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A Challenge to Thelemic Mathematicians 



Posted by Mordecai on December 05, 2001 @ 10:57 AM
from the anynumbercanplay dept.
It's well known that Aleister Crowley was a great believer in the scientific relevance of his revelation. Indeed, in "The Summons" printed in Equinox of the Gods, he writes of the Book of the Law, "Its solution of the fundamental problems of mathematics and philosophy will establish a new epoch in history." [emphasis mine] In his 1920 comment on verse I:28 ("None, breathed the light, faint & faery, of the stars, and two"), he tried his hand at some mathematical analysis of his own. I am not wellversed in higher mathematics, but I would be quite curious to see what any mathematicallyinclined reader out there makes of it as a piece of mathematical reasoning.
Now appears the plain statement of the Perfect Metaphysick. It may be as well to quote the essential passages from 'Bereshith' in connexion with this matter.
"I ASSERT THE ABSOLUTENESS OF THE QABALISTIC ZERO."
When we say that the Cosmos sprang from 0, what kind of 0 do we mean? By 0 in the ordinary sense of the term we mean "absence of extension in any of the categories".
When I say "No cat has two tails" I do not mean, as the old fallacy runs, that "Absenseofcat possesses two tails"; but that "In the category of twotailed things, there is no extension of cat".
Nothingness is that about which no positive proposition is valid. We cannot truly affirm: "Nothingness is green, or heavy, or sweet".
Let us call time, space, being, heaviness, hunger, the categories. If a man be heavy and hungry, he is extended in all these, besides, of course, many more. But let us suppose these five are all. Call the man X; his formula is thenX^{t+s+b+h+h}. If he now eat he will cease to be extended in hunger; if he be cut off from time and gravitation as well, he will now be represented by the formula X^{s+b}. Should he cease to occupy space and to exist, his formula would then be X^{0}. This expansion is equal to 1; whatever X may represent, if it be raised to the power of 0 (this meaning mathematically "If it be extended in no dimension or category"), the result is Unity, and the unknown factor X is eliminated.
Now if there was in truth 0, "before the beginning of years", THAT 0 WAS EXTENDED IN NONE OF THE CATEGORIES, FOR THERE COULD HAVE BEEN NO CATEGORIES IN WHICH IT COULD EXTEND! If our 0 was the ordinary 0 of mathematics, there was not truly absolute 0, for 0 is, as I have shown, dependent on the idea of categories. If these existed, then the whole question is merely thrown back; we must reach a state in which 0 is absolute. Not only must we get rid of all subjects, but of all predicates. By 0 (in mathematics) we really mean 0^{n}, where n is the final term of a natural scale of dimensions, categories, or predicates. Our Cosmic Egg, then, from which the present universe arose, was Nothingness, extended in no categories, or, graphically, 0^{0}. This expression is in its present form meaningless. Let us discover its value by a simple mathematical process.
0^{0} = 0^{11} = {Multiply by 1 = n/n} Then 0^{1}/n x n/0^{1} = 0 x ∞
Now the multiplying of the infinitely great by the infinitely small results in SOME UNKNOWN FINITE NUMBER EXTENDED IN AN UNKNOWN NUMBER OF CATEGORIES. It happened, when this our Great Inversion took place, from the essence of all nothingness to finity extended in innumerable categories, that an incalculably vast system was produced. Merely by chance, chance in he truest sense of the term, we are found with gods, men, stars, planets, devils, colours, forces, and all the materials of the cosmos; and with time, space, and causality, the conditions limiting and involving them all.
Remember that it is not true to say that our 0^{0} existed; nor that it did not exist. The idea of existence was just as much unformulated as that of toasted cheese.
But 0^{0} is a finite expression, or has a finite phase, and our universe is a finite universe; its categories are themselves finite, and the expression "infinite space" is a contradiction it terms. The idea of an absolute and of an infinite God is relegated to the limbo of all similar idle and pernicious perversions of truth. Infinity remains; but only as a mathematical conception as impossible in nature as the square root of 1."
This passage was written in 1902, E.V., before the revelation of the Law. It remains true that 'infinite space is a contradiction in terms', and so on; but this is no argument against the Cosmogeny of this Book. For above the Abyss every idea soever is necessarily a contradiction in terms; see Liber 418 for the demonstration of this.
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Re: A Challenge To Thelemic Mathematicians
by Mordecai on Wednesday December 05, @11:18AM

>Then 01/n x n/01 = 0 x ?
If your browser shows the final term of this equation as a question mark you should know that it is supposed to be the sign for "infinity".


