Again, a very fortunate thing happened in my life. Often what seems to be misfortune turns out to be fortune. I find that life is highly compensatory. Because I was very, very short-sighted when I was born. So short-sighted that, so very far sighted, that, I can't see when I have my glasses off, I see exactly now what I saw when I was four years of age. The correction has not been changed at all in all those years. This is my 76th year of these lenses. I see an absolute blur of faces I cannot see human eyes, I can actually make out some darkness where eyes are, and I can see more or less a shadow of noses, I can see the two sort of dark colors it's purely a color matter, there is nothing the matter with my spectrum of colors, so there is a pinkness this side of your face is a little lighter than that side of your face, and I get really just a sort of shadowiness that are the eyes. Very much like a Lorenzian kind of a painting. And there is a little bit more of a pinkness in here. I can make out a little color differential. So I didn't see a human eye until I was four and a half years of age, when I got my glasses.

Now, because of that, I tended to try to get my I didn't know, how would a little child know? what I see is not what everybody else sees, so I assumed that everybody else was seeing the same way. But my problem of understanding was really quite a different one from the people who could see the details. And I had a sister three years older than I was, and she was continually telling me the things she could see. And I thought she was making it up, so I didn't want every child has imagination, so I thought and I had been read fairy stories these are just fairy stories here, so I'd invent what I could see. And I could see some very extraordinary things, and I would always get laughs. And my sister didn't seem to get any laughs for her description of what she could see. So you can imagine what happened when I was suddenly four years of age, and I saw that she hadn't been telling me stories at all. And I suddenly saw hairs. Now, I spoke about, there is a compensation here.

I went to kindergarten before I got my glasses, and in the kindergarten, the teacher had some dried peas semi-dried peas, and she had toothpicks and she told us to make structures. To stick the end of the toothpick in the pea, and we found that they joined the tooth picks so that you could make structure. All the kids that could see, the minute they were told to make a structure, immediately tried to imitate houses. That was the first thing they thought of. So they were all rectilinear. Now what I did, because I couldn't see at all, I wanted to feel something that feels good, so that a square and those forms didn't feel right, but when I got to triangles, they felt great. So I could really feel that was nice and stable, so I made, literally a structure like that. And I remember the teacher calling in other teachers from the other school there to come over, and they were all very surprised as to why I had made this strange thing. But it was purely a consequence of my not being able to see. I was not trying to imitate something, I really she said, make structure, and I just got to where it felt right. You can understand that, somebody going around groping their way it's purely a matter of feeling. And anybody working in clay would just have that kind of feeling whether it's going to tip over or not or if it's cohering.

At any rate, I did do that. So it was something deep in me, also about that so when we have the moment of my being excited by Avogadro, he seemed to be giving me some Universal condition, and I had wanted to use vectors, and I felt this I said, I think I can make this. Now, this is called in mathematics an Isotropic Vector Matrix. Isotropic everywhere the same. Isotropic Vector Matrix. So I found I could make an Isotropic Vector Matrix, and that was just great, but then the Isotropic Vector Matrix turned out to be simply spheres in closest packing. Remember, the "two" the "me" and the "otherness", and then we suddenly come together, here, and suddenly we roll around on each other. These little Styrofoam balls are great to play to get the feeling of that rolling around, and from where I am, the fact that I'm rolling, you don't really notice that the profiles stay just the same. And so then I get three of them rolling together, and I get the one on top nesting in it the four. And then, there are your six vectors and. so spheres in closest packing, all the same radius unit radius spheres, closest packing, they simply, automatically come out the Isotropic Vector Matrix.

Now, we were interested in atoms and how the atoms behave and the volumes of numbers per volume and all those things. In every kind of a way this is a very satisfactory matter. It was at that point that I also said, I would like to see about a nucleus. And that's what brought me then, into finding the twelve six around one in a plane, and three on top and three on the bottom, giving us then, the vector equilibrium.

I would like, we have a lot of these balls, and I really would like you to do some experiments with them yourself. And I don't want to slow the picture down too much here. And you all are getting pretty well versed here. Now I've also given you tetrahedron, and I've also given you the idea of Euler's topology that vertexes and the numbers of the edges are not the same as the vertexes, remember. For every vertex we are going to have three edges and two faces. There is an absolute relative constant abundance of those in Universe, in addition to the polarity "twoness" which has to be taken care of, and that was what was not recognized by the topologists. They didn't realize that there was a hierarchy. It was never really understood that there is this hierarchy I am finding completely my own discovery to come then where the tetrahedron was unity. Which, you can see how absolutely logical it was. It was the minimum omni-triangulated vectorial model. And the cube just didn't work. It just was very uncomfortable, so you can see how quickly I really got into, sort of spontaneously, in here.

