Sunday, July 25, 2010

Sorry, the Golden Ratio is not "neo-pagan"

One of my favorite blogs for "eye candy" and occasional reading is the New Liturgical Movement (NLM).  The NLM's contributors almost always do a great job at showing beauty in liturgy -- architecture, art, vestments, music, and forms -- without sullying themselves with sectarian politics.  Their opinions are usually well-informed too, which is why a recent post ("Just How Golden is the Golden Section?") disappoints me all the more. 

The author, David Clayton, begins with a reasonable and informed argument that the "Golden Section" (known variously by the Greek letters Φ (phi) or τ (tau)) does not play such a large role in architecture and art as common wisdom assumes.  His assertion is supported by more mathematical articles cited in the comments.  However, the essay's final tangent (starting in the middle of page 3) speculates that the emphasis of Φ over other ratios indicates a "neo-pagan" world view, in which "modern man focuses more on what nature is, rather than what nature ought to be."  The author then continues with rambling, absurd numerological speculation:  that the ancients supposedly searched for meaning in the beginning of the Fibonacci series, whereas moderns seek the "ideal" at the series' end (i.e., the limiting ratio of successive terms of the series, which a little bit of algebra shows is Φ), and that this shows that the moderns "cannot see beyond the proportions of the fallen world."  (Wouldn't it mean the opposite?  Φ should represent an evolutionary view which finds the ideal at the Omega Point -- the end of time which is the consummation of all things.)  Clayton concludes with "A modern Christian interpretation of Φ," which makes the absurd claim that Φ represents the fallen material world and should therefore be called the "Fallen" or "Dark Section," rather than the "Golden Section."

The author's most offensive assertion in this essay -- that excessive veneration of Φ is a "neo-pagan" phenomenon -- is most offensive because it is entirely unfounded.  The article cites sources on architecture, art, and mathematics, but fails to cite a single source on what neopagans or "occultists" (i.e., students of the Western hermetic tradition, whom Clayton snidely derides as unworthy of his investigation) believe about Φ.  The author does observe the Pythagoreans would likely favor ratios of whole numbers, rather than irrational (in the mathematical sense) ratios like Φ.  Sacred geometry and numerology in the Western hermetic tradition seems to favor the Pythagorean approach, for example using the Tetractys in correspondence with the Tree of Life.  Irrational ratios do appear, but more incidentally, as part of regular geometric figures or Platonic solids.  Occultists do make use of the pentagram in rituals, but this occurs entirely independently of Φ. 

I'm not qualified to speak about what neopagans believe.  It is a point of controversy how much the 20th-century development of organized Western neopaganism has in common with (in)famous occult figures of the time (see e.g., Wikipedia's article on Gardnerian Wicca).  I would say, however, that both neopagans and occultists tend to be syncretic in their beliefs, and "take whatever they think is good from wherever they can get it."  Interest in Φ by a neopagan or occultist may be no more special than their usual interest in phenomena that relate the macrocosm to the microcosm.  (Clayton himself proposes Φ as an expression of this relation.)  Furthermore, a central premise of the Western hermetic tradition at least is the brokenness of the created world.  Human beings participate in the healing of that brokenness, a process known as the Great Work.  In that sense, the ratio Φ has no more to do with "fallenness" or "darkness" than any other ratio of physical quantities.

Despite my criticism of Clayton's article, I should point out that he presents his conclusions as provisional.  I would encourage him to consider not only evidence from art and architecture, but also from those beliefs which he critiques without understanding.

4 comments:

PhoenixAngel said...

Like your stuff Hilbert. Didnt know you blogged too! I'm definitely going to follow it! Thanks :)

HilbertAstronaut said...

i'm kind of late responding to comments -- and too lazy + busy to post as often as you! -- but your comment inspires me to work harder :-)

PhoenixAngel said...

Yes Please! I will listen. Anyone who has a Post-Doc in Linear Algebra (love matrices!) and can talk spirituality is GREAT!

HilbertAstronaut said...

i can talk the talk, but can i walk the walk? ;-)

Seriously, engineers are awesome -- the more i work with them, the more i realize that they have a consistent life philosophy: standardize, discover what is possible, use all the tools at hand, and solve real problems imperfectly rather than toy problems perfectly. Feel proud! You're in great company :-D