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.
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.
Next picture. I'm reviewing this quite rapidly because I want to get to some other things that I have added in, over and above what you had yesterday.
Next picture. There are the two halves of the three frequency.
Next picture. They come together as the tetrahedron precessionally again.
Next picture. And we have, then, the eight frequency, and they come together again as the tetrahedron, again.
Next picture. And, we then have the two one-eighth octahedra. And I'm sorry to say the top one is not clear, and they precess together to give us the cube. This is the first cube to appear in spheres. In other words, you can't have a sphere with eight cubes, just the corners that's all. There are in this, then, the base is six and the seven, so there are fourteen. So this first cube is apparently fourteen, and it's very possibly something to do with carbon. It seems very logically so.
Next picture. There we see the completion of the corners of the vector equilibrium by putting on the one-eighth octahedra in each corner.
Next picture. Then we take it off and we get the vector equilibrium itself.
Next picture. And then we take this whole thing apart in these various slices.
Next picture please. I also, then, want to remind you of something I gave you the very first day. The vector equilibrium, remember those shells, remember. First shell twelve, next shell forty-two, next shell ninety two counting up to 146 plus 92 gives you 238. I'd like to show you something about that that I didn't mention that day. So we have the formula for the number of balls in the outer layer was always, remember, frequency to the second power times ten plus two. Remember that? And I made it very clear why that was so. So we found then that we had this layer of twelve and forty-two, ninety-two and one hundred and sixty two and so forth two fifty two. Then, however, this was the first layer, but there was a ball inside, so it was zero layer. In other words, it can't be a layer, unless, I say, unless the ball itself really there is really a ball there, and it has an outside and an inside. And these layers have been enclosing, so I'll have to remember then this is a, being frequency to the second power times ten plus two; we then found that was ten and then we took so this was twelve was one was the number one, the first layer, this is number two, this is number three and number four. Those are the numbers that became second powered; so the center ball is zero, so I find out, remember what it's formula is. So it is frequency to the second power times ten plus two. So zero to the second power is zero, times ten is zero, plus 2 is 2. The value of the inner ball there turns out always to be 2. In other words it's own concave and its own convex. And I have given you, unity is two and you'll find this showing up time and again when we come to this extreme. I find this a very, very exciting point and I hadn't given it to you the first day, and it was very important that it come in today.
Next picture please. Here we have the knocking the central ball out you remember, from the vector equilibrium, and it immediately became the icosahedron. Same twelve balls simply the squares disappeared and they became triangulated as the pumping model shows very clearly.
Let's make a quick review of it, then we went from open vector equilibrium, down to here, and then we add these in here and here's the icosahedron. So like everything else it's the degree of contraction everything happens in the vector equilibrium, where the realities begin to occur there are always some degree of contraction. So this is a much further degree of contraction, and even further so when it came down to the tetrahedron.
Incidentally, there is another tetrahedron in the vector in the jitterbug which I haven't tried to make for you before this is a polarized one. See the precessional edges in my left hand and my right hand I have the double edges, and all the rest are single. All these things occur without ever breaking the edge. In other words, the integrity of the system is always there.
Next picture please. On the left you will see the these are pictures from Linus Pauling's book. And you will see a column there, he's got a polarized column, and he has the same picture I showed you, taking off one whole large corner of that cube. I'm sorry there's something else over on the other side that is very interesting. I made, in the late 30's and early 40's, I was able to get a hold of beautiful little clear crystal balls, and I found that they were transparent, and gluing them together I was able to make very fine models. I think we still have them, but they began to tell me, this upper row here, I began to really get faithfulness in respect to various atoms, and this is all a part of what kept me going.
You can imagine when I first began to discover all of these rational relationships, and I was able to really talk about them in the 30's and I began to confront scientists with what I was finding, and they found no identity with what they were thinking. . And they were not thinking models, and they felt any attempt to bring the models in was really tending to really roll backwards into the Platonic era, and this was all nonsense. So that, what I would have to say to myself. I would ask the scientists if they could find anything wrong with my arithmetic or my geometry. And they would say no. I had found this beautiful hierarchy of rational values, and I'd say, "Do you think I ought to go on?" And he would say "Yeah, I think you seem to have logic in it alright, you might as well pursue it, but it doesn't have any significance, you know, in physics, it's just sort of a mathematical pastime. And, so I finally had to ask myself a good question. I said "Am I so important that Universe would secrete a great cul-de-sac of incredible beauty and elegance, just to fool me?" I said "I'm just not that important." So I have to assume that it really is very important and that the other people are wrong. This had to be my argument, and I've carried that on since it's been really a very long time.
Next picture. On the left we then see our friend the tetrahedron with the octahedron in the center. I didn't have a nice model like that to show you the first day, so I thought I'd show you that again.
Next picture please. Something has gone wrong on my picture. That was going back. This is a picture of great importance because we are looking at the skeletonized tetrahedron with the octahedron inside it, and on the left hand side lower left hand side you'll see a blackened tetrahedron. It's base is on the table, and immediately to the right of its base, is then the base of an asymmetrical tetrahedron. It has the same triangular base both equilateral, but you'll see a dotted line going from the lower mid-right side of the big tetrahedron. There is a dotted line going to the top of the small tetrahedron in the left-hand corner, and that is, then, one of the x,y,z coordinates running between because the octahedron then has three corners, and this is one of the and that edge then makes an asymmetrical tetrahedron which is leaning leftwards a leaning tower of Pisa, but it has exactly the same sized base as the regular tetrahedron on our side. So the bases are congruent, so we know they are the same, and we know their top vertexes apexes are congruent, and the base is the same area, so their volumes must be the same. And that is a one quarter octahedron. You can see that it is just one quadrant of the octahedron if you study it carefully. So you can really feel very comfortable when I give you the octahedron as a volume of four when the tetrahedron is volume one.
Next picture. I didn't have the opportunity to show that to you the other day. I talked about it, but no model. I'm just confirming to you from the other day the count of the tetrahedroning instead of cubing. When instead of superscript 3, we call this then tetrahedroning instead of cubing.
And there is the count for each of those layers. The one, and then the two get up to eight, twenty-seven, sixty-four as they combine. So now you feel quite content to because we have also found that structure is triangle and if it isn't triangulated it's not a structure unstable. And that tetrahedron then was the simplest structure, prime structural system of Universe. And so when you count in tetrahedra, and cube take three, we are being more economical, and if you use a cube you use up three times as much space as Nature is using, because she is always most economical. So you want to catch on to what she is doing the most economical, and you've got to use the tetrahedron for your accounting.
Next picture. Again we really can't see. There is a vector equilibrium to the right and it shows the eight, little one eighth octahedra no the eight tetrahedra go in and the six one half.
Next picture. And that's showing a completion of one of the corners of the vector equilibrium to make it the cube, by the one-eighth octahedra.
