John, this is a strong claim, and I for one am skeptical. Of course,
you can keep pulling more signal out of a Mandelbrot set as you
fall into its infinite depths, but hey, in *some* sense, we *know*
what we are going to be getting out of it. The "fractal character"
of the curves that emerge from increasing levels of mathematical
magnification doesn't change much no matter how deep you go.
Going deeply into a grape, however, you run into, well, unknown
things. Who knows what's down in there? Superstrings? Membranes?
What? It's not as if the structure just stops at the level of quarks
and leptons... at least I suspect it's not, because the history of
science so far has been that the more you study a real physical
object, the weirder it gets.
If by "the shape of a grape" all you meant was "ellipsoid", well,
then you're just comparing a complex Platonic mathematical object
to a simple Platonic mathematical object, and you're not engaging
with Hara's Preal distinction at all. This is why I assumed you
meant the full three-dimensional curve of the grape in full detail,
interior and exterior.
-- Eric Watt Forste ++ arkuat@pobox.com ++ expectation foils perception -pcd