Next picture, and I'm now trying to make that a little clearer where he is now jumping from a boat to a little sloop and so forth, and you will see the arrows down at the bottom there will indicate the way the thing happens. The barred line, the barber pole part is where he is doing the jumping, and the white is the boat that he had jumped from and the red is the one he has jumped onto.

Next picture, and we have the same business here again where he is jumping from one onto the other. And the barber pole is where he's doing the jumping, and the white is the one he jumped from and the red is the one he jumps onto. And the triangle even comes back to itself.

Next picture. So we find all these different ways which the three vectors of "action", "reaction" "resultant", which are always in every system, can come out. They can be look like a Z, or they can come back to even look like a triangle. It's fun to make them look like a triangle, so that you can take two triangles like this, and you say, I have two triangles, and then you open them up and put them together, and you find they make the six edges of the tetrahedron. So suddenly, you had two triangles that you put in, and you come out with four triangles. In other words, there is always that invisible and I gave you the convex and concave, and the convex just has nothingness in that one.

Next picture. Now I'm going to look at two tetrahedra the black and the white tetrahedra, and they are I made this model out of very stout rods, and the white and black, they are congruent, and they're springy rods, and so they're able to sort of twist in and out of one another.

Next picture. I find that they one was locked into the other so that they couldn't get away, so they'd get to be where they were just vertex to vertex like that.

Next picture. Then they can be rotated in such a way that one is inside the other and makes a star called the eight-pointed star which makes the cube. And it is a fascinating matter to find that one of those tetrahedra can literally roll, just as if it were a ball, instead of a tetrahedron. The relationship of edge to edge no matter how you make it, they never get out of kilter. They are six edges, always touching. And, excuse me yes, six edges always touching six edges and they are always in contact, and one never pushes or pulls, they rotate around on each other superbly, either being congruent or in this position.

Next picture. Here is another one of the rotated positions.

Next picture. Then they can of course be face to face, the two tetra. And this, incidentally, was the atom clock where they pump where one vertex would pump through the base and come back on the other side back and forth, back and forth.

Next picture. Now I'm going to do things give you some information that I hope is going to help to understand in due course and feel quite strongly the model of yesterday when we saw the spaces becoming the spheres and the spheres becoming the spaces, and the transformation from being vector equilibrium, to octahedron, and so forth. So, here is a tetrahedron inside of a cube, giving the cube its shape. And I have also strung on the top of the cube, a single string. It goes from the far right corner back to the far left corner and then back to itself. It's a circle and it's strung over the pipes. And the edge of the tetrahedron is just lying between the paired circle of these two lines. And then we have a string that you can't really see at the middle of the top edge of the tetrahedron, and we're going to pull the tetrahedron out of the cube.

Next picture. We're starting to lift the tetrahedron. It slides, with its vertexes following beautifully the edges, and we find that the six edges keep sliding absolutely perfectly on the four square edges of the cube at the top. As we pull it up, that line which I said went back and forth from left corner to right corner, it went under the thing, over the top, under, over the top it makes it now it's a quadrangle, and as we are pulling the tetrahedron out, it gets spread.

Next picture. Now the tetrahedra has been pulled a little further, and you can see the line which I said is just a piece of rope, it goes round and the quadrangle is opening up all the time, and all the time all the part of the tetrahedron are touching the cube, very beautifully, sliding out.

Next picture. Now, it is half way out and the piece of rope has become a square. And that square, incidentally, is what you have your cross section of a tetrahedron if you want to make it really, really, you cut right here and the cut comes out right here, and you find that is where the octahedron is inside the section of the octahedron and so

Next picture please. Now the tetrahedron being pulled a little further and the quadrangle is now contracting from the square, but is now orienting for another corner. It is orienting at 90 degrees. This is one of those precessional things that went from going this way to going that way now.

Next picture. Now it is getting ready to be pulled out.

Next picture. And the rope goes, absolutely, right straight across now. And

Next picture. And take the tetrahedron out and the cube collapses. It's a very beautiful model this one that we made for the Institute of Design in Chicago long years ago.