Next picture. This, now is very, very important. We haven't come to this yet. Yes, we did, in the terms of spheres in packing, and let me remind you again, when we are talking about spheres in packing we are talking about vertices. And when we are talking about edges we are talking about when we see lines in structures, we are talking about the edges, and the counts are very different. There is one vertex, for two areas, and three edges, so you can see the difference. We are now looking at a skeletonized tetrahedron and the center of gravity of the tetrahedron. And we pull out from the center of gravity of the tetrahedron, a one-quarter tetrahedron, and that one-quarter tetrahedron, you may remember, we formed by we had a triangle of closest packed spheres, and it's edge read four and there was one ball on top. It was a three frequency. There was then nestability. Do you remember that? We found that where we had three balls there was no space for it, not until we had a three frequency, or four balls did we have then no, that gave us a ball at the center. It had to be five balls or four frequency before we get the one-quarter tetrahedron.
And, this, then was in a hierarchy of nestabilities. In other words it wasn't in just being arbitrary and saying we're going to have one-quarter tetrahedrons, and one-eigth octahedra, we found that those occurred where a ball could nest, and they were the sequence of the first time, and the second time that a ball could nest on top. Your first nest on top would make a tetrahedron. The next time it would make a one-eighth octahedron, and the next time it would make a one-quarter tetrahedron.
Next picture. Now those one-quarter tetrahedra up at the top. I've taken an octahedron, taken the octahedron and, that's alright, on each of its eight faces we put a one quarter tetrahedron. Again it is a regular equilateral triangle, it is all the same vector edge, so that it fits perfectly well. I've got one here, then another one here. And when you do, you'll find that the apex of those one-quarter tetrahedra are on the same plane as that line between the two. And what it does is to form the rhombic dodecahedron. It's a fascinating thing. As they come up here, this makes then for each of the twelve, there are twelve edges on the octahedron, and these apexes come up here and it becomes a flat it makes a diamond it makes a diamond on each edge of the octahedron. There are twelve edges so you get twelve diamond faces, and there is your rhombic dodecahedron. Now the rhombic dodecahedron is a very exciting kind of a form. It's volume is exactly six when the tetrahedron is one, and the cube is three, and the octahedron is four and so forth. Six. And its "sixness", what is this rhombic dodecahedron. Remember the vector equilibrium has twelve vertexes. And those twelve vertexes of the vector equilibrium are where every sphere in closest packing is in contact to the next sphere. Now, they are also the spaces and the spheres in closest packing, and what the rhombic dodecahedron does each one of those diamond faces occurs at the point of tangency. There are twelve of those diamond faces and each one, the center of it is where each sphere touches the other spheres. So what the rhombic dodecahedron the rhombic dodecahedron, like the cube, fills all space. So what it is, is both the sphere and the space. It goes in exactly, and there's an octahedronal space, and a vector equilibrium space, and it exactly goes to the center of gravity of that space. So it represents the volume of the sphere and the volume of the space that belongs to that sphere. And there it is, the volume is six. It's this beautiful rational number.
Now, we're going to see a lot more about this rhombic dodecahedron because it is then, the epitome of the behavior of the spheres in closest packing, and it is, I simply call it, "the domain of a sphere," and sometimes I call it a spheric. Because it is the domain of the sphere. It's a sphere and the sphere's own share of the space that is not a 20 like the vector equilibrium, nor 4 like the octahedron. It's a very important number. 6 is a spheric space a domain. And when we are dealing in spheres, in a way, we are used to thinking about spheres and so much of the Pi business, and somehow there are some very nice numbers coming in here without so far getting into any calculations of that kind whatsoever.
Next picture please. Now I have a very strange cutting here. Where we take the vector equilibrium, and we take the one-eight octahedron that we put onto each of the triangular faces to make it into a cube. Then, you remember that the vector equilibrium has, as a sphere, it had 25 great circles, remember that. And remember those 25 great circles, there were the 3 great circles, a 4 great circles that's 7. There was a 6 great circles makes 13. And there were 12 great circles, made a total of 25. If we had each one of those great circle planes were extended into the cube, and if I had those planes, then, come out I've got this corner over here, and they get outside the vector equilibrium and they cut up this little corner into pieces. Go back to that picture, may I see that picture again?
So what you see there on the lower right are the one-eighth octahedron corner. And you can see the lines on the surface of it, and it has been cut up internally by all the twenty five great circles. Now, back in 1947, I did my trigonometry carefully, and I found what the volumes of these were and they all counted out rational number. These little fractions are coming out rational numbers! Boy, you'd better work harder still. And, I'd just like to have that one mentioned.
Next picture. Now here is the, looking at the vector equilibrium, cut through the center, and we'll see a central vector equilibrium, and one, two, three there are four enclosures. I found that whereas I gave you for each layer in terms of spheres there were 12, 42, 92 and so forth, I found that the volumes were growing. The volume of the vector equilibrium is 20. And the sum total volume of the vector equilibrium is always frequency to the third power times twenty. For instance if the frequency were twenty then the volume would be three to the fourth power. This is a very we do not start with a zero, we start with an entity twenty is unity. Unity can never be less in a vector equilibrium unity is twenty. In the octahedron, unity is four. It never is less. That's where the number begins. So that when we, I found that the rate at which layers grew of the vector equilibrium, and I gave you the series of layers. If I took where the outer set of balls were occurring between that ball and the next layer in it, there would be a plane that could be struck; and that for any two layers, they combined to give me a very interesting number. Where the volumes were growing at frequency to the second power times six plus two. In other words there was something to do with this spheric space this number 6 being very unique to the rhombic dodecahedron or the domain of the sphere. So that those spaces that you're looking at now, pairing any two, will always be frequency to the second power times six plus two.
Next picture. What we are looking at here in this lower right hand corner is quite difficult to see. You are looking at the icosahedron, and it is you have the perpendicular bisectors of it, in other words we're looking at the 15 great circles which give you 120 spaces 120 right triangles on the surface of the sphere which I said the Babylonian's identified as very important. If I could have the picture back again. I found then that insomuch as the octahedron has eight faces, and there were 120 triangular faces showing there, I said, "Can you divide 120 by 8?" and I found you could. It's 15. And I said "It could be that if I took the icosahedron's face, and added around each of the three edges I would add, because I know that there are six inside, there are six triangles inside the icosahedron's face, so 6 from 15 leaves me 9. There are 3 edges. So therefore, if I could find a way of mounting 3 triangles on each edge of the icosahedron's triangle, in a symmetrical way, where it would make a corner of 90 degrees, like the octahedron, then I might have found an octahedron inside the icosahedron and sure enough we do have it. On the lower right hand side you will then see the octahedron in the icosahedron. They skew like this. Tomorrow I'll bring a model here where you'll see the icosahedron inside the octahedron and you'll find that literally it is rotatable. Will you bring that, Meddy, from the office tomorrow.
