Buckminster Fuller

Described as an "inventor, architect, engineer, mathematician, poet and cosmologist" in his biography at the Buckminster Fuller Institute (http://www.bfi.org/).

Inventor of the GeodesicSphere and all things dymaxion, a unique and original thinker, too original to be understood in his own time. Some of his ideas on reforming the housing industry have yet to be tried, though they would probably make many things better for many people. His version of basic physics (SynErgetics?) is unique and fully worked out. It's surprisingly clear once you get past his unique language. It may be all wrong, but at least it's wrong in a creative and inspiring manner.

Disagree - I have looked through some of his physics, and it has all sorts of very clear problems that a fully developed theory should never have, wrong or not. For instance talking about the cuboctahedral nature of space he does not hesitate to connect Planck's constant with the numbers of cuboctahedral components, even though it is not exact and is not dimensionless. This is the kind of creativity one sees habitually in ether theories. Not to take away from the man - Fuller has a good and deserved reputation in most of the above categories, it's just cosmology should not be one of them.

This guy has a substance named after him: buckminsterfullerene. It's 60 carbon atoms arranged in a spherical shape, sort of the three-dimensional analogue of the benzene ring. The discoverers of the substance were reminded of his geodesic designs. There is also a hydrogenated form of buckminsterfullerene, called buckminsterfullerane.

Aren't these known colloquially as BuckyBalls?

Also the inventor of the (patented) DymaxionMap projection, which achieves, bar none, the lowest distortion ever in mapping the globe of Earth. By mapping the globe onto an icosahedron (a geometric solid having 20 triangular faces) and then unfolding it such that no landmass or nation is cut and no landmass is distorted beyond single digits, a flat map with the North Pole at its center is produced.

This was (reportedly) inspired by his analysis of a Phoenician "map of the world" which has been variously interpreted to be a partial map only. He supposedly looked at it from the viewpoint of "what if it actually does cover the whole world?"

Looking at one of these things, I was finally able to get an undistorted view of the relationships of Canada, Alaska, Greenland, and so on.

Very cool.

I don't mean to detract from the brilliance of this map projection, but had you never just looked at a globe?

That's a fair question. The answer is "not really." There are things I notice more in flat maps than on a globe's surface. I typically survey particular regions or global routes on a globe, as opposed to comparative sizes. The flat presentations make comparisons of non-adjacent land masses more obvious -- but distorted. If I were a more assiduous student of global land masses, the impact would certainly have been less.

Online books and material

Synergetics: http://www.rwgrayprojects.com/synergetics/synergetics.html
A Fuller Explanation: http://books.google.com/books?id=F6n2dZJ1POwC
See also the Buckminster Fuller Institute (http://www.bfi.org/).

Quotes

"When I am working on a problem I never think about beauty. I only think about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." - BuckminsterFuller [love this quote -- AndyPierce]

"You have to decide whether you want to make money or make sense, because the two are mutually exclusive." --BuckminsterFuller [submitted by KrisJohnson]

"In order for a world-around democracy to prosper, world society must learn how to prosper." -- Buckminster Fuller [from the .sig of BenTremblay]

Author of CriticalPath.

I found Synergetics to be a good workout. Some of it is impenetrable though. I'd be interested in an experts view of a number of his geometric statements. For example he does a 'proof' of the four colour map theorem in about three sentences. I keep reading it and my brain goes 'whaaaaaat?'.

Very few experts would agree with his statement that all triangles inherently have four corners, two of which are overlapping. Sometimes things are hard to understand because they involve difficult ideas, and sometimes because they don't make any sense. Three sentences should be enough to quote here, would you mind letting me see?

I thought someone might ask so I looked it up (praise the Web). Here it is and it makes perfect sense but then...:

: 541.20 Solution of Four-Color Theorem
: 541.21 Polygonally all spherical surface systems are maximally reducible to omnitriangulation, there being no polygon of lesser edges. And each of the surface triangles of spheres is the outer surface of a tetrahedron where the other three faces are always congruent with the interior faces of the three adjacent tetrahedra. Ergo, you have a four-face system in which it is clear that any four colors could take care of all possible adjacent conditions in such a manner as never to have the same colors occurring between two surface triangles, because each of the three inner surfaces of any tetrahedron integral four-color differentiation must be congruent with the same-colored interior faces of the three and only adjacent tetrahedra; ergo, the fourth color of each surface adjacent triangle must always be the one and only remaining different color of the four-color set systems.

