Fitting the Lo Shu square into the Tetractys triangles

[imagenerator]

In the first Lo Shu #1 mirror and subsequently in the "The Abrahadabra Grid" discussion , there has been mention of placing the digrams of the Tai Swan Ching into the chambers of the Tetractys of the Decad. This got me thinking about how the digrams would be most elegantly placed. I started to wonder, what would a "magic triangle" look like ? Mapping the concept of a line in the magic square to a triangular grid, what would be the equivalent to a line? That is to say, if one were to place the numbers from 1-9 inside the chambers, how would the 8 groupings of 3 numbers that add up to 15 be arranged amongst the chambers ? I sought out an elegant configuration, and came up with this:

http://tn3-1.deviantart.com/fs13/300W/i/2007/023/7/5/Magick_triangles_by_imagenerator.jpg


There are 8 groupings of the digrams outlined in grey, 3 equilateral triangles, 3 straight lines, and 2 scalene (uneven) triangles. This becomes more evident if you take apart the image in it's native svg format (http://www.deviantart.com/download/47250738/) (if you don't have a program to do so, I reccommend Inkscape (http://www.inkscape.org)). An easy way to spot the groupings is to look at the lines; each group has each type of line in both positions (makes sense?).

Has anyone else come up with a configuration of the bigrams in the chambers that works particularly well ? I'm unsure of how to procede with testing such arrangements. I haven't thoroughly encoded the meaning of the Lo Shu arrangement into my being, so I maybe I need to return to that.

Sometimes I worry that proceding into the unknown with a lack of adeptness for this work is dangerous business, but then other times I think that my strength is in figuring things out in my own way. Any wisdom concerning this situation would be appreciated.

[Okazaki Castle]

Interesting set-up imagenerator. I especially like the emphasis on the six-star within the tetractys at a smaller level. I use a similar approach to this one myself, but with a progressing principle which takes it to smaller and bigger dimensions/sizes: ike mirrors within mirrors within mirrors sort of thing...

I find it is useful to have the actual bigram (or longer grammatic configurations) shifting and changing with the needs of what they encounter. Also makes them less predictable, and so capable of nasty, or benevolent, suprises...

Funnily enough your geometry in that one is very similar to my Zhedhi symbol. I'll post a copy of it on this thread sometime soon-ish if you like. Funny how things like that happen occasionally...

all the best,
Oazaki.

[Anibis]

Neat diagram. I'm not entirely convinced that there arent more 'groupings' in the figure. for example there appears to me to be more than two scalene triangles. There's at least 4 right angle triangles through the centre. Since 7, 2 and 6 are connected as an equilateral triangle, but also 7, 2, and 5 (scalene), it is impossible that those two triangles will ever be equal in any arrangement. I am sure that a number of the groupings will also have this deficiency. Still, it may be possible to construct a figure with nested mathematical features... I hope someone will double check the math for me, but it appears that three equilateral triangles each total 15 (the Big one(1+5+9), and the Magen Star in the Centre(7+6+2, and 4+3+8). Now that's very nice. Very very nice. And they said it couldn't be done... hmm. Anyone else notice any cool patterns in this arrangement? Keep up the good work.
Don't worry about the dangers of going out on a limb, just keep your patterns stable. You have more adeptness than you are letting on...;) As for the procedure, it is simple: try and find the most elegant and comprehensive pattern and run with it. Revise your position if you turn out to be mistaken. Easy as pi. All we are reallly doing here is cathexing (http://en.wikipedia.org/wiki/Cathexis) mathematics... Just poke at the step before you put your weight on it.
-Ibisis

[MythMath]

Perhaps some color coding...?

[Anibis]

Aye! That would be nice...
-Ibisis

[m1thr0s]

I think perhaps this art form is being grossly misinterpreted. I have of course played around with all of this but here's the rub...this kind of art owes a certain responsibility to clarity and logic. If you cannot justify why these bigrams should go precisely where you have placed them...you have essentially posed an argument with no supporting evidence. This stuff isn't just about kicking out a lot of nifty looking gadgets...any school kid could do that. You need to present your arguments or there is simply not much reason to take your arrangement very seriously...

So while I applaud the general effort...the conclusions are ambiguous at best. Care to explain why this arrangement is any better than, say, its exact inverse? It doesn't even have to be conclusive necessarily, but the omission speaks to a general lack of recognition of the art form itself.

m1thr0s

[Anibis]

I thought the 3-fold occurance of 15 looked pretty nice. Even with squares, there will always be reversals and such: Fundamentally they are the same pattern. Since it impossible to have a fully magic triangle in terms of rows of cells, I do think it is somewhat of a clever move to do it in terms of the triangles themselves. There's some merit there.
-Ibisis

[MythMath]

Speaking for myself, I engage these various
images and forms in graphic designs in an
attempt to become more familiar with them...

I'm always assuming that I'm mangling the
underlying energies and that all of you
who are intimately knowledgeable with
them will roll your eyes and laugh... :(

I am however manipulating them
and once they start popping up in my
dreams, I feel like I'm making progress...

All of this makes it a little easier to comprehend
more of the subtleties when I read things here,
in books and in other opportunities for research...

I appreciate the patience and advice that you've all shown
to me as I try to grasp the basics of these bizarre realities...

[m1thr0s]

Numbers are fickle in some cases...conclusive in others. I have yet to find a single arrangement of bigrams to chambers that convinces me of their unique superiority...yet I believe a key is there right in front of us. I don't buy the 15's as especially compelling but it is a useful observation. I think there is some other key here that we are all overlooking...

And I am not trying to come down too harshly...I will be blunt where I think it is important. That doesn't mean I am trying to be a hyper-critical asshole...

The Lo Shu is very clear...yet even the Lo Shu provides a number of allowable variations. I think we need to pinpoint what our "governing dynamic" will be here...if such a thing is even possible.

m1thr0s

[MythMath]

No, you're right, being critical is important here...

When my little squirts show me their art,
I respond in a positive and non-critical manner...

That's not what is needed here...

Just keep dishing out the experienced guidance,
and we'll end up with the most efficient,
elegant and energetic schematics in the universe... ;)

[m1thr0s]

Personally, I think there must be some way of using the points to identify their corresponding contents...some way of counting the points that reveals a chronology in the chambers. It's just instinct, but if such a thing were found this would amount to a very compelling argument I think...

Another possible approach is comparing the Tetractys chambers to other known 9-based systems. So we have several possible ways to proceed I think. But our end-result should be able to demonstrate a powerful justification.

m1thr0s

[Okazaki Castle]

Personally, I think there must be some way of using the points to identify their corresponding contents...some way of counting the points that reveals a chronology in the chambers. It's just instinct, but if such a thing were found this would amount to a very compelling argument I think...


Well, a neat little trick I often use to save time and live beyond current ability and knowledge state is, when I get a clear instinct impression in a particular area I just tell subconscious mind: 'Right, do it that way, move the specifics into place whatever they may be.'. You don't consciously know what's going on exactly in that way, and indeed to attempt to do so would slow things down whilst you paused and brought thru the knowledge. So you colour it balck, call it Mystery and let subconscious get on with it in practical application. Then you'll more often than not get the specifics brought to you by the life process, eg in synchronicities around you, to the extent of getting the precise pattern delivered to your doorstep and an explanationof how it works yielded up also.