Next picture. Now, remember, I am looking at, again I'm not seeing enough. I'm going to go to the board to show you your squares, and triangles and your counts were all perfectly clear; but we have the two triangles to the square but I want to show you something about triangles and squares, which then also applies to rectilinears. (Bucky goes to the board now). That model is here. Oh beautiful! We won't go any further without it. You recognize your yellow octahedron, now, and your red icosahedron. And notice, it is skew in there. The points like that. And I'm going to do this. It will rotate right in there. Fantastic. The beauty of these two coming together. So I want you to get into the rationality of the interrelationship of this icosahedron, which is always bothering you because it's volume is 18.51 all the others are rational. And you have to realize it is a very special behavior, that icosahedron, because it can only have one layer of the balls in closest packing due to the contraction there is no room for the second layer. The vector equilibrium position there is room for the layers, but when it is contracted, there is only room for the outer layer the outer layer can be triangulated, but you can have no more layers, because it is inherently a single-layer affair. So, again, it makes me feel that it is very much the electron behavior, and I have to note these kind of reciprocities.
Now, I was going to come over to talking about. If I make a any quadrangular form, but not equal edges if I bisect those edges and interconnect, I do not get four similar forms. That's not so. But if I take any triangle and bisect its edges and interconnect, I get four exactly similar triangles. That is, the triangle is inviolable in the matter of its it can look like anything to you in this Universe, but the accountings I have been giving to you always come out exactly the same whether it looks like a regular tetrahedron or not.
And the same thing if I made that a rectilinear thing, it would be a whole lot of trouble as you know. So that but in the tetrahedron can look like anything you want, and it still comes out this way. Now, there were two forms that showed in the last pictures where I saw that they were not clear enough to really bring to your attention. But I now am going to get into an accounting, just doing this for you myself.
I'm going to make a I've got a tetrahedron made I've got rubber bands coming from me, and I'm going to hold the base of my tetrahedron between my two feet. This is a basic one. And you can take a hold of the vertex over there, and I am going to make a line parallel to my feet over her. And I'm going to hold this tetrahedron's top here, as long as you just move it in this line always parallel to me, the area of the triangle it forms with the base here, will be the same base and the same altitude, because the lines are parallel to one another. Agreed? So then I find that I can move that base line and I also can move my top here in a plane parallel to the floor. So I find that out of the tetrahedron's four corners I hold two of them, I hold one edge fixed only. And the other five edges are continually changing. But it always remains the same size tetrahedron. So I can move this vertex way, way over there. Or I can move that one on the floor over there. Always the same altitude, the same base. In other words, you could get to an extraordinarily asymmetrical tetrahedron here, but it always holds true. And I am quite confident that this has a whole lot to do with the fundamentals of tuning. Where I said, I could sub-divide those triangles any way I want. It doesn't make any difference at all. It all comes out, always, the same value. I think it's a whole lot to do with electromagnetic tuning, where you could tune in here, and I could tune in any place in the Universe and we simply come in. I haven't made that particularly clear that point, but as time goes on, that will clarify.
Next picture please. On the first day I tried to have a stick standing up here and it didn't work. Then I had a picture over here, but it didn't really do much better. I've got two sticks standing in the lower left hand side, and they can swerve anywhere, but over on the right they fall towards each other. And so they engaged these other tops, and now they can act as a hinge.
Next picture. And here we have the three of them falling towards each other and making the tetrahedron. But it's legs can go out, so we must have a set of tensions down there.
Next picture. That's part of what I've just been talking about.
Next picture please. About the distortions being in there. Here you have a drawing I was making of tetrahedra. These very simple things where they get very narrow, and get to be like the tree, so I gave you the other day a tree as we know, the cambium layer. Each year the cambium layer encloses the next one, and we find they literally do grow, the top is now, they are tetrahedronal. They might look more like a cone to start off with, but, no, you'll find the roots that as they do the stretches tend to go out tetrahedronally. So that I said each layer of the cambium layer the trees continue, one tetrahedron enclosing another, and the branches themselves go out as tetrahedra, and you find the wing root is really exactly that, the bottom of the wing root in here it's deep, and the flap goes that way that's the shape of the wing root. So that each branch is a tetrahedron, and it gets its cambium layers, and each twig is the same, and they are continually this way with tetrahedron embracing tetrahedron, and so the bud and the whole thing comes out there.
Now, I was just making pictures here of tetrahedra, and I had them perpendicular to the earth. The earth's surface was upside down on the bottom there, that's alright. There's no upside down in Universe, so it was valid. I had been making that picture, when the next day somebody gave me a picture of radiolaria.
Next picture. And this are radiolaria and they look so much like my sketching that I thought I'd like to show these two coming together.
Next picture please. Here I have three ships. I was in the navy, and I had been taught about Galileo's parallelogram of forces. And I had been taught that you had the way you make a parallelogram of course is that you have two masses moving at such a velocity in such and such a direction. So you make the vectors that length respectively. Then you make two lines parallel to them, you're making parallelogram. Then they had you make a diagonal of the parallelogram to the point of impact. And then extend that diagonal outwardly right thru the point equal length to its diagonality, and it would be the resultant of the forces.
Well, when I got out of the navy, I began to feel that this was utter nonsense, because I said that when two ships run into each other, they don't go waltzing north-northeast 12 miles or whatever. They, one goes to the bottom, and that wasn't on the diagram! And I think you're going to have to have a little different kind of a diagram. I found that both ships were in great acceleration, and the fact is that when they do hit, they rise because the resultant is outwardly with Earth. They are both in acceleration their trying so the total resultant is really primarily upwardly like that, then one goes down and one rolls way over to that side there. And one goes to the bottom. I found it really made the music stand form, and really made then, our friend, the tetrahedron again because of the three legs and the vertical of the tetrahedron.
Next picture. While we are looking at such forms I thought it would be interesting to look at the, may I have that back please. This is the looking in a cloud chamber. And I spoke to you the other day about two lines can't go through the same point at the same time. And this is where they bombard with the neutron bombarding a whole lot of atoms this is a typical kind of a cloud chamber picture with these resultant angles of the bombardment.
Next picture. And put all the light you can in on this please. I spoke to you the other day about being going to the Island of Crete, because I can read this picture well today. I took photographs in the great palace of Knossos. And on the wall there you'll see a hexagon. This is what is called the "kings sign." And why they call it the double ax I don't know, because I think that is really a very foolish kind of way to talk about it quite clearly it is the hexagon.
Next picture please. And blot me out and let's just have these pictures. Here we have this is another one. It's a little cocked though.
Next picture. And there you see the distaff side like the English flag with the vertical cross and the diagonal cross. That is the distaff side. I just wanted you to see these things that were on that wall, and I spoke to you about then the possibility that this great invasion, the breaking down of Crete which had been the stronghold of the water-people was broken down by lesser water people who were more landed, the Ionians coming out and suddenly the mathematics breaks into the open. But it breaks into the open on the distaff side, with the x, y,z coordinates rather than the 60 degreeness which I think remained very secret to the navigator and calculator.
