> > > Nice. I see beauty in the Mandelbrot set. However, there seems to be
> > > a lot of deja vu, similar repetition on a theme.
> >
> > Right. But full of subtle variations.
> > It is all normal to have a lot of deja vu when you make a journey
> > across a multiverse ...
> >
> > > I have never been
> > > able to find anything resembling a beautiful girl,
> >
> > You are not looking close enough, and also, the zoom movie remains a
> > pure third person description. Consciousness is more related to a
> > internal flux or to some stroboscopic inside views in the Mandelbrot
> > Set (assuming the conjecture).
> > It is a bit like looking to a picture of a galaxy. You will not see
> > beautiful girls, unless you look close enough, and from the right
> > perspective.
> >
> > > or even a mother-in-
> > > law, or a white rabbit. This seems to go against your conjecture.
> >
> > (remember also that "not seeing something" is not an argument of
> > not-existence, like seeing something is not an argument for existence).
> > If you want to see a white rabbit (*the* white rabbit), the best
> > consists in looking at
> >
> > http://fr.youtube.com/watch?v=Z5XfQWKgf4M&feature=related
> >
> > As for the mother-in-law, I am not sure about your motivations ...
> > (Holiday jokes :)
> >
> > Bruno
> >
> >
> >
> >
> >
> >
> >
> > > Tom
> >
> > > On Aug 12, 8:30 am, Bruno Marchal <marc....domain.name.hidden> wrote:
> > >> On 09 Aug 2008, at 09:44, Tom Caylor wrote:
> >
> > >>> I believe that nature is not primarily functional. It is primarily
> > >>> beautiful.
> > >>> And this from a theist? Yes! This is actually to the core point of
> > >>> why I am a theist. I don't blame people for not believing in God if
> > >>> they think God is about functionality.
> >
> > >> If you remember my conjecture that the Mandelbrot Set, (well, its
> > >> complement in the complex plane), is Turing complete (that is
> > >> equivalent in some sense to a universal dovetailing), then zooming in
> > >>
> > >> it gives a picture of the arithmetical multiverse or of the universal
> > >>
> > >> deployment. And I do find most of them wonderfully beautiful. Here is
> > >>
> > >> my favorite on youtube:
> >
> > >>http://www.youtube.com/watch?v=G0nmVUU_7IQ
> >
> > >> Is that not wonderful? Awesome ?
> >
> > >> Bruno
> >
> > >>http://iridia.ulb.ac.be/~marchal/<http://iridia.ulb.ac.be/%7Emarchal/>
> >
> > http://iridia.ulb.ac.be/~marchal/-<http://iridia.ulb.ac.be/%7Emarchal/->Hide quoted text -
> >
> > - Show quoted text -
> >
>
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Received on Thu Aug 21 2008 - 17:24:04 PDT