The Triangle Theory

[FutureLeFunk]

Caveat: This is an evolving thread, theory & infinite conclusion!.

Background

A post that I made with respect to the interview with Charles:


Thank you Bill and Sepia for this video :)

I present to you "Allegory: A crowned eagle standing on a globe and a wolf steering a boat" by Leonado da Vinci.

http://img268.imageshack.us/img268/6921/alleory.jpg

Please note the firm grip of the eagle on the Earth. Perhaps the wolf and boat represents the journey that we all face in the eyes of the dominant eagle. The emphasis on the mast as a tree may signal the wisdom of a tree and the earthy connection between the two. But what strikes me is the royal crown, which I see as a sign of purity. It is also placed not on the head but above, to me this points to the sovereign position of the eagle but not the purity associated with that position.


Its awkward because Common Law and contract law goes back to the beginning of nation states and the organization of tribes. The entire foundation of contract law is about honor and dishonor. You have two people, or corporations who have what is known as a "meeting of the minds" and they sign a contract. One receives a value and the other receives consideration. Then the contract is valid. There are specific terms and conditions on how the contract is to be executed.

If one makes a claim against the other for breach of contract, then there are specific remedies for redress. I accept your claim with honor, or I conditionally accept your claim with honor upon proof of claim, or I dishonor your presentment and file a counterclaim, or I dishonor your presentment and do not redress.

This is strictly business. Any Attorney will tell you that.

This is a very relevant post IMHO. The contract is joined between minds, but more importantly placed on the body. What if the body supported by Mother Earth is of more significance than the mind and even the soul within it. If we are placed on Earth for a reason, no matter what the exact nature of the experiment may be, our salvation may be in the purity of Mother Earth, but our ascension may be from that but of the body.

Indeed a two dimensional structure such as the pyramids may effect the mind, body and soul. Perhaps a three dimensional structure may be the answer. A structure may be a three dimensional object, but I point to the significance of design dimensions not constrained by the structure itself.

I looked at the significance of the 33 in two dimensional design, but they only became significant when held to that and the design extended further into three dimensions. This design still appears to hold the same principals of the pyramids, but more importantly gives a position of the body being carbon based.

Regards

By no means a perfect starting point, but this gives me something to focus on and develop.


Interesting science facts about the number 33:

* The atomic number of arsenic
* A normal human spine has 33 vertebrae when the bones that form the coccyx are counted individually
* 33 is, according to the Newton scale, the temperature at which water boils.http://en.wikipedia.org/wiki/33_%28number%29


Three General Principals - Based on Dimensions

1. Humans are of 3d: 1d Mind, 2d Soul & 3d Body
2. Design in 1d, 2d & 3d : relates to any construction etc
3. Molecular Covalent Dimensionality: 1d Chains, 2d Plates, 3d Network

* All of these are held within Mother Earth, a creation of 4d. The basis of the Earth's dimensions are founded by the classic elements:

Earth
Fire
Water
Air


http://img254.imageshack.us/img254/8957/333pxfourelementsrepres.png
http://en.wikipedia.org/wiki/Classical_element
-------------------------

* From herein everything is evolving. Please take the opportunity to read the background research first (http://projectavalon.net/forum4/showthread.php?10991-The-Triangle-Theory&p=94772&viewfull=1#post94772). The basis here is to gather an understanding on dimensions. My feeling is that everything we need to expand is within us all, but we may have to use dimensions in order to release that. :)

Brainstorm




*Humans are carbon based lifeforms.

*Carbon if the foundation for our existence, which in the purest sense is our network with each other.

*A two dimensional system of control is in place to define that network. But if our carbon body is considered a three dimensional object why is our network reduced to two dimensions.

*You don't need to look too close at the the system to see it's imperfections. Considering social interactions constrained within a two dimensional network, the extra dimension overlooking all of this this is a belief based system. If equality is the principal failure in this belief system, it's success would be to answer the question of our existence.

*A belief based systems purpose is to constrain our social interactions within a two dimensional network. In a three dimensional network then surely the question of existence would be known if our interactions were to be equal.

*In the greater sense, a belief system is there to give the masses a sense of purpose. The question for those outside of this two dimensional control system is how to give those held within it the answer to the question of existence and for what purpose.

*If our existence is defined within us all, then to remove those within a two dimensional network the answer is to give them a purpose.

*If a belief system is there to contain all of the questions within the planet Earth. Our purpose is to find the network connection of carbon based life outside of this planet.

*The answer to the greater question of existence, is this the three dimensional network, a meeting of mind, body and soul. The rewards are the different energy levels in that three dimensional network connection.

The Triangle Theory (http://projectavalon.net/forum4/showthread.php?10991-The-Triangle-Theory&p=94777&viewfull=1#post94777)

Before clicking on the link above, please note that I'm still working towards evaluating the significance and further building on information that I've found. I've only just downloaded some CAD software which I'll use in order to clarify some issues. At present figure 5 needs improving on as it's not easy to relate to figure 1, but in essence you discount all the triangles not equal (count the small black ones).


Some thoughts to ponder regarding dimensions:

To consider the parallel relationships between the principals based on dimensions as equals. Evolve my basic belief that dimensional differences can both add and subtract. Consider dimensions constrained by the three principals, all must be equal to move forward, an unequal dimensional principal layer subtracts.

