[lit-ideas] Re: How long is the coast of Britain?
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sat, 23 Oct 2010 11:57:07 +0100 (BST)
--- On Sat, 23/10/10, Richard Henninge <RichardHenninge@xxxxxxxxxxx> wrote:
> ------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.
One thing the history of ideas, science, and even philosophy, may usefully
teach us, is that the truth, or a valid argument, is often counter-intuitive.
[This truth is itself counter-intuitive for some, and this may help explain why
they give it so little weight as opposed to their intuitions].
The difficulty here is, in part, separating out a mathematical explanation for
shapes in the real world from the accuracy of a mathematical description of
shapes. Even if we accept that any 'real world' shape might be accurately
described by mathematical formulae that would not mean that the explanation for
why that was its shape lay in the field of mathematics.
As Richard puts it:-
>"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...
We might come up with a perfect geometrical account of, say, the shape of a
mountain crest without that mathematical description being the explanation of
the creation of the shape of the crest - which might lie rather in the
contingencies of erosion, the buckling of tectonic plates, lava flows etc.
Yet this would not exclude the possibility that some patterns in nature may be
explained in what we might call a "quasi-mathematical" way:- a way that
combines mathematical modelling with a Darwinian account of "strategies" that
would likely proliferate as against other alternatives. This
quasi-mathematical, Darwinian approach has perhaps more purchase when dealing
with cases of "natural generation, such as procreation" (i.e. cases of organic
evolution) than it has with the evolving shape of a mountain range or coastline
(non-organic evolution). The mathematical description of shape affords no
explanation per se, but in its simplicity and economy the description may
reflect a rule or pattern that would likely proliferate for the reasons the
underpin Darwinism as a research programme. We might ponder that while the
'double-helix', 'fractal' and 'Fib sequences' cannot be taken as logically or
mathematically the only way nature could possibly take shape,
they are 'shapes' or 'constructs' with highly generative potential in
Darwinian terms - because they embody two things that are rewarded, generally
speaking, in any evolutionary system governed by selection pressures - they are
both highly stable structures and highly adaptable.
Seen this way, Richard's following comment is of less weight than it might
seem:-
> 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).
Is it true that the operation of a self-replicating 'rule' in nature would
always "be subject to outside influences which would destroy, or at least
compromise the perfection of its rule-generated structure"? Is this true of the
"double-helix" for example? [A "double-helix" being after all a "perfect"
geometrical structure in an important sense]. And where such influences did
"compromise the perfection" - so that just as in nature there is no 'perfect
circle' there is no perfect fractal either - that would not mean a
"rule-generated structure" was not part of the explanation for why things are
as they are and not some other way.
> Despite what I say, I can still hope that someone will do
> the heavy lifting that Mandelbaum has apparently avoided.....
[This surname-slip might be explained because a tree/baum is more fractal than
bread/brot, and Richard is in a fractal mood. On the other hand, the later
"Mandelbrod" looks like a fractalisation too far.]
Rather than "heavy lifting" it might be 'careful sifting' that is required here
- to talk through specific examples and see what aspects of explanation are
mostly mathematical and what are mostly empirical in a field where explanations
may often have a quasi-mathematical and quasi-empirical character [consider
Fisher's quasi-mathematical explanation for why, counter-intuitive as it then
seemed in Darwinian terms, gender ratios in most fish species are 1:1 -
counter-intuitive because 1:1 seems wasteful an evolutionary strategy when one
male can fertilise many females; and consider how, long after his
'quasi-mathematical' explanation was accepted, this explanation was then
empirically tested and corroborated].
D
TTFN
Ldn
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