So, sort of, you yield control (conscious awareness) first, then on the return motion conscious awareness yeilds unto you and renders herself up. The advantage is speed.

all the best,
Oazaki.

[Okazaki Castle]

There's at least 4 right angle triangles through the centre. Since 7, 2 and 6 are connected as an equilateral triangle, but also 7, 2, and 5 (scalene), it is impossible that those two triangles will ever be equal in any arrangement.

Riemmanian geometry. Curving the space you can approximate corners, or nodal points. Similarly, you can use this technique to produce some sort of interface between triangles and other geomteric figures, eg pentagrams, squares. Not sure how to explain that one or put it in words, see it clearly when focusing on these things but it's like one of those images which you can't relate through 3D mind. A bit like some of the astral colours which don't really exist down here and can just be approximated, even though you see and feel them very clearly when there.

Another interesting point I'd like to raise here is: has anyone thought of redfining numbers and number gates? Words change definition all the time, and even letters (which are geometry) can be played around with. For example, a 9 gate can fairly easily be correlated to a 12 gate. That approach allows for the inclusion of further sephiroth above, below or in between the traditional 11 (or 10) normally used. A rather astounding application of that which fits in nicely here I think is that you can add another line of five below the base of the tetractys, giving fifteen nodal points. Generally I'm all for simplifying and reduction, compression in other words, as it makes things go faster. But expansions are also useful, provided you can contain that within your field, and the 15 expansion is especially useful I feel - if for no other reason than it is the original beat that I based my working for Bush & co on, and is also the configuration I got from the 'three pentagrams' series of occurring alignments within 3 degrees of orb over 2004.

Again, there is much here that is very technical and that I don't really get in it's totality yet. But some ideas perhaps...?

all the best,
Oazaki.

[Anibis]

It appears to me that, the 'proof' with these things is in the elegance of the structures managed to be teased out of the figure.

A word about magic squares. it is possible for a given 'order' magic square, to enumerate all the possible 'different squares' (not including rotations and reflections) of say order 1, 2, 3, and so on....

The number 1 is a magic square, with no rotations or reflections. The number 2 has no magic squares, there is only one order 3 magic square (the Lo Shu), although it can be rotated or reflected (I believe there would be 8 variations), There are something like 880 fourth order diferent squares, and so on.... it increases dramatically as the orders increase.

As for the triangle, it should be possible to prove what is or is not possible to do with it. from what I understand, a magic numeration of the chambers (rather than the points) of Tetractys is impossible. It would be nice to look at the math proving this, but I'm not sure I'd understand it. Still, some things ought to be possible. I'm not looking for the definitive 'true form' but rather which form has the most synchronistic internal patterns...

Some squares are 'more magic' than others. For example there are square which are called 'pandiagnol', which means that as usual all the horizontals, verticles and diagnols total to the 'magic sum', but so do the 'broken diagnol'... which would be as follows:

xxxx
xxxx
xxxx
xxxx


or

xxxx
xxxx
xxxx
xxxx


This ends up contributing alot of crazy features, not the least of which is that if you take a given pandiagnol square(of say, order 4), and put any number of them side to side, then any 4x4 selection of numbers in that array will be a magic square. This is called a Nasik array.

Anyways, I am digressing, but the point is that if we can find an especially elegant emergent pattern in an array of numbers, then perhaps that's proof enough...

I agree the 3 15s are fairly weak, since they are just 3 independent sets of numbers... still it may be possible to find some interesting 'crystals' in the lo shu in this way. What if you expanded it to a tetrahedron? then perhaps there could be 'lines' traced over the edges and around the figure itself whilst numbering the various cells.... WHo knows, just trying to open up territory.

How many basic arrangements to the 9 chambers are there? If we can come up with a number for that, we might be able to design a composite figure that holds all the variations withing itself; a crystal of some sort...

Okay that's all for now.
-Ibisis

[imagenerator]

Neat diagram. I'm not entirely convinced that there arent more 'groupings' in the figure. for example there appears to me to be more than two scalene triangles. There's at least 4 right angle triangles through the centre. Since 7, 2 and 6 are connected as an equilateral triangle, but also 7, 2, and 5 (scalene), it is impossible that those two triangles will ever be equal in any arrangement. I am sure that a number of the groupings will also have this deficiency. Still, it may be possible to construct a figure with nested mathematical features... I hope someone will double check the math for me, but it appears that three equilateral triangles each total 15 (the Big one(1+5+9), and the Magen Star in the Centre(7+6+2, and 4+3+8). Now that's very nice. Very very nice. And they said it couldn't be done... hmm. Anyone else notice any cool patterns in this arrangement? Keep up the good work.
Don't worry about the dangers of going out on a limb, just keep your patterns stable. You have more adeptness than you are letting on...;) As for the procedure, it is simple: try and find the most elegant and comprehensive pattern and run with it. Revise your position if you turn out to be mistaken. Easy as pi. All we are reallly doing here is cathexing (http://en.wikipedia.org/wiki/Cathexis) mathematics... Just poke at the step before you put your weight on it.
-Ibisis

Just to clarify, I was using the term "grouping" to refer to a group of 3 that add up to 15. The grey lines are formed by connecting each point in the group to itself. So, structurally there are actually only 5 triangles and 3 lines. MythMan's suggestion of color coding is well-taken; it did occur to me something that would add clarity.

I don't quite understand your question about the 7,2,5 and 7,2,6 triangle. Is the definition of "equal" mean forming the same shape ? Do the shapes have to be the same size ? Even if we answer "Yes" and "No" respectively, any two triangles with 2 of the same points will never be equal. For me, the focus of this experiment is the relationship between the "groupings" as defined above.

Thanks for the encouragement to explore this branch of mathemagick Ibisis. I like this term cathexis; I can really relate to it ;). It reminds me of something said about Kundalini yoga and steam engines on this forum.

[Anibis]

So there are 8 groups of three that make 15? Okay... let me look deeper...
-Ibisis
Edit: Okay, so I found the three straight lines. Could you present a version in which the scalene triangles stand out. OR just tell me their numbers. There ARE more than two scalene triangles in this figure, see? 8 rows of 15 are precisely what you'd get in the Lo Shu anyways... I think this is kind of neat. Is there any other way (other than by reflection) that this many 15s will appear in the figure?

[imagenerator]

I think perhaps this art form is being grossly misinterpreted. I have of course played around with all of this but here's the rub...this kind of art owes a certain responsibility to clarity and logic. If you cannot justify why these bigrams should go precisely where you have placed them...you have essentially posed an argument with no supporting evidence. This stuff isn't just about kicking out a lot of nifty looking gadgets...any school kid could do that. You need to present your arguments or there is simply not much reason to take your arrangement very seriously...

So while I applaud the general effort...the conclusions are ambiguous at best. Care to explain why this arrangement is any better than, say, its exact inverse? It doesn't even have to be conclusive necessarily, but the omission speaks to a general lack of recognition of the art form itself.

m1thr0s

Point taken. The characteristics that made me choose this one were:
- corner chambers correspond to the doubling of each line so that each force is an extremity of the triangle
- there are 3 equilateral triangles, and 2 form the magen star as mentioned earlier
- the straight lines form beams to support the triangle in all directions
- and those 2 uneven triangles ..... well, .... they were just what was left over

To be honest, after posting that, I decided "what I really need to do is write a computer program to output ALL possibilities".