1d + 2(2d) + 3(3d) + 4d = 5d product (add)
4d + 3(3d) = 3d product (equal)
4d + 2(3d) = 2d product (subtraction)

That above the 3d and up to the highest level in 5d the square rule applies inversely.

Square numbers:
0*0 = 0
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25
6*6 = 36

Inverse Square:
? = 36
0d = 25
1d = 16
2d = 9
3d = 4
4d = 1
5d = 0

Curiously these are triangular numbers. Perhaps this signifies the significance of triangle numbers on different dimensions, based on 3d humans.........


My perception is the following sequence based on the principals:

0d - 1d - 2d - 3d - 4d - 5d - 4d - 3d - 2d - 1d - 0d

If the 5d signifies space and that is inversely connected to the Earth then equality suggests that conversely there must me a second link to another.


Perhaps a greater sense or perspective is needed here. There appears to be no depth in the connection between us and 5d space. Considering that there appears to be a significance based on inverse square, to be balanced it would make sense that inverse triangle theory must apply to a positive square.

So:

-5d, -4d, -3d, -2d, -1d, 0d, 1d, 2d, 3d, 4d, 5d, 4d, 3d, 2d, 1d, 0d, -1, -4d, -3d, -4d, -5d

The 3d relative to the -3d must only be a difference of perspective. Indeed the difference must only be in the reality that we see and the unwritten rules that we do not.

I do not rule out the possibility of a 6d. If the number 36 is of significance to us based on sacred geometry and a triangle theory, perhaps our own significance is the link between us and 6d life........

Without going into any depth on this just consider three sixes. There is no beast just us and them :)

[AlkaMyst]

FutureLeFunk

I mean no disrespect by this, but "Please" correct your math and your geometry for they are both wrong........there are way more than just 36 triangles here and what you're trying to convey doesn't really makes sense."

If you are interested in the subject of sacred geometry, then you should look into "Drunvalo Melchizedek's Flower of Life Books".......which I happen to have in the FTP Account, please let me know if you're interested!!!

Again, I mean no disrespect and I know you meant well, but let's not try to confuse this community more then it already is.

With Love and Blessings!!!
AlkaMyst

[FutureLeFunk]

Background Reading - Theory Development


A tetrahedron is a 4 (tetra) sided object. A tetrahedron has six edges, four
(triangular) sides, and four vertices (corners). The methane structure is
tetrahedral. Lines connecting any three hydrogens outline a triangular side.

Combining two Egyptian pyramids at their bases forms an octahedron (8-sided
object).

sp{3} bonding, such as for the carbon atom in methane is a tetrahedral
bond. The
bonds between carbons in diamond are also tetrahedral and these tetrahedra
form an
extended 3-D network that is diamond. On a larger scale than a single
tetrahedron
the diamond crystal structure is face-centered cubic. To see this you
might need
to locate a chemistry text that talks about crystal structures.

Greg Bradburn
http://www.newton.dep.anl.gov/askasci/chem00/chem00377.htm

---------------------------------------
This is quite an interesting video that I found:

http://www.youtube.com/watch?v=-qDykfU9JYU&feature=player_embedded

http://img20.imageshack.us/img20/4732/networkcovalentdimensio.jpg

http://meta-synthesis.com/webbook/38_laing/tetrahedra.html
----------------------------------------

In the early 1980′s, Dr. Robert J. Gilbert, Ph.D, was an instructor in the U.S. Marine Corps, in the field of nuclear, biological and chemical warfare survival. During that time, he became aware of a thriving sub-culture of advanced scientists who are studying geometric shapes as a key to everything from Human Biology to Nuclear Physics. This includes studies that have been commissioned by NATO. Dr. Gilbert found that, in experiments in Nano-technology, which is the study of the control of matter at an atomic and molecular scale, scientists were unsuccessful in their attempts to create matter until they studied sacred geometric shapes, such as the pyramid.[ii]
http://hiddenlighthouse.wordpress.com/category/star-tetrahedron/
--------------------------------------------

The Divine Triangle

The twin flame soul merge is symbolized by the divine triangle in sacred geometry. The two lower points of the triangle represent the divine masculine and feminine principles of the soul and the top point represents your higher self. The divine masculine and feminine energies that merge within the higher heart of your higher self are unconditionally loving. Being here for selfless service, twin flame partners who have merged with their singular higher self tirelessly work together for the good of all.

Once one has sufficiently raised their vibration into higher consciousness through inner work, they will attract their twin flame. They may come in the form of an embodied human, as is the case with Jesus and Mary Magdalene, or as a being of light who is not incarnate at this time.

When the merge occurs, the union will be experienced as exquisite pleasure that is felt multidimensionally within the mental and emotional bodies, as well as the physical one. This is true whether your twin is incarnate or not. When your twin is a light being, the merge will take place in one’s light body but will be felt physically just as if they were there in person.

How can this be? When, through inner work, someone ascends into their higher selves, they develop exceptional meditative abilities to see the unseen and hear the unheard. They even develop the ability to feel the unfelt. Though spirit exists in a non-physical dimension, they are just as real as the embodied spirits who exist in this one. There is only a thin veil that separates our two dimensions. It is created out of belief. When one believes they can’t see beyond the physical dimension, they don’t develop the skills to do so. The individual who has ascended into their higher self knows a higher truth and is ready and willing to interact with a higher dimension.

