Ouroboros in Futurama Episode 13: Fry & The Slurm Factory

Tuesday, July 29, 2008

Can't find the right frame online, but in episode 13 of Futurama, Fry & The Slurm Factory, there is a very clear, blatant ouroboros (snake biting its own tail) symbol.

In this episode, modeled after Willy Wonka & the Chocolate Factory, the gang visits a Slurm factory where it is revealed that the secret ingredient is-- (no, not people, that's Soylent Cola)-- waste from a giant worm.

But, what's interesting is that in the scene depicted in the image to the right, the worm forms a perfect ouroboros by drinking Slurm from its own tail.

I can't find the exact screenshot online but here are some other representations of the ouroboros to compare. Note the crown (or horns) in some of these:



Posted by Jonah Dempcy at 3:56 PM 2 comments  

Bertrand Russell on Education

http://chaosandoldnight.files.wordpress.com/2006/07/bertrand-russell.jpg

Education in a scientific society may, I think, be best conceived after the analogy of the education provided by the Jesuits. The Jesuits provided one sort of education for the boys who were to become ordinary men of the world, and another for those who were to become members of the Society of Jesus. In like manner, the scientific rulers will provide one kind of education for ordinary men and women, and another for those who are to become holders of scientific power. Ordinary men and women will be expected to be docile, industrious, punctual, thoughtless, and contented. Of these qualities probably contentment will be considered the most important. In order to produce it, all the researches of psycho-analysis, behaviourism, and biochemistry will be brought into play.
- Bertrand Russell, 1931

I think this quote is a great example of the mentality of the elites. Keep the masses content so they will be docile, industrious, punctual and thoughtless. Meanwhile, reserve hidden knowledge for the chosen few.

In another Russell writing he discusses what should happen if one from the lower ranks were to be of high intelligence. He concludes that should this situation occur, that person should be invited into the elite circles. If they refuse, they should be killed, for if they continue to live in the lower ranks they will inspire others and cause civil unrest (presumably through revolution or uprising).

I can't remember the book which this horrific sentiment came from, but I think it's the same one where Russell discusses the need for children to be taught that snow is black, if only for the reason that it proves their utter obedience and loyalty (agreeing with something even though they know it isn't true).

Remember, this is coming from the same guy who proposed "preventative warfare" measures, i.e. nuking civilian areas as a way to scare the world into peace. And some people think this guy is a genius! Go figure.

Posted by Jonah Dempcy at 3:42 PM 1 comments  

Synchromystic Analysis of Futurama - A Fishful of Dollars

Sunday, July 27, 2008

I saw Episode 6 of Futurama last night, titled A Fishful of Dollars, and I noticed quite a few synchs.

Here is a synopsis of the episode and some screenshots:

"A Fishful of Dollars" is episode six in the first season of Futurama. It originally aired in North America on April 27, 1999. The episode was written by Patric Verrone and directed by Ron Hughart and Gregg Vanzo. Pamela Anderson guest stars as her own preserved head in a jar. This episode marks the first appearance of the character Mom, the series' recurring antagonist. The title of the episode is a play on name of the film A Fistful of Dollars.[1]

http://www.gotfuturama.com/Multimedia/FrameGrabs/1ACV06/Grabs/pic00532.jpg

Fry's Nemesis: "Mom"
Fry's Nemesis: "Mom"

http://www.gotfuturama.com/Multimedia/FrameGrabs/1ACV06/Grabs/pic00144.jpg
The whole character of Mom and her use to sell products was a major synch to me. She has a heart-shaped hair-do, her advertisements have bright pink, thus associating consumerism with receiving a mother's love. For more on this, see this YouTube video.

An excerpt from the script during Mom's advertisement follows:

               MOM
Call me old fashioned, but when my
robot starts to squeak like an old screen
door well, that's when I reach for a
can of Mom's Old Fashioned Robot Oil.



BENDER
Mmm, tasty!


MOM
And remember: Mom's oil is made with
10% more love than the next leading
brand!


[She smiles.]


ANNOUNCER
"Mom", "love" and "screen door" are
registered trademarks of Mom Corp.