This is a horrible non-proof. First of all he is taking the map and dividing it into triangles, something which could quite easily affect the number of colors the map needs. The tetrahedra are made by joining each triangle to some point in the sphere, but are really superfluous, since adjacent tetrahedra having common faces is the same thing as adjacent triangles having common edges. That reduces his argument to each triangle being surrounded by three others, so at most four colors being needed for them. That proves local 4-colorability, but that is not at all the same thing as global 4-colorability, or we'd have solved the problem a long time ago - on a torus, for instance, there exist maps that take more than 4 colors, despite the same conditions applying.

Yes, I thought that immediately. Then I thought about partitioning of a precolored map and realized (please correct me if I'm wrong) that if we add a region by partitioning any region of the map, we can always color the region with the color which is simultaneously isolated on the other side of the partition. This is easier to show than describe. My mathspeak isn't really up to it. Still, here goes. So we can always partition the set locally without incurring a non-local constraint violation. We can do this up to the fully triangulated set as Bucky has. My brain starts to melt when I try to run this process backwards. I feel there's an assumed symmetry which doesn't quite gel, or rather cannot be assumed.

I don't think there's any obvious way to run the process backwards at all. Whenever you fuse two regions, you are faced with the prospect that the combination might need a new color, and that is not necessarily possible within a four color limit. In that case you would have to recolor the whole map and if you can do that, well, you already have the result. So your reaction is perfect - the statement makes no sense, and you shouldn't worry about it too much.

Incidentally, and possibly off-thread (we can move it), in ToroidalColorMap?, do you always get one singularity of the fifth color or a whole heap of "tie-breaker" patches?

I'm not sure, but I would guess the latter, since some tori need as many as seven colors. [From memory, the usual example has only seven regions, each of which is surrounded by the remaining six.]

Thank you, I believe I understand. Hmmm, I must look up the complexity of any coloring algorithm and test Intel's finest. Thanks again. RichardHenderson.

The tough thing is that since the 4-color theorem is actually true (we now know), one can't concoct a counter-example to disprove his would-be proof. One can only argue that the premises don't necessarily lead to the conclusion. His retort would be, of course, "show me an example of where it doesn't work", and one can't. -- AlistairCockburn

Tensegrity

...which leads me to think of a MeshNetworking? protocol based on same. Let the data packets be distributed equally among all connected members.... To be completed later...

Conceptualizing torque lead Bucky to the dome structure (GeodesicSphere) we've come to know, and here's how it matters [plagiarized from Imaging the Imagined; Modeling with math and a keyboard http://www.frontiernet.net/~imaging/]: Beams and cables have strength in compression and tension respectively, but both are poor in resisting torque; under shear forces, walls act as levers, creating torque, and so the building deals with the stress by destroying itself. Bucky's lightweight structure was designed so that a horizontal force above the base creates compression and tension but no torque. Neat trick! -- BenTremblay

Some of his ideas on reforming the housing industry have yet to be tried, though they would probably make many things better for many people.

StewartBrand argues that his ideas (pre-fabricated mobile housing units) have been tried with great success, but in a much more pragmatic form than Fuller's dymaxion house. Instead of expensive round shapes made from exotic materials and air lifted into location by helicopter we have cheap rectangular shapes made from traditional materials rolled into place on roads. Of course, mobile homes lack the glamour of dymaxion houses. But they meet all of the requirements that really matter.

As I seem to remember, the 'buckyball' fullerenes are very hard (like diamond) Carbon based molecules, Which can even be used to hold gasses inside that 60-C poly-whatever-dron, and a important point would be that cell plasma (the inners of human cell or brain cells) have a lot of 'strange' materials like microtubule, and also these buckyballs in it. By nature, that is. -- TheoVerelst

Microtubules and buckyballs have nothing in common. Buckyballs are not found in cells, though they are found in soot. Perhaps you are thinking of the pure carbon bucky-tubes that have recently been constructed?

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