Once you experience the twin flame soul merge, you will continuously vibrate in love and bliss feeling this as pleasure in your body which you will wear like a cozy garment of love. You will feel so completely fulfilled by this inner sensation of divine love that you will feel like you are the luckiest person alive even though your twin flame may not have a physical body for hugging and kissing.
http://img130.imageshack.us/img130/7733/divinetriangle.jpg
http://seekingenlightenment.net/2010/11/29/twin-flame-soul-merge
-----------------------------------------------


http://img842.imageshack.us/img842/6474/sierpinskigeometric.gif
The Sierpinski Triangle raises all sorts of little questions that relate to topics in chaos theory not covered in the last few pages. For example, the Sierpinski Triangle is a canonical example of a shape known as a fractal. But soft, you ask, pray tell, what is a fractal?

Most simply, a fractal is a geometric construction that is self-similar at different scales. This is rather dry. More clearly, a fractal shape will look almost, or even exactly, the same no matter what size it is viewed at.

This is a pretty unintuitive concept. But let us look at the Sierpinski Triangle. The first step in the geometric construction of the Sierpinski Triangle involved splitting a triangle up into three other triangles. When we look at the finished Sierpinski Triangle, we can zoom in on any of these three sub-triangles, and it will look exactly like the entire Sierpinski Triangle itself. In fact, we can zoom in to any depth we would like, and always find an exactl replica of the Sierpinski Triangle.

This is deep. This is very deep.

http://www.zeuscat.com/andrew/chaos/sierpinski.html

[FutureLeFunk]

Caveat: Currently being updated for clarification.

My basic philosophy is based on equality and purity. I hold onto this philosophy dearly and project this from my soul. From my experience in life I consider a two dimensional system of control, based on the mind but placed on the body.


The Triangle Theory

Start with the number 33:


33 is the largest positive integer that cannot be expressed as a sum of different triangular numbers

Divisors: 1, 3, 11, 33

Consider always the significance of something that it is not.

I decided to look more into this. Something also seemed to resonate with me in the video with Charles, "triangle craft that can form shapes and be joined together". Perhaps a triangle that's made up of others.

Trianglular numbers: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Triangles made up of others: 1, 4, 9, 16, 25, 36


I understand that a multiple layer triangle can be made up of more than stated. But I decided to go exactly with what I saw, 36 individuals joined together.

In this context of a 2D design the 33 it only appears significant because of the remainder that it produces: 36-33 = 3 a triangular number. Figure 1 represents the remainder 3 as A,B & C in what I consider the most significant overall position.


Figure 1
http://img98.imageshack.us/img98/4545/triangle33.jpg

However it stuck me that the outside faces of the object must be of some significance as there was 3. Counting the points of the triangles which face inwards on one face comes to 6, another triangular number.


Considering a two dimensional system of control, it seemed more relevant to look at 3D objects.

One thing that has always struck me was the significance of The Great Pyramids. From a basic level of design they're a 2D square/rectangle extended into 3D by a central point. With four triangle faces pointing to the skies. Researching some design theories attracted me to the idea of the four corners representing the four elements, which goes along nicely with the four triangle faces.

So going back to a basic 2D triangle and extending it into 3D based on a central point produces a tetrahedron. Considering the four elements it seems perfect with four points an faces. For me it appeared to be a perfect alternative to the pyramid design.

Stepping back from this it became apparent why the pyramids design based on the four elements position of a 2D cube.

In the 2D a square is significant because it's not a triangle. However in design structure consider the importance of square numbers, 2D design and 4 outside faces in 3D. But in 3D a pyramid has five faces, this leads me to the conclusion based on equality and significance, that pyramid design is only of significance if the bottom face is disregarded and entered through. Only natural sources such as light, wind and rain can enter through it's faces.


Extending from the two dimensions of control. I conclude that in terms of pyramid design, any influence could only have an effect of two dimensions. Based on the 3D design flaw it cannot have a three dimensional effect. The pyramids significance was mainly beneficial for a two dimensional system control. It was without pure power.

So I'm naturally drawn to the significance of 3 & 4 based on 3D design. Straight away I consider a tetrahedral, and as a consequence the molecular structure of methane.

But drawn back to 2D design and the triangle I consider the missing four again. I've always related pyramid design based on the four elements, this gives a natural balance.

Considering the 2D design and A, B & C, therein lies a problem of which of the four elements to project to a 3D object. Sticking with the 2D design principal I simply use a circle to represent the Earth.


Figure 2
http://img3.imageshack.us/img3/9348/pumpt.gif

To extend this design out into the 3d, I simply used the centre of the circle representing the Earth and ended up with a tetrahedral.


Da Vinci may answer that question with the "Vitruvian Man". But for don't forget to consider what's missing?, where is the Vitruvian Woman?


