Mathematics
I was originally aimed to be a mathematician, you know. I remember those long-ago days when I was a teaching assistant in the math department at the University of
eπi + 1 = 0Though I think my favorite (quirky choice, I know) was:
i² = j² = k² = ijk = -1Then there's Parseval's theorem, in Fourier analysis; if only I could figure how to represent it in HTML, which I can't; though you can find it here.
posted by paul @ 7:24 AM
8 Comments:
I keep wondering whether that's not beauty but wondrousness. If beautiful things (in Aquinas's formulation) are those which, seen, please, then wondrous things are those which, seen, rule. Or something like that.
In my own Hermetic language, the beauty of mathematics would be mn'athlo, which is sometimes (quite inadequately) rendered into English as "splendor." If something is athla, it exemplifies something like the mysterium of Rudolf Otto's mysterium tremendum.
To quote from the notes I penciled into the flyleaf of my copy of Otto almost 20 years ago: "mysterium, stupor, the wholly other, θατερον, θαμβειν, astounding, amazement, wonder, the 'beyond' (επεκεινα), transcendent, mn'athlo, mn'olthro, mn'olthraona, mna thijizmona."
Or to quote from myself elsewhere: "How can I convey the meaning of Hermetic terms such as dhnamo and athlo? Each denotes awesome power, and yet dhnamo is the power of lightning, of the sword stroke, of main and might. While athlo is the power of the unforeseen chess gambit, of architectural form, of perfect balance, of the craftsman's master touch. To the Hermetic mind, it is obvious that the sun is dhnama, while the moon is athla."
It sounds like your athlon is an aspect of what I would mean by "beautiful" -- it's about cognition that enhances feeling & affectivity -- athlon seems to pertain particularly to the feeling of being arrested, struck, impressed (which I would call the "first stage" of the apprehension of the beautiful). Well, "impressed," etc., are mild words compared to "astonishment," but I like to cover the whole range. The stage is Joycean in conception, but I don't associate it with that which Joyce called "wholeness" but instead with that which one might technically call "due directed magnitude."
What I mean by "wondrous" is neither athlon nor dhnamo which latter seems sheer concentrated directed force. By "wondrous" I mean something which, by one's sheer apprehension of it, commands one and perhaps frees and empowers one -- it's about cognition that enhances volition, choice, conation, etc.
I think that there's a resonance, an echo, between wondrousness and beauty as athlon to the extent that athlon means things like "astounding," "majestic," etc. (due directed magnitude), which is to the extent that athlon is beauty in its most dhnamo-like aspect. Splendor, radiance, the lovely bloom, the vital feeling & energy, these seem to me to be another aspect of beauty, though of course they can be great enough to be astounding by that very greatness. Anyway I'd associated with the third stage (also Joycean in conception), that of enchantment, becoming rapt, even enraptured. The arrival at the essence, its blooming for the mind.
I've borrowed a few of your words there, but, independently, I've been at this a long time. Nuances of semantics -- in philosophical thinking, it seemed for some time almost all that I had, drifting among all those echoes.
Sorry I kept writing athlon instead of athlo. I was just at the Perseus-Tufts Greek dictionary looking up thambein and got caught up in Greek forms.
It sounds like your athlon is an aspect of what I would mean by "beautiful" -- it's about cognition that enhances feeling & affectivity
Well, yes, though at the same time mn'athlo is about feeling & affectivity that enhance cognition— something like Goethe's approach in his plant morphology, his theory of colors, etc., insofar as I understand those correctly. Will have to blog about Goethe some time, if I can find a way to pry him loose from the clutches of spooky doo-doo doo-doo Rudolf Steiner, whose followers have in these latter days pretty much monopolized Goethe on that front, alas.
Or to take another example which is quite athla... the aesthetics of the Go board, with its not quite square grid, the white and black stones with their slightly differing shape and size and texture, all contribute to enhancing the players' visual grasp of the game. Wish I could locate the psychological study done years ago which found that Go neophytes were able to play better, at a higher level (kyu ranking or whatever), with a traditional Go set than with other, at first blush no less suitable but quite nontraditional Go sets.
By "wondrous" I mean something which, by one's sheer apprehension of it, commands one and perhaps frees and empowers one
Hmmmmm, along with the Hermetic language I also developed a Hermetic culture (or loose cluster of overlapping cultures) which is often implicit in the language and its usage. In fact, in Hermetic thought there is a sort of dialectic, a cosmic dualistic struggle, between mna dhnamo and mn'athlo. A bit like yin and yang. Or, to be exact, a struggle between the Sun (dhnama) and the Moon (athla). When one recognizes Dhalbembu the Moon as athlona, not only is one having certain feelings and cognitions, but in some sense the Moon is striving to increase his rule, his command over one, and over the world.
In my epic Mna Sipri Cilama (The Celestial Labors), for which I really ought to produce a satisfactory English translation some time, the king Dhalathlo goes on a cosmic journey, a great circular trek through earth and sky, in which he is changed and transformed. To use a Tolkien analogy, he starts out like Frodo Baggins and ends up like Aragorn, the return of the king. All due to the struggle within him (unbeknownst even to himself) between mn'athlo and mna dhnamo. In the end Dhalathlo passes over the tipping point, as his personal transformation triggers a vast cosmic transformation... (Always thought that scene would make great Japanese anime... ^_^ )
I'm not sure if any of this aligns with the distinction you're trying to draw. Arrrgghhhh, if I start blogging about Hermetic culture there'll be no end to it, and it just gets more and more and more arcane...
Cognition that enhances affectivity can be produced in works through cognition with regard to affectivity and, in particular, through understanding in what effects one feels things. I mean not a psychologist's understanding, but an artist's understanding -- that understanding, formed as a discipline, is his/her art.
Likewise affectivity that enhances cognition can be produced in works through affectivity with regard to cognition -- valuing with regard to cognition -- feeling and valuing in what signs & evidences one cognizes things -- and including love of knowledge, philosophy in its earliest and now somewhat buried sense, and including the valuing of standards of evidence, standards of signs, and so on. Love of truth, clarity, evidentness, even obscurity. Love of the imaginative. More generally, what do we value as true and legitimate and real?
I'm not sure about our alignments, I'll have to think about that a while. There's one other thing which you mentioned but that's for off-blog.
At your linked page The Hermetic Language, you wrote "here it was the evil sun-god, Rotas, who was trying to free the world from multiplicity and return it to the undivided unity of the primordial point. While it was the good moon-god, Dhalbembu, who was struggling to preserve the "myriad-faceted jewel" of this tangled world in all its diversity."
It reminds me of the last line of Hypocritic Days by Douglas Woolf, where the central character thinks of how the Moon is pale compared to the sun, "but at least it was something a man could stand to look at."
Yes, it was sort of a gnosticism-in-reverse, with Rotas the sun-god (cf. the gnostic demiurge) wanting to "reformat the hard drive." And Dhalbembu the moon-god wanting, not to "exit the Matrix," but rather to purify and perpetuate the Matrix; as if alchemically transmuting the blue pill into the red pill.
"The myriad-faceted jewel" (mna camno calpila): I keep using that phrase, though oddly enough it doesn't even occur in Mna Sipri Cilama!
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