Here I have taken two of the DNA-RNA tetrahelix, three of them. And you'll find that as you make one of these, you can make it spiral positively, or you can make it spiral negative. But you'll find that if you make them all positive, then they will nest in one another. But, if one is positive and one is negative, they do not nest. They have to be, and this is when you're twisting rope, they both have either positive or negative twist to settle one into the other. Now one of the things that have been very fascinating to the Watson-Crick-Wilkins, and all of the people who studied along with them, all the virologists trying to understand what's going on here that the design is codified and controlled by the DNA and the RNA, we find that the child unzips from the mother as the prototype form, just zips apart like that. It might have quite a lot to do with trying to put these things together and see how they were nested with one another, and why they might let go. And because I also do my trigonometry in very extreme depth to be sure that I really have my figures very close on, I am really quite familiar with the form that the chemist or the biologist, the virologist, making a model like this, simply find that he had 36 degree increments, so he found it was a helix, and so ten times that was 360 degrees, so it seemed to be a cycle. I found that it really was not exactly so, because, we take the tetrahedron, I cut a plane perpendicularly against this line, through here, that this angle is 70 degrees and 32 minutes, and so the octahedron when we balance, and one sits in here so this angle is 109 degrees and 28 minutes, and 70° 32'. They are absolutely discrete. So that I found that there was a very interesting set of information coming in where the, when great plates of steel are sheared in great testing in navy work and so forth, that they always tend to shear at an angle which the metallurgist has been calling 70 and 110 which add up to 180. And so too, the earthquake faults and so forth earth faults continually showing up in the 70 and 110. I said, I'm sure they are not 70 and 110. They are 109 degrees and 28 minutes and 70 degrees and 32 minutes. But it makes a great deal of difference when you make sharp accounting. And I found then that when you make the tetrahelix, the tetra is coming around because there is accumulation then of the hedral angles as you come to the top. Lots of people take the tetrahedra and try to put them together edge to edge like this and you seem to be able to get, if you're just doing it with things like this, you say "I am getting five around one". But you find there is a little opening there.
And it's always there. So we find out exactly what that opening is. You take five times 70° 32'. 352° 40'. So we take 360 degrees minus 352° 40', 7 degrees and 20 minutes. This is the difference. So that when we get in that tetrahelix going up like that, we find that the 70 degrees and 32 minutes is in there, and yet there is enough torque in my models when I make this long thing, so that you can pull them together. In other words, in the twistability you can get one to wind in tight enough so that it will hold. But, they want them to spring. That was one thing that they couldn't quite understand that the child wants to, tends to unzip from his mother. So here is the unzippability, suddenly there. I was able to explain this to the Watson-Crick Wilkens group, and that has found considerable favor with virologists. It's probably so. But their model looks so strange, that they don't think about it as being tetrahedronal. But I find that human beings are just not tending to think. If you want to get the kind of experience that you are having with me, you are going to have to always think tetrahedronally, and realize that really all helixes are really brought about there are many ways that you can make them by taking strange match boxes and other tricks and put them together but it always comes out following the same rules and laws.
Next picture please. This is simply a picture of the, when I gave you the hammer thrower, and showing precession and why the wheel tilted the way it did. This is part of my if any one of you would like to, you can go back and look at the May, 1940 FORTUNE magazine and you'll find my explanation a double spread page of the gyroscope. Which the Sperry Company said was absolutely faithful, and they didn't think it could be done, but it was done.
Next picture. Now, I'm just looking at a large tetrahedron, and inside of it.. And the octahedron, and so forth.
Next picture. I'm doing some I want you to think of a big tetrahedron now in which something else is going on. There is a center of gravity there is a center of the base triangle, you can see that. Above it, there is a point, and that is the center of gravity of the tetrahedron. That's where the one quarter tetrahedron comes into it, and above it, an equal increment there is a vertex of a one-eighth octahedron, which is superimposed can you get me out of the picture, I'd like every bit that we can get of the picture that we are looking at there. There is, then, a tetrahedron, and it encloses with the same common base, a one-eighth octahedron and enclosed within it is a one-quarter tetrahedron. Now a one-eighth octahedron has a volume of 2, remember, an octahedron has a volume of four so one eighth turns out to be 2. And the one quarter tetrahedron, then, has a volume of where the one-eighth octahedron is two, and the tetrahedron, itself, in this case, I'm going to make it a volume of 4 where the volume of the tetrahedron is 4, the one-eighth octahedron will have a volume of 2, it has the same base as the big tetrahedron, but half the altitude, and the one-quarter tetrahedron has one quarter the altitude and the same base, so it is if the big tetrahedron is 4, the small tetrahedron is 2, and the bottom one is 1. That is, the volume of the one-eighth octahedron turns out to be exactly twice the volume of the one-quarter tetrahedron. One-eighth octahedron is twice that of one quarter tetrahedron.
Next picture please. We're going to have some very interesting things showing up here. Now I've got four black one-quarter tetrahedra coming out of the big tetrahedron.
Next picture. Now, there is a regular one-quarter tetrahedron. And as you know the regular equilateral triangle has three perpendicular bisectors. I'm taking a plane perpendicular to the base plane, three three such planes and chopping, they come down to the perpendicular bisectors, and they cut the one-quarter tetrahedron into six parts. Remember, if I stepped tetrahedron up to having a volume of 4, for convenience, and we made, then, the one-eighth octahedron a volume of 2, and we made the one-quarter tetrahedron a volume of one. I'll now chop these all up into units, so that each one will be one-sixth of one. For a moment I'm going to multiply everything now. So each one of these blacks would be 1/24th of a tetrahedron. There were four faces, and they break into six parts it is 1/24th of a tetrahedron. And I call that unity. Then the tetrahedron has 24 and all the other numbers multiply the same way.
Next picture. That 1/24th of a tetrahedron is a very interesting thing, because you can make it out of one triangle. I have the dimensions over there. It is not a right triangle, but it is a triangle and so you can fold it up out of one triangle. When you fold a tetrahedron out of one triangle into a tetrahedron then it has, for instance, you can take an equilateral triangle, bisect its edges, interconnect, and you get four triangles and then you fold on those truncated corners and you get (a tetrahedron). So when you do, energies that would bounce around inside of a triangle then keep bouncing around inside the tetrahedron. So, this is an asymmetrical tetrahedron that is folded out of all one triangle. And therefore it is an energy inhibitor. It will hold energy bouncing around on the side of it.