Figure 3
http://img602.imageshack.us/img602/9202/vitruvianmantriangle254.jpg



Further Background Reading that I found:


Figure4
http://img810.imageshack.us/img810/3378/backba.jpg
http://www.korncirkler.dk/cccorner/universe2.html



Figure 5
http://img407.imageshack.us/img407/5447/tetrahedral.jpg
http://www.korncirkler.dk/cccorner/universe2.html

[AlkaMyst]

FutureLeFunk,

Go here (http://projectavalon.net/forum4/showthread.php?9448-***The-FTP-Site-is-Back%C2%85.Just-for-Avalon-Forum-Members!!!***) to find out about the FTP Account.......I think I should have made myself a bit more clear (There are over 70 triangles in this image), the untrained eye will only see those 36 you mentioned maybe 37 if the count the whole triangle, but in reality there are more than 70 here and that can not be discounted, I love math/geometry and have a good eye for this things.

Maybe I'm the one misunderstanding your theory, and maybe a little more elaboration might help :)

[FutureLeFunk]

Caveat: Currently being updated for clarification.

Perhaps the most interesting 2D design that I've found is figure 5. If you check the link it shows pictures of corn circles, of course these could just be man made or indeed clues.........

I did find a 2D design which further increased my ideas on a 2D design. Please bear in mind that I take this to represent the two dimensional base of a tetrahedral. Again it all appears to fit into a triangular theory, which I will need to expand on.


Figure 5
http://img407.imageshack.us/img407/5447/tetrahedral.jpg
http://www.korncirkler.dk/cccorner/universe2.html

The essential concept is to look in terms of triangles and equals, which leads to figure 6.


Figure 6
http://img213.imageshack.us/img213/2966/sierptriangle.gif

We end up with three equal triangles represented in red, green & blue. It may be essentially four triangles but the central fourth is disregarded until later.


Figure 7
http://img842.imageshack.us/img842/6474/sierpinskigeometric.gif

Again the important thing to consider when subtracting such as above is three. For example:

(1) Start with the overall triangle.
(2) Split into three and subtract one.
(3) Split into three and subtract one.
(4) Split into three and subtract one.
(5) And to return back to (1) simply multiply by three, three times

There are three levels of subtraction and conversely three levels of multiplication to return back to (1).

Taking into consideration figure 1 and the significance of the number 36, look at what remains at (4). If you count the number of equal triangles, lets say in blue then you get:

3*3*3 = 27

This is of no significance until you consider the equal blank triangles:

(4+4+4) * 3 = 36

It seems a little far fetched until you reflect on the Molecular Covalent Dimensionality Tetrahedral in my background reading post. First you need to consider that the triangle theory is limited to this design. If figure 6 represents the base of 3d tetrahedral and that this base in the interface between the 1d and 0d of molecular covalent dimensionality. Further consider that figure 6 also represents the x,y axis of a 3d tetrahedral, lets say that the red/green combined represents the base. The central blank or open equal triangle is a tetrahedral in 3d, it's top is represented in molecular covalent dimensionality also in 3d, further imagine that it has also three natural entrances at ground level.

Going back and considering a circle with a triangle in it as a pump, my theory is that a 3d person enters in and the structure descends them to -3d.

But I was struck that there should be a sense of balance so a pump should be opposed. This led me to consider an equal opposing tetrahedral and so a star:


Figure4
http://img810.imageshack.us/img810/3378/backba.jpg
http://www.korncirkler.dk/cccorner/universe2.html

Working in reverse you end up with a very interesting structure. Imagine if a 3d person enters, descends to -5d and it sent to an equal planet where he is re-assembled. Perhaps the corn circles are not ufo's but just arrivals.........

[AlkaMyst]

That's quite alright my friend, I know you meant well :)

I just PM'ed you the login info to the FTP Account......just login and go under books (Search: The Flower of Life)

ENJOY!!!

[FutureLeFunk]

Thanks I got a pm and will check it out.

I'm sorry again but I rather stumbled through this with a strange sense of focus. It appears that I need to work backwards from the top, which is not a problem :)

I've found a few old books clearing out as I have to move next week. Mathematics in Western Culture is now on my list too!

[FutureLeFunk]

Ok! my posts have been updated and I've tried to clarify whilst evolving my theory.

My general idea was to throw together something and then evolve it with further research etc.

I now feel comfortable to expand my knowledge. Please understand that I rejected a formal education when I was younger. It is very unusual for me to expand this way unless I feel a natural sense of purpose.

Thank you all! :)

[AlkaMyst]

Much better my friend, but I'm still somewhat confused at what you're trying to get across......maybe as the thread develops more it would be easier to understand and see your point.

Just a thought that I think may help some......


* All of these are held within Mother Earth, a creation of 4d. The basis of the Earth's dimensions are founded by the classic elements:

Earth
Fire
Water
Air




Where's the Aether (Ether) in this whole equation, because that is also an element and happens to be the most important one which is what connects all the other elements together.......I think that if you try and incorporate this you might be a bit closer to what you're trying to get across here.

Just my input, but great job FutureLeFunk....keep up the hard work!!! :)

Blessings,
AlkaMyst

[FutureLeFunk]

Much better my friend, but I'm still somewhat confused at what you're trying to get across......maybe as the thread develops more it would be easier to understand and see your point.

Just a thought that I think may help some......



Where's the Aether (Ether) in this whole equation, because that is also an element and happens to be the most important one which is what connects all the other elements together.......I think that if you try and incorporate this you might be a bit closer to what you're trying to get across here.

