I am now going to switch over to tensegrity structures, because all of the geometries that I have been identifying for you in the terms of topological analysis and volumetric analysis and energy analysis quantum and so forth. All of those geometries can be made tensegrity. And so I point out to you also, that one of the things that inspired me very early in the game of structures was getting into the push-pulls and how they're accomplished, and finding that and I went over that with you. That compressions had limited length in relation to cross section and tension didn't. We went into all that. Discovering that the Universe is actually designed with islanded compression, usually spherical as the most effective use of the energy that way, and the whole thing cohered tensionally. And the tensions the compressions are inherently discontinuous and the tensions inherently continuous. We have a Universe with inherent continuous tension. And that was not the way man was building.

But when I found all the geometries and all these interrelationships and all this coordination I was looking for nature's own coordinating system, I was sure it was rational due to the chemistry, and I found the rational coordinating system, and I found that all the geometries could be produced in tensegrity. I was looking for this and then I had the word.

At Black Mountain College I was a visiting professor the summer of 58 and 59 I was the summer Dean. And there was a student there in 58 and 59 both, Ken Snelson, he'd been in the Navy, and his father was a photographics camera store man in Oregon; and Ken had a great he was fantastically expert in cameras moving pictures and still. But he had real, real feeling about art, and he liked painting. And he'd come to Black Mountain on account of his painting, and to study with Albers there, and Ken Snelson fell in love with I talked to him and gave him my energetic geometry, and he was absolutely in love with my energetic geometry. And he was incredibly good at model making, so that for a whole year after Black Mountain he came to New York to wherever I was and worked. And then I went out to the Institute of Design in Chicago, and Ken Snelson moved out to Chicago.

Then in the second summer at Black Mountain, Ken showed me a sculpture that he had made, and, in an abstract world of sculpture, and what he had made was a-a tensegrity structure. And he had a structural member out here two structural members out here, that were not touching the base, and they were being held together held they were in tension. And I explained to Ken that this was a tensegrity. Man, I had found, had only developed tensegrity structure in wire wheels and in universal joints. Universal joints where he had a steel shaft, and the reason for needing a universal joint because you were changing the angle of the drive, and you had two shafts, and each one of them came to three arm points like this, tetrahedronally like this. They had forged members steel, and came to a pad with a hole in the end of the pad. So there were three pad holes, tripod like this, and they would bring those together at 60 degrees from one another with a flexible disk and they would try all kinds of fabrics and leathers, and so forth, to see how long they would last, and they would then rivet these onto that flexible disc, and as it drove this way, the disc would accommodate. In other words it was a tensional interconnection. So man had used tensegrity in this drive shaft of the universal joints. He had also made it with the wire wheel where he had an island of compression as the hub, and an atoll of compression at the rim, and the whole thing was tensionally cohered. So this is the only place I found that man actually had tensegrity. So when Ken Snelson showed me this little extension thing he did it was really just an arbitrary form, he saw that you could do it, but he was just, as I say, an artistic form or something startling to look at. And I said, "Ken, that really is the tensegrity and it's what I'm looking for because what you've done I can see relates to the octahedron and this gives me a clue of how this goes together in all the energetic geometry.

So Ken opened up my eyes to the way to go into the geometry. And, Ken, himself is an artist, and he's gone on to make all kinds of tensegrity sculptures that are getting to be very well known as one of the most, in the higher demand artists. But Ken himself kept himself alive by doing moving picture work, he has got a moving picture camera man's union card, and he turned out to be really one of the best, so anytime he wanted to work he'd go and make a whole lot of money on some big project and then go back and commit himself to his art work. At all times in my carrying on I have come to phases where I could see that something might be attractive from an art form you can suddenly get insights, I could suddenly see new patterns and then people would say and this could be extremely interesting, and I know personally I am deeply moved by it, that I could exploit it by stopping and just being an artist, but that was my commitment, I told you last night how my whole commitment was to be absolutely responsible to never exploit for self, and never just for self or fame or whatever, you must not exploit. And if people tried to make you fancy, then you must do everything you can to make sure that is deflated. So that I've never gone off with these forms, but it is interesting how many I have an enormous number of artist friends, and really deep friends, and they are very simpatico with what I do, and they do then go off, and they like what I can find out, also technically, which gives them a chance to do various things but at any rate. It couldn't be a more beautiful life than I have had with my artists friends.

But I cannot talk about tensegrity without talking about the fact that Ken Snelson really was a catalyst to my discovering how I really connect this up with all the geometry and all the coordination of everything I wanted to do, doing more with less. And, so I'm now going to go into the tensegrity with you and give you a little feeling. But I also did earlier in our time talk to you about pneumatics and tensegrity showing you how and why it did get into the regularities it did. So we don't have to get into that and you'll recognize that as we go.

May I have the first picture. Here I am also pointing out to you that where we have a balloon or a football, or somebody said, they think about it as impervious, but if you look at it with a very fine microscope, it is full of holes. The only thing is that the holes are smaller than the molecules of the gas that are inside, so they are really like a fish net, where the fish net is smaller than the fish and the fish simply hits the net. And I saw them really operating very much as fish. The molecules of gas hitting the bag and hitting it in so many places whatever it's stretchable shape is, it takes that shape. So you can make strange looking balloons of special shapes that are always getting pushed outwardly.

