Re: Is The Mandelbrot Set Real?

Hara Ra (
Mon, 18 Aug 1997 02:03:19 -0700

John K Clark wrote:
> Eric Watt Forste <> Wrote:

> >>The shape of the Mandelbrot Set is more complex than the shape of
> >>a grape
> > John, this is a strong claim, and I for one am skeptical. The
> >"fractal character" of the curves that emerge from increasing
> > levels of mathematical magnification doesn't change much no
> > matter how deep you go.
> The Mandelbrot Set never repeats itself exactly and it's been proven that
> the boundary line of it is as convoluted and random as it is possible for a
> line drawn on a flat surface to be. We know for sure that the shape of
> The Mandelbrot Set is infinitely complex, we don't know for sure that
> anything about a grape is infinitely complex.

Ah, serious confusion here. Indeed, to our perception, the Mandelbrot
Set is infinitely complex, in its overwhelming amount of detail. In
terms of complexity theory, the Mandelbrot Set is a simple object. The
mathematical definition of complexity is basically the length of the
string describing the algorithm used to create the object. The Peano
Postulates describes the algorithm used to create the integers. The
algorithm used for the Mandelbrot Set is only slightly longer. Both
objects are not very complex in this sense. A grape is much more
complex, simply due to the length of the active DNA used to build a

> But is complexity really the issue here? You seem to be saying that
> The Mandelbrot Set is not real because it's not complex enough, Hara was
> saying it's not real because it's too complex.

Let me make a slight modification to my terminology:

Areal - Abstractly Real, ie, Platonic reality
Preal - Physically Real, representable in the physical universe
Mreal - Mentally Real, representable in the mind

Mreal is a subset of Preal. Preal is a subset of Areal.

The set of integers, and the Mandelbrot Set are Areal objects. Said sets
cannot be represented in the Preal or Mreal. The definitions or
algorithms for these objects are Mreal, and therefore Preal. The
definitions are not complex, and the sets themselves are.

BTW, to all readers of this list, Hara Ra is a single word, ie,
Hara(space)Ra. (I would use Hara_Ra but my email server won't accept

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