Just my input, but great job FutureLeFunk....keep up the hard work!!! :)

Blessings,
AlkaMyst

Hiya

Thanks for the input!, it's very much appreciated :)

I think you need to disregard the classic elements and consider them purely symbolic, only a clue to develop theory. It probably makes more sense to think of it as a chemical equation of different dimensions. The elements are at a basic level only relevant as an input.

Consider this a strange but natural experience for me. So I'll explain in terms of how this theory is developing:


There is a duality to everything in life, take for example communication.

I can phone you, you can phone me. Thirdly there's a natural connection requiring no apparent input or output, from either you or me.

You could consider telepathy for instance as being a natural connection. But for the purpose of this example lets say that this connection is simple e.g. speech.

Ok! so to further expand on this and instead of a quick natter, lets say a 3d picture. If I was to convey a 3d picture to you using telepathy and speech it would take longer and a require more effort.

Now further expand on that and lets say that I communicate to you exactly what I see through my own eyes. Consider how easy it is to look in a direction and how natural that image is processed. If you think not in terms of time, think how big the first computer would need to be to process all of that and the energy required. Technology reduces the size and the energy needed to do that, consider nano technology with the aid of sacred geometry assists that. However instead of telepathy, there is a natural network between us to transfer that instantly.

Essentially the theory is that if there's a natural connection between equal carbon life forms on this planet, the only restriction is that a direct transfer is limited to information and not physical objects held within the Triangle rule. This is not to say that there's not advanced technology based on other rules , but lets limit it to triangle and square for now.

Considering the possible limits of these two rules, it may however be possible to naturally add or subtract from physical objects. My theory is that this natural network extends from objects to planets, through space and can return to equals. So no beaming up to the moon, but possibly a human/carbon life transferred to another planet such as the Earth.

The hard part is validation. My feeling is that catalysts which work naturally on products of reactions may be a good starting point. Something tells me to look at the products of combustion.

It's strange I know, but perhaps the key is subconscious and forced natural connections. On a subconscious level a natural connection doesn't need to be direct.

Thanks

[AlkaMyst]

I more or less understand where you coming from.......it will be interesting to see your theory develop!!!

Blessings,
AlkaMyst

[FutureLeFunk]

I'm moving this week and reading up to further develop it.

Here's one out in the Nevada desert.........

http://img96.imageshack.us/img96/5247/nevadaw.jpg
http://www.bibliotecapleyades.net/offlimits/offlimits_area51_07.htm

[Intraphase]

This is great stuff. Very helpful to me to reinforce the connection between fractals and triangles as methods information uses to contract itself to instantaneous size for immediate timespace transfer and then re=expand itself to resynchronize to the size required at its destination point.

[FutureLeFunk]

Apologies as I was a little distracted with moving home and developments in the Charles threads. But back to work :)

Centred Triangular Numbers

Following on from the Sierpinski Triangle, it made sense to look at centred triangular numbers.

Figure 8

http://img213.imageshack.us/img213/6796/centredtriangular.jpg
http://en.wikipedia.org/wiki/Centered_triangular_number

So the relationship between the two is quite simply the centres.

Figure 9
http://img703.imageshack.us/img703/8817/centredtriangularnumber.jpg

Looking back at figure 8 and the first expansion in figure 9, in a way it resembles to me The Eiffel Tower.

http://img593.imageshack.us/img593/2263/eiffeltower431x300.jpg



Named for its designer, engineer Gustave Eiffel, the tower was built as the entrance arch to the 1889 World's Fair.

The tower stands 324 metres (1,063 ft) tall, about the same height as an 81-storey building. Upon its completion, it surpassed the Washington Monument to assume the title of tallest man-made structure in the world

Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n.
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325.........., 1711
http://oeis.org/A000217



The difference compared to height is only one (324 metres +1 = 325)
The same height as an 81 (9*9) storey building.
It surpassed the Washington Monument, which on it's eastern face bears the inscription "Laus Deo/praise be to God".
The monument was inaugurated on March 31, 1889. On that day, Gustave Eiffel climbed the 1,710 (http://paris.eiffel-tower-faq.com/construction/) steps of the Tower to plant the French lag at its peak. As with the height you add one to get a triangular number.


It was designed by Alexandre Gustave Eiffel (http://en.wikipedia.org/wiki/Gustave_Eiffel). He also designed La Ruche (http://en.wikipedia.org/wiki/La_Ruche), an old three-storey circular structure that got its name because it looked more like a large beehive than any dwelling for humans.


Now that I've dragged you down here with me, I may as well explain what it is I expected to see. In the year of the Universal Exposition of 1900, the sculptor Alfred Boucher bought some vacant land in the Vaugiraud area as a brainstorm.

After the exhibition, he purchased the Médoc wine pavillon, a forged gate from the Pavillon des Femmes, the caryatides of the British East Indies pavillon and some other items of the exhibition's architectural bric-a-brack, and plopped it all in the Passage de Dantzig, along with either 80 or 200 rudimentary ateliers for artists. The whole kabob was inaugurated in the spring of 1902, with the ministers of education and culture helping out.