One of the themes was advertising, and it's revealed that in the future advertisements are implanted in peoples' dreams. When asked how this works, the professor says, "It's very simple. The ad gets into your brain just like this liquid gets into this egg," and he injects and egg with liquid from a hypodermic needle. The egg explodes on the crew, then the professor continues, "But in reality, it isn't liquid, but gamma radiation."

So, advertisers of the future use microwave devices (ala HAARP) to beam ads into peoples' dreams? Serious mind control theme here. In fact, the very next line is Fry exclaiming, "That's awful, it's like brainwashing!" The Futurama opening also says "Presented in Brain Control where available", parodying the normal "Presented in Closed Captions where available" message.


Some of the synchs I noticed were:

  • The number 1077 seems prominent in the episode as Fry makes a point of saying it again and again, even though it is his "secret" PIN number. It is also the price of a cheese pizza and a large soda at Panucci's Pizza, the New York restaurant where he worked in the year 2000.

  • Fry had 93 cents in his account at Big Apple Bank but 1000 years later this accrued to 4.3 billion, due to the 2.25% interest rate.

  • Dialogue from the episode:

     LEELA
    You're Fry's relative. Do you have any
    idea how he got so crazy?


    FARNSWORTH
    Uh, wha? Oh, yes, they say madness runs
    in our family. Some even call me mad!
    And why? Because I dared to dream of
    my own race of atomic monsters. Atomic
    supermen with octagonal-shaped bodies
    that suck blood out of...


    [He walks out still blabbering. Enter Fry.]


http://www.gotfuturama.com/Multimedia/FrameGrabs/1ACV06/Grabs/pic00039.jpg
Fry has a nightmare where he is in a class on Ancient Egyptian algebra. This probably has zero relevance but my ears perk up any time Ancient Egypt is mentioned (which is quite a lot!) so I thought I should mention it.


http://www.gotfuturama.com/Multimedia/FrameGrabs/1ACV06/Grabs/pic00439.jpg
Mom explains that they can take a slice of this DNA from a sardine ...

http://www.gotfuturama.com/Multimedia/FrameGrabs/1ACV06/Grabs/pic00441.jpg
And combine it with DNA from third-world children to make .... Oil! Genetically engineering third-world children to make them easily "convertable" into oil that can be used by robots. Pretty blatant commentary on the mentality of profiteering capitalists who will commit atrocities in third-world countries just to get rich.

Sunday Mind Control Linkfest

From Wikipedia ...

Methods

Researchers

Miscellaneous


External links


Pages in category "Mind control"

The following 46 pages are in this category, out of 46 total. Updates to this list can occasionally be delayed for a few days.

A

B

C

D

E

G

H

I

J

L

M

N

O

O cont.

P

Q

S

T

U

W

Z

Posted by Jonah Dempcy at 2:02 AM 0 comments  

The Fountain (2006) by Darren Aronofsky

Saturday, July 26, 2008



Just finished watching The Fountain. Pretty heavy movie, I wouldn't recommend it unless you want to see a real downer. That being said, it has some very nice imagery, interesting storytelling and a wealth of symbolism.

A gold-hued scene in which Tom (Jackman) faces a hallucination of Isabel (Weisz) beside the Tree of Life
A gold-hued scene in which Tom (Jackman) faces a hallucination of Isabel (Weisz) beside the Tree of Life

According to Wikipedia, "The Fountain explores the themes of love and mortality, drawing influences from the The Fountain of Youth and The Tree of Life. The film is framed with visual language by using transition scenes, light, and shapes." I wish more movies used a "visual language" like this. It makes for some images that are aesthetically pleasing, yet still rich in meaning.

Here are some of the themes and memes of the film:

Death/ego loss, acceptance, reincarnation, the Maya, the land of the dead (namely, the Mayan underworld, Xibalba), The Fountain of Youth and Tree of Life (as Wikipedia mentions), the search for El Dorado, gold and the color yellow, nebulae and dying stars, parallel realities, spiritual enlightenment, writing a novel, the Garden of Eden and tree of knowledge

Miscellany:

The main female lead, played by Rachel Weisz, is named "Izzi." I thought that this is a somewhat strange name because of its symmetry.