Now, this picture I am sorry to say, doesn't show it very clearly, but you'll see a cube. There are three cubes, one above the other. And in that cube you will find that there is a position where a triangle inside the cube sits near the lower right hand side in the top picture, that triangle is in there. It's actually following, the position remember I had a tetrahedron inside the cube and it's taking one of the faces of that tetrahedron and going up like this and back. So it's inside there. Now I rotate that triangle inside the cube, and it continually it shuttles back and forth and goes to the left side. It's coming from the lower right up towards the upper left corner. I'm sorry that you can't see all of those pictures, but it is a very beautiful thing, so we made the model.

Next picture, we have a model where you can see the, I made just such a frame so that you can literally see the triangle shuttle back and forth.

Next picture. Here we made a steel cube. Can you block my head out. We have a steel cube and it is made in a general chassis, a frame, and that cube was made in two halves. You can look at the right hand side of your picture, the white, light cube, and you see going up the middle of it here a groove the two halves, there is a groove that goes completely around it, zig-zag, zig-zag, zig-zag. Six parts. And there is, the cube is mounted rigidly, and two halves a part like that, and there is an axis, two journals in the end, and there is a handle that moves a rod running through the diagonal of the cube which is horizontal in our picture. And mounted on it, near the left hand side, you'll see a triangle. Three struts coming out from the shaft to the triangle, and there is a point of that triangle sticking out at the top of the cube right now. We rotate the handle of that shaft and we find that the triangle's end which is up through the top of the cube, moves down the far left side next picture. Can you see that moving down the far side the far top side?

Next picture. It is now moved clear down to the bottom, and is at the far side.

Next picture. Now it is starting to shuttle back again.

Next picture. Now, this business of the triangle pumping back and forth inside happens to be nothing more than what happens you remember if you complete a vector equilibrium's eight corners by putting one quarter octahedra on them you've got a cube. Do you remember that? O.K. That being so, then, this could be a cube. And if it were so, this triangle would be in the corner of that cube. Now what happens when I the big cube represented by completing those corners, that consists of eight cubes. You can make a big cube out of eight little cubes, two cubes to the edge. I want you to assume that, so for each of the eight triangles here there will be eight cubes, and this triangle in my hand is in the cube in this corner here. And when I pump this down to become the octahedron, it simply shuttled from one side of the cube to the other. I found that there was a triangle in cubes doing very strange things, so that I really wanted to study what they were doing, and I found that by making these models that sure enough the triangle can rotate in the cube. But what happens is that, I made my triangle a little smaller than the cube, and each corner of the triangle that steel model the frame, we had a little steel pipe running out from each of the three vertexes of the triangle out through the runner to be guided, and we found that as it goes through the cube, it literally makes a circle, makes an arc, the end makes an arc, in other words the end goes outwardly as it goes through and then back flush. And, we made that model in such a way that those are all tubes, and we made it so that we could have lights. So that when you'd find that as you did this, on each of the with the eight triangles that can be in any cube, they would all be pumping and they would be going two ways on the edge of the cube, and with the little lights you can see a sphere. You see a spherical cube. And see it being defined by shuttling lights going both ways as a consequence of the pumpability of these triangles in them. All these things have to do with experiences we have when we try to explain all kinds of phenomena, absolutely, just as an inventorying of data of energy, but I am quite confident these relate to all the kinds of different kinds of physical phenomena we do have.

Next picture. But they do explain how and why, when the vector equilibrium became an octahedron, and the octahedron became a vector equilibrium and each of the spheres became spaces, and spaces became spheres; as they did so each of the triangles bulged a little, so that, inasmuch as they, everyone of them, bulged in the transformation, it made the whole system bulge uniformly in all directions, so that it became a spherical bulge. And this is what brought about the our visibility of the electromagnetic wave.

Next picture please. Now, block me out please. Here is something we had yesterday. The precessional effect of the two edges of the three ball edged tetrahedron, or two frequency tetrahedron coming together precessionally.