I didn't consider the cronological progression of the numbers as a path. In this particular arrangement, it's messy, unlike the cronological path formed on the Lo Shu square, which is somewhat symetrical. Maybe I'm just not scrying hard enough:laugh:.

[Anibis]

Okay, I found the 2 scalenes. Interesting. What would this thing look like if you superimposed an inverse figure? That is, what would a Magen star made of this figure look like? THat would seriously require color coding though. It seems, it would double up the internal magen star, and complete the triad on the outside. WHat I would like to know is what those two 'wing' triads would end up looking like. I can sortof pick out the octahedron in it... maybe that would come out in full form if it was done as a Magen star?

-Ibisis

[Okazaki Castle]

Hey cool developments here. You see, this is the sort of stuff which is not in my ability set really, and holds little interest for me in fact. So it is good to see others covering it and pick up pointers here and there.

I think it's productive when we each focus on our own areas of specialty and agree to let others cover theirs. That way, we can all do each others' work for each other, whilst each doing what we like. That makes for more fun and less work all round I think...

Thanks then... :)

all the best,
OC.

[Anibis]

It's no doubt that the brain-pool here is awesome indeed...
-Ibisis

[Okazaki Castle]

It's no doubt that the brain-pool here is awesome indeed...
-Ibisis

:yes::yes: Most intelligent people in existence I think. It's what the abra mutations do to you I think...

all the best,
Ibisis.

[MythMath]

I found some inter-related stuff here:

http://www.drking.plus.com/hexagons/magic/index.html

And these:

http://www.drking.plus.com/hexagons/magic/thexs1.pnghttp://www.drking.plus.com/hexagons/magic/oe.png
http://www.drking.plus.com/hexagons/magic/thexs1.png

[imagenerator]

Well, I re-scripted my program to accept any permutation of numbers and I was about to make it churn out all the possibilities, when I thought "wait a minute, exactly how many permutations are there ? " And the answer is 9! (9x8x7x.......x1), which is 362,880 ! Of course, a whole bung-load of them are rotations and reflections. How many.... I've yet to figure out. If I pin down the corners and only allow the middle to move around, then there's 120 permutations, which is a bit more managable. Well, back to the drawing board as they say ....

[imagenerator]

I updated the original figure to include color-coded groupings.
http://tn3-2.deviantart.com/fs13/300W/i/2007/024/d/8/Magick_triangles_by_imagenerator.jpg

[m1thr0s]

interesting site MythMath...very useful. These two hexagons give us a clue what we are up against. We can only actually count 3 rows in the Tetractys itself having the same number of triangles.
http://www.drking.plus.com/hexagons/magic/hexagram1.png
http://www.drking.plus.com/hexagons/magic/hexagram2.png
The author claims that these are the only two possible ways to balance the interlocking triangles which then gives us 6 rows. He has a little program in C that can verify this ( C program (http://www.drking.plus.com/hexagons/magic/MagicHexagram.c) ). I have no idea how to run this program on my system. Does anybody have a way to run this against the Tetractys itself?

edit: handsome image imagenerator...

m1thr0s

[m1thr0s]

let's assume for a minute that we do find the pattern that works out in the numbers. It is still possible that it will not suit us aesthetically, though I would still like to see it if something does exist (of course). There are a couple of other criterion we can use however. One alternative is to count hashmarks themselves...the Chinese were actually fond of this system. A yang counts as 1 hashmark, a jen counts as two and a yin counts as three in the ternary system. So that's one possibility. Another possibility is to balance our symmetry against the Tree of Life, disregarding numbers altogether and looking solely at geometry. In a sense, we are already doing that when we assert the 3 primaries at corners to the Triangle. To balance against the Tree, the yangs should actually be on the right-hand corner (following the right-hand pillar) and the yins on the left (following the left-hand pillar) with jens at center (following the middle pillar). The vertical axis should parallel Heaven in the Above, Man in the Middle and Earth in the Below as nearly as we can get it. This then, becomes a balanced geometrical standard. As such it has profound tantric value just in the way it "stands", providing a kind of physical "asana", like a geometrical Buddha of sorts.

We can do this for several reasons, but perhaps the most compelling reason is that we already have the Lo Shu to satisfy the demands of numerical supersymmetry. It may not be necessary that the Tetractys adheres to the same exact criterion. Finally, there are other ways of running numbers in the Tetractys that may be of use to us such as were used by Pythagoras, Pascaal and others...one of these arrangements may yield something especially attractive to our purposes here.

just a little food for thought...

still, if something 1-9 can be found...I think we'd all like to see it.

m1thr0s

[Kain]

The author claims that these are the only two possible ways to balance the interlocking triangles which then gives us 6 rows. He has a little program in C that can verify this ( C program (http://www.drking.plus.com/hexagons/magic/MagicHexagram.c) ). I have no idea how to run this program on my system. Does anybody have a way to run this against the Tetractys itself? Well, the program ran but wouldn't stay open for the viewer to actually see the result of the calculations. I made some tiny corrections to it to have it portray the results in the end. I have here attached both the original executable and the modified one (so you can all use it now), and the source codes of both for anyone interested. The results are a bit skewed compared to the image you posted m1thr0s, but it is correct I think.

Very interesting thread!

Kain

[m1thr0s]

Thanks Kain. I was able view it but it wasn't what I thought it would be. Is there any way to modify this so it will run the same check on the Tetractys Itself? It looks like it's scanning for the interlocking hex only. Is there some way to tweek that?

m1thr0s

[Dragon]

Something exciting here...a form which incapsulates the 12. I'll be damned. Just mumbling to myself. Laters. More verification needed.

~D~

[Kain]

Thanks Kain. I was able view it but it wasn't what I thought it would be. Is there any way to modify this so it will run the same check on the Tetractys Itself? It looks like it's scanning for the interlocking hex only. Is there some way to tweek that?Yeah, this is because it is scanning the interlocking hexagram only. I suppose it could be adjusted to the Tetractys, but it would have to be re-written as the structure of the program as it is doesn't really allow such a maneouver easily I think, it being built for an interlocking hex check...

Kain

[m1thr0s]

http://upload.wikimedia.org/wikipedia/en/b/b9/Yggdrasil.jpg

The Nine Worlds of YGGDRASIL (http://en.wikipedia.org/wiki/Yggdrasil)

1 : HELHEIM, HEL's Domain of the Dead

2 : NIFLHEIM, the frosty Realm of Ice

3 : JOTUNHEIM, Land of the Giants

4 : NIDAVELLIR, the Land of Dwarfs

5 : SVARTALFHEIM, the Domain of the Dark Elves

6 : MIDGARD, Middle-earth, our bit, the Realm of Mankind

7 : ALFHEIM, the Land of the Light Elves

8 : VANAHEIM, the World of the VANIR

9 : ASGARD, the World of the AESIR

m1thr0s

[Ci Celli Ddu]

As far as Trees of Life go, I think that the Celtic Tree of Life has 9 spheres actually, although I am not as familiar with it. It's always good to keep in mind that there isn't just one Tree of Life...here's an artistic variation I sort of like:


Argh! Another neo-druidic invention. The Norse have Yggdrassil, but there is no Celtic Tree of Life in our myths. The closest to it is this, from the tale Peredur fab Efrog:

And he came towards a valley, through which ran a river; and the borders of the valley were wooded, and on each side of the river were level meadows. And on one side of the river he saw a flock of white sheep, and on the other a flock of black sheep. And whenever one of the white sheep bleated, one of the black sheep would cross over and
become white; and when one of the black sheep bleated, one of the white sheep would cross over and become black. And he saw a tall tree by the side of the river, one half of which was in flames from the root to the top, and the other half was green and in full leaf.