Aronofsky described the astronaut period as a homage to David Bowie's "Space Oddity"; the protagonist's name "Tom" originating from the Major Tom of the popular song.[18]

It seems that the Garden of Eden and Biblical symbolism makes an appearance as well ...

The Fountain begins with a paraphrase of Genesis 3:24, the Biblical passage that reflects the fall of man. Hugh Jackman emphasizes the importance of the fall in the film: "The moment Adam and Eve ate of the tree of knowledge, of good and evil, humans started to experience life as we all experience it now, which is life and death, poor and wealthy, pain and pleasure, good and evil. We live in a world of duality. Husband, wife, we relate everything. And much of our lives are spent not wanting to die, be poor, experience pain. It's what the movie's about."[24] Darren Aronofsky had also interpreted the story of Genesis as the definition of mortality for humanity. He inquired of the fall, "If they had drank from the tree of life [instead of the tree of knowledge] what would have separated them from their maker? So what makes us human is actually death. It's what makes us special."[36]


The Kabbalistic tree of life is one of the most prominent symbols throughout the film. It is acknowledged on the Wikipedia page:
In The Fountain, the Tree of Life was a central design and part of the film's three periods. The tree was based on Kabbalah's Sefirot, which depicts a "map" of creation to understand the nature of God and how he created the world ex nihilo (out of nothing). The Sefirot Tree, being two to three hundred feet tall in lore, had to be resized for The Fountain to fit in the camera's frame.[19]
More analysis from Wikipedia:

The theme of thanatophobia is described by Aronofsky as a "movement from darkness into light, from black to white", tracing the journey of a man scared of death and moving toward it.[37] The theme is highlighted by Aronofsky's use of visual language, such as shooting Jackman's characters in shadows until the story's light-saturated conclusion, while Weisz's characters are awash with light in each period.[38] Along these lines, Aronofsky made use of the color of gold, as gold was the sought-after treasure of the conquistadors. "When you see gold, it represents materialism and wealth and all these things that distract us from the true journey that we're on," Aronofsky said.[37] The director also used similar geometric constructs in the film to distinguish the three chronological narratives. The 16th century conquistador's tale reflected triangles through pyramids and constellations, the 21st century researcher's period reflected rectangles through doors, windows, and computer screens, and the 26th century contemplative's journey reflected circles and spheres through the spacecraft and stellar bodies.[39]

Darren Aronofsky emphasized that the narratives in their time periods and their respective convergences were open to interpretation. The director maintained that the film's intricacy and underlying message is "very much like a Rubik's cube, where you can solve it in several different ways, but ultimately there's only one solution at the end".[40] Critics have observed recurring, mythological references to themes of enlightenment, redemption, the Hindu concept of cycle of birth and death and moksha, the Biblical Tree of Life,[41] the Buddha,[41] and the world-tree Yggdrasil.[42] In the same vein, Jackman views the story as a modern myth that helps people to understand the meaning of life, explains the unexplainable, and fosters understanding. "These fables may not make scientific sense, but somehow they explain the world to us," said Jackman.[43] Aronofsky later explained the film has an atheist meaning. "It's about this endless cycle of energy and matter, tracing back to the Big Bang", he said. "We're all just borrowing this matter and energy for a little bit, until it goes back into everything else, and that connects us all."[44]

So, as I said, it's chock full of symbolism! A good film for discussion and analysis, though its overly long pacing and sometime hokiness (doing yoga flying through space was especially cheesy) reduces the impact of an otherwise powerful film. But, with this slow pacing and at times dreadfully repetitive and melodramatic score, it was a pain to sit through the last 20 minutes or so. Even before that, I thought they really over-did the whole emotional side of it, at the expense of exploring the themes in greater detail. This is definitely not a "talky" film, quite the opposite. And, that's fine; Film is a visual medium, after all.

