Sunday, November 11, 2012
i was thinking about this when the image of Crowley's rendition of Atu XIV came to mind. Unlike the traditional angel image, his deck shows a being with two sides, two faces, even two genders, but one current mixing and flowing down from its heart into the vessel below. To me, this is a natural interpretation of the motto behind the figure. The most "interior" of the "interior of the earth" to visit is the interior of the self, the first place one must "rectify" before attempting to rectify any other place. Rectifying the self literally means "to make oneself straight," to remove impediments to singleness of heart. However, in the image of Atu XIV, i see a being acknowledging and even working with its multifarious nature. It's comforting to see that this is possible. i certainly use my education in two different fields (mathematics and computer science) in my daily mundane work, and i find being a big sack of opposites as useful (and perhaps entertaining) as it is frustrating sometimes.
Sunday, November 4, 2012
Sunday, October 21, 2012
Saturday, June 23, 2012
Soror PhoenixAngel's recent post pleasantly reminded me about the real analysis and mathematical logic courses i took a number of years ago, and about Paul Halmos' lovely little textbook "Naive Set Theory." (It's "naive" not because it's easy, but because Prof. Halmos didn't focus too much on avoiding the minefield of potential paradoxes when discussing the infinite. Take a look at the cover for a hint at the easiest of the paradoxes.) These topics share in common with other branches of mathematics the intention to find the minimal set of axioms needed to construct everything -- or at least, as much of mathematics as possible. The Peano Axioms are a good example; from them comes all the real numbers. It didn't occur to me at the time that they also define a concrete representation of the integers, from which one can construct a machine to do arithmetic. The resulting "unary" arithmetic is slow compared with other number systems, like the binary numbers found in modern computers, but it's still perfectly functional. When I took a one-semester course tracing the development ofGoedel's Incompleteness Theorem, it became more clear to me how a set of axioms or even the process of deducing theorems can be a computational process. Goedel proved the theorem by translating mathematical statements into numbers, and operating on those numbers. Without realizing it, he had defined a computer for mathematical logic: a terribly slow and space-inefficient computer, but plenty capable. That was a hard semester for me, but i saw computer science in an entirely different way afterwards.
Essays like the respected Soror's remind me of the central role of computation in understanding the universe, whether that be mathematical understanding, as in Goedel's theorem, or metaphysical understanding. Abstracting metaphysical processes as symbols and transformations on symbols has a long history in esoteric thought. Furthermore, both practicing mathematicians and practicing metaphysicians realize that symbols aren't detached from that which they symbolize. This is because we pick symbols as tools to model reality. A hammer has the shape it has because it's useful for pounding nails, and it lacks that which would interfere with that task. Similarly, good mathematical definitions (or good source code) are good because they point back to the concrete examples they model, without including details that would interfere with their utility in making deductions. It's good mental exercise to make and refine definitions, to refactor source code, and to draw analogies and pare away unnecessary details. It's always fun for me to read articles like Soror PhoenixAngel's and watch that process of drawing analogies in action.
Sunday, January 29, 2012
A conversation last week with a dear friend on the gift economy reminded me of a poem from Charles Williams' Taliessin through Logres, called "Bors to Elayne; on the King's Coins." This poem belongs to a sequence on Arthurian themes, and Williams assumes quite a bit of background knowledge on King Arthur's Court and the "Matter of Britain." This poem deals specifically with King Arthur establishing his independence from the Roman Empire by minting his own coins. The "dragon" depicted on the coins represents Arthur's house of Pendragon. Kay is (as mentioned) the king's "steward," which means something like "chief procurement officer." (Remember that wars were won or lost by supply chains, and you'll understand Kay's importance.) Taliessin is the king's poet (and a figure of the author himself, who despite his success as a theologian and career as an editor at Oxford University Press considered himself foremost a poet). Finally, Bors (the Younger) is a Knight of the Round Table and a lord in his own right, and the only one who returned from the Grail quest.