[m1thr0s]

ahhh...ok...thanks for the correction Ci Celli Ddu...

funny that so many people refer to it though...makes it tough to know what the real deal is...

m1thr0s

[Ci Celli Ddu]

ahhh...ok...thanks for the correction Ci Celli Ddu...

funny that so many people refer to it though...makes it tough to know what the real deal is...


Yes. I like to think that the people who came up with it have their own private wickerman awaiting them on the other side...:devil:

[Anibis]

Something exciting here...a form which incapsulates the 12. I'll be damned. Just mumbling to myself. Laters. More verification needed.

~D~

I have found a number of magic figures encapsulating the 12, more in a bit. For starters, go here (http://forums.abrahadabra.com/showthread.php?p=11982#post11982).
-Ibisis

[imagenerator]

Thanks for all of this interesting feedback folks. My recent mutations have been in finding a chronological leyline (from 1 to 9 and back to 1 again) that is triangularly symetrical and that also produces an elegant pattern of groupings. I've yet to find anything particularly satisfying. There are some appealing patterns you can make by tracing out positions in the chambers though. I like the idea of using the line valuation addition as criteria m1thr0s. More to come, now ...

[m1thr0s]

I've yet to find anything particularly satisfying.This was exactly what I ran into imagenerator, which is why you don't see any of my own assertions of this kind. There is something inherently amiss with trying to shove a square peg into a triangular hole. It may ultimately be that the Lo Shu Square is simply the best way to express this relationship. Nevertheless...the quest itself is rather addicting...lol

take a look at this link. There may be something in this...
http://www.hyperflight.com/

then again, the guy may just be a nutter...

m1thr0s

[imagenerator]

This was exactly what I ran into imagenerator, which is why you don't see any of my own assertions of this kind. There is something inherently amiss with trying to shove a square peg into a triangular hole. It may ultimately be that the Lo Shu Square is simply the best way to express this relationship. Nevertheless...the quest itself is rather addicting...lolAddictive indeed. I managed to generate all 720 possibilities of "Lo Shu Triangles" with fixed corners (my mistake earlier, it's 6!, not 5!). I've found a couple more that have symetrical groupings. I've also used the concept of mirroring leylines as in the Twinstar to render the cronological path into something with symetry for each of these. I'll post the notable ones when I get through all the possibilities. They make pretty patterns.... but maybe you're right, the lo shu may not be fit to be triangular :p. I'll have to chew on that link some other time.

[m1thr0s]

there's a subtle principle going on here I don't quite know how to explain imagenerator. What the points themselves have revealed about the Tetractys is something more profound than anyone really seems to recognize. Unfortunately I am not a trained quantum physicist or I might be able to explain this better. I have heard it said that there are 10 stable topologies in the known universe. This may come from string theory, I am not sure. The TwinStar appears to be revealing an eleventh...which, while rooted in number is also somehow rooted in "being", for want of a better term. So in this respect the chambers...at the level of the Tetractys, are more akin to "organs" than numerical slots, and we may need to look to a different anatomical standard to resolve their technical (ie elemental) identification. We do have the Lo Shu Square as a fall-back point with respect to numbers which works well enough to order not only all of binary reality but ternary reality as well. That's big...bigger than people can actually comprehend because it's not just a matter of adding these things together...this is a synergistic interplay we are talking about between the binary and the ternary systems.

Naturally we want to know what numerical symmetries can be found and eventually we will know, or at least be able to validate up or down what is possible in the numbers. But at the end of the day it almost doesn't even matter since the TwinStar is still there...is still a stable topological totality awaiting the proper application to be wholly manifest in the scheme of things. We tend to think of that application in numerical terms. This is our training...this is our strength in most cases. But there appears to be something more...something only tantra itself is able to effectively approach.

Very lofty thing we are looking at here...I've been studying it most of my life and only feel I have just barely begun to grasp its real meaning...

Ah well...here's a little comic relief: the magic triangle (http://www.file-online.com/games/triangle/triangle1.htm)

...and a tetractyl puzzle (http://puzzlemochalov.com/Nunber/magic_krygi.htm)

m1thr0s

[m1thr0s]

Let me demonstrate one way we might go about attempting to resolve this question "organically", just to give you some idea how this might work. In the following diagram (which I am not going to make pretty for now) we have the 9 bigrams being expressed as elements and we are dispensing with any issues involving numbers. Here we just want to arrive at an arrangement that "feels" strong and balanced and is as "correct" as we can get it relative to other maps we are aware of...

http://abrahadabra.com/images/elements01.gif

Ultimately this type of approach can only be hammered out through trial-and-error. We have no numbers to guide us, but then we had no numbers to teach us how to walk or talk or feed ourselves either. We have to bear in mind that as important as numbers are, they actually are not everything...not all knowledge necessarily revolves around them as some would like to assert. Even Pythagoras fell prey to this assumption and it's a noble assumption, albeit a wrong one in the final analysis. Many things have their root in stature...in physicality and anatomy etc... It makes it a little more difficult to "prove" that one thing is more correct than the next, yet it can still be possible to determine what is correct on a purely physical basis, so long as we have some means of testing that physicality, just as walking/running/jumping etc is the practical litmus test for functional feet & legs...with or without regards to the numbers.

m1thr0s

[Ci Celli Ddu]

What do the plain circle, the aterisk and the cross represent?

[m1thr0s]

Sorry CCD...you can find the basic elemental key here:

The 9 Principal Bigrams

http://abrahadabra.com/images/elements03.gif

The 9 Principal Elements

http://abrahadabra.com/images/elements02.gif

Elemental Key

1 = Fire
2 = Sun
3 = Air
4 = Lingam
5 = Spirit
6 = Yoni
7 = Earth
8 = Moon
9 = Water

m1thr0s

[Ci Celli Ddu]

Thanks, m1thr0s. I'm guessing that Yoni and Lingam are the sanskrit Ying and Yang?

[m1thr0s]

Basically yes, Ayurvedic stuff just as Sun & Moon are. What really happens here is that you have 4 Cosmic and 4 Organic with Spirit balanced at center, since in this instance, Sun & Moon are not planetary so much as they are representative of organic lifeforce energies... These elements are typically found in Tantric iconography...Shiva is always adorned with these etc...

One of the things that is so remarkable about the Tetractys as a magickal tool is that it is as rooted in physicality as much as it is rooted in number. It's actually not all about numbers at all...it just happens to be very forthcoming in terms of numbers. Squares are not especially "organic"...they don't fit people very well actually, although the mind is quite partial to them according to their logical qualities. Triangles are logical too...but they are also very physical.

