So it was not until we got to the here's a frequency phenomena. Just pay attention to this triangle in here. We have, while you see four balls to the edge, it's a three frequency one, two three one, two, three one, two, three. It's a three frequency system. Three frequency then has a ball at the nucleus. Therefore, as I begin to build up the vector equilibrium, and each edge of the vector equilibrium shows four balls, it's a three-frequency system, and at that level there is a new nucleus showing but it is not a nucleus because it is just showing on the surface. There is a nucleus at the center of the thing, there is a nucleus on the surface, but it's not a nucleus until it, too, is equally enclosed with the original nucleus, which apparently always gets two good layers of its own. So this one is going to have so I could get a four frequency five frequency, after five frequency I suddenly am really enclosed and have a new nucleus vying with the original nucleus.

So we find that the this nuclei idea is one which the first nucleus shows up at the layer the first layer was this 12 42, no nucleus not until we get to 92 do we have a new nucleus showing. But we say it wasn't one it too would have to have another layer on the outside of it here. Still isn't a nucleus. It's not really a nucleus until it gets to this one, and then it suddenly has, now it is really enclosed. You can see here this 92 isn't an enclosure point. This number 92 becomes a very important number, and I'm going to take the 12, 42, and 92 and I want to add them up. This is not including the ball at the center of the system it's just the layers. We find it has six. He adds 146! That's the number of neutrons in uranium which is the chemical element number 92! That gets to be very impressive suddenly. And then you find that you add to the 146, this is 92, there is a matching, always 92-ness there is always a twoness on the outside of the system, so there is another 92 that comes out of here, that gives you 8 uranium 238. So if you want to make it fissionable you knock out four. So, these numbers suddenly get to be very intriguing, there is compatibility with both, accommodating both Einstein's radiation and the Newtonian gravitation, which was what Einstein hoped for very much, this is your unified field theory suddenly showing up.

I want you to realize, I'm concerning these with you in really a very "kindergarten" kind of way, but this is the truth . So you can imagine how excited I became about energetic geometry as I began to get into it a great many years ago.

Because, I 'd just like to recite once more, as a little boy there were things that I was only being told "Never mind what you think, pay attention to the teacher," and I was trying very hard. But the teacher would say things from time to time, that I couldn't help but have some reservations about it.

Now, another thought, as we get going to learning first fractions and we learned all about how you manipulate fractions, and everything was going great. And one day the teacher said "I'm going to show you a better way of doing it." I wondered why she didn't give us a better way the first time "it is called decimals." So she had a .125 that's l/8 and .25 that's a quarter. .333 goes out the window and over the hill. Every once in a while things would go out the window and over the hill, and other things would stay in the room I wondered if she really knew what she was talking about. It didn't seem to me a very good classification.

So I began to really ask myself a lot of questions, and particularly where it came to geometry, because I loved geometry. And she had a point, she put it on the blackboard, and said it didn't exist. So she went and then she said, now I'm going to take a number of these points and put them side by side, and that makes a line, and that doesn't exist and she wiped that out. Then she took a number of these lines that didn't exist made out of points, and laid them parallel to one another, and got a plane. And said that doesn't exist. She wiped that out. And then she stacked a number of planes that didn't exist made out of lines that didn't exist made out of points that didn't exist, like this and says it's a cube and now she says it exists! (Audience laughs). So, I wonder how you get existence out of non-existence to the fourth power?

So I said, "If it exists? How old is it?" And she said "Don't be naughty?" And then I wanted to know how much it weighed, and what it's temperature was? because the word existence has something to do for me with existing. And, of course she couldn't identify it was an absolute ghost cube of her imagination.

Now, then I want to come back to something else I call the dilemma of mathematics and it's imaginary phenomena. We find the mathematicians, then, talking about lines, and lines that go to infinity, and from the Einsteinian viewpoint that doesn't make much sense because, I say, he is entirely operational he's never been to infinity, so he doesn't say that. He finds that all energy is in finite packages and seem to be an aggregate of finites. Einstein is not talking about any kind of infinity at all. But you find the mathematicians have what he calls a beautiful straight line I said, "Well draw it," and he takes his ruler and goes to the board; and I say, "Well, it's really quite crooked look at, see that chalk going up and down there." And he said "You're not in the spirit of mathematics this is just an imaginary straight line absolutely pure." So I said, "I don't know how the word imagination comes out of experience, and the word line was invented by me for an experience I was having either the trajectory of leaving some smoke behind, or leaving some chalk behind, or I've taken a chisel and am clearing something away. I've left a tracery of my action, and that is always going to be very crooked." Anyway, the mathematician said, "I mean a line of sight it's straight. Get yourself a surveyor's transit." and I said, "Alright, we'll put the surveyor's transit on the sun, just kissing the horizon, in the evening, and we find that the sun hasn't been there for eight minutes, so you're looking right around the curvature of the earth." And the mathematician said "You apparently just don't want to get into the spirit of mathematics here. You'll never understand it." So I finally came to a discovery which I find begins to work fairly well.