I came in; I saw you stand, in your hand the bread of love, in your head lightness of law. The uprightness of the multitude stood in your figure; my fieldsmen ate and your women served, while you watched them from the high seat. When you saw me a southern burst of love tossed a new smile from your eyes to your mouth, shaping for that wind's while the corn of your face. It was said once that your hair was the colour of corn; he who said so was capable only to adorn the margin of parchments drawn in schools of Gaul; their doctrine is your hands' main. I am come again to live from the founts and fields of your hands; colour is art, but my heart counts the doctrine. On the forms of ancient saints, my heroes, your thumbs, as on a winch the power of man is wound to the last inch; there ground is prepared for the eared and seeded harvest of propinquant goodwill, drained the reeded marshes, cleared the branched jungles where the unthumbed shapes of apes swung and hung. Now when the thumbs are muscled with the power of goodwill corn comes to the mill and the flour to the house, bread of love for your women and my men; at the turn of the day, and none only to earn; in the day of the turn, and none only to pay; for the hall is raised to the power of exchange of all by the small spread organisms of your hands; O Fair, there are the altars of Christ the City extended. I have ridden all night from organization in London, ration and rule, and the fault in ration and rule, law and the flaw in law, to reach to you, the sole figure of the organic salvation of our good. The king has set up his mint by Thames. He has struck coins; his dragon's loins germinate a crowded creaturely brood to scuttle and scurry between towns and towns, to furnish dishes and flagons with change of food; small crowns, small dragons, hurry to the markets under the king's smile, or flat in houses squat. The long file of their snouts crosses the empire, and the other themes acknowledge our king's head. They carry on their backs little packs of value, caravans; but I dreamed the head of a dead king was carried on all, that they teemed on house-roofs where men stared and studied them as I your thumbs' epigrams, hearing the City say Feed my lambs to you and the king; the king can tame dragons to carriers, but I came through the night, and saw the dragonlets' eyes leer and peer, and the house-roofs under their weight creak and break; shadows of great forms halloed them on, and followed over falling towns. I saw that this was the true end of our making; mother of children, redeem the new law. They laid the coins before the council. Kay, the king's steward, wise in economics, said: 'Good; these cover the years and the miles and talk one style's dialects to London and Omsk. Traffic can hold now and treasure be held, streams are bridged and mountains of ridged space tunnelled; gold dances deftly across frontiers. The poor have choice of purchase, the rich of rents, and events move now in a smoother control than the swords of lords or the orisons of nuns. Money is the medium of exchange.' Taliessin's look darkened; his hand shook while he touched the dragons; he said 'We had a good thought. Sir, if you made verse you would doubt symbols. I am afraid of the little loosed dragons. When the means are autonomous, they are deadly; when words escape from verse they hurry to rape souls; when sensation slips from intellect, expect the tyrant; the brood of carriers levels the goods they carry. We have taught our images to be free; are we glad? are we glad to have brought convenient heresy to Logres?' The Archbishop answered the lords; his words went up through a slope of calm air; 'Might may take symbols and folly make treasure, and greed bid God, who hides himself for man's pleasure by occasion, hide himself essentially: this abides-- that the everlasting house the soul discovers is always another's; we must lose our own ends; we must always live in the habitation of our lovers, my friend's shelter for me, mine for him. This is the way of this world in the day of that other's; make yourselves friends by means of the riches of iniquity, for the wealth of the self is the health of the self exchanged. What saith Heracleitus? -- and what is the City's breath? -- dying each other's life, living each other's death. Money is a medium of exchange.' I have come now to kiss each magnanimous thumb, muscles of the brain, functions of the City. I was afraid the Council had turned you into gold, as was told of Midas who had ass's ears. What can be saved without order? and how order? Compact is becoming contract; man only earns, and pays, the house outside the City burns but the house within is enslaved. What without coinage or with coinage can be saved? O lady, your hand held the bread and Christ the City spread in the extensor muscles of your thumbs. Say -- can the law live? can the dead king's head live? Pray, mother of children, pray for the coins, pray for Camelot, pray for the king, pray.
The key in the first part of the poem (before "The king has set up his mint...") is to contrast "organization" and "organic." Bors and Elayne reign feudally over "your women" and "my men"; there is no need to romanticize feudalism. Any "organization" is morally ambiguous; any abstraction of symbol from substance risks dehumanization. (Be sure to read the bit about apes by imagining yourself a pre-WWI Brit.)
Friday, January 20, 2012
It did help, though, to take some time to cultivate consciousness of the Higher Self. This is about all the religious discipline i can manage these days without feeling ridiculous or ashamed. My impression is that the Higher Self has a Name which can be used devotionally. This use helps reminds myself that the end goal is returning to the Source and that the access mechanism is through the Higher Self, which functions as an interface. (i realize i'm using computer science terminology; i suspect Pythagoreans would prefer it (or even category theory) to geometry as a source of metaphysical vocabulary, if they came about today.) Daily life then aims towards that goal of returning to the One. (Honestly, i tire of my individual personality and am really hoping that i get to give it up at the end of my days.) i'm not sure whether this is accurate, but taking this approach during my trip seemed to help me gain perspective on being alone in a place that can sometimes feel alien (not at all due to my spouse's lovely family, though!).