Wednesday, April 28, 2010

When Geometers Attack!

A little detour today.  Geometers sometimes have different views of things.

Followers of R. Buckminster Fuller commonly subscribe to his view of the universe summarized in his seminal work, "Synergetics."

One of the principal notions at the core of Synergetics is the space-filling shape Bucky terms a "MITE." 

Here Frank Zubek (my bias: I like Frank's ideas) disputes the claims of MITE supporters, and proposes an alternate view of space filling.  There is an on-going dispute between Frank Zubek and Kirby Urner, two very knowledgeable geometers.  Kirby is a proponent of Fuller's views, Frank offers an alternate view. Forgive me for finding this dispute somewhat amusing.  Note how Frank says "Hi Kirby."  Oooohh, careful Frank.

As an observer, it's been very interesting for me to watch this geometrical dispute.  Like Clash of the Titans, only more instructive and less bloody (so far).

Here are some videos from Frank Zubek:
first video
second video
third video

Now just calm down everyone, we'll get to the bottom of this.  Maybe we mite.


  1. I am not sure where you are getting all of your information. Cyber battles are fought on different fronts. The main bloodshed is pouring from Zubek's Elusive Cube. This can be found in a Yahoo group called Synergeo. Godzilla has come in and straightened everything out. Essentially, RBFuller's A&B modules which make up the MITE can build all of Zubeks coarse modules. Yet Zubek cannot make A&B modules with his three chunks. Case closed. Note to students of architecture, it may be in vogue to trash Bucky Fuller, but when it just isn't funny anymore, you will appreciate that he was around.

  2. Thanks for your comment. I had been a member of synergeo for over a year, until Rybo's insistent nonsense drove me away (no reasoning with that guy). If a module is fundamental, it should not have a sidedness, i.e., left and right; which mites do. Zubek's notion does not have this handedness, it is more fundamental. I recognize that this is a matter of opinion. If left and right parts are OK, then why stop there? How about front and back parts (for both left and right) top and bottom, etc? This is how I see Frank's work as addressing the notion of being more fundamental than Fuller's mite. In other words: mite makes right (and left...)

  3. Amazingly, you are incorrect about the MITE and you should correct this error. The MITE does not have left or rightness as a module in itself. Zubek halves the MITE into two pieces one left and one right handed. You sir, have that backwards. You have done a major disservice to Synergetics and it shows your ignorance.

    Frank Zubek is on a fanatical mission to "destroy" Synergetic geometry. It is very simple to understand why. He has a proprietary interest in having his clunky blocks be the end all in modularization of four-fold symmetric forms. Of course they are not and Synergetics shows this with the A&B modules.

    Here is the gist of it. Take a cube of side "a", it can be sectioned into lessor sized pieces. One way is to break it down into Fuller's A&B module forms. Exactly 48 A and 24 B module forms. A = B in volume, so 72 equal volumed parts. Zubek can break down the cube, edge = "a", into 6 equal volumed parts, but requires more than one cube to demonstrate all of the different possibilities.

    Interestingly, each of Zubek's modules are composed of 12 A&B modules in different agglomerations. All of Zubek's unit can be described in the cube of edge "a, by A&B module forms and they do not have to be repositioned to demonstrate such.

    To get around this, Zubek claims that the cube he is using is edge ="a/2", shrinking his units so they can not be made of A&B modules forms from a cube, edge = "a". He then states that 8 of these "a/2" cubes make the cube, edge = "a". The latter is true, but then there is no sound or reasonable basis to halve the cube. Why not just acknowledge how these units can be made from A&B module forms?

    A MITE (minimum tetrahedron) is composed of 2A and 1B module. It is not left or right handed, one could argue that internally they are left and right handed, but as a building unit in itself, it is neither left or right handed.

  4. Thank you for your comments.

    I argue that internally mites are left and right handed, precisely.

  5. You should question your association with Zubek, for he just used this link recently and he never bothered to point out the errors. He has no shame or humility. Being correct takes a back seat to him being "right".

    Trivializing good geometers because of a dogfight that amuses you is not all that becoming. I am impressed with the work you are doing and I hope that we can spend more time discussing the detail and nuances of your icosahedral brick:

    And the discussion on DNA:

    David Koski

  6. "I argue that internally mites are left and right handed, precisely."

    --Peter Roberts

    So, as a mason, you contemplate the internals of a brick and knowing that it could be geometrically sectioned into lets say an asymmetric way that it is no longer a brick? Is not the form of a MITE, just what it is, a MITE?

    As a builder would you reject a form because of knowledge of its internals even though its external behavior performs to expectation?

    I want you to apply your logic of rejection of MITEs as being left and right handed to everything since it seems necessary to apply here. Bad argument. Stay away from Zubek is my advice. It is extended in friendship.

  7. Furthering this argument. The most classic form of masonry is a brick. We use them in an overlapping way. Of course for windows and doorways we do cut them in half. As a potential customer, I would want as many full bricks as possible. Using only half bricks would weaken the structure with more joints and lose the integrity of overlapping. Also the amount of labor would double the cost in time and mortar.

    Zubek cuts the MITE in half, besides the structural integrity loss, one would have to order equal amounts of left and right handed units. Anyone familiar with construction management knows that this is only a potential opening for more errors in ordering and movement of the objects. An apprentice may follow orders and gather more of the appropriate amount, but maybe bring all lefties for instance. Even the most experienced may make mistakes on this level.

  8. I thank you again for your comments, Mr. (Dr?) Koski. Thanks also for identifying yourself. I do not mean to trivialize the significance of the ongoing discussion regarding synergetics. I am a huge fan of Bucky! I simply suggest that because MITES require both A & B modules means that it is less than fundamental, in that it takes more than one shape to fill space. I believe that these arguments point more to the inherent difficulty of filling space with one fundamental shape than to whom is right (and wrong). I believe these discussions are enlightening, to anyone who bothers to pay attention. Forgive me for finding humor in these exchanges, I do not mean to insult or offend. To me, Zubek's perspective adds to the discussion. I do not see one side as "right" and the other as "wrong", I see both sides as more fully illuminating the problem of space filling. I find humor in the very personal nature of the ongoing attacks and rebuttals which have continued back and forth for some time now. I love a good argument and I love a heated exchange, in that it more fully informs an impartial observer. Life would be less interesting without all the passion invested in such an esoteric subject. Hi to everyone at synergeo!

    1. I concur that the Mites exhibit handedness, based on the (arbitrary) polarity ("positive" or "negative" per RBF) of the b-module. See Amy Edmonson's A Fuller Explanation: and for illustration. These alternate forms mirror about Zubek's cleaved plane. Make some models. Convince yourself. Enjoy! Tell your friends.

  9. To me it has always been obvious that MITEs exhibit handedness (left and right). I don't think I have a special gift, or a weird brain, or a unique ability to tell left from right. Instead I think that Fuller's followers (some call them "true believers") have blinded themselves to the obvious. I am confounded by this, because many of these people are very gifted geometers. This should not be taken as a personal attack on anyone, I am simply stating the obvious. Thank you (anonymous, above) for the links to Amy Edmonson's insightful work. MITEs are comprised of left and right handed units; as such they are something other than fundamental, in my view.