Re: A Challenge To Thelemic Mathematicians
by Xnoubis on Wednesday December 05, @11:36AM

Oh dear. Could someone who's seeing a question mark in that line in the article comment on whether an infinity sign shows up below?
∞
If it does, I'll mark it up that way in the article (as a named character entity rather than as a Unicode value, for the geekish out there).



Re: A Challenge To Thelemic Mathematicians
by jcat on Thursday December 06, @09:18PM

...perhaps the cat is a minx
perchance there is a no chance
wherin the intent of extent
is zero content...
where as all possibilities
are impossibel and impossible
at one and the same time...
were time to arise in any given
set of sequences...therefore
eternity would return to the scene
of the X crime...to the nth dimension
cat in the city with two tales
in one version the cat is let
out of the given bag...
in the other cat finds a fine finite
and proceeds to use it as a kind of
shoo stone....wherin the cat is
promply shooed....into the infinite


Re: A Challenge To Thelemic Mathematicians
by johnadreams on Friday December 07, @08:31PM

how about this for math?
sator
arepo
tenet
opera
rotas
do what thou wilt shall be the whole of the law,
love is the law, love under will
v.v.v.v.v.
johnadreams


Re: A Challenge To Thelemic Mathematicians
by Mordecai on Saturday December 08, @11:46AM

Not exactly relevant, useful, or original, but thanks anyway.



Re: A Challenge To Thelemic Mathematicians
by Fra. T_H_A_M on Saturday December 08, @03:29PM

Interesting, although I lack any apptitude for mathematics. It does in, certain respects, compliment some current research I've concluded. I've just finished a heavy paper on how Qabalah informed the output and anarchism of the painter Barnett Newman. I had to go and wade through alot of Lurrianic Kabbalah, and was amazed at how prescient it seemed. The manifestation of form from 0, by the process of tzimtzum, seems curiously like descriptions of creation by modern physicists and cosmologists. I am by no means a scholar of this branch of kabbalistic epistimology, so i wonder if anyone else has encountered it? Sorry for my tangent.


Re: A Challenge To Thelemic Mathematicians
by Fluffy the Wonder Vole on Saturday December 08, @06:34PM

He doesn't really seem to say much of anything. How did he display that zero was dependent on categories? I duuno. Why does he equate the dimensions of measurement applied to a thing with exponentiation? I dunno. Why does he not refer to any of the number theory that was around at the time? He didn't know it, I guess. I'm trying to extract some meaning from the piece in order to respond to it and I find that I can't.
(Oh, and zero times infinity is zero, and imaginary numbers appear in our descriptions of nature constantly.)
"The Universe Explained. By A. Cambridge Dropout. Two pence."


Re: A Challenge To Thelemic Mathematicians
by Ulan Batar on Thursday December 20, @07:06AM

There are a number of fallacies in this argument.
1. You define X as man and separate it into categories. You don't define any relations between those categories. Nor did you define what you mean by "category". I don't understand how "being" can be separated from the others. If there is no extension into "being" then the other categories are irrelevant! X itself should thus be "being", no?
and then all of a sudden X becomes an "unknown factor". Are you now saying man that is an unknown factor?
2. (0^1/n) * (n/0^1) is meaningless by itself. x/0 is termed "undefined" in mathematics, not
infinity, and there is a good reason for it, which stems from the mathematical definition of "division".
If this issue arises in a physical problem,
then you take the limit:
lim x>0 [n/x] = inf.
this means n/x approaches infinity as x approaches 0. (read: it never actually equals it!)
Your equation ( (0^1)/n ) * ( (n / (0^1) ) can be analyzed with calculus.
lim x>0 [(x/n) * (n/x)] =
lim x>0[(x/x) * (n/n)] =
lim x>0[1 * 1] = 1
in other words, 0^0 approaches 1, but NEVER equals it.
3. multiplying the infinitely great by the infinitely small DOES NOT result in SOME UNKNOWN FINITE NUMBER. If you want to be "mathematically correct", you'd either say "undefined" or you'd study how the the two extremes approach their respective limits (inf or 0). For example
(2x/x), as x goes to infinity, you get a classic example of the infinitly large (2x) times the infinitly small (1/x). however, regardless how big or small x is, it will always be 2, even though the infinitly large gets large twice as fast the the infinitly small decreases.
4. just because something can be stated using mathematical terms, it in no way makes it correct.


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