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Transfinite numbers and magic

23:18 / 29.04.02

Does anyone know of any magical subjects relating to magic and the transfinite numbers? Whether its numerology or a kind of Gematria thing or anything else?

It seems like the kind of thing magic-folk would absolutely adore, but I don't know if I have ever heard it mentioned.

If not, then does anyone have ideas about how we could start to make one? And how we could use it?

23:44 / 29.04.02

OOooohh...math and magick.

Math and Magick

The previous link is a pretty good overview of Mathematics and magick. I'm not quite sure what you're asking here exactly.

04:54 / 30.04.02

Non-Euclidean geometry and transfinite arithmetic might well serve a similar purpose in mystical thought, but
exploration along these lines has been almost non-existent.

That answers my first question, I suppose.

So does anybody have any idea how we might begin to fill this void?

12:56 / 30.04.02

1/0 = infinity

1 = the self, the ego
0 = void, dissolution, nothingness, zen

Eastern mysticism expressed as an equation.

Or, as I prefer to view it:

1 = infinity * 0

Somewhere within the dualistic conflict of nothingness and infinity lies the true self, the soul. Conflicting infinite dualities as the dynamo of creation. One gives rise to 2 whose interaction brings about the 10,000 things.

Those are the bits I like to play with.

15:38 / 30.04.02

Define: transfinite number.

solid~liquid onwards

17:17 / 30.04.02

i read a book about sacred geometry ages ago, if its of any interest.

dunno any sites, suppose you'll just have to search

17:44 / 30.04.02

Check out this page and then follow the link to "Cantor's Solution: Denumerability" at the bottom of the page.

If I understand right, a transfinite number is a number which describes "degrees of infinity"... i.e., there are the "same" number of natural numbers as even natural numbers because these sets:

{1, 2, 3, ...n}
{2, 4, 6, ...2n}

can be matched up element by element. But you can't match up the natural numbers with all the real numbers--there are more real numbers, even though the natural numbers and real numbers are both "infinite."

Anyway, check the link, in case I screwed it up.

Wrenching myself back to the abstract: the idea of infinities which aren't as big as the next infinity up the line might be an appealing way of dealing with gods, or in invocation... hm.

Maybe looking at degrees of infinity could be a way to deflate yourself if you're feeling like a GREAT AND POWERFUL ARCHMAGE and need to get knocked back to earth. Work that idea into a banishing or something?

18:12 / 30.04.02

One divided by zero does not equal infinity; it’s an undefined number, which is far stranger.

IMHO, the real magic in math is in the math, not in the fanciful systems we’ve constructed around it. Math is the music the universe dances to--how cool is that?

22:08 / 30.04.02

doubting thomas is describing cardinality. Cardinality is the size of a set. It refers to both finite and infinite sets. So a set {0,1} has two elements and therefore a size (cardinality) of 2. In symbols, this reads
card({0,1}) = 2

When I say a transfinite number, I mean something just a little bit more general. I mean an ordinal number.

Here are the first few ordinals
0, 1, 2, 3, 4, 5, ...

"After" all of those ordinals is an ordinal called omega (written as a lower case omega, which I will write "w" unless someone knows more about html than I do)

w, w + 1, w + 2, w + 3, w + 4, ...

2*w, 2*w + 1, 2*w +2, ....

3*w...

4*w

5*w
:
:
:
w*w

and so on. All of the transfinite numbers I've written so far have the same size, namely w.

But there are numbers of larger size. The next largest size is w_1 (where 1 is usually a subscript)

We have defined this number mathematically, but we really don't know what it is.

What doubting thomas described with the size of the real numbers versus the size of the rational numbers is very interesting. We know that the size of the set of rational numbers is w. We do not know what the size of the set of real numbers is. We just know a few things it isn't! It is not w, for one thing. It might be w_1 or w_2 or w_3. But it cannot be w_w.

And other stuff like that.

I hope I'm explaining this well.

23:47 / 30.04.02

Good explanation SMat, though there is a lot of wierdness hidden in the explanation. To reiterate your point, ordinals are things that have both a size and an ordering - the objects come in a sort of infinite list. Cardinals just have size - they are actually ordinals where you forget the order. With ordinals you can do addition, multiplication and exponentiation - even infinitely often - but you can't do subtraction or division, as far as I know.

One small niggle - its not that we don't know the size of the real numbers. Its more that we haven't decided on what choice to make regarding where on the list it should go.

01:31 / 02.05.02

Well, I tend to think that everything that exists is a transfinite number wrapped up by our interpretations of things. I mean, take the room that you are sitting in now, it is full of seemingly discrete objects, ya? But we enfold the reality of those objects into apparent finite units, but you can see how they are not what you think they are. The connections that any given thing has to anything else in the world are likely at least countably infinite, but I tend to think that we could probably come up with a logical proof which shows that for any given list of relations that you can create which is intended to be comprehensive with respect to a single object in the world, then you can show that at least one relation has been left off your list. This would be similar to Cantor's diagonalization proof to show that the Real numbers are larger than the Natural numbers. I tend to think that we might also be able to give it a "godel" which is also a sort of diagonalization that depends upon self-referencing--indeed, anything in the world must relate to itself, so there ya' go off to infinity: like the set of all sets (ain't no such thing 'cause you can then take your set of all sets and put it into itself, but then it is now larger then it was, and then you can take the new set and add it into itself, but then...ad infinitum)!

So, in short, when you work in the world, you are working with the representations of transfinite numbers all the time. There is nothing that you can observe, interact with, etc. that is not itself infinite. However we have trained ourselves to fold things up because we can't handle an infinite number of infinite objects. Simply start seeing things a little more at a time. As William Blake wrote:

"How do you know that the bird that doth cut the airy
way
Is but an immense world of delight enfolded by your sense
five."

Or something like that.

{0, 1, 2}

09:01 / 02.05.02

Thank you, mod3. I understand everything you're saying, but I'm not really sure how I can use it (outside of mathematics itself). We are indeed srrounded by infinities, but there are two things that I think we're missing. One is that the beauty of ordinals is that they can distinguish between different infinities. The other is that, when numbers are used in magic, they don't have to be associated with "This many." They're just names, but they're names with a spirit attached to them. The Gematria has numbers associated with love, God, mother, father, and so on...

23:41 / 02.05.02

Oh, I certainly agree, but all the associations of gemetria are generated via finite numbers standing in for finite concepts/archetypes, or whatever. So we have things like, 6 = The Lovers, or 23 = synchronicity, or whatever. The idea being that the whole is always reflected in the parts, so really, maybe The Lovers = 6.1362547586979458049284374635141627486978463528590470945302927645392450291981348764139784250964098538732636...spiraling off to how knows where as more and more of its complexity is made aware to the practitioner. We get, from this string:

Lovers = {Lovers, Magician, Empress, Lovers, High Priestess, Hierophant, etc. or perhaps, Tiphareth, Kether, etc. or perhaps both!}

The idea, it seems to me, is to force isomorphic mappings whenever plausible (kether in malkuth, ya?), and leave the remainders close to your heart.

{0, 1, 2}