But, I guess I felt that the themes didn't really progress-- sure, there was a minor character arc for the protaganist, who felt the transformation of enlightenment, or of fear into love, or whatever you want to call it. But did the audience feel any divine sparks from this? Was the character arc genuine? I certainly felt sad from the movie constantly slamming the fact home that death takes away what we cherish most, but I somehow don't think that the movie took the audience along for the transformation that the central character felt. I just couldn't relate to him doing yoga in space, or killing the Mayan priest and claiming the tree of life.

His "transformation" and change just felt tacked on, like throughout the film he didn't really have a character arc. He didn't truly change much, he just kind of kept going along as he was, until the very end where he suddenly became enlightened.

In any case, it's quite interesting to analyse the symbolism of the film, and it sure has a lot of that!

On the Radar July 2008

Tuesday, July 22, 2008

Beck - Modern Guilt
http://farm4.static.flickr.com/3015/2589335341_8174995f58.jpg
"I can't even believe what we've seen outside, you and me watching the jets go by." So croons Beck in the track Chemtrails off his latest album, Modern Guilt, released this month.

I really enjoyed Mellow Gold and Odelay, but I can't say as much for his music since then, this album included. It's produced by Danger Mouse, who has done some interesting work in the past (his debut, The Grey Album, mashed up The Beatles' White Album with Jay Z's The Black Album), but this album just falls a bit flat for me.

http://www.neumagazine.co.uk/upload/beck300.jpg

But the song Chemtrails caught my attention as it is a popular topic of conspiracy theorists, and many of Beck's songs have focused on rather eclectic topics in the past. Here are some more excerpts from the lyrics:

"You and me
Hit by a cloud of an eagle
Watching the jets
Pass us by
...
We're climbing
A hole in the sky"

Christian Bale
I just watched The Prestige on Blu-Ray a couple nights ago, a 2--6 film starring Christian Bale and Hugh Jackman. It was the second time I'd seen it, the first being in the theater. I think this is an underrated but great film, and under repeated viewing and close scrutiny, the plot held up quite well.

http://www.eiu.edu/~history/ha/images/ha2007/poster_the-prestige-poster-1.jpg

The film has some fun steampunk contraptions and lots of great symbolism about sacrifice and the nature of illusion. From a synchromystic perspective, there is a wealth of material, including a mysterious box that is shaped like a truncated pyramid. The box contains a marvelous yet horrible invention devised by Nikola Tesla (played by David Bowie).

http://nudo.nu/wp-content/ThePrestige.jpg


Interesting turn of events today in tthe Weirdest Celebrity Arrest in Recent History where Christian Bale—star of this weekend's history-making blockbuster The Dark Knight—was arrested for allegedly assaulting his 61-year-old mother and 40-year-old sister. Splashy British tabloid coverage comes from The Sun. Respectable mainstream media coverage comes from Agence France-Presse.
Slog -


The Dark Knight: Christian Bale & Heath Ledger
Of course, Christian Bale is the star of the new Batman film, The Dark Knight...

http://blog.seattlepi.nwsource.com/spi/library/300tdkposter.jpg

This film itself is so mired in synchromystic symbolism I will leave the analysis to other, more informed bloggers in the synchro-sphere:

Heath Ledger Syncfest: Crows, Ravens & Bats

...wake of Batman (also 1989)." Darker than the Bat? Hmm! (enlarge pic on the left)Mirrors are used in both The Crow & the original Batman as well as The Brothers Grimm in which Heath stars too. In the first Batman movie Jack Nicholson breaks a handheld mirror and starts laughing, in the Crow movie Brandon Lee smashes the window at the desk of ...
Dedroidify - http://farm3.static.flickr.com/2128/2110025535_8e488fd438_o.jpg

6 MK Minutes of The Dark Knight

...of The Dark Knight, because of what happened to Heath Ledger (his mind controlled existence and his subsequent demise) and because it was so obviously going to be full to the brim of mind control themes, and I wasn't disappointed. The film begins with the camera moving towards a glass building, with the windows creating a grid pattern (squared/b...
Pseudo-Occult Media -



And here are some other more-or-less related posts:

Batman Begins (warming up for Dark Knight)

