J.W. Power was an Australian artist who, while at one time very
significant, seems to have fallen out of the history books. Born in
1881, he studied medicine at the University of Sydney, and then
moved to London in 1907 for further study. He was a military
surgeon during World War I, and after the war decided to become a
full-time artist, spending much time in Paris. He became a
member of the avant-garde group Abstraction-Création in
company with other leading artists in Paris, and was involved with
both cubism and surrealism.
Power left a large sum of money to the University of Sydney for the
purpose of making the latest ideas and theories in art available in
Australia through lectures and through the purchase of
artworks. The bequest eventually led to the establishment of
the Museum of Contemporary Art in Sydney as well as the Power
Institute within the University of Sydney. Power as an artist
is currently attracting attention, with a major Power exhibition, in
the form of a recreation of Power's solo exhibition in Paris in
1934, coming up at the University
of Sydney's art gallery.
My interest in Power comes about because in 1932 he published a
geometrically-based book (in Paris; both French and English versions
appeared). The English version has the title The Elements
of Pictorial Construction: A Study of the Methods of Old and
Modern Masters. I recently had a chance to examine
copies of both versions at the University of Sydney, thanks to
Anthony Green, Senior Librarian of the Schaeffer Library and Ann
Stephen, Senior Curator of the University of Sydney Art
Collection.
I also found that the whole work (in French and English) is
available online through the National Library of Australia (go to
http://catalogue.nla.gov.au/ and search for "elements of pictorial
construction"). However, the physical book has a unique
feature: six pockets at the back, each of which contains a
photograph of an artwork and one or more transparent sheets with
lines drawn on them, which are to be placed over the photograph
according to instructions in Power's text. These reveal
features of the construction of the work, according to Power's
analysis.
What is the basis of Power's work?
Power considers that he is recovering a method of construction used
by the Old Masters. He starts from the idea that all the
significant points in a masterpiece of painting are carefully
placed. He draws horizontal and vertical lines from each such
point to the edges of the painting, and considers in what proportion
the edges are divided, expecting this to be significant. Apart
from the midpoint of the edge, the Golden Section point
(approximately 0.618) is a natural choice, but Power introduces
others, including a point on the long side which is √2 or about
1.414 times the length of the short side, being the diagonal of the
square on the short side. Then Power has a method of
"transfer": for example, take the distance between the √2 point and
the end of the long side, and mark off this distance on the short
side. He even makes a second transfer of the remaining
distance on the short side back to the long side. The result
is a large number of horizontal and vertical lines (27
horizontal lines and 16 vertical in the case of the "Mond"
Crucifixion by Raphael, in Power's first detailed
analysis). Power also identifies an equal-sided nonagon
(nine-sided figure) connecting significant points within the
painting, and a hexagon surrounding the painting.
Power also has an idea of "movable format", the same configuration
appearing in different parts of the one painting. He applies this
to a Last Judgement by Rubens, with the movable
configuration consisting of a perspective drawing of a cone with an
inscribed square pyramid, which he sees as being used in
approximately eight different positions. Having a actual piece
of cellophane to move about is a great help! According to
Power, the positions are not arbitrary, but each is obtained by
rotating the configuration about a specific point, or a similar such
move.
There are some other ideas about construction in the book as well,
but the division of the edges of the painting and the "movable
format" are the most important.
What do I think of the book?
Power sticks very closely to his subject of construction and does
not consider colours in the book, let alone things like symbolic
content; there is a complete absence of mystical waffle. The
book is also clearly written and generally easy to follow.
However, in my view Power has not made a convincing case for what he
claims.
It is uncontroversial that large paintings were frequently first
done at small scale and then transferred to a wall or panel by some
process of drawing up a grid. However, as far as I know the
grid was made up of equally spaced lines (extant examples indicate
this). Also, although the golden section was known and used,
again as far as I know there is no historical evidence for things like
Power's √2 point, let alone his "transfers" of such points.
So if there is a lack of historical evidence, the evidence must be
internal to the works; indeed Power says: "[The Old Masters']
studies and sketches handed down to us show very few traces of these
methods, while the finished pictures show a great many."
