Twenty two objects in a single body

Is this structure stable? it seems like it would be, but I'm not sure. the reason i ask is, I see your double-cube basis of the Tree and think its a fascinating perspective, but what would have caused the ancients to intuit this design? it would seem that an actual, complete double-cube would be pretty straightforward, and i could se them using it, but this one with some pieces missing, i"m not so sure.
do you think they knew of this structure, or have you just discovered a happy coincidence, or is it just an 'artistic' version of the Tree?
sorry for all the pestering :)

A very incisive series of questions. Let me take this one at a time.

Is this structure stable?
Yes and no, and this is part of the magic of it, it seems. It depends on how you make it, really. Made of wood and string, if the joints are tight and the pathways rigid it can be perfectly stable If some joints are slackened, or some rigid paths replaced with flexible ones (rope for instance) then the structure can become fluid, flexible - it can curl this way and that, lying flat to either side. It is like a snake. Modelled in paper or papyrus the form displays some startling characteristics and can be deformed into a number of fascinating configurations.

What would have caused the ancients to intuit this design?
This is a little trickier. I believe it stems from the flat diagram. That the ancients were aware of seven-circle Seed of Life seems certain. The ten-circle natural tree is a simple extrapolation from this, which leads naturally to an array of 3/7/12 pathways. This particular physical structure is the only arrangement which satisfies the requirements of the flat plan. Any other arrangement leads to overlapping or multiplication of the pathways - ie you end up with a structure with more or less than 3/7/12 - the structure and the plan to not match. This arrangemnt is the only one I can find that satisfies both the textual requirements of the Book of Formation and the geometry described by the Tree of Life. I realise that the two 'missing' uprights are unnerving, unnatural perhaps, but try as I might I cannot justify their presence according to the given text. For example here (http://img.photobucket.com/albums/v40/fotthewuk/build.jpg) is an example of an early development which addresses this - as you can see, there are 8 doubles.

...it would seem that an actual, complete double-cube would be pretty straightforward, and I could see them using it
A double cube is without question of great significance in the histories of mathematics, religion, art and architecture.

do you think they knew of this structure?
I am convinced of it. Without it, the Sefer Yetzirah is meaningless. Among other things it seems to me that this struture formed the basis of the tabernacle. I realise this is quite a stretch, and I have some way to go regarding the precise relationship, but this is the theory I'm working under. I would further suggest that this could have formed the basis of the hitherto unknown ancient Egyptian system of mathematics and calculation. I feel a madman for saying all this, but this is not mere trivia - this is fundamentally significant in a way I have trouble putting into words.

Pestering? On the contrary, thanks for listening.

I think the one point we disagree on is that this double-cube is the only way to create the Tree without duplicated parts. As i showed with that plastic model, i think it can be done another way in 3-D, with the advantage of having all paths be the same length.
still, i find it interesting that in your double-cube, the 7 'verticals' of the flat Tree do not all belong to the same group. this has some interesting implications.
and yet, combined with the other 3 'mothers', all 10 of these have a diagonal length, while the other 12 have an edge-length.
lots of things to ponder here...

I've a great deal of respect for your 3d model of the tree, it's extremely elegant. What I can't do is relate it's structure to the pathway attributes as given in the Book of Formation, and for it to make sense. By 'sense' I mean in the most basic structural terms: that north and south must lie opposite each other, up must be above down and so on. I'd like to know how you would relate these terms to your 3d structure:

10:(start, end, good, evil, up, down, east, west, north, south)

3:(ascent, balance, descend)

7:(up, down, east, west, north, south, centre)

12:(east height, west height, north height, south height;
north east, south east, north west, south west;
east depth, west depth, north height, south height)

I just can't make it self-consistent, you know?

what I'm thinking is that the key to making it fit Sefer Yetzirah is to do what you've done, and that requires paths of two different lengths.
i see what you mean about the consistency problem, and this is what is baffling to me, because i would think the ancients had some kind of model, in 3-D, and then described it in the SY. but apparently that model couldn't have been 'my' 3-D version, (at least i don't see a solution as of yet).
it would make sense then, that the model was the double-cube. but if so, then why take out the 'extra' uprights, unless they simply wanted to dispense with any redundancies?
its like qabalistic sleuthing, trying to use inductive reasoning to figure out where they were coming from.
what your double-cube with the 'missing' members reminds me of is Bucky Fuller's Vector Equilibrium. Essentially, this is a cuboctahedron with rigid struts and flexible joints. it will fold down into an octahedron, (with the struts doubling up). but halfway to the octahedron stage, it makes the outline of an icosahedron, only 6 of the struts are 'missing', just like your cube. this may lend weight to your hypothesis, and perhaps your double-cube arrangement is an intermediary stage between the figure all flattened out, and the figure collapsed into one square with all of the struts doubled or tripled up. (don't know if that made a lot of sense, but i tried :)

i appreciate your comments and will continue to ruminate...well, not literally ;)

http://www.livejournal.com/users/fotthewuk/89463.html

looking at your excelent graphic from July 15, its easiest to compare to my little plastic model. it seems that everything works out on a one-to-one basis except that Begin & End and Above & Below are not 'opposite' each other like on your double-cube, rather they are all in the same plane. everything else seems to fit the bill in terms of 'oppositions' based on physically opposite sections of the double-cube.
what i did try was to make the top part of my Tree concave, and leave the bottom part convex. this solves all problems but one; the 'Centre' strut would have to be twice as long to join Begin and End. hmmm... having a strut exactly twice as long is not any more far-fetched than some struts having irrational lengths :)
the nice thing is that it resembles your double-cube idea in the sense of hinging about the center portion of the diagram.

well, being close is nice, but not quite enough.
back to ruminating...metaphorically speaking.