I want you to see that this is how a child carries on. I'm just going I think of all the things that were, I find important I don't think anything is quite so important as naivete. Just cherish your naivete. Don't let anybody try to belittle you because they say you are naive. This is the most beautiful thing we have. So I think I have been very naive many times, and the as a sort of off character, seeing the wrong way at first with the teacher and everything; and then, I didn't wear my big glasses. I was a kind of ugly looking character anyway, and I NEVER was any teacher's favorite, I assure you. And often, my friends discovered that to such an extent they found that they could play tricks and I'd be the one who'd get the blame. It was sort of a standard matter in every class I was in. I was continually having to stay after school and so forth, and when you stay after school and the teacher is rather nice, and got to saying, you really like mathematics very much and I'll teach you some more. Actually at Milton Academy where I was the mathematics teacher said, "I think you might just as well go on into college of mathematics ." So, I went through a whole lot of mathematics while I was still in school. Simply, this was afternoon time when I was being penned in anyway, so, it came out fine. As I said, there are compensations that go on. And the kids didn't know what a favor they were doing me. I didn't know either.

I don't want you to think at anytime that I'm being something abnormally smart here. Everything that has happened in my life here so far, as far as I can see it, comes really out of the physical circumstances. And, of all the things I think my not being able to see properly nothing was quite so important. Because at four and a half imagine if you had never seen a hair and you suddenly see a hair. And you'd never seen a dew drop before. Can you imagine. I hadn't seen eyes particularly eyes. And particularly eyes of creatures, and eyes of those kittens and eyes of the snake. And I seem to be able to talk with people's eyes. I just love snakes and toads and they like me and we get on, and I fill my blouse up with them and people would holler about that. But I want you to understand, I don't think anything went on with me here, that wasn't just a very, fantastically normal, average character, with certain physical deficiencies at the outset which get fixed up. Cause at four and a half I really started life all over again. Imagine getting a second chance. I'm sure that through the years when things went badly, I would say, because I couldn't see at first, I'd say "When I don't see or I don't understand what's going on here, I think all I have to do is to wait a little." There must be something in me psychologically that came about through that delay and that second sight. That second take where you really suddenly understood. I think this has helped me to hold on and to hold on many times to the total package. And certainly that business of not being able to see details I was having to put together smelling, and hearing, and touching. Which were very much less effective than the seeing. So I was using the three-way system to sort of zero in.

And, personally, my grandson says to me now that he's not sure whether I'm really being effective with human beings when I say this thing, but I am confident that the only thing that is important about this particular character me is that I do represent an average character, more or less getting peeled off by something wrong, like the kids fooling you so you get to peel off for the afternoon. I found myself getting isolated more and more but it gives me more and more perspective on the show.

And tending then to see long distances, to put together big patterns. When I say, then, as far as I am concerned, I am very clearly a demonstration of what any human being can do if they are disembarrassed of the game where society is trying to make you a specialist no question about society doing what it did in great love. The grownups really feeling an enormous affection they are sure they are doing the right things for their kids. There is anything but malevolence in here. I don't think, again, that you can see anything if you assume bad or good in here, you have to understand how people got caught in the picture they are in, why people do what they do, and you may find out something.

Now, I have some more slides I'd like to go on with. Oh! there is something I'd like to show you here, because I find there are five of these balls and five sets of the tetrahedron have been put together. You remember how when we had a tetrahedron, just look at it in the corner, you can get four tetrahedron and one octahedron in the center. You remember that. So that's getting clearer and clearer to you. But I also pointed out to you that vertices and edges are not the same. So sometimes you're looking at tetrahedron and they look like this. And when you're doing that, these are entirely vertices. The spheres are the little points enlarged. This is vertexial topologically. And then when I see it as a line, then I can make it out of solids, and those are areas. They really are, these are three different topological phenomena, and the counts come out differently. It's very important to realize this. Then we have two balls here, but there is only one edge between them. That's one reason why we came out where four balls had six inter-relationships. They are not the same number .

So, I wanted to show you how what you are very familiar with now, putting a tetrahedron, four tetrahedra in each corner, and one on top. So here is a tetrahedron. Another tetrahedron here. Another tetrahedron sits here. Now, we've learned it in areas where it looks like solids. Then you put a tetrahedron on top and you put an octahedron inside here. That's not what you do at all. You say the octahedron I'm going to take a tetrahedron and put it upside down. Excuse me. This tetrahedron I'm going to lay it in upside down, and each of these four are going to come in the middle of those like this, it fits right down there. Now, I'm going to take one more and it fits right on top there. Now we've got a three ball, or a two-frequency tetrahedron made out of five tetrahedra. Gives us the number five showing up quite interestingly, where you've got an octahedronal kind of four that's a prime number difference in there. It is very, very important not to get fooled about see it is very neat.