My first comment is that Power's method is on the whole not
perceptually based. We know that a division of a line in a
ratio somewhere in the range 3/5 to 2/3 is perceptually attractive,
and this explains the photographer's "rule of thirds". But
there is no reason to suppose that the exact value 0.61803... of the
golden ratio is perceptually markedly better than say 0.625 (which
is 5/8). There is no perceptual reason for things like the
"transfer" of twice the short part of the golden section division of
the long side (which occurs in Power's analysis of Raphael's Disputa).
So we are dealing with Power's geometrical ingenuity rather than
perceptual givens, and Power has provided an array of lines and
construction methods that I suspect can yield a good approximation
to any ratio. The question is then whether the Old Masters used
geometrical ingenuity in a similar way. It is not out of the
question for a Renaissance master to be playing mathematical games
in a painting, certainly with the golden section, but Power has not
made a good case for the Old Masters to be playing his
mathematical games. There is a range of geometrical ideas that
Power could have discussed and didn't. Power doesn't provide
the derivations for all of the lines in his analyses, but it is
notable that he doesn't discuss equal divisions beyond the midpoint:
there is no mention of thirds, quarters, fifths, etc. It
is also notable that there is essentially no mention of the
possibility of the same configuration occurring at different scales
within the same painting. In geometrical terms, Power is
concerned far more with congruence than with similarity. And
there are always further possibilities: for example Power introduces
ellipses but doesn't mention their focal points.
The "movable format" idea is intriguing; certainly for a swirling
composition like the Last Judgement by Rubens, something
like it appears more appropriate than fixed horizontal and vertical
lines. However, I found the use of a pyramid drawn in
perspective problematic. Power is not attempting to construct
a three-dimensional model of the space implied by the painting; he
is simply moving the perspective drawing of the pyramid as a flat
object around the surface of the painting. This makes nonsense
of any perspective within the drawing of the pyramid. On the
whole, Power isn't much concerned with perspective. Raphael's
Disputa has lines near the bottom whose spacing is determined
by perspective, not by the sort of division that Power is interested
in; Power doesn't consider these lines in his analysis.
I think that Power has driven his methods much too far, seeing
things that are not there; I suspect that similar methods could
provide quite different analyses of the same painting. The
choice of significant points and lines is of course up to the
judgement of the interpreter, and I am reluctant to challenge Power
on this, but in Raphael's Crucifixion, for me the nail
through Christ's feet is a prominent point in the painting; Power
doesn't mention it, though he does mention other less prominent
points. Then I could draw diagonal lines through the angels'
feet and the nail to the faces of the kneeling figures, and start
looking for similar triangles, and so on. If it is possible to
give two quite different geometric analyses of the same work, both
are likely to be illusory. I was somewhat more convinced by
Power's discussion of cubist construction, since in cubist work it
is reasonable to find both simple geometric shapes and the use of
plan and elevation as described by Power.
As an aside, although the title The Elements of Pictorial
Construction brings to mind Euclid's Elements of Geometry,
Power is not using Euclid's methods (and does not claim to use
them). The nine-sided figure Power finds in Raphael's Crucifixion
cannot be constructed exactly by ruler and compass. Also Power
has not read all of Euclid's Elements: he refers to the
"dodecahedron and icosahedron, the proportions and structure of
which had then [by the later Renaissance] been worked out".
But the dodecahedron and icosahedron are discussed by Euclid.
It is interesting to consider what has happened in mathematics since
Power's time. Power's geometric viewpoint comes across today
as far too rigid. Power was not a professional mathematician,
and it is not fair to the history of mathematics to take him as
representative of his era, but certainly an emphasis on more
qualitative approaches such as topology has become stronger.
Topology was already well established by the 1930s, but may not have
been accessible to people in Power's position, or
may not have been seen as relevant. However, D'Arcy Thompson's
On Growth and Form, published in 1917, might have caught
Power's attention. Since Power's time a major impetus away
from simple formulas has come from the computer. Chaos theory,
fractals, and things like strange attractors and percolation theory
have all given us new geometric objects that are quite different
from the cubist cone and cylinder; although these new forms have
been given solid mathematical underpinnings, the computer has helped
in the discovery and investigation of the phenomena. And in
general the absence of simple formulas in an area of investigation is much less of an
obstacle than it was.
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