...create the Batman. But later in the movie Alfred also lets us know that their deaths sparked the rich into action to start cleaning up the city. And even later in the movie Ra's Al Ghul shares this:He says that the League of Shadows (secret society) had attempted to use economics as a means of destruction, which led indirectly to the murder of B...
Dedroidify -

Room 101

...s Batman movie, he visits an underground "hospital" where a doctor who surely doesn't have a license to practice medicine operates on the Joker trying to fix his skin color and fixed smile. This room reminds me of the tourture Room 101 in 1984 with it's terrible appearance. After leaving this room of pain, the Joker confronts his boss who had h...
The Stygian Port -

Heath Ledger and the Five Points of Rennes le Chateau

...like a knight on a chess board a game he loved so much.Ledger was a self professed antichrist. He did not believe in Jesus Christ and is on record saying so many times. It would appear from the occult nature of his films that he did believe in something though. “ I am the Widows son” he cries out from horseback in the film Ned Kelly. Ned Kelly w...
ATLANTEAN TIMES -

Metal Gear Solid 4

Easily my favorite game of the year and most likely my favorite game of all time. This is one of the most detailed and impecabbly crafted games ever made. And it's fun, too! For those not in the know, the Metal Gear Solid series are known as the creators and thus-far best examples of games in the sneaking genre. You play Snake, an old CIA agent who sneaks around on "wet ops."

You start the game with 'octocamo', which allows you to blend into the surroundings like an octopus. See if you can spot Snake in the image below:

http://www.metalgearps3.com/images/metal-gear-screenshot1.jpg

After beating the game once on normal difficulty, I tried again on the hardest ("The Boss Extreme") mode, but failed because I hadn't procured the solar gun on the way through. After a second playthrough on easy mode, I had procured not only the solar gun but also the bandana of infinite ammo and stealth invisibility, Predator-style. (These were obtained by playing through the entire game without ever getting spotted and with zero kills).

There is a wealth of symbolism
in this series, including a recurring theme of 4 enemies who must be defeated, each associated with an emotion and a totem animal.


http://dimensionz.files.wordpress.com/2008/01/metal-gear-solid-4-guns-of-the-patriots_beauty-beast-unit.jpg

Pictured above, the 4 bosses in Metal Gear Solid 4, which are based on similar sets of 4 bosses in the previous games. This particular installment in the series focused on the modern day war economy, paramilitary corporations, nanomachines and artificial intelligence used to control the masses.

In the game, there is a massive conspiracy carried out by a secret society (revealed to be controlled at the highest levels by an AI) to maintain constant war around the world as a means of control. This same control apparatus is so pervasive that anyone who has been 'chipped' with nanomachines (highly advanced microchips) cannot so much as utter the name of the secret society, The Patriots. Should they try to say this name, they will instead say "la-li-lu-le-lo", a Japanese string of syllables similar to "a-b-c-d-e" in English.

The Patriots are controlled by 4 AI programs, named after US presidents: GW, TJ, TR and AL. That's GW for George Washington, not Bush jr., according to Wikipedia. The man behind it all is known simply as 'Zero'. Here's an excerpt from the Wikipedia article: "JD sought ways to control the masses through manipulation of the economy, (which lead to the War Economy), digital information (which lead to the creation of Arsenal Gear) and eventually personalities (which became the SOP system)."


For more, check out my shared Google items.

Posted by Jonah Dempcy at 6:32 PM 0 comments  

The Lost Ring: Building the Earth-Omphalos

Thursday, July 17, 2008

As a follow up to my last post on The Lost Ring, check this out.

James showed a map with 27 Theo headquarter locations. These cities are places where we can build city labyrinths to complete the Earth-omphalos, that is needed to send the six home.
Strange stuff indeed. So what the heck is an Earth-omphalos? From wikibruce...
Returns:
MAKE OMPH KNOT: One rock, covered by a net, with at least 27 knots.
OMPH STRENGTH: K1 + K2 + K3 ... + K27. K = (C x S)/6
Trace a labyrinth (any design) at least 3 stadia wide. The bigger the labyrinth, the more powerful it is.
The labyrinth must have AT LEAST 3 circuits. The more circuits, the stronger the knot.
Earth-scale omphalos knots must be created within omph city limits. OMPH CITIES PENDING.
Without diving in too deep to this Lost Ring nonsense, it seems that the plot revolves around 6 amnesiacs who must return to another universe. Apparently by creating 27 labyrinths (and accompanying earth-omphali) at key points around the globe, a 'stargate' will be opened and the 6 will be allowed to return home.