La Ruche, the original building, was - is? - round. The ateliers dividing each floor are described as triangular, or as Zadkine said, "It is a sinister wheel of Brie." The artists worked in rooms like wedges of cheese. From the one old photo I have, it looks like a flying saucer wearing a Chinese hat - but I do not see this at all today. Maybe a higher angle is needed to see it all.
http://img843.imageshack.us/img843/228/laruche.jpghttp://www.metropoleparis.com/1999/426/426ruche.html


http://img218.imageshack.us/img218/9373/eiffel.jpg

The first drawing by Koechlin and Nougier reveals their phantasmagorical intention: A tower as high as the Notre Dame, the statue of liberty, the arc de triomphe, three obelisks and a 5-storey apartment building stacked up, altogether 1000 feet high. It was the tallest building of the world until the 1930´s.

Koechlin and Nougier contacted Stephen Sauvestre, an architect, to embellish their project. Sauvestre proposed several modifications, among them the arches which would connect the base with the first level of the tower. Nevertheless, the bridge-turned-upside outraged his contemporaries. While nobody was objecting against Eiffel´s bridges, the fact that he was building a tower in Paris horrified the Parisian art and architecture establishment. With the tower, Eiffel left the context of the “utilitarian” which contained his bridges in a territory outside- and below- the area of “art” claimed by the architects of his time. He was intruding in architectural territory with a naked, technical construction, higher than anything else in Paris or the rest of the world. http://ideas.mgstrategy.com/


ps. I will update this later today after further research.

Thanks :)

[FutureLeFunk]

I more or less understand where you coming from.......it will be interesting to see your theory develop!!!

Blessings,
AlkaMyst

Yes! sorry I'm having some difficulties translating the design using a CAD package :embarassed:.

But here goes anyway! :)

Figure10

http://img691.imageshack.us/img691/1624/sierpinskiexpansion.jpg


Figure 11

http://img545.imageshack.us/img545/7989/xyzcoordinates.png

Considering the star in figure 4, I was keen to attempt to translate the Sierpinski triangle into a 3d design.

Figure 10 shows an equal 2d design based on the x & y axis, which doesn't seem to work. (Although considering it two opposing cones would make an interesting 3d object)

The hard part is representing the Sierpinski triangle on the x & z axis and then extending the design on the y axis (I need to develop my CAD skills).

[FutureLeFunk]

Apologies! I found Google Sketchup which thankfully is much easier to work with :)

Figure 12

http://img25.imageshack.us/img25/8991/yellowstarq.jpg

My initial thoughts about the significant sides of the structure are shown above. The three top yellow faces (at the pointer level) and the lower tetrahedra representing opposing connections.

Figure 13

http://img214.imageshack.us/img214/8536/yellowstarxray.jpg

But it seems prudent to look closer at the internal connection of the two joined blue/yellow tetrahedra. Above shows the connection a little clearer.

Figure 14

http://img203.imageshack.us/img203/5954/sellacentrexray.jpghttp://img8.imageshack.us/img8/8196/stellacentrewired.jpg

With the outside tetrahedra removed you end up with above, which is two opposing pyramids. The wired shows this in a different orientation. I'll consider the difference in orientation more when the design gets more complex.

Before that I'll look at a 3d Sierpinski Triangle.

[Intraphase]

A logic based summary paraphrasing the ten episodes of:

DANGEROUS KNOWLEDGE
Covering Cantor Boltzman Godel & Turings journey wrestling with:

The Continuum - Probability - Incompleteness = Halted Vs Solved


http://www.youtube.com/watch?v=Cw-zNRNcF90
Part-01

00:00 The matrix of rules known as science.
01:00 The fear encountered by understanding The Infinite Vs. The Eternal
02:00 The four stories begin in Holland
03:00 Georg Cantor "How big is infinity" Commentator: "Like being on drugs"
04:00 "He dies alone in an insane asylum"
05:00 "Suspected certainty could lead to man transcendance"
06:00 "Did not identify with Jesus Identified with God"
That which is hidden shall be brought into the light. Corinthians
07:00 The Creator God "AS" Eternal Mathematics
08:00 Yet there are complications understanding "Infinity"
09:00 The mystery of The Infinite as understanding The Circle


http://www.youtube.com/watch?v=wpWXT9yMBnw&NR=1
Part-02

00:00 Two lines radiating outward from a circle grow apart to seemingly infinite distance apart
01:00 Cantor marries while wondering can I add { Infinity + Infinity }
02:00 1872 grasped infinity as inward and outward infinite convergence and infinite divergence
03:00 Starts to "size" infinities. Realizing inward verses outward of the smallest verses largest.
04:00 Introduces (GC) Gregg Chaitin. "A multitude of infinities are discovered and found unnameable"
"Has nothing to do with building bridges or airplanes simply profound insights"
05:00 G.C. "Here... we are down in the forest struggling up the mountain... if lucky you get there."
06:00 There is a liberating effect but also a precipice of unmeasurable possibilities (theme= superposition)
07:00 Cantor is blocked from publishing and attacked personally "Poincare - a sick mathematics."
08:00 Safe set theory is developed to overcome Cantors revelations of infinite possibility.
09:00 Cantor asks himself "Is there a logic that ties all the infinities together?"
He grows isolated and his bipolar disorder begins troubling him.