Next picture please. Now, move my head out. You'll see the one-quarter tetrahedron and there are on its sides there, excuse me, we have not done this here properly, so that I'm going to ask you to go back, if you will remember where I had that black skeleton where I had the tetrahedron, and under the eighth octahedron and under it the quarter tetrahedron and there were a whole lot of little lines there. I not only took this vertical plane of cleavage of the perpendicular bisectors of the quarter tetrahedron, but also of the one-eighth octahedron, so it too broke into six parts. But because the one-eighth octahedron had the volume of 2 and the one-quarter tetrahedron had the volume of 1. When I took one away from the other, one is under the other, then what the difference the space between the one-quarter tetrahedron and the one-eighth octahedron is also one. Because it's total volume is two and the thing enclosed is one, so the space between them is one. So then when I have these vertical planes cutting both the one superimposed on the other, the perpendicular bisectors of the base triangle, each one breaks into six, and the six ones on the
Next picture, I'm going to have, the top ones will be gray and the bottom ones are going to be black. That's what you're seeing there on the lower left-hand side, are the gray ones that lay on top of the black ones. And they will fold in on top of it, and
Next picture. There they are the greasy are on top of the blacks. Can you see them there in the lower left hand corner? And each one the gray is exactly the same volume as the black one. In other words the space between the one-quarter tetrahedron and the one-eighth octahedron was equal to one total volume being two which was the volume of the one-eighth octahedron. So, I find then, that the, if I'm going to call then the black 1/24th, I'm going to also then, and let them be unity, so that would make the tetrahedron, it will have to be 24, and then we find that each gray there and each black have a volume of l. So what you're looking at is a set of 6 sitting on top of 6. The volume of 12 involved in what you're looking at there. These are very asymmetrical. These are what I have here laying on the table. There is 1/6th of a quarter tetrahedron. I call that an "A". And here is a sixth of the 1/8th octahedron sitting on it, and it's a "B". They are obviously very different shapes. And we call this the "A Quanta Module" and the "B Quanta Module" because remember then that octahedron and tetrahedron do fill all space. And when we break them up, both "A" we get something common to both tetrahedron and octahedron, you suddenly can make all the geometries. The "A Quanta" and "B Quanta" these two alone complement one other to make all the geometries. So they've got to be very, very, very important. This is one of the most important of all the discoveries I ever made.
I'd like to just pass that to you, and hand it around so that you can get a little feeling of it.
And now the next picture, there you'll see two one-quarter tetrahedra fractionated which equals one one-eight octahedron.
Next picture. Now I am making a large, you're doubling the size of a one-eighth octahedron. On the lower right hand side you'll see a one-eighth octahedron, and I have put three of those on the corners of the thing on the left. I'm doubling the size of the one-eighth octahedron. And you'll see then there is that one-eighth octahedron in each corner, and then there is one sitting on top of it there. You can see six one-eighth octahedra there. But you remove those three top ones,
Next picture, and you'll find that you have what was inside there was a tetrahedron. Now, this is now a new, this is the one-eighth no this is a one-quarter tetrahedron doubled in size, and in order to make it you'd have to take, you have three regular one-quarter tetrahedra on the corners, and then inside them, you start piling you remember, now, the blacks are the A's, so there is A, A, and then the B. A,A,B. But I found that that space, in which they are. Notice, you've got a three-pointed star here haven't you? Of greenness. So I'm going to be able to take those A's and B's out of that space and rearrange them so they don't look like that at all, but they'll still fill the same space. In other words, they are reorientable within the same space.
Next picture. Now, there are the same ones, but their narrow ends are in and they were not that way at all before. To find, then, they are all radiant from the center, do you notice. Can you go back one picture? This one where they are radiant from the mid-edge inwardly. They are butt-end, they are putting their energies inwardly.
Next picture. Now they are radiant from the center out. They radiate energy out. The same phenomena, same A and B, rearrangeable in space. Brings about completely different energy conditions. This began to really get me. And you realize if you took the center of gravity of each of those A's and B's, the center of gravity's are deployed in this picture, in the first one they are conserved. I don't know whether you've ever seen X-ray diffraction where you hit metals and so forth, and you really can see these displacements take place like that.
Now I'm going to talk some more about these A's and B's. They are very, very fascinating. I found then, what I was putting together was this group right here, and they can be put together two ways. Here's an A and an A. But the B has been put here. In this hand I've got an A and an A base to base and the B is out here. An A and an A you can put them that way, but the point is, when you then turn them like this you find that they are, this is an isosceles here, the isosceles in a number of different directions. This is an isosceles triangle. So they are rotatable. They are a right angle, a right angle, a right angle. Three sets of right angles in the inside here, which allows changing the right angles around because that is an octahedronal center. You realize how rotatable that is. And they're all these isosceles forms, so that they can really be changed around.
Now, the next thing about those A's and B's. You can go on and make all, and I have, I've made all of the geometries there are. But when I handed those to you, if you'll look at them carefully you'll see that there is also, a little line, a curved line in there as they come together here would you come take this one and pass it around? This then, this point is the center of the spheres in closest packing, and these are spheres in closest packing. You'll see how much of the what some of them, part of them, occur in the space, and part of them are inside the spheres. And so, as they keep coming together, they continually put spheres together. Now, the next thing I discovered which was really I told you then, this fills all space, the rhombic dodecahedron, and it's face, it's mid-face is at the point of tangency between the adjacent spheres in closest packing. And then I found this extraordinary thing. I can make this into an octahedron. Because of all those different 90 degrees. I can rotate this piece around an incredible number of ways, and this thing fits down into the rhombic dodecahedron here, so this is what I call the "coupler," between any two spheres. It is also all space filling just as the rhombic dodecahedron is. You'll see the two spheres kissing one another in here. So it's volume consists now of each one of those is 1/24th of a tetrahedron, and there are obviously 3,6,12 and 12 there are 24 of them which is the same as one tetrahedron, isn't it? There are twenty four of them, so it's back to our friend unity like the tetrahedron. And, I call this the coupler. And I find then what it does, now you're going to see a series of pictures where, you can rotate, you can make these in different colors the A's and the B's, to see what you're getting. But the numbers of rotations in place within the coupler, seem to be very close to the same number as the periodic table of the atoms it looks like it's 92 rearrangements within it.
Next picture please. I'm just going to show these to you fast so that you can have a little feeling. Oh, there you are looking at the octahedron one half of the octahedron is broken up into the A's and B's, the top part.
Next picture. At the upper right hand then, is an A and the white is a B. The only difference between these is another unit of altitude with the same base. As long as you have the same base, and increase one unit of altitude, then each is always the same fraction. So the orange, then, is one unit more of altitude, and the black is the top of the tetrahedron. Then it goes another one, and another one, always the same increments, therefore the volumes are always the same. They get thinner and thinner and thinner. We find then, energies that are putting on a conductor like this, really tend to keep going the waves going outwardly , and out, getting flatter and flatter, getting more and more parallel to the conductor itself, and then trying to precess off of it. This is one of the problems with conductors.
I want you to understand, how a wave, because this can act as an energy input, each one of those a wave going on a conductor system. You don't have to get very much altitude then, and they seem to be absolutely parallel.
