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.

Theoria and praxis, distillation and inspiration

We love books.  While we haven't quite stooped to keeping books in our oven, our little apartment has long ago run out of shelf space.  Books stack in precarious piles around the edges of the living room and reach for the ceiling on top of shelves.  Many of these are spiritual and mystical books, ranging from the most orthodox of orthodox Christianity (St. Francis de Sales' "Introduction to the Devout Life") to the least orthodox (but perhaps more interesting!).  I've read all of them, some several times, but i can't say that i've truly absorbed the implications of any of them.  St. Maximus the Confessor said that "Theology without action (praxis) is the theology of demons."  I don't think i know any more about demonic theology than i do about angelic theology, so perhaps i missed out on the content as well as the implications!

Anyhow, the point is that i look back on my ~ 15 years of devotional study, and wonder what "progress" i made.  I did certainly mature from a pious but naïve youth to a more open-minded, broadly educated adult (who finally finished school not long ago, after an education of nearly epic length!).  My religious perspectives certainly have changed.  I can't say that i'm a kinder person, that i'm more charitable (not just in the "dropping money in the basket" way), that i'm any closer to getting in touch with the Divine -- but perhaps this is because my work and familial responsibilities demand more attention and resources.  There are those books, though, mocking me.

I was thinking about that this morning when i drew two cards out of the Tarot deck:  Temperance and the Star (the latter link might be a bit NSFW if your boss can't handle nonsexual art nudes).  (I took the images from Wikipedia's depiction of the Rider-Waite-Smith deck, which i don't use, though i like Pamela Colman Smith's artwork.)  Temperance and the Star both depict a female figure with two water vessels in the midst of pouring.  The difference is that Temperance transfers liquid from one vessel to the other, while the Star pours them out, one upon the waters and the other upon the earth.  One can understand the water here as inspiration or the "stuff" of spirituality.  Pouring it between containers is an allegory of distillation or refinement (compare the alembic); pouring it out is an allegory of divine or heavenly inspiration.  Distillation and inspiration aren't opposites, but they do involve different agents.  The former is the work of the mystic or "spiritual alchemist" who refines received ideas,  extracting out the "aqua vitae" ("water of life" -- the "living essence" of the idea).  The latter comes from above.  The Star's work happens in secret, at night, without an obvious human agent to receive the results.  (Perhaps our mystic slept too soundly and missed a midnight date with Lady Star!)


The previous two paragraphs introduced two dualities: theoria and praxis, distillation and inspiration.  I would certainly be overextending my rhetorical abilities to put them in correspondence.  They do make an interesting constellation of analogies for understanding how the "stuff" of spiritual life flows around and through a person.  Collected inspiration can be refined and purified through the work of Temperance or nepsis (spiritual sobriety -- the virtue keeping one on the hard, long, but ultimately rewarding path).  Theory has practical implications, and practice influences and inspires theory. 


The personal implication is the necessity of patience in one's spiritual growth.  Inspiration comes when it wills, not when i will.  Distilling it is a lifelong internal work.  Careful praxis may take time to work out, so that it forms a partnership with theoria, rather than fighting against it.  (Just because some group is oppressed, doesn't mean one should immediately rush the barricades with them!)  Perhaps this is only self-justification, but it also seems wise to be patient with one's one nature.  If it takes me a long time to gather and to distill, to refine myself and my ideas, then as long as i'm following the path of true spiritual sobriety, i should let things develop naturally.

Distillation and sublimation

i'd better start up this blog again before the spammers take over!

Was poking around the bookstore for Dion Fortune's "The Mystical Qabalah," which i never had the chance to finish, but found her "The Training and Work of an Initiate" instead.  Surprising to see the book as "The Mystical Qabalah" bought from such a conventional bookstore.  Sometimes i look down on the simple folk in this town, but there must be an interesting reader among them!