Read more

Posted by Jonah Dempcy at 5:10 PM 0 comments  

McDonalds' Game "The Lost Ring"

The International Herald Tribune reports:

"The Lost Ring" is part of a gaming genre called alternate-reality games that blend online and offline clues and rely on players collaborating to solve puzzles.

While corporate sponsorship of these games is common - one popular game called "The Beast" was created by Microsoft for the Warner Brothers film "A.I. Artificial Intelligence" - this is McDonald's first foray into the genre.

The game kicked off with 50 bloggers receiving packages with an Olympic-themed poster and a clue pointing them to TheLostRing.com. The site presented a dramatic trailer, replete with sci-fi lighting and a narrator with a British-accented baritone speaking over footage of a woman waking up in a field with "Trovu la ringon perditan"- an Esperanto phrase - tattooed on her arm.

Ten characters deliver clues via YouTube videos, blogs, photographs on the Web site Flickr and updates from Twitter, a social network.

Online clues are supplemented by offline ones: Last week, players found documents in a mailbox in Tokyo and the fireplace in a bookstore in suburban Johannesburg.

[Full article]

I'll have to check out the game a little more before writing too much on the symbolism, but it's certainly an interesting tie-in to the 2008 Olympics.

The name and implied object of the game is a lost ring, so a good place to start might be with the meaning of the Olympic rings themselves.

According to the Olympic Charter, the five-ringed symbol "represents the union of the five continents and the meeting of athletes from throughout the world at the Olympic Games." Baron Pierre de Coubertin conceived of both the symbol and the flag. Not coincidentally, Coubertin is the founder of the modern Olympic Movement. The Olympic Committee adopted the flag in 1914, and it was first flown at the 1920 Antwerp Games. [source]
So, it seems that the rings primarily signify the unification of the world, an effort echoed by other global organizations such as the United Nations.

The ring is already considered a unifying symbol as it is used in the union of marriage- I suppose it follows that the interlocking rings representing the 5 continents are about unification on a global scale.

And, the Olympics truly are a global event. In this context, the use of Esperanto in the game makes sense: it is ostensibly the most popular global language, after all.

More info at olympics.wikibruce.com.

Posted by Jonah Dempcy at 2:55 PM 0 comments  

Crop Circle Points to December 23, 2012

Wednesday, July 16, 2008

An interesting crop circle appeared July 14-15 which seemingly depicts the configuration of the planets in our solar system on December 23, 2012, the end date for the Mayan Long count calendar.

Crop Circle at Avebury Manor, nr Avebury, Wiltshire. Reported 15th July 2008:



Images Gary King -

WCCSG
Copyright 2008

Avebury Manor of July 15, 2008 reminds us that the Mayan Long Count calendar will end on December 23, 2012: by showing precise orbital locations for all nine planets of our solar system on that date, plus an accurate elliptical orbit for Pluto

The 5125-year Mayan Long count calendar will end on December 22-23, 2012. Given the long period of time which it represents, all nine planets of our solar system need to be shown in order to mark its end uniquely. Such a clever astronomical diagram was shown at Avebury Manor on July 15, 2008. All nine planets appear there precisely as they will be located in space four and one-half years from now on December 23, 2012, with one exception.

Thus, the outermost planet Pluto has been drawn in this new crop picture somewhat further to the right (or closer to Neptune) than should be the case. Yet Pluto still seems to be located correctly relative to the crossover of its highly elliptical orbit with the orbit of Neptune. Three weeks ago at Secklendorf in Germany, two different dates from the year 2012 were indicated astronomically in a crop picture, one of which (December 21, 2012) was essentially the same as that shown here (see HERE).








