On 21 Aug 2008, at 18:32, Tom Caylor wrote:
>
> 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.
I agree. Recall that truth about "just numbers" is far bigger 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.
Yes, although her peculiar state of consciousness is "terribly"
distributed, and we have to distinguish the many pov ...
> 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.
I think so to. But not all undecidable set have to be universal.
(Actually I am not sure of which undecidable properties of Koch
Snowflake you allude to)
>
>
> Have you heard of fractal Turing machines, which incorporate real
> numbers? Perhaps this is something to be explored in the Everything
> discussion.
You mean the work of Blum, Shub and Smale? Yes, it gives a proof of
the undecidability of the Mandelbrot set with an "enough good"
generalization of computability on the real (or on any ring actually).
But its universality or creativity (in Emil Post sense, or its Blum,
Shub Smale variant) remains to be proved.
Bruno
> 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/~marchal/- Hide quoted text -
>>
>> - Show quoted text -
> >
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Aug 22 2008 - 17:24:22 PDT