Dion Fortune makes a useful point in the latter book: for someone on the path of hidden work in the world (the "occult path"), all the "things of this world" that distract from the Work are not for renunciation, but for sublimation.  The technical image there is of carbon dioxide ice passing directly from the solid to the gaseous state, but the esoteric image is that of "gross matter" being "spiritualized":  the sculptor carving beauty out of stone, the poet shaping everlasting words out of changeable feelings.  Related images are the crucible and the still:  two different ways to express the same idea of separating a noble material from its impurities.

This reminded me of a conversation i had with an experimental chemist.  His experiments require exceptionally pure ethyl alcohol.  Even the alcohol he purchases from chemical supply houses isn't pure enough, so he has to refine it further by distillation, in a process not much different from what moonshiners use.  i asked him whether he couldn't just start with the same raw material (fermented mash) used to distill strong liquors for human consumption, but he said that he can't, because that raw material has water in it.  It's physically (i.e., thermodynamically -- barring the work of Maxwell's Demon) impossible to use heat to separate a mixture of water and alcohol completely.  Some 5% of the water will always remain.  The raw substance with which he starts, therefore, contains no water; it must be made using a different process than used for distilling liquor.

This conversation suggests an esoteric analogy, which should give pause to those who want to practice sublimation: Is it possible to sublimate all human emotions and experiences?  Can everything be spiritualized?  i don't speak of things that are definitely wicked -- that clearly harm others or oneself.  Some things may not be wicked, but they may not be good material for spiritualization: we may need to drop them completely, to renounce them, rather than try to carve them into the desired shape or burn them into a more pure substance.  All things are good, we are told; but are they?

The pen is mightier than the sword?

According to Wikipedia, the word "athame" (referring to a knife used in ritual magic) is a corruption of "artavus," a quill knife ("a small knife used for sharpening the pens of scribes" -- "cultellus acuendis calamis scriptorii," as found in early editions of the Key of Solomon).  Of course the use of such knives in ritual magic has changed over the years and has been subject to fanciful interpretation and outright invention.  However, the subtle meaning (as I see it) is that the pen is equivalent to the knife or sword: a tool that cuts between good and evil.  Truly writing is a "Scheidekunst," though I see that word not as Novalis sees it (as a perverse artificial separation of philosophia into separate scientific fields that do not inform one another), but as "the art of decision."  Surgeons wield the scalpel to access diseased tissue and remove it; critics wield the pen to reveal disorders of thought and excise them.

Vermouth straight: "Trouble in Tahiti"

Over breakfast this morning, I caught a scene from a movie adaptation of Leonard Bernstein's opera "Trouble in Tahiti":  after walking out of a particularly cheesy movie, Dinah works her way through the liquor cabinet in a fit of 1950s confined-housewife-with-selfish-husband misery, singing the whole while.  The staging in a suburban home of the time was full of artifacts and colors of the time (I'm always struck by how enthusiastically 1950s families covered their counters with the latest in kitchen technology).  Amidst all the richness, though, a tiny point stood out:  after Dinah had already drunkenly poured herself a few, the last pour was from a bottle of Vermouth.  That was such a subtle point in the staging, but it meant so much: the only reason for a 1950s American household to keep a bottle of Vermouth around is for martinis, and if she is drinking Vermouth straight, it means she has already exhausted the gin supply and is desperate to continue her drinking binge.  Even though it's a sad, ironic moment, one still appreciates the aesthetic sense, the historical awareness, and the thought that went into the staging.

Consensus: chant and community

This Sunday morning, our schola was joined by a professional singer with expertise in early music -- Gregorian chant, pre-Bach polyphony, and the like.  Different scholae sing chant very differently, and I could tell during rehearsal that she was feeling her way around, trying to figure out how our director and our schola interpret various musical directions.  This led to an interesting discussion between our director and her about how a schola decides on a musical interpretation of chant -- of a particular piece and of a whole style of chant (Gregorian, Mozarabic, Ambrosian, etc.).  It was fun to listen in and talk about the way I learned to sing chant.