Squares are not without their physical qualities, but these are mostly rooted in vertical and horizontal axis which has special significance to the brain in particular as this is how we navigate our way through life. Vision is based on this and equilibrium and so forth. The triangle carries these as well but has more dynamic focusing qualities than squares. Triangles "concentrate" energy as much as they partition it.

m1thr0s

[Kain]

Squares are not without their physical qualities, but these are mostly rooted in vertical and horizontal axis which has special significance to the brain in particular as this is how we navigate our way through life. Vision is based on this and equilibrium and so forth. The triangle carries these as well but has more dynamic focusing qualities than squares. Triangles "concentrate" energy as much as they partition it. Yes, that's a very good point and I think a very important one at that. This is one of the many reasons triangles are so crucial in energy work I think. Perhaps our most basic instrument as all-around manipulation endeavors go.

I like the Tetractys's Nine Chambers with the elemental symbols within m1thr0s, very good representation.

Kain

[m1thr0s]

It's interesting that anyone would want to tackle this so soon, although I suppose it is one of those questions that seems to be begging for some sort of resolution. The problem I have always experienced with placing the bigrams in the Tetractyl chambers is twofold: first, they never add up anywhere half so correctly as they do in the Square and, second, they look funny...look out of place...like a fish out of water. It is possible that we are simply dealing with a sort of context-confusion here, since otherwise it is perfectly obvious that the Tetractys does indeed comprise 9 Chambers. But it seems to want those chambers expressed in a different sort of way than in the Square. We haven't actually lost anything by doing things this way and the arrangement is not without its logic...there are, in fact, very logical reasons for this particular placement. What there is not, is an "empirical" proof that this is necessarily the best or the only way to arrange things.

It is questionable if there is any empirical proof that any of us even lives, yet we seem to live...we consider ourselves alive. All the circumstantial evidence at our disposals tells us we are alive, so on the basis of this "common sense" knowledge we conclude we are alive. None us can actually prove it, empirically. Yet we tend to want to keep looking to find some way to get a perfect alignment in the numbers with respect to the Tetractys chambers. I am no different. I return to this puzzle periodically and until I know specifically how to resolve it up or down I will probably keep looking. I am reasonably certain that there is some gradeschool math teacher out there someplace laughing his ass off that I do not seem to know the answer and this is, of course, completely annoying. But my point here is to demonstrate that even if we never can resolve it in the numbers, this doesn't mean that we are left without viable options.

"We know ourselves chiefly by hearsay" [eric hoffer]

m1thr0s

[m1thr0s]

I have a question for any math wizards out there (of which I actually am not one). How do we calculate the total number of unique arrangements of elements to chambers here? Is it a simple 9 x 9 = 81 solution or are there more? My instinct tells me it may be 9 x 9 x 9 = 729 which is too amazing to even discuss without knowing first.

thanks in advance...

m1thr0s

[Kain]

I have a question for any math wizards out there (of which I actually am not one). How do we calculate the total number of unique arrangements of elements to chambers here? Is it a simple 9 x 9 = 81 solution or are there more? My instinct tells me it may be 9 x 9 x 9 = 729 which is too amazing to even discuss without knowing first.

thanks in advance...

m1thr0sI think permutations (http://en.wikipedia.org/wiki/Permutation) are what you're looking for m1thr0s. From wikipedia:

In set theory (http://en.wikipedia.org/wiki/Set_theory), a permutation is an ordered sequence (http://en.wikipedia.org/wiki/Sequence) containing each symbol from a set once and only once. Neither "1, 2, 2, 3, 4, 5, 6" nor "1, 2, 4, 5, 6" are permutations of the sequence "1, 2, 3, 4, 5, 6" A permutation is distinct from a set (http://en.wikipedia.org/wiki/Set) or combination (http://en.wikipedia.org/wiki/Combination) in that the ordering of elements in a set is not considered relevant. In other words, the set-theoretic definition of permutation is that of a one-to-one correspondence, or bijection (http://en.wikipedia.org/wiki/Bijection), of labeled elements with "positions" or "places" that are arranged in a straight line. Since what we're essentially looking for here is a permutation of the sequence "1, 2, 3, 4, 5, 6, 7, 8, 9" that has a size of 9, I think the number of possible permutations is (9!) , which is 9! = 1*2*3*4*5*6*7*8*9 = 362.880 .

Kain

[m1thr0s]

wow. more than I thought. Thanks Kain...

m1thr0s

[Kain]

wow. more than I thought. Thanks Kain...

m1thr0sYes, quite a lot of possibilities here. I think however that, as you yourself pointed out in a different thread where I inquired the possible permutations of navigating the Tetractys, actually intelligent and alchemically auspicius permutations are certainly a lot less...

Kain

[m1thr0s]

Yes, quite a lot of possibilities here. I think however that, as you yourself pointed out in a different thread where I inquired the possible permutations of navigating the Tetractys, actually intelligent and alchemically auspicius permutations are certainly a lot less...
I guess what I am not sure of is if all 362,880 combinations would be unique without any duplications...

m1thr0s

[Kain]

I guess what I am not sure of is if all 362,880 combinations would be unique without any duplications...Well, they certainly are I think as the point of permutations is that they count linear correspondances where each element of the set appears only once but all of them have to appear once. So there are no duplications of elements nor are any elements omitted, making it the way for counting unique correspondances, their defining characteristic being their numerical linear placement.

Kain

[m1thr0s]

right...so we should actually be looking at 362,880 unique sets?

m1thr0s

[Kain]

right...so we should actually be looking at 362,880 unique sets?362,880 unique ways of running the same set, yes.


For instance, if we were looking at the permutations of {1, 2, 3} it would be Per = 3! = 1*2*3 = 6.

Which would analytically be: {1, 2, 3} , {3, 2, 1} , {2, 1, 3} , {2, 3, 1} , {3, 1, 2} and {1, 3, 2}, thus giving us 6 unique ways of running this set in total.

Kain

[m1thr0s]

interesting...I'll have to look into this number more.

found an intriguing article googling "362,880 + Pythagoras"

http://members.aol.com/johnkeely/scale.html

m1thr0s

[Kain]

interesting...I'll have to look into this number more.

found an intriguing article googling "362,880 + Pythagoras"

http://members.aol.com/johnkeely/scale.html
Very interesting article m1thr0s...

Kain

[m1thr0s]

the funny thing is...in all those variations, there are still ways to narrow things down, but you have to choose which criterion will be more important than others first. The arrangement I settled on is fairly easy to grasp once you know the underlying assumptions. The middle-pillar (middle 3 triangles) simply pulls from the middle 3 bigrams and positions heaven in the above, man in the middle, earth in the below as per the Fu Hsi standard. It is then flanked by the "four corners of the universe" in the two diamonds to each side. leaving a simple remainder of sun and moon. moon is placed on the left and sun on the right following the Tree of Life pillars. The specific arrangement of the four corners is based on the symmetry of hexagrams 63 & 64 which we know to represent "Completion" in the nuclear hexagrams. So it winds up being kind of a slam-dunk, once you have determined what your priorities will be...

