[lit-ideas] Re: How long is the coast of Britain?
- From: "Richard Henninge" <RichardHenninge@xxxxxxxxxxx>
- To: <lit-ideas@xxxxxxxxxxxxx>
- Date: Sat, 23 Oct 2010 04:13:36 +0200
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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