I'm going to take, I spoke about Boole the other night, Boole developing his Boolian algebra when you can't find the logical way, take the most absurd way. Take the most absolutely absurd you can get, and get something a little less absurd, and you'll gradually get working toward something that might be reasonable by elimination of absurdities. At any rate, I'm going to take a deliberately nonstraight line, and instead of saying I have a straight line, I want to be invariably sure of it, so I take the rope which is obviously curly it's all twisted, and I'm going to take this and one of the definitions of a straight line is that it never returns upon itself, so I'm going to take the ends of my rope and deliberately splice them together, so I have a most clearly deliberately non-straight line, either along the local service or the ends coming together. It is a closed circuit and then I'm going to take that piece of rope, and I find that I'm going to take any two parts of it and put them aside like this and put a clamp on it then I'm going to massage the rope from the clamp on like this, keep massaging it very evenly, and I come to where it turns around very sharply, back on itself. It's a tight little radius, and I keep it pinched, and I make a mark and put a little red ribbon on that turning point, and I go to the clamp and I massage the other way, and come to where it turns around again. Anyway I get just as close as I can to the middle of that arc, and put another ribbon on. Quite clearly I've now divided the rope into two parts that are fairly, reasonably each is just about half of the rope. Heisenberg makes it absolutely clear we can never be exact, so that we just only struggle so far. I'm really content that I've taken unity and divided it into approximately two parts. Now I'm going to take each one of those parts between the ribbons and pair them up the same way. And I'm going to get a quarter point. I'm going to do it the same way. And I'm going to get a quarter point. I'm going to do it the same way keep halving the distances between points. We're not increasing or multiplying here, we're simply continuing locally, halvings so that each one is a reasonably good half. And we get down to sixteenths, and thirty seconds and sixty-fourths and so forth. All nice clear marking distinctions so we know which point we're dealing in. Now we're going to go to the wall and put up some nails, and I'm going to put a nail on the wall this is the wall we're looking at over here. And we'll put a nail here and I'm going to ask you, I'm going to take the piece of rope and put the first marker on here. I'm going to ask you to really hold it nice and tightly, and I'm going to go over to the quarter marker, quarter way around the rope and I'm going to pull it tautly from you, so it swings as a radius here, and I can put in another nail, anywhere I want on that radius. So this distance between this is, I know, is one-quarter of my rope. Then with this same thing I'm going to come down here, another quarter point and I can swing it anyway I want in here, so I say, let's put it here; excuse me it should be about over here so then I'm going to get to another quarter point. There's I've got somebody holding it, and I've got holding it here there's a slack piece in here now, and I come down to the marker, pull it tautly and put in another nail. So now my rope is stretched over that; and the rope is we've got a diamond, and it's an equilateral parallelogram. You're very familiar with that, and there is nothing you've learned in geometry that as far as just playing games with lines, that I will not go along with. It's fine. This is an equilateral parallelogram.

But I have very clearly already marked on here other points, so I'm going to take the 1/8 points, and I'm going to take the rope off of this nail here and pull it down firmly; and so the rope is now going to come down to here. I'm going to take it off of this nail here and pull it firmly up like that, and it's going to come up to here. We have now two parallelograms, and I can eliminate this one out here. This is the same piece of rope, now, but it is two diamonds end to end. And it's very easy all the way through it is equilateral parallelogram, holding absolutely true. Same length between "a" and "b" all the time here. Now it's no trouble at all to do that again. So each time I'm going to half it here, and we eliminate this, and then eliminate this, and now we have four four diamonds in a row. There it goes. In no time at all when we get to this 32nds and 64ths and so forth, we get down where every time I do this I half the distance.

So what we have now is this baby. And those vertexes again closer but it's always the same length, it's always the same non deliberately non-straight line, but it keeps getting straighter and straighter. By the time you get to the 64th and so forth, in almost no time at all it begins to look like a straight line, and it gets straighter and straighter. And I have a way of getting it straighter and straighter which the mathematician didn't have, at least I've got a progression towards straighter he didn't really have anything except making kind of "get a line of sight or so forth" he didn't have any really methodical way of getting there, but I know it's non straight. So I'm going to be able then to get a line for the mathematician which I can probably prove mathematically is a little finer than any straight line he's ever used, but I know that it is deliberately non-straight.

Now the physicist when he wants to get the student feeling wave we're getting into quantum and wave we really want to feel wave. One of the first tricks he does is to put a nail in the wall and fasten a rope to it, and stand over here, and throw a whip into the rope, and it goes to the wall and comes right back here and stops. It's a fundamental characteristic of a wave that it comes back where it started. Beautiful thing. What's going on here, is then from "a" you whip here from "a," it goes out here to "b" and it comes right back to itself. It's a wave. See it? Now when he said, "I meant a line of sight," that is always a wave phenomena. This is the line of sight. Now I'm really able to show him what his real line of sight really was, it is a wave. Physics has found NO straight lines; ONLY WAVES, ONLY CURVES.