Next picture please. I'm just showing A's and B's a little closer here. Next picture. And there we are seeing, I put together, I handed to you just a minute ago, three of them. And, this is the negative A B. Because one is a positive and one is a negative which way I do it. You can fill all space with the negative one. These are very extraordinary tetra, because you remember a regular tetrahedron can't fill all space, but this one can fill all space. Or the positive can, or they can do it together. And I call this there are two ways of putting the six together positive and negative. They can go this really long way, and they I call these the SYTE the little one is a MYTE, and these are the SYTES. And you can see them in the two different arrangements. And, they fill all space. So here, if we're using a Quanta as unity where tetrahedron now must be 24, and octahedron is 4 x 24, that's 72 and so forth, we then find, that these have a basic unit of 6 6 quanta. This is very interesting to have six quanta, because we found there were 6 quanta when we spoke about the basic putting the proton and the neutron coming together around the two models and we got the "sixness" the basic six quanta. There are six quanta in there, and they will fill all space, both positive and negative, so that they do all the tricks you can possibly do.
Next picture please. These pictures just go on making sytes and mytes.
Next picture, please. This was part of the rhombic dodecahedron. I found I could open it and fold it, putting tapes to the edges, and they would all fold together again.
Next picture. There's the coupler. Next picture.
Now, that's the way you could make either a positive or a negative. You must start with two A's and then either a B on the right side or B on the left side.
Next picture. And I'll identify then where the rhombic dodecahedron is, you can see on each vertex of the vector equilibrium, and then where the coupler occurs. Now there is going to be a series of these.
Next picture. where you see your spheres at the center.
Next picture. Next picture. Not very sharp.
Next picture. These are beginning to show you some of the strange combinations that begin to occur with your reds and blues. At some places they are conducting, at sometimes they are not conducting. Sometimes they are fortifying, sometimes they are subtracting, and so forth.
Next picture. Next picture. I'm going to just keep right on with you, just a little flick because there is a whole series of them.
Next picture. I made a series of all the possible combinations. These are all in the Synergetics book.
Next picture. And there is an analysis of each one, how the energy values are, and what it does in the way of shunting, blocking, conducting or not conducting.
Next picture. Just keep it on please. I would like to go through this series quite rapidly, you can just do it at will. The quicker you do it the more rhythm you get out of it.
Now, I'm just going, quickly that's the end of the A's and B's.
But into some studies of the complexes of the octahedron and tetrahedron, which I made.
Next picture. If you look at the complex of a big vector equilibrium made of octahedra and tetrahedra this is a two frequency. You'll find that there are very different aspects of them. You are going to see five different aspects.
Next picture. You see through it in quite different ways.
Next picture. Next picture. Keep right on. Next.
Now, keep on, next picture please. This is getting into when I began to find the great strength you get in such trusses. This is in North Carolina State back in the early 50's. And we found that they make very, very powerful structures. And,
Next picture. Then we began to get into fascinating mathematics. If you'll remove my head from the picture. These are octahedra and tetrahedra in complex trusses made out of single sheets of paper, strips of paper that you find that you can triangulate it and they simply come together.
Next picture. Next picture. And this one is done with a single set of wires and so you make it with bed springs and so forth. The wires can coil and let you make them.
Next picture. Next picture again. These are out of Linus Pauling's book. Next picture. You can see the chemists paying great attention to these things.
Next picture. Next picture. Now we are coming back to joints of the octahedron-tetrahedron trusses. Since the rhombic dodeca occurs, we found where the twelve radii come together, these are then the perpendiculars to where all those lines come in. This then, becomes a very natural joint for, so you'll find a number of studies of that going on here.
Next picture. There is a this thing comes apart in one, two, three, four in these four parts and you, may I have the picture back please, and you can see it open like that where the faces, then, and the perpendiculars coming in.
Next picture. And here is one with crevices, and you can find that all of these things can be brought together.
Next picture. It was along these lines that I made the truss, this is in the beginning of my studies for what became the Ford Motor Company's Dome.
Next picture. Where we made our struts out of sheet aluminum, just angled, and found that the angles could overlap. Around the vector equilibrium's twelve vertexes, there is a turbining. I've showed you where balls can get to two layers begin to turbine, so literally these surfaces turbine around one on top of the other. So it was possible to have them overlap and just turbine on one another.
Next picture (From the technician "That's the last picture).Very good.
In the coupler that I in the asymmetrical octahedron, and being an octahedron has really very interesting properties of octahedron. The mathematical properties. You are used to the x, y, z coordinates and to the fact that if you get into cartography and so forth, you would find that the latitude/longitude grids anything that happens in one octant of the x,y,z coordinates tells all the mathematical stories things upside down, reverse and so forth they go positive and negative, but all the number relationships are all covered by your octant. I find this of great importance because I would like to really know why that is. Can I give any kind of a mathematical, geometrical proof of why that would be so. And I find it really quite interesting, because you and I know, then, the tetrahedron is then the minimum system dividing Universe into insideness and outsideness, the minimum structural system, and it is then, has it's four sides so that there really are only total systems really only requires four facets to tell the whole story. And I am going to then look at an octahedron where we'll have, this is a solid sheet , and then find that this is a solid sheet here, and this is a solid sheet here, and this is a solid sheet here, so you can make the octahedron with four triangles with single-bonded instead of in the tetrahedron the four triangles are edge bonded doubled bonded, and here, this is single bonding. And, yet, they really cover the whole story. So it goes plus, minus, plus, minus, and that's exactly the way the we get into our trigonometry now our trigonometric tables. This being a plus, and a minus, a plus and a minus. We're going around any one point, the main, the clock you get going around the point there is plus, minus, plus, minus this is your straight trigonometric basis for doing everything.
Now, I found it very interesting to get into that, because then the this octant, I was able to when I was trying to find out how many different relationships exist in there, this did come into play in a very big way. Now, the next thing I would like to talk about in that relationship is something I have come to in numbers. When we do our spherical trigonometry, I'm going to talk about spherical trig with you a little more. I mentioned it quite a lot the other night, and I pointed out that when we were brought to trigonometry we were bothered by the idea that signs and cosines, the trigonometric functions, were fractions, and that the fractions were seemingly different phenomena of edges and then angles, but I've shown you then if you start with wholeness, if you start with Universe and System, then there are the central angles and the surface angles, and one of the things that I discovered that I found was fascinating as I did those great circles, that I showed you, as I went from the four great circles, the angles in there when I spun it where you went where a line went altitude of a triangle and altitude of a square and altitude of a triangle it only went through two sets of vertices when I spun it where the altitude of the triangle was 54°44', and the altitude of the square was 70 degrees and 32 minutes, and the triangle 54°44' again. We'll just look at those. Looking at the vector equilibrium, when I spun it on these six, there are twelve vertices so there are six axes, this is the one that went altitude of a square, and then altitude of a triangle, and then altitude of a triangle. Now, in doing that, we have, I said this altitude here is 70 degrees 32 minutes which is an interesting number because I am also familiar with the dihedral angle of the tetrahedron. And this is 54°44'. and this is 54°44' again. Altitude of the triangle. Those numbers are interesting as I think about 60 as being the normal angle. So let me take 60 in relation to 54°44', and that's 6 and 5-4=1, and 9-4=5, and there we are 5 degrees and 16 minutes. Two times 5 degrees and l6 minutes should be 10 degrees and 32 minutes, so it is very interesting, 60 plus l0 degrees and 32 minutes is 70°32'. So if I use 5 degrees and 16 minutes, as a basic increment this one is saying minus one, minus one, plus two or it goes plus two, minus one, minus one... plus two, minus one, minus one as it goes around. That I found very typical, and when we went then, from this first phase of the vector equilibrium to where I made the, we got this set the six great circles which we did get from this when I did that, you'll find it dividing the surface of the there is also the oh yes the three great circles, which are those of the cube, and the three great circles of the cube come about from the three square faces and they do this. They never get into the triangles, they only get into the squares.