Next picture. Then this represents, look in the upper right hand side, or middle right hand side, what I gave you are the two swimmers coming together and shoving off from each other, and then hitting going careening off of the and there is no line that you can make inside there, in essence a radius that wouldn't be a chord. It could be a very deep chord, it could be a very light chord, and I find it really going around like that, hitting the skin a glancing blow. Now because there are two of them action and reaction shove off from each other, they each hit the skin a glancing blow. The fact is then that a chord, an arc, stays in the circle, but the center of the chord is nearer the center of the circle than an arc's ends, so it's ends are always emerging, hitting the skin at a very small angle, and there is a net of the two one going this way and the other both pushing outwardly, means that there is a single force going out like that, and the magnitude of that force is governed a great deal by that angularity of the but a frequent enough episode keeps it all moving out. So, you can get the bag harder by putting more gas in so increasing the frequency of the hitting very, very greatly.

Next picture. Then I showed you how what seemed to be randomness automatically worked itself into the circles and the omni triangulation and on the hexagons and the pentagons are simply incidental to the triangles here. The triangles are here. And these are just basic the triangles do all the stabilizing.

Next picture. Now, the simplest, could that picture be dropped, or turn it sideways? The simplest thing you can do for a tensegrity is two members like that, have their oneness one bowed like this, the other bowed like that our precessional effect of the two coming together. These are very much like taking a tetrahedron. I've got two balls and two balls coming like that at each other. Or let's take a tetrahedron, consists of four triangles, so pair them into two diamonds, so you take two diamonds and precess and come like this and grasp each other. And that is exactly the way that you make a baseball. A baseball skin, the two lobes in it, like in a tennis skin is really two of those balls. It is each lobe is a triangle of a tetrahedron, which you can then also draw as a circle, and then have, between the two complement that same radius. So you have two pairs of triangles, and two pairs of triangles precess them like that, and grasp them like that, and that's your baseball.

And, incidentally, your baseball, if you draw it, it is quite interesting because it is this. It is yin/yang. The yin/yang are these two complements, not in a plane, but really in the Universe. And the baseball form is exactly that, this uniform radius all the way through. It's a lovely thing. Baseball is telling you precession. Yin/yang to me tells me a great deal. I'm sure the Chinese thought in the terms of the whole too, and they came to a flat representation. I'm sure they were thinking this way. So they really felt the power of that yin/yang. So the complementaries do precess like this. O.K.

So in this first one here, you can't take two straight sticks like this you can if you want and they are two edges of a tetrahedron. Makes a very flat tetrahedron. All I have to do is having one tension member go right around, you call it a kite, you can make a diamond shaped kite. And you don't have to fasten these two to each other because it is simply a very flat tetrahedron, and by pushing, the tighter you make the perimeter the tighter this comes against it here. But it doesn't have to be fastened. It is the beginning of tensegrity, so it is two member tensegrity, so the two member tensegrity is really then a precessional affair, but it is a little set of arc a little like this the pull of those lines will make them do this to each other. That is what that model is that I have there. You can see how you can take a ship, now, a Naga ship, with great ends, and the ends come out of the water like that, and you could have a spar going like this in the sky, which is then supported from the ends of that spar to the end of the ship here, and out the other end of the spar, right to the other end of the ship which is sticking out of the water very far. And then you'd have to have a fore and aft tension to the top of this thing so it wouldn't fall over. It would be quite possible to make a boat that way, and I'm surprised that people have not built boats this way because it would be possible to drop sails from this thing just connect in tension. I think we probably will see just such a device one of these days, because we'll get into very, very light weight instead of having a mast that has to go vertical like that, this is a very much lower thing, yet can drop you a great square still, and give you an enormous amount of sail. At any rate, that is the simplest tensegrity.

Next picture please. The next one is one where you make the octahedron. It has x,y,z coordinates, and I suggest you try this someday and before you tie put tension from end to end, you take some little a box, say a cubical box, and you tape one of the tubes onto it. The box has six faces so we go on another face here and have one going that way, and have the x,y,z coordinates fastened onto the box, but a little away from each other. Do you understand that? Taped on. Then you take your tensions, omni-triangulated, you have eight triangles in high tension, then you remove the box from the center and you find they just don't touch each other, so here we have very clearly the non touchingness of the octahedron, and it makes it quite possible then with a little mild bowing by the tensioning, to make them quite fairly accurate. We find in nature all the crystals that are octahedronal or whatever they may be, always have, they skew one way or another. They are always turbining either one way or the other. Now this was turbined, there are two ways of turbining this.

May I have the next picture. No, I haven't come to it yet. This is a four member. I had three members, now I have three struts. This is the this is a tetrahedron made by Ken Snelson. It is really a very fascinating tetrahedron by the way. It's a four strut tetrahedron and it relates then to the vertexes and the opposite faces you have a suspension of the opposite face.