During the warmups before Mass, I was assuming the professional singer would remark on the interpretation method.  When she asked a question about interpretation, I remarked that we do "parish Solesmes" (referring to the French monks who revived Gregorian chant in the West in the 19th century), meaning that we interpret vaguely according to Solesmes rules, bending them either to make the music easier for amateurs or to make it more musical.  In the discussion after Mass, though, it came out that she was thinking of something entirely different than a set of rules.  The word she used was "consensus":  guided by the text, the melodic line, and by historical investigation, the schola members gradually come to agree together on the subtleties of interpretation.  She contrasted this with a director imposing rules upon a choir that must learn them.  Consensus is most often not a conscious verbal act; it emerges as a group phenomenon from individuals, who both have unique characters and seek unity and agreement. 

Consensus involves an interesting balance between individual leadership and submission to the group.  Individuals have to have an opinion, and lead -- otherwise the director just ends up imposing a rule, and dragging everyone else along, like a string of five-year-olds on a class outing.  However, people have to compromise on strict interpretations if they realize that the choir just isn't going along.  Everyone has horror stories of that one stubborn person whose rigidity precipitated open conflict.

What I like especially about consensus is that it makes each group unique.  It evolves out of practice -- out of common practice, together -- and thus it shows progress towards forming a real community.  Of course it makes trouble for singers who have to learn all those subtle, unwritten cues when they have to work outside their normal group, but to me that lends so much character to the art of sacred music.

Knowing he is God, he stripped down and washed their feet

Tonight is Maundy Thursday -- Maundy coming from "Mandatum," for Jesus commands tonight in the Gospel reading: 

Si ergo ego lavi pedes vestros, Dominus et Magister: et vos debetis alter alterius lavare pedes.  Exemplum enim dedi vobis, ut, quemadmodum ego feci vobis, ita et voc faciatis (John 13).

"If I, your Lord and Teacher, have washed your feet, then you also ought to wash one another's feet.  For I have given you an example, that as I have done to you, so you do also."  What struck me from tonight's Gospel reading, though, was not so much the familiar command, but John's introduction:

Before the festival day of the Pasch, Jesus, knowing that his hour was come, that he should pass out of this world to the Father, having loved his own who were in the world, he loved them unto the end.  And when supper was done (the devil having now put into the heart of Judas Iscariot, the son of Simon, to betray him), knowing that the Father had given him all things into his hands and that he came from God and was going to God: he rose from supper and laid aside his garments and, having taken a towel, girded himself.

I have to quote the whole introduction to the chapter to get the grand effect.  John reiterates Jesus' unbearable foreknowledge, his sense of purpose and intense love and fully willful, unconstrained and unforced self-sacrifice, and then -- Jesus strips down and puts on a towel.  It's a strange letdown: the language sets you up for a grand, heroic gesture -- perhaps a second, more impressive ritual to follow the first Eucharist, or a revelation of a great new teaching -- and then Jesus does something completely humiliating and weird, something that not even a slave would be asked to do.

In some sense, this act encapsulates the Incarnation:  it's a completely weird thing that such a grand and infinite God could want to be so close to Creation as to become part of it.  Earlier today I saw an article discussing the symbolism of the four-petal jasmine flower that appears on the image of the Lady of Guadalupe.  For the Aztecs of the time, the flower represented the four directions of the universe -- and thus, universal authority, along the same pattern as the circle-cross or spherical scepter topped with a cross.  It symbolized Ometeotl, the Twofold God, "Owner of the Near and Far," "Lord of heaven and earth," "Creator of people," "Inventor of Himself" -- an abstract god without a cult of worship or a temple, a god too grand, high, and remote to have an interest in human affairs.  And yet -- the Fourfold Flower appears engraven on the womb of the Mother of God.  The Lady comes bearing God, the same God that was or that seemed completely inaccessible, yet here appears tiny and weak and helpless, wrapped in swaddling clothes or a towel or a burial cloth.