[lit-ideas] Re: When do we know enough?
- From: John McCreery <john.mccreery@xxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Fri, 16 Dec 2005 22:50:24 +0900
By coincidence, I happen to be reading a book that speaks to the
question that occasioned this thread. The book is _The (Mis)behavior
of Markets: A Fractal View of Risk Ruin, and Reward_ by Benoit
Mandelbrot, the father of fractal geometry, and Richard L. Hudson,
formerly the European regional editor for the Wall Street Journal. The
voice throughout is Mandelbrot's. "Consider," he says, "two ways of
looking at the world: as a Garden of Eden or as a black box."
"The first is cause-and-effect, or deterministic. Here, every
particle, leaf and creature is in its apointed place, and, if only we
had the vast knowledge of God, everything could be understood and
predicted....
"Enough. How realistic is that? We cannot know everything. Physicists
abandoned that pipedream during the twentieth century, after quantum
theory and, in a different way, after chaos theory. Instead, the
learned to think of the world in the second way, as a black box. We
can see what goes into the box and what comes out of it, but not what
happens inside; we can only draw inferences about the odds of input A
producing output Z."
Interestingly, too, Mandelbrot not only likens the scientist's
imagination to that of the artist, achievement in both fields
depending on a willingness to discard conventional wisdom, he
frequently cites artists in relation to his own thinking. Here he is
talking about the nature of fractals. He says,
"A fractal has a special kind of invariance or symmetry that relates a
whole to tis parts: The whole can be broken into smaller parts, each
an echo of the whole. Think of a cauliflower: Each floret can be
broken off and is, itself, a cauliflower in minature. Painters,
trained to observe nature closely, have know this without waiting for
science."
Here he cites Eugene Delacroix who himself refers to Swedenborg and
concludes the remark quoted by Mandelbrot by saying,
"I often said that the branches of a tree were themselves complete
smaller trees; pieces of focks are similar to larger rocks, small
handfuls of dirt to very much bigger heaps. I am convinced that many
more such examples could be found. A single feather is made of a
million feathers."
Clearly the difference between the ways in which scientists and
artists perceive the world is less sharply defined that some of us
would like to believe.
John Mc
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