This begins to make a set of triangles you see these triangles in here. These are the central angles of those, if we do have two tetrahedra inside of a cube giving it shape, and the central angles, those are the angles in here. And those angles, interestingly enough, from the 60 degrees it was outside in the vector equilibrium and a central here 54°44' and 70°32', I find that the next one, what were the inside angles become the outside angles, and the outside angles become the inside angles. As if it were a succession of the great circling, the thing turning itself inside out. So surface angles become central angles, and central angles become surface angles. So I found a hierarchy of this kind of intertransformation going on.
Now, I'm going to seemingly switch a little bit with you here now, and go into "number", because I have been talking to you about the geometry we're using numbers, but I became also, I've paid a lot of attention in my life to things that often are not too well thought of we'll say astrology, I haven't done as much with astrology because I but I would reckon there is something that makes astrology highly creditable, and so many people get into it. Somebody taking women's menstruation the very word monthly, the word month comes from moon that is in discovering the tides of our earth, and the absolute connection of the tides of the earth, and the moon, and the month and I'm quite there are tides in women, and this is a perfectly clear demonstration of their being astronomical effects on human beings on planet. That seems to me to be implicit. Therefore, I would say I think the people who have done astrology have gotten into too much of the myths that go along with constellations and what constellations are supposed to do in the integrated azimuth what twins do, and I don't think that is very valid particularly as I began to find that these stars are enormous distances, one behind the other one even in the same constellation, but from where you and I happen to sit, we've got that appearance. So we're taking a black board effect, where there was not really such a cartoon in the sky. So I felt that there were too many stories came in there to make me have time to really fathom it out I would like to get to be a great astronomer, and I would like to know much more about this, and I would like to be able to use the planetarium to advance things and but also take the real distances of two stars and so forth, and see what would be the ones that were really having some force at that time. I think something like that could be done, but the point is, the big thing is, I tend to I will not dismiss something that my intuition has given me any clue that this has good reason to exist. So much superstitions, and so forth, obviously walking under ladders is a pretty stupid thing, because people are always working on ladders, that's why there's a ladder there, and you're liable to get something on your head, and I think that's a fairly good probability one but, I pay attention to all the little superstitions I've been told about, on the basis of someday I might learn something.
And one thing that really impressed me a whole lot when I was young was numerology. I don't know how many of you have ever played games with numerology, but there are where you take the letters of the alphabet and give them their numbers. And you discover some very interesting combinations of things that happen. And, I was interested enough in numerology to really begin to try things out in a mathematical manner. And I'm going to tell you something about that tonight.
First place, we have human beings counting in 10's, which is the logical way you see he has five fingers and five fingers counting on your hands. There are, however, other people who have counted in twelves. And twelve is a very convenient way to count, because when you count on your hands the decimal doesn't even include the number three, and there are going to be a lot of triangles in the world, and anytime that three comes in the number is not going to come out evenly for calculation purpose. But people who liked the twelve had a very good reason to have it in there. But the twelve itself, didn't include the "five", so it may be that when you got to some other kind of module it would be better. And then there are, if you think about the single integers, you have the 1,2,3,4,5,6,7,8,9,10 and if you did even get into the that's the 60 degrees this is where it is comfortable that prime number 1, prime number 2, and prime number 5, and then prime number 3. Multiply 1 times 2, is 2, times 5 is 10, times 3 is 30. So, if you were if you get to the number 30 and 60 you are going to be able to accommodate the first four primes. But it does not accommodate the prime number 7, so when we get into trigonometry, we're using the 60 degrees and 60 minutes and so forth, every time the prime number 7 shows up any division will not come out even. It just automatically throws waves of error into systems. I saw that it was very interesting that, it was Plato, tried multiplying the 7 quite clearly because it's in his notes, but he never talked about it, 7 x for instance 360 degrees. Gives you, would somebody do that, I think it's 5040, isn't it? Or 2520? Does it come out 2520? So 2520 is an interesting number because it could be 5 0 4 0 so but Plato has, you can see where he wrote about 2520, which made it clear that he was possibly trying to bring in a prime number 7 accommodation in trigonometry. Those kinds of thoughts, also appealed to me when I was trying to find I've been looking for Nature's own comprehensive coordinate system that was what I was after if I could possibly find it. And therefore it certainly was going to involve number.
So I've had to pay quite a lot of attention to number. Then I saw that the, I'm going to give you something really quite interesting, we'll do a little counting here. Now, in the game of numerology, where you give what they do is to take numbers, you are given a number for a name, and you add your integers, and if you get to more than 10, you go instead of 11 it is a 2, and you simply integrate the integers. And if you did that, for instance, in the way we count numbers here. This would be a 1 and 1+1 would make 2, and I'm going to use another color. So this would be a 2 and this would be a 3 and this would be a 2 and this is a 3 and this is a 4. 3, 1 and 3 is 4. This is a 5. 5, 6-6,7 7,8, this would be 8 and 9, and this would be 1 and 8, would be a 9. And this is 2 + 8 10, this would be a 1. And 1, 9-10, is a 1; and 2 + 9 is 11 this would be a 2. And this would be 2 + 3, no, no that's that. Yes, this is a 2 and this is a 3. So we've got, it is, things are not coming out it's gaining all the time, so I tried doing the counting in 11's, and I'd tried counting in 9's, and tried counting in 8's. But I found that just let me try the 9 now.
So this one is a 1, and this one is a 1 and this is a 1, 9, 10, this is a 1, so 1, 1,1, 2,2,2, 3,3,3, 4,4,4, 5,5,5, 6,6,6, 7,7,7, 8,8,8, 9,9,9. This was nice because they are neither gaining nor losing. If I tried it in 8's, I find it loses 1. And if I tried it in 7's it loses 2. If I tried it in 6's it loses 3. If I tried it in 5's it loses 4. 1 obviously gives you a +1, 2 gives you a +2, and 3 gives you a +3, and four will give me a +4, but 5 gave me a -4, and 6 gave me a -3, and 7 gave me a -2, and 8 gave me a -1. And then there is the 9 gave you a 0. This is interesting. There seemed to be, I saw a positive and negative 4 that is going on here it's effect. But the 9 had a 0 effect. Now the 9 have a 0 effect is something well known.
