Re: SUO: 4-D representations in relativity and cubism
Hi John,
I don't really understand what you meant with this posting, esp. your
bottom line. Sorry, I won't try to discuss the subject matter of the
book, I'm a little leery about that sort of analogies between
theoretical physics and art. I must be a beotian, this sound to me like
another platitude, better kept for holiday family reunions, maybe
praised for their poetical value at the end of the meal when there's
only brandy left and no more decent red wine.
Did you mean to make a case that a theory based on and serving
"commensensical representations" (or call it whatever) should include a
fragment treating of special relativity?
I don't really fancy this idea. For the few things I understand, I don't
see special relativity as mostly common sensical. I don't see the need
for introducing special relativity in order to account for anything
close to everyday understanding of physical phenomena.
Maybe the question should be: did you mean that a formalization adequate
for the purpose of building a theory of reality based on and serving
"commensensical representations" should also include ressources fitting
the purpose of contemporary fundamental physics?
The only suggestive reason I found to date for considering a 4-d
framework seem to be based on Einstein's conception of spacetime (I
should mention also some unimpressive antirationalist new-agy
orientalish lucubration.) I still can't really grasp what's so curcial
about the alternative. In particular, I fail to see clearly how to
distribute the merit between formalisms. But you seem to mean that
appeal to Einstein stuffs provides additional evidence. My understanding
is that appeal to relativity theory is dispensable for most purposes
having to do with "common sense". I guess I just fail to see the
evidence.
To be fair, I cherish the idea of leaving some room for the upcoming
novelties. I'm just afraid of utterly painful contorsion for the sake of
doxtrinal completude or mere manierism.
I think you'll have to provide another of those pointers to articles of
yours (I apologize for not keeping track of this.) I'm confused by what
you actually claim should be done with the lattice of all possible
theories. But anyway, I'm more puzzled by trying to imaging what would
be an non-open-ended framework. If you have an ontology at time t and
want to account for novelties overflowing your intitial setting, can't
you just extend your ontology, your language, your theory? Can you do
otherwise anyway?
Happy New Year!
yours,
Pierre
"John F. Sowa" wrote:
>
> The discussions about the merits of 3-D or 4-D representations
> have raised many questions, including the issues of how commonplace,
> or commmonsensical, or widely applicable such representations might be.
>
> The following review of a book about Einstein and Picasso draws
> attention to the fact that Einstein invented his theory of relativity
> around the same time as Picasso invented cubism. Arthur I. Miller,
> the author of the book, points out the many influences on both
> Einstein and Picasso that led them to their respective inventions:
>
> 1. Poincare's 1902 book, _Science and Hypothesis_, which directly
> influenced Einstein and indirectly influenced Picasso.
>
> 2. H. G. Wells' book, _The Time Machine_, which appeared in 1895
> and which popularized the notion of time as the 4-th dimension.
>
> 3. Common speculations in both scientific and artistic circles
> about the fourth dimension.
>
> 4. Henri Bergson's writings and lectures about time, consciousness,
> memory, etc., from 1889 to 1934, which contributed to the popular
> interest in time and its relationships to perception and thought.
>
> This book illustrates the wide variety of influences that affect
> the representations used in both science and in what is often called
> "common sense". It provides further evidence for my point that no
> single collection of axioms can ever be adequate to cover all the
> possible variations that are needed in ontology.
>
> Bottom line: As I have said many times before, the ontology must
> be based on an open-ended framework that can accommodate any and
> all representations that might be invented. That is the fundamental
> rationale for organizing the ontology as a lattice of all possible
> theories with systematic ways for navigating from one to another.
>
> John Sowa
> ________________________________________________________________________
>
> Source: http://www.physicstoday.org/pt/vol-54/iss-12/p49.html
>
> _Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc_,
> by Arthur I. Miller
>
> Basic Books (Perseus), New York, 2001. ISBN 0-465-01859-X
>
> Reviewed by Stephen G. Brush
>
> Arthur Miller addresses an important question: What was the connection,
> if any, between the simultaneous appearance of modern physics and modern
> art at the beginning of the 20th century? He has chosen to answer it
> by investigating in parallel biographies the pioneering works of the
> leaders of the two fields, Albert Einstein and Pablo Picasso. His
> brilliant book, Einstein, Picasso, offers the best explanation I have
> seen for the apparently independent discoveries of cubism and relativity
> as parts of a larger cultural transformation. He sees both as being
> focused on the nature of space and on the relation between perception
> and reality.
>
> The suggestion that some connection exists between cubism and
> relativity, both of which appeared around 1905, is not new. But it has
> been made mostly by art critics who saw it as a simple causal
> connection: Einstein's theory influenced Picasso's painting. This idea
> failed for lack of plausible evidence. Miller sees the connection as
> being less direct: both Einstein and Picasso were influenced by the
> same European culture, in which speculations about four-dimensional
> geometry and practical problems of synchronizing clocks were widely
> discussed.