Nevertheless...it is highly likely that there is at least some useful application to any of the 362,880 variation possibilities...

m1thr0s

[Dragon]

Good find m1, and relates directly to the research MM and I are embarking on.

I'm doing the math to verify Kain's find, but it looks like it totals up, just needed the equations. funny when you do it on paper it starts building triangles naturally in the permeatations of the sets -

I'll be back on later tonight with a better explanation once I do all the math...I'm doing the equations by hand just to be sure.


~D~

[m1thr0s]

oh good...you saw the link. synchronistic, eh?

gotta love that stuff...

embarrassingly, imagenerator already brought this out earlier (the 362,880 bit), but somehow I missed it...

362,880 = 27 sideways. I know. cheap thrills...but still...kinda cool.

m1thr0s

[MythMath]

Last week my daughters came home from highschool and
told me they're covering factorials(!) in their calculus class...

When I confessed my general unawareness of the applications
they said that there was probably something I could do
with them since I'm 'always talking about permutations'... :laugh:

[oak]

probably not worth much or anything since i don't know anything about which numbers are "important" or "special", but here's one of the arrangements i came up with when trying to make the vertical and horizontal "lines" of tetractyst chambers sum up to primes since i like them. :)

1
2 7 4
8 5 3 9 6

chose that one because i liked the image it made with its' mirror arrangement:

http://www.tuubi.net/oakie/pics/abr/tetra.gif



yeah, nevermind, was just fun playing around with numbers, been a while..

[m1thr0s]

it's ok Oak...it's a very interesting pattern...

playing around with these things at random is pretty much how everything happens anyway...

well...and researching, experimenting, and screwing around some more...:cool:

m1thr0s

[MythMath]

oak,

Your chamberpaths reminded me of
something I first saw years ago:

http://www.richardsnotes.org/pictures/michael_moschen3.jpg

Michael Moschen* bounce-juggling balls in a triangle...

If I recall, each of the three sides had a different pitch... :yes:


Ib, ever try this...?

_____________________

*In a work beloved by Moschen aficionados,
he also choreographed and performed with crystal balls
as David Bowie's hands in the Jim Henson film Labyrinth.

[Dragon]

Confirmed. 362880 is the correct number of combinations of 9 integers in 9 places without duplications.

Divided by 3 is 120960
by 6 is 60480
by 9 is 40320
by 729 is 497.77777777777777777777777777778

I tried several divisions, pi, etc., but the most coherent was -

by 64 is 5670.


~D~

by 5 is 72576
50 is 725.76
etc etc

[Kain]

the funny thing is...in all those variations, there are still ways to narrow things down, but you have to choose which criterion will be more important than others first. The arrangement I settled on is fairly easy to grasp once you know the underlying assumptions. The middle-pillar (middle 3 triangles) simply pulls from the middle 3 bigrams and positions heaven in the above, man in the middle, earth in the below as per the Fu Hsi standard. It is then flanked by the "four corners of the universe" in the two diamonds to each side. leaving a simple remainder of sun and moon. moon is placed on the left and sun on the right following the Tree of Life pillars. The specific arrangement of the four corners is based on the symmetry of hexagrams 63 & 64 which we know to represent "Completion" in the nuclear hexagrams. So it winds up being kind of a slam-dunk, once you have determined what your priorities will be...Yes, that's what I mentioned myself earlier...it really becomes clearer when a few basic principles are attended as given. Certainly worth checking out the ramiffications of all possible permutations though.

Confirmed. 362880 is the correct number of combinations of 9 integers in 9 places without duplications.

Divided by 3 is 120960
by 6 is 60480
by 9 is 40320
by 729 is 497.77777777777777777777777777778Yeah, I tried these myself yesterday. Didn't think about dividing with 64 though, good call Dragon.

Kain

[Anibis]

oak,

Your chamberpaths reminded me of
something I first saw years ago:

http://www.richardsnotes.org/pictures/michael_moschen3.jpg

Michael Moschen* bounce-juggling balls in a triangle...

If I recall, each of the three sides had a different pitch... :yes:


Ib, ever try this...?

_____________________

*In a work beloved by Moschen aficionados,
he also choreographed and performed with crystal balls
as David Bowie's hands in the Jim Henson film Labyrinth.


Not personally. In our circus the two jugglers (and by this I mean specialists, rather than hobbiests like me) did a rebound act with various blocks that they would move around and do various different configurations with. Cool stuff.
-Ibisis

[imagenerator]

Confirmed. 362880 is the correct number of combinations of 9 integers in 9 places without duplications.


I think a more relevant number than all possible permutations is the possible permutations without duplications created by rotations and reflections. I haven't figured out how to calculate that number yet. For example in the set with no rotations or reflections
1
2,3,4
5,6,7,8,9

would exclude as a permutation

5
7,6,2
9,8,4,3,1

because it is a rotation of the former

and as well exclude
1
4,3,2
9,8,7,6,5

because it is a reflection of the first figure.

[imagenerator]

Let me demonstrate one way we might go about attempting to resolve this question "organically", just to give you some idea how this might work. In the following diagram (which I am not going to make pretty for now) we have the 9 bigrams being expressed as elements and we are dispensing with any issues involving numbers. Here we just want to arrive at an arrangement that "feels" strong and balanced and is as "correct" as we can get it relative to other maps we are aware of...

http://abrahadabra.com/images/elements01.gif

Ultimately this type of approach can only be hammered out through trial-and-error. We have no numbers to guide us, but then we had no numbers to teach us how to walk or talk or feed ourselves either. We have to bear in mind that as important as numbers are, they actually are not everything...not all knowledge necessarily revolves around them as some would like to assert. Even Pythagoras fell prey to this assumption and it's a noble assumption, albeit a wrong one in the final analysis. Many things have their root in stature...in physicality and anatomy etc... It makes it a little more difficult to "prove" that one thing is more correct than the next, yet it can still be possible to determine what is correct on a purely physical basis, so long as we have some means of testing that physicality, just as walking/running/jumping etc is the practical litmus test for functional feet & legs...with or without regards to the numbers.

m1thr0s


This arrangement resonates with me strongly. I may have overlooked the elegance of it had the bigrams been in place of the corresponding glyphs.

My first impressions of this glyph:
The sun and the moon, heavenly bodies, balanced by anatomical yang (or the less formal wang :p) which can reach them, fire and water balanced by the anatomical yin, that can contain them, and earth and air, the "limited" elements balanced by the limitless spirit. And as you descend the right pillar, you get a yang-yin-yang property going on, and as you descend the left pillar, you get a yin-yang-yin quality, which creates a sort of "weave". I've seen these types of attributions mapped onto the qabbalah's left and right columns, but I forget the exact context (references anyone ?).

Beautiful ! I feel like I have been taught a very valuable lesson. Thank you m1thr0s for a different view. That is not to say that I will completely disregard my work with the multitude of permutations I have generated, but rather, I'll just let it be a tempering force in my modes with codes:yes:.

[Radiant Star]

How would you fit the elemental symbols on the Abrahadabra points since there are not ten?

Can this be done?

[Anibis]

You could use spirit twice if you wanted to, since it has two modes....
-Ibisis

[Kain]

How would you fit the elemental symbols on the Abrahadabra points since there are not ten?