http://www.youtube.com/watch?v=1AAvWb5wYNk&NR=1
Part-03

00:00 The natural ability to live the seemingly unnatural hermetic isolated life
01:00 He once got a letter from father saying "He was the family's key hope for the future."
02:00 1884 His theory two years work on "The Continuum Hypothesis" is attacked regularly
03:00 He has a breakdown and goes to an asylum. Speculation is Manic-Depressive with Mania and Grandeur
04:00 He can't stop working on the hypothesis. Cycles through inner voices with extreme highs and lows.
05:00 Writes to his publisher off and on "I proved it" and "I can't prove it my work is ruined" again and again.
06:00 Rigidity of his perceptual stance and inability to let go causes him to describe infinity as "The Abyss"
07:00 (During blood tasting scene voices whisper; "I must I must I must I must." ) He never recovers.
08:00 1899 is in asylum (Still working the Hypothesis) when his music inspired son Rudolph dies four days short of 14 years old
09:00 He once loved music like Rudolph did. He wonders why he left music


[][][] The second of four great minds (Louis Boltzman) is now introduced into the historical context. [][][]


http://www.youtube.com/watch?v=qUL-x8Gm1h4&NR=1
Part-04

00:00 "The equation which killed Boltzman"
"Cantor undermined the logic in math Boltzman undermined the logic of physics
01:00 "They craved certainty" ... "The old order was dying." "Hapsburg monuments probably doomed."
02:00 "The rich always in castles the poor men always at their gates"
03:00 The End of Empire - University of Vienna "They oppose his place in the pantheon of physics"
04:00 "Order emerged from disorder because of natural patterns of random bumps" "He understood atoms"
05:00 "A new kind of physics ( Probability )" "Exactness is now fading... Probability is gaining"
06:00 "Boltzman genius was he accepted ( Probability ) to assign positions and motion tracks"
07:00 "Boltzman was in the right place at the wrong time. Twenty years later he would be hailed as hero."
08:00 Eternal Structure Vs Unpredictable Probability
"Timeless never changes but it is dead, yet change brings death and decay."
09:00 "The accumulation of disorder and decay is the ( ENTROPY ) Boltzman understood as:

[] S = k.log W [] AS []

S-State of Gas Cloud = K.log-Possible Number of Internal shuffled Positions (X) Frequency Each State Appears

http://www.youtube.com/watch?v=So9RAbBy1ps&NR=1
Part-05

00:00 "The idea of time is now revolutionized. Time moves only forward only equations can run backward."
01:00 "Entropy is decay with decay nothing lasts forever. Mortality is captured in an equation."
02:00 "With the equation of entropy he brought the idea of constant (Eternal ) change into the heart of Physics."
03:00 "He liked Darwins view as a dominant philosophy of 1800's" "Viennese are searching for stability"
04:00 "The radicals and conservative trap Boltzman in the middle" "He is a passionate man."
05:00 "His mood swings deepen " No sacrifice is too great."" Writes "repeating the doctrine" style books. "The last years of his life he does no research at all."


http://www.youtube.com/watch?v=fqKQ0-T3swY&NR=1
Part-06

[][][] Here Boltzman goes to the place he has chosen to die/commit suicide at. [][][]

00:00 "Boltzman discovered a fundamental equation of how the universe works'
"The great discoveries comes as a revelation like a palace emerging from an autumn mist"
01:00 "Exhausted and demoralized he killed himself leaving no note of explanation"
02:00 "A clue is a Faust qoute in his science paper intro.
"Bring forth what is true. Write it so its clear. Defend it to your last breath.""
03:00 "Faust's pack with the devil was he could have all the knowledge and experience he wants as long as he never asks to stay in one place or one moment. Boltzman craved the stopping of time right there.
04:00 He is vindicated as an accurate revolutionary 20 years later.

[][][] Back to Cantor's struggle with The Size of Infinites [][][] They are desperate for logic now.

05:00 The Principia Mathematica - It takes a whole volume just to prove 1+1=2 based
The Finite Verse The Infinite ..... is now the struggle for logic. It seems to float in the air
06:00 1917 Cantor begs to be let out of asylum. 01-06-1917 He dies alone his Continuum Hypothesis unfinished.
07:00 "Without God how is it all held together. The believed god died during World War One."
08:00 "Even Descartes believed God must exist as some sort of higher intelligence."
09:00 The Principia Mathematica is nothing but a patchwork to logic that isn't holding.

[][][] The third of four great minds (Kurt Godel) is now introduced into the historical context. [][][]

University of Vienna. "The limits of *strict* logic"
Kurt Godel born in 1906 The same year Boltzman died
Godel finally brings the castle of logic down. "His family called him Mr. Why"
Germany slow to recover from WW1 is vulnerable to Hitler's political aspirations.


