i realize that i should really just get around to learning calculus (one way or another), if i am ever to functionally utilize the concept of infinity... meanwhile, this is still fun, for the moment... but eventually, there must be a limit!

meanwhile, i think that i will continue in the “uniting of consciousness with infinite space by the exercise of love...”.

on a related note, this surprisingly concise description of thelemic cosmology comes from religioustolerance.org:
"Thus, the Book of the Law conceives of each conscious individual as a perfectly simple, and therefore indestructible, point of view in an infinity of possibilities all striving to return to their source and origin in Nothingness by gradually extending themselves over time to build up into their conscious sensorium an ever increasingly complex system of point-events, until they incorporate into themselves the totality of all that is, i.e., infinity."

for further clarification, this is from an article called, Zero Points & Heart Spaces:
"The Law is for All, elaborates these mysteries – in explanations of Hadit and Nuit. Hadit is an infinitely small and atomic point, while Nuit is infinite space, the root principle of creation which allows for the manifestation of Hadit. The conjunction of Hadit, the supernal point within cosmic space, Nuit, is the root for all manifestation. Hadit and Nuit are identified with various dualities; the masculine and feminine principles, yang and yin, motion and matter, the star or point of light within the darkness and emptiness of space. "

of further curiousity are the entities of Azathoth & Yog-Sothoth in Lovecraft's cosmology... according to The Necronomicon Research Group:
"Azathoth, the ultimate nuclear chaos that emits the random waves that govern the universe, seems to be the principle opposite of Yog-Sothoth, who embraces the expanses of infinity. Whereas Yog-Sothoth is infinitely large, Azathoth seems to be infinitely compact (e.g., the quantum center). HPL researcher Philip A. Shreffler states in _The H.P. Lovecraft Companion_ that the acting principles of Yog-Sothoth and Azathoth are "infinite expansion and infinite contraction" respectively."

infinity also appears in crowley's descriptions of the naples arrangement, which i have always thought a fascinating system; but perhaps y'all will enjoy this piece of skepticism about crowley's theories:
Of Myths and Maths (third in a series of articles)

or these contemplations of the unicursal hexagram by a satanist, and a thelemite

but here's some fascinating artistic theory, anyway:
Projective Synthetic Geometry in Lady Frieda Harris' Tarot Paintings and in Aleister Crowley's Book of the Law, by Claas Hoffmann (also q.v. my links to rudolf steiner & his anthroposophical theories of infinity, in my previous post about infinity)

oh, and although wikipedia has a less controversial listing for infinity that specifies: "Infinity is a term with very distinct, separate meanings which arise in theology, philosophy, mathematics and everyday life." ...there is also a discussion called Talk:Infinity at wikipedia that has been referred to as, "a mushy mix of philosophy, intellectual history, and mathematics, (containing) a lot of outright errors"

also, amusingly enough, the World Peace Translation of The Tao Te Ching uses the word "infinity" to represent the Tao.

To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.

--William Blake, Auguries of Innocence


the roots of infinity as a symbol used in mathematics are often traced back to John Wallis in 1655, and Bernoulli in 1694.

although the truth is that there's an even deeper history when you scratch below the surface...

the leminscate (from "lemniscus" ...which, according to Gérard P. Michon, Ph.D. of numericana.com, is Latin for "pendant ribbon") is perhaps related to the analemma (which, according to Brian Tung of Astronomical Games, comes from the Greek word "analambanein", meaning "to take up, to resume, to repair")

i also found some anthroposophical stuff that incorporates the idea of the leminscate one way or another...
from an anthroposophical criticism forum, "mysplum" wrote:
A leminscate is a sign that resembles the figure 8 which stands for eternity. The leminscate is a very holy symbol in Anthroposophy. Steiner's first Goetheanum (mystical temple) was built to represent the leminscate (eternity). If you read Anthroposophic books you will notice that many illustrations explaining Steiner's "science" utilize the leminscate. For example Steiner drew a leminscate to show how the astral body travels at night in the cosmos. It is an important and basic symbol of Anthroposophy with healing powers. I read once that children knit in order to be exposed to the healing powers of leminscates. The fingers make leminscates with the wool around the needles.

also, q.v.:
The Ogdoad
ouroboros
Möbius Strip
M.C. Escher's Moebius Strip I
M.C. Escher's Moebius Strip II
Deep Mathematics and Meta-systems Theory

...and my further explorations of the nature of philosophical perspectives on the idea of infinity