Can this be done?How about



*

Moon Sun

Yoni Spirit Lingam

Water Earth Air Fire



The relationship between the point of Unity and the apex is quite apparent and Spirit certainly can be said to occupy "both" positions...

Just a thought,

Kain

[Kain]

I think a more relevant number than all possible permutations is the possible permutations without duplications created by rotations and reflections. I haven't figured out how to calculate that number yet. For example in the set with no rotations or reflections
1
2,3,4
5,6,7,8,9

would exclude as a permutation

5
7,6,2
9,8,4,3,1

because it is a rotation of the former

and as well exclude
1
4,3,2
9,8,7,6,5

because it is a reflection of the first figure.I think these rotations and reflections influence an energy construct's attributes quite substantuially, so they should certainly be included I think. Even a vertical reflection like the one you describe would have quite potent ramiffications, switching the left and right pillars' inertia (and thus the solar and lunar currents' inertia) and thus affecting the constitution of the whole construct quite extensively. I can see this happening in less dynamic structures though so I see your point imagenerator...however triangles are quite sensitive to alterations of this sort.

Kain

[m1thr0s]

How would you fit the elemental symbols on the Abrahadabra points since there are not ten?

Can this be done?A lot of things can be done Ricci...if it serves some sort of purpose. Remember that the points already have Planetary Attributions and for my purposes at least, this altogether suffices my primary application of the Tetractys itself. I am content to relegate the 9 elements to the 9 chambers and leave it at that because I don't really need them at points. I have Numbers and Planets at points already (also Letters).

Some things just wind up being busy-work...it's not always clear. If you have a strong need to resolve 9 elements into 10 points you will probably come up with something that works. One suggestion might be to look to small cards, for instance...

not trying to criticize here...I hope that is clear.

m1thr0s

[oak]

it's ok
nice :)

i tested that sequence and like it! counterclockwise movement all the way and clockwise movement for the mirror sequence, easy to remember too because it fits nicely if sitting in lotus posture.

played around with photoshop, and here's an aproximate picture of the flow to both directions:

http://www.tuubi.net/oakie/pics/abr/lotus_tt.jpg


also figured out how to do gif animations with it, and here's a sequence of the 10 primes between 9 and 45:

http://www.tuubi.net/oakie/pics/abr/tetra_23.gif

[m1thr0s]

you rock oak!!!

very cool...thanks brother...

m1thr0s

[Dragon]

One of the mysteries of interlocking one number with the next up or down is to look at a star diagram. The next number up being the center point as defined by the circle of the other points around it. so if you build an intersecting star, pentagram or a pentagon it reveals the 6th point in its center. When that point is then moved out to the edge of the circle the next star (hexagram/hexagon) manifests, same with a cross and a pent, or a triangle and a terahedron, or a hexagram and a septagram.

~D~


edit: p.s. nice work Oak.

[Radiant Star]

A lot of things can be done Ricci...if it serves some sort of purpose. Remember that the points already have Planetary Attributions ... If you have a strong need to resolve 9 elements into 10 points you will probably come up with something that works.

It is for something I have been working on but since you have pointed out that there are already planetary attributions, then I will have a rethink.

Thanks, very useful.

[m1thr0s]

Just a quickie cheat-sheet...

Planetary Attributions to Sepheroth (or Tetractys Points):

1 - Neptune
2 - Uranus
3 - Saturn (feminine)
(-) - Saturn (masculine)
4 - Jupiter
5 - Mars
6 - Sol (sun)
7 - Venus
8 - Mercury
9 - Luna (moon)
10 - Earth

note: I have seen other assignments to Daath (-) but I don't really care for them all that much. But at least be aware that Daath may be the more flexible in terms of planetary assignments... There is a lot of traditional backing for placing Saturn counter-pole to Luna in the Hexagram of the Planets, which places it at Daath on the Tree of Life...

m1thr0s

[Ci Celli Ddu]

Interesting that the newly discovered Neptune and Uranus are included. Why is that?

[MythMath]

Really nice stuff, oak...!
_____________

Kain,

*
Moon Sun
Yoni Spirit Lingam
Water Earth Air Fire


Very similar to the Tetractys Tarot spread that I like to work with...

[Dragon]

Another attribute of Daath is a pole of Earth.

[m1thr0s]

Interesting that the newly discovered Neptune and Uranus are included. Why is that?Probably mainly because we can. Prior to this there were no actual planetary assignments to the Supernals at all (sepheroth 1-2-3) and the Hexagram of the Planets was all that there was...

Presumably Pythagoras had his own set of 10 planetary attributions though for the Tetractys...I will need to dig these out as I don't have them handy in my brain...

Another attribute of Daath is a pole of Earth.Absolutely, and another very dynamic mystery surrounding the action of running the (-) to Crown in the TwinSar Meditation...

m1thr0s

[m1thr0s]

Beautiful ! I feel like I have been taught a very valuable lesson. Thank you m1thr0s for a different view. That is not to say that I will completely disregard my work with the multitude of permutations I have generated, but rather, I'll just let it be a tempering force in my modes with codes:yes:.My pleasure imagenerator. I don't usually crack that one out but as you have been busting your hump on this issue I thought you might find it useful. I have actually been working on it on-and-off for some years...mostly fact-checking and trying different variations etc. From a purely tantric standpoint, it is hands-down the strongest arrangement I have found to-date.

And yet...it doesn't yield squat in the numbers! lol...kind of an amazing thing in itself actually...like a principle of non-number or something...

like this: what is the numerical value of "beauty"?
impossible...yet we know it when we see it, even within certain "subjective" constraints...

m1thr0s

[Radiant Star]

Just a quickie cheat-sheet...

Planetary Attributions to Sepheroth (or Tetractys Points):

Thank you m1thr0s, this is perfect for my needs. :D

[Dragon]

like this: what is the numerical value of "beauty"?
impossible...yet we know it when we see it, even within certain "subjective" constraints...

m1thr0s


About a decade ago I came across some studys into the 6:10 ratio. It seems that people were attracted to objects and forms that had this particular ratio in its composition. They deveoped a model for faces that reflects this mean, and it is used in the modeling industry to assess the symmetry and potential attractiveness of fashion models faces...plastic surgeons make a lot of money reshaping faces and bodies to get as close to as they can.

It is both a subjective and an instinctive response in the human animal. although I can't remember if they experimented with non-humans...hmmm...worth a look.


6:10.

do the math.


~D~

[m1thr0s]

I'm having a hard time finding any links on it Dragon...probably searching it wrong...let me know if you know of any please.

m1thr0s

[oak]

thanks guys :tsmug:

have had some interesting effects and think i'm gonna spin "it" like that for a while. i also noticed it has breathing/tempo guide too; 1-5 inhale, 5-6 exhale, 6-7 inhale, 7-8 exhale, 8-9 inhale, 9-1 exhale. :p

changed the constitution of the prime 23 in the animation btw, pretty nice progression visually now i think.

[imagenerator]

So, promised to show my further research in this field, and so I return, return, return....

