Now, next picture. I'm looking at an aggregate here of vector equilibria plus octahedra. Where there are octahedra, the external octahedra are put on the outside triangular face of the vector equilibrium, and the interior octahedra go in between the two square faces. You're going to see some more pictures that will help.

Next picture. That is a vector equilibrium with the four removable spheres in the four faces which are very important to chemical compounding.

Next picture. Now you see red vector equilibria and you see a white octahedron which is, I said, this is an external octahedron. Where it nests down between any four, because there are triangular corners in every vector equilibrium, and when you bring when eight of them come together more or less cubically, and they have an octahedron between them.

Next picture. Now you are looking at red I'm sorry to say there are red and yellow ones, and there are white ones. Every other one of those, one is where a sphere is going to be and the other is where a space is going to be. They could all be actually cubes and you can stack a bunch of cubes together, as you know you can, close packing, but if you then realize that where the corners of the cubes come together are where the external octahedra are and where the faces of the cubes come together are the internal octahedra. That is a pack that you are looking at right now, but I want you to realize then that you're going to find in closest packing that the arrangement of centers of spheres and centers of spaces is this arrangement. Where you are suddenly going to discover that the vector equilibrium, I gave you originally the vector equilibrium flat, and then I gave you where it curved the edges, where it became convex, or it could be concave. The same vector equilibrium can become concave or it can become convex. And so can the octahedron. So we have, then, spaces that suddenly become spheres, they blow up and the spaces contract. So there is something terribly exciting going on here.

Next picture. Now you're looking at. Would you remove me again? You're looking at, I made a steel frame, it's a cubical frame, and there are brass rods or wires that run with the cubic frame I told you that the perpendiculars to the faces of the vector equilibrium are the same as the perpendiculars of the four faces of the tetrahedron which is our basic system of all. If you run there are eight corners to the cube and so if I run a line from one corner of the cube, diagonally down thru the cube to the opposite corner down on the floor, I get then four diagonals for the eight corners, and they are the lines which are perpendicular to the faces of the tetrahedron, or the eight triangles of the vector equilibrium. I have now mounted in there, you remember how I made the jitterbug. And the jitterbug, then, remember can go from being open it's a vector equilibrium. It can become octahedron. And what you're looking at I've made, I've put little transparent Plexiglass red triangles and white triangles. And I've mounted them on the rods. Could you go back to the picture itself now? You are going to see that there are eight octahedra showing there. But if you look very carefully, you're going to see some white or clear sheets. Those are the vector equilibria. There are vector equilibria and the octahedra those are the external octahedra. Now, each of those triangles has a, we put a stove pipe rivet through it a journal made of brass. We are able to mount those triangles on the rods. The triangle's corners are tied together with just a little Dacron thread so that they are vector equilibria. So the vector equilibrium is open, and the red ones are vector equilibria that are closed into the octahedronal state like this. We found on that frame, we put carbon dust so that everything would slide it's very best, I took one pencil and pushed one face of the white, clear vector equilibrium that is open, just push on one face, just one force operating the whole system, and the vector equilibria collapse, all the vector equilibria collapse, and all the red octahedra open up. But it is a very three-way kind of affair I assure you, because due to the internal and external octahedra. But what happens when I push on there every sphere becomes a space and every space becomes a sphere. Now when you come to this kind of an aggregate, for instance in a liquid, you begin to see how you can pierce thru a liquid. Because the spheres keep getting out and keep becoming a space. This to me is a very extraordinary matter, because now this is made symmetrically. There are the eight octahedra that you see showing and there are the I think there are the same number, yes, there are the same number of vector equilibria, and they simply interchange.

What you're in this model because they are all mounted on those wires, as remember this thing rotates as it opens therefore the corners of the triangles take a little more space. And there are a number of other models I am going to be showing you tomorrow and Monday in which you'll see then tetrahedra rotating in cubes. It's a fascinating thing but they do. Float absolutely beautifully through cubes. But anyway, you'll find that the way the tetrahedra rotate in cubes, make the cube's sides bulge out every way like that. So when I make one sphere become a space in a system, and have the space become a sphere, the whole all the wires bulge outwardly symmetrically. Pulse outwardly like this. They are changing from sphere to space it makes it do this. You see for the first time, remember when we dropped the stone in the water you see a wave. This is the first time you see electromagnetic waving propagated. Actually, the model does it.

Can I have the next picture please, and you'll see it happen. Now all the red octahedra opened in the vector equilibrium form, and all the little white octahedra nested. I have this model in our Cambridge office. It is quite old, it's l951-71, it's 23 years old and it's getting a little poor, but to me this was sort of the supreme moment of Synergetics. When I realized you were really seeing electromagnetic wave form in the eye.

Now, I think this is a very good place to stop for Sunday. It is now almost half past three twenty after three. I would like to keep myself fresh. Can you tell me how much time we have done today? (From the audience "We've got about 4 1/2 hours') We got something then worthwhile do you feel? I would think that I might go a little slow on you now, and I'd like not to do that. So let us break up. I would like you to realize we have enough tape for sixty hours. I don't think we're going to make the sixty hours. If we did four hours today, and I think we had let's see, we're about at twenty, and we have just about the same amount of run ahead. I think we may get up to forty, and it is my suspicion that I have learned to say things more compactly. I know that I am really covering a whole lot of territory today, where I used to go quite detailed following, I'm exploring myself and now I'm so much more familiar that probably I am compacting the sixty hours into the forty. I feel that way about it. So that I think we're going to have the total experience. If we get to the end of the time, I'm quite certain that I'm not going to be withholding from you some of the things that I feel are all this important interrelatedness, because I do come into you time and again with new kinds of thrusts, and yet you find everything getting back into the same fundamental world. It really gets more and more thrilling. Thank you.