>
> The French mathematician Henri Poincaré provided inspiration for both
> Einstein and Picasso. Einstein read Poincaré's Science and Hypothesis
> (French edition 1902, German translation 1904) and discussed it with his
> friends in Bern. He might also have read Poincaré's 1898 article on the
> measurement of time, in which the synchronization of clocks was
> discussed--a topic of professional interest to Einstein as a patent
> examiner. Picasso learned about Science and Hypothesis indirectly
> through Maurice Princet, an insurance actuary who explained the new
> geometry to Picasso and his friends in Paris. At that time there was
> considerable popular fascination with the idea of a fourth spatial
> dimension, thought by some to be the home of spirits, conceived by
> others as an "astral plane" where one can see all sides of an object at
> once. The British novelist H. G. Wells caused a sensation with his book
> The Time Machine (1895, French translation in a popular magazine
> 1898-99), where the fourth dimension was time, not space.
>
> Picasso actually incorporated the fourth dimension into his creations
> before Einstein did. Miller discusses in great detail the history of a
> single painting, Les Demoiselles d'Avignon--completed and first
> exhibited in 1907, now in the Museum of Modern Art in New York City. It
> is generally considered a seminal painting, which led directly to what
> is now called "modern art." In its final form, "the painting represents
> five prostitutes in a bordello. Although in close proximity, they do
> not interact with each other, only with the viewer--the client." From
> left to right we see: "a partially clothed demoiselle . . . with an
> Egyptian-Gauguinesque face, whose seemingly disembodied arm is pulling
> open a curtain; then there are two more attractive demoiselles of
> Iberian-Oceanic likeness . . . The standing demoiselle on the far right
> is also parting a curtain, while the squatting demoiselle is in a
> grotesquely impossible posture, with her back facing the picture plane
> and her head turned 180 degrees as if on a swivel . . . [with] a face
> that is shockingly hideous in comparison to the others" (page 89). The
> "plot" of the painting is the increasing geometrization of the figures
> as one goes from left to right, ending up with a four-dimensional view
> of the squatting whore.
>
> In striking contrast to Marcel Duchamp's Nude Descending a Staircase
> (1912) where the figures represent successive points in time, seen as
> coexisting in the fourth dimension, Picasso's painting culminates with a
> superimposed set of three-dimensional projections of an object in four
> spatial dimensions. One is seeing the object simultaneously from (a
> sampling of) all possible perspectives rather than from only one as in
> classical painting.
>
> Einstein did not appreciate the value of four-dimensional geometry in
> 1905 but came to it only later, with the help of Hermann Minkowski and
> Marcel Grossmann. Poincaré's influence was significant here but not so
> crucial; in fact Einstein rejected the "conventionalist" philosophy that
> led the Frenchman to the view that no uniquely determined geometry
> governs the world -- you may choose whichever one is most convenient.
> Poincaré even proposed a "principle of relativity" but failed to grasp
> the consequences that Einstein drew from it.
>
> Miller's point is that both Einstein and Picasso discarded the
> empiricist view--"what you see is what you get"--in favor of the
> realist-intellectualist view--thinking, not seeing, leads to the truth.
> The purpose of science is not to provide the most economical
> representation of the facts (as Ernst Mach claimed), and the purpose of
> art is not to provide the most accurate representation of what we can
> see (Why compete with photography?). The purpose of both science and
> art is to discover the reality that lies hidden behind the appearances.
>
> This reality must, of course, conform to the highest aesthetic
> standards. Thus, as Einstein pointed out at the beginning of his 1905
> relativity paper, the basic defect of classical electromagnetic theory
> is that it fails to give a symmetrical description of electromagnetic
> induction, one that is independent of the frame of reference of the
> observer.
>
> In addition to giving detailed accounts of Einstein's discovery of
> relativity and Picasso's creation of Demoiselles, Miller provides
> fascinating biographies of both men. Both were isolated from most human
> concerns by their preoccupation with discovery; for instance, both
> attracted women whom they felt free to discard at will. Picasso had
> more lovers than Einstein did, but it was Einstein who "had the kind of
> male beauty that, especially at the beginning of the century, caused
> such havoc." (This anonymous quote, on page 50, provides part of the
> subtitle for the book.)
>
> I strongly recommend this book to anyone interested in physics or art:
> It enhances a reader's understanding of the connection between art and
> science. It also underscores the breadth and pervasiveness of an
> epoch's intellectual ferment.
>
> --------------------------------
>
> Stephen G. Brush is a historian of science at the University of
> Maryland, and is coauthor with Gerald Holton of Physics, the Human
> Adventure: From Copernicus to Einstein and Beyond (Rutgers U. Press,
> 2001). He thanks Elizabeth Alley for information about art history.
--
Pierre Grenon, Cycorp, Inc, Austin, Texas.
Tel: 512 514 2982 - Fax: 512 342 4040
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