Posted by Jonah Dempcy at 9:24 PM 0 comments  

Vector Equilbrium Resource

Check out this great resource I found on Vector Equilbrium:

Vector Equilibrium and its Transformation Pathways


1: ***

  1. The structure remains coherent in what ever way it is twisted and in whatever configuration it takes
  2. Some configurations are more elegantly symmetrical and reveal this unity more clearly
  3. This unity acquires special significance when the structure is in any of the classical three-dimensional configurations: tetrahedron, octahedron, icosahedron (known as the Platonic solids), or vector equilibrium (an Archimedian solid) also known as cuboctahedron
  4. Vector equilibrium: can be folded up to a single triangle configuration beyond which it can be reduced no further by "conventional" manipulation
  5. In contrast to many other configurations, a few can be kept with the application of force at only one point. These include: tetrahedron, square pyramid, double square pyramid (force at common vertex), double tetrahedron (force at common vertex)
Link

Posted by Jonah Dempcy at 1:29 AM 0 comments  

Omnidirectional Closest Packing Around a Nucleus

Excerpt from Bucky Fuller's magnum opus, Synergetics.

Figure 413.01
:

Fig. 413.01

Fig. 413.01 Vector Equilibrium: Omnidirectional Closest Packing Around a Nucleus: Triangles can be subdivided into greater and greater numbers of similar units. The number of modular subdivisions along any edge can be referred to as the frequency of a given triangle. In triangular grid each vertex may be expanded to become a circle or sphere showing the inherent relationship between closest packed spheres and triangulation. The frequency of triangular arrays of spheres in the plane is determined by counting the number of intervals (A) rather than the number of spheres on a given edge. In the case of concentric packings or spheres around a nucleus the frequency of a given system can either be the edge subdivision or the number of concentric shells or layers. Concentric packings in the plane give rise to hexagonal arrays (B) and omnidirectional closest packing of equal spheres around a nucleus (C) gives rise to the vector equilibrium (D).

Posted by Jonah Dempcy at 12:41 AM 1 comments  

Cuboctahedron as Vector Equilibrium

I found an interesting article on the cuboctahedron as vector equilibrium:

Amy C. Edmondson
A Fuller Explanation
Chapter 7, Vector Equilibrium
pages 90 through 93

Cuboctahedron as Vector Equilibrium

We can understand the symmetry of the plane by observing that although any polygon can be made to have equal edge lengths, only the regular hexagon can have edges equal in length to the distance between the polygon's center and its vertices. In the same way, although there are many regular and seniiregular polyhedra with equal edge lengths, there is only one spatial configuration in which the length of each polyhedral edge is equal to that of the radial distance from its center of gravity to any vertex: the cuboctahedron (Fig. 7-5). (3) This shape therefore is the only one that allows the requisite arrangement of vectors to demonstrate equilibrium.

Vector equilibrium

Fig. 7-5. Vector equilibrium.
Click on thumbnail for larger image.


Cuboctahedron, twist cuboctahedron
Fig. 7-6. (a) Cuboctahedron; (b) twist cuboctahedron.
Click on thumbnail for larger image.


We first saw the cuboctahedron as the degenerate truncation of both the cube and the octahedron, but at that point in our investigation we were only looking at surface topology. Now diving into the interior shape, we discover this unique property of equivalence. Table IV compares the radial lengths of various familiar polyhedra given unit edge lengths. Only in the cuboctahedron—hereafter referred to by Fuller's term, vector equilibrium or VE—can the radius be of unit length.



Table IV
____________________________________________
Unit-edge polyhedronRadiusCentral AngleAxial Angle
Tetrahedron
0.6124
109.47°
35.26°
Octahedron
0.7071
90.00°
45.00°
Icosahedron
0.9511
63.43°
58.28°
Cube
0.8660
70.53°
54.76°
Pentadodecahedron
1.4012
41.81°
69.04°
VE
1.0000
60.00°
60.00°
____________________________________________

Posted by Jonah Dempcy at 12:30 AM 0 comments