After quickly flipping through all 720 possibilities of triangular Lo Shu arrangement (with corners fixed as the doubled-line bigrams) I discovered 16 of those possibilities fit the criteria that all of the groupings' lines combined form a symetrical pattern. Here is the page from my deviantart account (http://www.deviantart.com/deviation/50726644/) demonstrating this, preview:

http://tn3-2.deviantart.com/fs13/300W/i/2007/071/f/b/Lo_Shu_Triangulation_by_imagenerator.png


The intention in narrowing things down to these possibilities is to resolve the triangular 3-fold symetry with the horizontal 2-fold symetry. The lines on the Lo Shu are what give the elements relation to each other, and it has been my understanding that seeing a given element in relationship to the others that are in line with it are what allow you to balance them out. When you interlock the Tetractys of the Decad with the Lo Shu, scrying all of the 8 lines of the Lo Shu Square into triangles (or lines) inside the chambers is a useful operation. That being said, I have not given these combinations a good scrying myself, which may amount to all of this being a load of poo. I will give them a run in time and report back.

The source file contains all of the 16 maps that present this symetry. Notice that by picking apart the layers of the source image (http://www.deviantart.com/download/50726644/), one can remove the black lines that aid in seeing the symetry to reveal the color lines that help to reveal the groupings.

My next trick will be to figure out all of the arrangements of the mentioned 720 where the chronological tracing of the bigrams forms triangular symetry.

[m1thr0s]

Insofar as scrying applications go, I can't say I am especially compelled by any of this. One of the things to understand about the Tetractys is that it is all about simplification and consolidation at its most rudimentary levels. This is already accomplished in the TwinStar itself, so I am having a difficult time figuring out what actual purpose is served here. This is just a gut reaction but it seems you have taken something very simple and elegant and rather made a mess of it. We will have to see where it leads and how it all pans out over time I guess.

Still, the arrangement into 16 is interesting as it might correlate to Geomantic characters, Court Cards, and other related 4 x 4 correspondences. The 81 Shou of the Tai Hsuan Ching can be divided into 5 suits of 16 with a remainder of one, ie, 5 x 16 = 80 + 1 = 81. It happens that it is possible to identify a unique system of Court Card relations to all of these divisions. In a case like this such a division is useful since it interacts with other things. Here I would not be certain how we could rank these 16 variations into similar character distinctions, but there might be some way to do this.

The source image link does not display on one page on my computer screen yet it brings up no scroll bar. Are you saying that these are set up in layers that can be dismantled and looked at with or without the overlays? What type of program are you using that can do this? Photoshop can't read it at all for instance...

m1thr0s

[m1thr0s]

Ok...I found it...looks like Illustrator will read this stuff and also let you dig into the layers...

I guess I am still not seeing what you are shooting for here imagenerator so you'll just have to endure a certain amount of blunt reaction. It doesn't mean this stuff might not have some value...just that it looks like a hell of a lot of busy-work on the face of it. I'm a pragmatist at the end of the day. I'm not just into all the patterns that can be created from this stuff since I already know the sheer magnitude of it is more than we could make a dent in over the course of a lifetime.

What I am personally after is that which expedites and consolidates and simplifies the work of mastering the Body of Light itself. But I do recognize the value of exploring many different angles, so just keep that in mind please. You are pretty much taking my stuff and running off with it and that's ok...but since this is where you are going I am going to address some of these issues at a Magus level of sophistication whether you are ready for that or not. We have a certain obligation not to succumb to a lot of stupid games here...we are not dealing in crossword puzzles et al.

The 16 factor is a good snag I think. This has some merit as I stated above. How would you go about identifying, say, the Knight of Wands from the Princess of Cups in this system? I think that if we can sort this out, we are onto something that may have a more permanent sort of value... If the 16 holds up in the numbers, then we must have some kind of Tetractyl Geomancy at play. The next issue is one of identifying who is who and why...Beyond this we can then begin to look at how to "call" these particular intelligences, since they will have then distinguished themselves as archetypal kingpins... The Key of Jupiter is nothing to sneeze at so we need to approach this with a certain degree of severity...

Note: To make it a little easier to actually see the variations, here is a modified color version (click to enlarge):

180
m1thr0s

[Radiant Star]

I think it is good to test out and explore ways of bringing meaning to it all in the beginning - it kind of clears the decks a bit I think.

Its also good to play with it but in my own experience, the real understanding comes from working with it and that seems not to be expressible in ordinary terms.

[m1thr0s]

It's actually very helpful having the svg file since the lines themselves don't make it clear what triangles are specifically involved...I'm going through the numbers right now...

note: I notice that aside from triangles they all include a vertical line as well...is that cosmetic or also part of the formula?

m1thr0s

[imagenerator]

It's actually very helpful having the svg file since the lines themselves don't make it clear what triangles are specifically involved...I'm going through the numbers right now...

note: I notice that aside from triangles they all include a vertical line as well...is that cosmetic or also part of the formula?

m1thr0s

Thanks for drawing out the colors in this one.

The vertical line is a consequence of spirit being "in line" with every other element on the Lo Shu Square, so that, no matter how you fit it, there will always be a triangle/line connecting the top and bottom-middle chambers.

I have taken into consideration your previous comments on this work. I sincerely appreciate your honesty. It challenges my tendency to play with things without having a sound understanding of their fundamental nature. I still sense that there is something to this problem that has some merit. At worst, it has been a little practice for my imageneering skills. When I think of all of the time I've spent doing impractical exercises in school, it doesn't seem like such a big deal. That being said, I do strive for efficiency in my undertakings ... uhhh.... I mean, birthings :laugh:. Particularly, I have a lot of work to do to make my tools useable by others. :yes:

An interesting numerological note: 720 = 16*45, and 45 is the sum of all the numbers in the Lo Shu square. I also noted that there are 729 THC hexagrams, and 729 = 720 + 9. Hmmm....:o_O:

[m1thr0s]

yeah...this is good stuff imagenerator. I couldn't quite get the whole picture without being able to dig into the layers. You really need a whole set of sub-graphics for each one to make it very clear both for the numbers and the lines...

You've got 15's flying off the page here...very cool...still sorting through the numbers...but I see you've got line values triangulated here as well...

technically I suppose we could rotate the whole collection on its sides flipped front and back and still get the same numerical and line symmetries, right? Which may screw our 16...but maybe not...up is still up...just cuz it's standing on its head doesn't make it something else etc...

Strictly speaking this is probably not so much a tantric application as it is a computeristic one. But there's the thing...this whole logic handles both dynamics with equal agility and that's big...that's the late-breaking news the whole damn train has been waiting on... cuz look...if the Mind is not a godamm supercomputer of the highest possible order...what good is it? It's just a transitional vessel in that case awaiting something bigger and better to come along...something that can actually navigate universal parameters...the velocities...the magnitudes...the whole kit-n-kaboodle. What we begin to grasp here I think is that it's already there...probably been there all along...What we have historically called the "spiritual" is actually a higher anatomical rung of the same essential physics we slog around in day-to-day. Freed up and stripped of cumbersome inessentials, but otherwise the same basic mechanism...

It's only really been very recently that we have begun to scrutinize that "mechanism" with the kinds of tools acquired through modern science...the logic...the protocols...the technologies etc... So we really are in a position to observe ourselves with greater precision that at any other known point in history.

m1thr0s