THE INCOMPLETENESS THEORUM

http://www.youtube.com/watch?v=oldUAw2Aux0&NR=1
Part-07


00:00 "Chaos was liberating but created to much uncertainty... math *could!!!!* be made whole again."
01:00 "The completion of mathematic was *impossible* Godel begins the "Incompleteness Theorum"
02:00 1930 "Godel believes all systems of logic are limited... Some true things can not be PROVED"
03:00 "The great renessaince dream of god like knowledge is dying-it is truly OVER. (logic as god)
04:00 "Hilbert very angry at Godel's Proof. The argument is very clear and accepted that Cantors work can not be solved and that the paradoxes were unsolvable and unprovable.
05:00 "Where's Godel's bust IN Vienna ???????? What are they afraid of in his PROOF that logic is limited."
06:00 "He begins to understand what he has done by destroying math as a system replacement for "God.""
07:00 "Yikes he goes all the way back to what drove Cantor crazy "Continuum Hypothesis" even using his book.
08:00 "He calls it his worst year and has a nervous breakdown ending in an asylum just like Cantor."
09:00 "Perkosdorf Asylum. Driven mad by symmetry and logic he is in a building designed to embody it."


http://www.youtube.com/watch?v=0ZcErXdR_eQ&NR=1
Part-08

[][][] The fourth of four great minds ( Alan Turing ) is now introduced into the historical context. [][][]

Cantor of the "Continuum Hypothesis" is now deceased
Boltzman of the "Probability Theory" is now deceased
Godel of the "Incompleteness Theorum" leaves Germany

Turing seizes on Godels idea above and describes it as "The Halting Problem"


00:00 "Turing is much more practical" "He makes the Incompleteness Theorum a theory beyond question"
01:00 "The vision he has to make Godel incompletness theorum provable is THE COMPUTER"
02:00 (GC) Gregg Chaitin "Its devestating what Turing does with Godels idea that some things are unprovable"
03:00 "Turing recasts the problems as unsolvable because the machine never stops trying or finding a solution."

HOW DO YOU KNOW WHEN TO STOP... ??? aka The Halting Problem

04:00 "I finished.. whoops I guess not... yes I did... nope.... shucks hmmm" Computer Crunching logics.
05:00 "Turing wonders "Are we or are we not computers"" He loved Christopher a homosexual friend.
06:00 "He falls in love with the idea that computers could one day be like children and learn." "Turing believes if our minds are like computers then here is the means to understand ourselves."


Cantor & Boltzman as Pure mathematics - Infinity & Probability
Godel & Turing as the Limits Of Logic and the limitations of The Human Mind = Outcome "Aha!!! Intuition"

The four great ideas have evolved as: Continuum - Probability - Incompleteness - Halting Problem / Solvability

07:00 Psychiatrist "He vascilates between people are and are not machines"
08:00 (GC) Gregg Chaitin: "His mathematics does not have to agree with his personality. He proves that the human mind must be more powerful than machines because it can smash problems with intuition."
09:00 "Turing personal philosophy was to be free from hypocrisy compromise and deceit." "If we were computers then we would be the type of humans Turing desired but we are not."


http://www.youtube.com/watch?v=SYB8KXwQ69E&NR=1
Part-09

00:00 "He believed we were partly computational machines"
01:00 "The tension between the Human & Computational was a tension he needed to progress." He is arrested charged and found guilty of homosexual acts and chemically castrated
02:00 "The treatments affected his moods, body and mental effectiveness. He poisons himself."

[][][] Back to the sole survivor in the: Continuum - Probability - Incompleteness - Halting or Solvability

03:00 "Kurt Godel is at Institue for Advanced study working obsessively behaving peculiarly."
04:00 "He believes in bad air, bad food and various paranoias but believes THE MIND IS NOT A COMPUTER."
05:00 "Why did he believe in the DIVINE SPARK aka *Quantum Self* ?? the same as Einstein
06:00 "How ever complicated the universe is there shall always be useful rules. God is not malicious."
07:00 (GC) Gregg Chaitin: "INTUITION itself *IS* the connection to the eternal forms and boundaries between infinities."
08:00 "Computers are limited. Humans are not limited. Yet! Hmmmm.... but it can not be proved. Intuition is beyond.
09:00 "Minds create systems and then leave them running; but move BEYOND. He tries to prove *INTUITION.*"


Part-10
http://www.youtube.com/watch?v=_8dczB1rY-Q&NR=1

00:00 "He has identified a paradox. "The mind thinking about the mind thinking about the mind thinking about......"
01:00 The Self Reflection Paradox - Logic Contemplating Logics Own Being "He begins starving himself" (This is similar to using a flashlight or laser beams between two mirrors - some radical new theories involve this)
02:00 "He desperately wants to prove logically; that logic is not logical" He can not seperate himself from the process.

Cantor discovered uncertainty searching for certainty.
Boltzman verified Probaility was more of a tool to measure
Turing and Godel proved uncertainty was inescapable and must be lived with.

03:00 "Logic had revealed the limits of logic. The search for certainty had revealed uncertainty"
04:00 (GC) Gregg Chaitin: "This notion of... ABSOLUTE Certainty is silly. Our knowledge of The Totality shall always be a finite amount because we are finite but our journey through the knowledge is unlimited therefor infinite as permutations"
05:00 "Are we grown up enough to live with uncertainty or do we pledge blind allegiance to some new illusion of certainty."


The End.

My fourth full viewing of this and I came away with a symbolic summary as above.

Human Vs Eternal
AS
The Finite Vs. The Infinite
AS
Computation Vs. Intuition

Outputs:

Continuum - Probability - Incompleteness = Halted Vs Solved