In response to three responses from Mr. Palma:
(1)
says who?
On Wed, 20 Oct 2010, Richard Henninge wrote:
> What's this I hear about fractals describing nature? If fractals
> describe
> anything, what it describes is on the Kantian "this side" of nature.
> Fractals are just fancy grammatical and syntactical constructions.
> Fractals can only be created by computers, hence by us, nothing outside
> of
> us.
------Says me on the basis of the counter-intuitiveness of nature's
creating of objects or "shapes" that have been generated by the following
of a rule. Granted, people too can create fractals, but it is so tedious
that their "discovery" would not have occurred without the development of
computers. Further, even if nature could work by following a rule, the
object so created would immediately and constantly be subject to outside
influences which would destroy, or at least compromise the perfection of
its rule-generated structure (unlike the hermetically propagating
computer-generated fractals).
Despite what I say, I can still hope that someone will do the heavy
lifting that Mandelbaum has apparently avoided, or simply left undone--it
*is* daunting--and demonstrate why nature does, if it in fact does,
"choose to go" or "have to go" the fractal route in generating structures.
As long as he spoke of such structures in relatively small,
organism-internal structures, such as ferns, one could have imagined he
was interested in the "why" or "how" question and investigated the
fractalization of growing plants. But as soon as he waxes fractal over
such obviously amorphous structures as coastlines and clouds, he showed he
was content with playing the part of the advocate of the
pseudo-explanatory power (consisting only of heuristic analogies) of these
"cool" computer-generated shapes.
One basic error is to confuse mathematical "generation" (the forming [of a
geometric figure] by describing a curve or surface) with natural
generation, such as procreation. There is about as much rhyme or reason to
a mountain range's crest as there is to a city skyline, and by "rhyme or
reason" I am referring to the kind of patterned, concerted, purposeful,
intentional, and eventually rule-based products as those produced
exclusively by humans with their basically dumb, but rigorously obedient
flunky processors churning out fractal upon fractal--resembling--the
natural world, if only in complexity.
(2)
what if we find that coast is fractal?
is that kantian coast?
On Wed, 20 Oct 2010, Richard
Henninge wrote:
> What's this I hear about fractals describing nature? If fractals
> describe
> anything, what it describes is on the Kantian "this side" of nature.
> Fractals are just fancy grammatical and syntactical constructions.
> Fractals can only be created by computers, hence by us, nothing outside
> of
> us.
Kant's checker on that one, as it was for Wittgenstein the engineer, was
to submit the "findings" of the "Kantian" subjectivity to the unbiased
jury of mathematics and/or truth-value logic: unbiased in that the
scientist cannot approach the coast with the fractal figures dancing like
sugar-plum templates in his head, ready to be sprinkled over the chaotic
world, until "PAFF!" it organizes itself into the desired fractals. The
more realistic alternative, acceptable, I would venture, to both of them,
would be a mathematical measuring as-if structure, holdable by multiple
minds simultaneously in the mathematical and rigorously truth-value
logical way that allows for effective discussion and, eventually,
consensual adjustment.
(3)
> >
> > "The best prophylaxis to brake these hubristic heuristic tendencies
> > is
> > Wittgenstein's checker: The world is everything that is the case, and
> > that
> > of which we cannot speak, of that we must remain silent.
>
>
> precisely. and what told anybody that the coast of x is not fractal?
> Or Wittgenstein also predicted it?
>
If it is the case that the coastline of x is fractal, then we would be
able to speak of it by reproducing its form in a fractal equation, we
would be able to program a computer to generate just that coastline. The
equation corresponding to the curve of that coastline would then image the
world. You can bet that Wittgenstein would have begged Mandelbrod to
exercise a more judicious restraint in his speculative utterances.
Richard Henninge
University of Mainz
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