We left off at the experience of witnessing the every sphere in closest packing, changing and becoming a space, and a space becoming a sphere. We've been through discovering what the shapes of the spaces between the spheres were. They were concave vector equilibrium, and concave octahedron, and I had pointed out to you that the vector equilibrium itself, then, could go convex or concave and the spheres I see then in convex forms. Remember, the vector equilibrium is using the most space in Universe and all the things happen by contracting, so that when it's edge vectors became curved, they reached a lesser distance. So these spheres in closest packing are actually in a they produce a what is called-an isotropic vector matrix the centers of each one are equidistant from one another. But it produces an isotropic vector matrix whose chord length or vector length is a little less than the length of the vector equilibrium before all this starts. I think I had pointed out to you that everything that goes on inside the vector equilibrium, I am convinced is what goes on within the nucleus. And everything that goes on outside the vector equilibrium is what goes on in chemistries of association of atoms into molecules. This is the internal affairs of the atom.

And, incidentally, just saying that, in World War I, I mentioned to you the other day they had physics, and there was something called electricity in addition to physics. physics is mostly mechanics. And after W.W.I., suddenly the electron became of the greatest importance. So physics was really electronics. And then W.W.II saw physics become nuclear physics. And we saw that the physicists and the chemists then getting to crossing lines with one another and the chemists and the biologists crossing lines with one another, so that after, well after W.W.II at MIT they decided to have a sorting this out. And they decided from there on that chemistry was now dealing with atoms, but chemistry was dealing with external affairs of the atoms, and the physicists were dealing with the internal affairs of the atoms. So the kinds of things that go on inside my vector equilibrium, these contractions and so forth, I am assuming, really, are the internal affairs of the atom, and what I just want you all to remember then, as the vector equilibrium is contracting, and it is contracting by virtue of its edges becoming either convex or concave when they become concave they become the space in between the spheres; if they become convex they become the spheres. And they occupy the spheres then occupy, or the spaces occupy the same positions.

If you had a complex of cubes many, many, many cubes stacked up layers after layer all tightly packed; if you were looking at it like a checker board, every other cube is black and then white, black and then white. Then you would have the whites would be the spaces, and the blacks would be the spheres. So when this transformation occurs, then, the white then becomes the sphere and so forth. I want you to have that feeling about what is going on here quite strongly, and the model that I photographed and made it possible to demonstrate that is still in existence in Cambridge, and someday we hope to have a better model made. A fresh one today.

In respect to our whole experience together and my starting and operating entirely spontaneously and finding my way in, not knowing just what I was going to say as we started, I have gradually found, now, what it is I have said, and I can remember all the things. We've now done approximately 20 hours, and now I can see, having done the 20 hours, I can really feel the things that I'm going to have to do in order to be complete as we would like to be. And I hope I will be able to do it in the available further 20 hours we have. That's all we have now. And I don't want to lose any more time at the beginnings or ends of our meetings than necessary. I am planning, then, for your questions. And I thought that your questions had best be the last day. Because I am sure there are many things you will ask me that I would like to bring in. For instance I have been asked very many questions about philosophy and about God, what I feel about such matters, and I plan to do that in the next to the last day. In other words I am beginning to see exactly what we have available, and what we better do with that time, and I'd also like to point out that I'm hoping someday you will all be interested enough in what we have experienced together to wish, for instance, to make models on your own experience. Because with the video as a medium, it is possible, as with all tape, to come back at any point, and actually run over that point, and superimpose take out the old image, and put in the new. So we could keep the voice going and put in a better picture of a model at various points as we see fit. If we are unhappy with what we have as the total result. I think it will be primarily due to the feeling about models. We, ourselves, could, if we liked out product, could very greatly improve it by making models at various places that would be better than the pictures we see there.

Now, I am going to have some of those slides, please. And there are some that I am going to do tonight that will review fairly fast some of the things that we already have been through the other night, but I think I found some slides that seem to be a little better.

Now you remember dealing in that topology, and we have this inventory of relative numbers of vertexes, faces and edges that when we took out the two polar, or axial vertexes, remember the accounting, then we found that the relative abundance was such that for every vertex there were always two faces and there were always three edges. And this told us then, because everything is double there is an inside and an outside so there is a multiplicative two there are six of the vectors.

In this picture right now, we see on the tetrahedron to the left, there are three of the edges have been shadowed. I want to try to follow those three increments. You see in the cube, three red ones, and three black ones and three white ones. And there is one other color, but they are always in threes. We will see in the octahedron.

Next picture. You can make any of the polyhedra, always in sets of threes, and those threes, remember, were also our friends "action", "reaction" and "resultant". So that the vectors are always "action", "reaction" and "resultant" and they always come together to make sum total structures.

Next picture please. Now this is the one I mentioned something to you the other day when we came to the three frequency vector equilibrium made out of spheres, which shows four balls to an edge, but is three spaces I also mentioned that in the square faces of the vector equilibrium where the outer shell was the number 92, there were, in each of the square faces, four spheres which could be loaned out of the system, without in any way hurting the integrity of the structure of the system. And, we find, then, that, we do find atoms in combination combining in chemistry where they are able to loan one can loan up to four to the other. And we see that, "fourness" in those square faces and those square faces you remember were half octahedra, and they were the internal octahedra, where the two vector equilibria came face to face, and the octahedron hid between the two, and that could be where the four could be exchanged to do the bonding between them.

Next picture please. Now here I've you see, it looks like a lot of circles. What I did was to take a metal floor in a subway where people are walking over it all the time, scratching, scratching, scratching. And there was a bright light. But at any rate, you'll find that if you look at any scratched surface, you will always see circles. And you keep moving along, but with the beautiful sun it is always circles, every time. And it is very important to explain to yourself how all the randomness can disclose to you a set of concentric circles. Well, it's fairly easy to realize that the shadows so as long as there is a light, the scratches actually have shadows. And like a mountain range, there is a dark side and a light side to the mountain range where the sun shines on it. And what happens here, with the light present, is that all the lines that are approximately at right angles, or precessional to the light are the ones that get lit up. So you'll always find then that the other ones don't get illuminated. So you always get then this beautiful sunburst. I find this a very important matter, because it really shows how any kind of an event can find it's own set of orders in what seems a set of very great randomness.

Next picture please. Now we're looking at a sun shining on a spherical surface. A very shiny one which had also been scratched polished a lot. And you see there a star pattern. Not only are there the circles, but it makes into the hexagon. It breaks down into that. It sorts itself out in that no matter where you look.

Next picture, please. Here I was studying the action-reaction. Several of the items in this picture are not there, but we have a man in a rowboat and he jumps from one rowboat to another making one shoot very fast. But you find that the rowboat he jumped out of and the one he goes for they both tend to steer right around they don't go off in