Is The Mandelbrot Set Real?

Eric Watt Forste (
Tue, 12 Aug 1997 11:42:24 -0700

John K Clark writes:
> 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.

Given that a short while ago you were asserting that none of the
definitions of complexity currently in use are satisfactory, it
seems strange for you to be claiming the "we know for sure" anything
about the relative complexity of different things.

> But is complexity really the issue here?

I doubt it. What I was questioning was your straightforward assertion
that the shape of a Mandelbrot set is more complex than the shape
of a grape. I don't think we know enough yet about the shapes of
grapes (or about complexity) to be able to make claims like that.

I think that Hara Ra's Mreal/Preal distinction is an ontological
division between kinds of information structures that can be grown
in human brains. Some, like brain-models of grapes that we use to
perceive and think about grapes, originate mostly in sense-data
and are "open" to being further informed by further examination of
physical objects and processes (e. g. grapes). Others, like
brain-models of Mandelbrot sets that we use to perceive and think
about Mandelbrot sets, originate relatively independently of
sense-data and are relatively "closed", since all the information
about them is *implicit* in a short, complete definition which
algorithmically compresses the entire Mandelbrot set into a
comprehensible (to humans) piece of mathematics. I doubt that grapes
are thus losslessly compressible, and so in that sense, grapes are
more complex than Mandelbrot sets. But is that sense the sense most
people are trying to get at when they talk about relative complexity?
I don't know.

I suspect the sense of complexity discussed above is the sense
used in algorithmic information theory, but I'm not sure. Does
anyone want to fill us in on this point?

Eric Watt Forste ++ ++ expectation foils perception -pcd