One of my first jobs in business before W.W.I, I had an accounting job after becoming a mechanic, and in this accounting job accounting job for a big packing house, Armour and Company, and they had on the meat markets of New York, the wholesale markets and enormous amounts of food were being shipped, then to New York. So the accounting, keeping track of cutting up food and so forth was a very powerful job for the branch houses. And the auditors came around quite frequently, and the auditors taught me a trick of their's which they called "casting out 9's". What they would do was to cast out the 9's in the input and the answer, and they could tell very quickly if you had made an error. Now the fact that human beings, and this has apparently been known for a very long time, and the more I thought about it the more fascinated I became, because, quite clearly the name "nine" in our English and Latin-none-and in German nine these all mean no, no, no, "0". In other words it must have been known for a very long time, because I also said to you the names for the numbers are amongst, in etymology, amongst the old names nobody knows what they stand for. But suddenly that you find that the "nine" is associated with the noneness, it must have been known a long while ago. And again, I'm always suspicious around my number world, and my geometrical world, because of the realization, that the navigators, did then, hold the great secrets, and the King respected them fantastically, he didn't know where they got all their So the Priest was always being able to give the Emperor or King something very tricky, and he absolutely guarded his mathematical capability. I don't think there is any question about this, and it keeps showing up.
At any rate, this then began telling me that Nature had a way of counting here which was really pretty interesting where you might have, I really do have a "0" level. This is zero. And then she had her plus 1, and plus 2, and plus 3, and the plus 4. And then she drops straight down to the minus one, minus two, minus three, minus four. So she seems to have a system going here of 1,2,3,4 then she drops right down to -4, -3, -2, -1, 0, this being the zero, and she seems to then this one would go on like that, and go on like that. But there is a connection like this. There seems to be a wave phenomena, and this could even double back on itself, make a bow tie out of it. It could look like this. That's what it looks like, and that is part of a great wave system, where you simply have these bow ties. I think she's using then, I think Nature is very definitely using this. This is number itself. And give me the positive 4 and the minus 4 that again sounds very familiar along with the tetrahedron's faces and with just the octant accounting and so forth. That's all there is. These are all the faces, and all the characters there are. And I'm quite sure that this number must relate very much, then, to the way what are all the variables of the system. And there are only four positive and four negative every time. I find it very, very exciting that's why I say this octant had then a great appeal to me when I came to realize the coupler was an octahedron. That it had, really all the variables were in it completely.
Now, in relation to what I have been saying to you and talking about prime numbers, I'm going to give Meddy, I checked, look at that, somewhere in the back here, Meddy, is a sheet of paper that I'm not allowed to look at right now. Here it is (Meddy says, "do you want me to write it on the board?) Bucky again Oooom, here it is. This one. The bluey. Now you keep it to yourself. I began to find some very extraordinary things going on in numbers as I began to explore more and more. You can sit down and keep it to yourself. And saying, I was interested in accommodating if we're dealing in octants, then, just mathematically, I don't know how much you've looked at trigonometric tables and so forth the sines and cosines but the complementary of the sine is the cosine, and the two together have to keep adding up to 90. So, in, let's get to a quadrant with it's right angle like that. It's an isosceles triangle where it is 90 degrees. Now this is 45 and this is 45. Now any other triangle where it is 90 degrees, but say it's a 60-30-90. So 30 and 60 and here 90 and so forth. They are complementaries. But, I say, you can look at one column or the other column for the sine or cosine, because these things can exchange. So, the largest number you can get to on the small side is 45. From there on, this is the biggest one, and you can always find out in terms of the small number and the tables are right there so it's simply a matter of whether you want to use the positive or the whether you go with the cosine or sine and so forth.
Now, this made it very interesting. I said then, if I want to really accommodate all of Nature's transformings, I really have to have all of the prime numbers up to the number 45, or else the calculations will come out badly. I need to have a comprehensive dividend that will accommodate all those prime numbers, and I probably better have quite a few of those prime numbers because a 2 will show up quite a lot, so I have such a number and Meddy has it there. And I call it a Scheherazade Number because, I'll explain that to you in just a little bit. Or maybe it would be fun to see what a Scheherazade is first.
I want you to take the prime numbers that are not included, if we are going up to, I've got a positive octave, and a negative octave in an octahedron I've got to have both the positive and the negative. The positive side has a 4, 4, and then the other side. The so I'd like all the prime numbers up to 16. Or possibly all the prime numbers, maybe up to 18. But, let's say up to 16 which takes two octaves. So then there's been a prime number 7 that's been left out, and 11 7, 11, and 13 anybody tells you those are very bad numbers. They are crap numbers, and numbers to be avoided. 13 is an absolutely awful number. So, I want to see, if we take these numbers which the myth makers of the great priesthood made VERY, VERY BAD numbers. I want you to multiply 7 by 11. Very nice, 77 x 13 21, 3 and 7, 21, 23, 77, 1001 very interesting number 1001. Now you know why I talk the Scheherazade. Scheherazade remember, had the 1001 Arabian Nights tales, she kept telling them stories, in that great Arabia, where the Arabic numerals are the big story. And, I say, let's try to multiply 1001, by 1001. We get 1001 and we get a zero, and another 0 and then we get 1001 again.
That makes a very interesting kind of a number 1 002 001 it's almost like a binomial A square, plus 2AB plus B square. There's a 2 in the middle 1 002 001. It is a beautiful symmetry. Lovely number isn't it?
So let's try multiply 1001 again. So we get l 002 001 x 1001 and we get 1 002 001, then you move over one place, two, place; so it goes 1 002 001, so we get 1 003 003 001, always coming out mirror! every time a mirror, and this is the most extraordinary thing, because it suddenly introduces symmetry into number. No wonder they call that 1001 they didn't want anybody to know about those lovely numbers, and it makes some very very extraordinary things.
So I find that, for instance if you want to just take 1 x 2 x 3 x 5 = 30, then let's just get the second power of 30 so that would be 900. So I'd like to take the second power of the first four primes times the second power of the next three and you'll find that multiplying the 900 times this number, and you'll find that it comes out again, a beautiful symmetry number. Now, I'm getting a whole lot of prime numbers in here, and it is highly rememberable what I call sublimely rememberable numbers. They are so symmetrical that you can't help but remember them and they actually build up to a center, and down the lovely hill! So I found a whole series as I went on into very large, numbers. Because I thought, maybe I have to have more 17's and so forth, and I began to get into all the prime numbers up to 45, and I have this rememberable number, and I have to prove it, because Meddy has it over there. And it reads, I'll say it to you back and forth, 3,128,581,583,194,999,609,732,086,426,156, I'm not going to have room for it all 130,368,000,000 and read what that number is Meddy. You know that multiplication is simply a dot between the two numbers, right. Not a decimal. So this is 1 to the nth power and 2 to the 12th power it is 3 to the 8th power 5 to the 6th power times 7 to the sixth power times 11 to the 6th power times 13 to the 6th power times 17 to the second power times 19 x 23 x 29 x 31 x 37 x 41 x 43. So it has a very large number of the first 1,2,3,4,5,6,7, the first 8 are highly accommodating and so forth, so that I am quite confident this number used as if we use this number for the circle, or even just if we would make it four times this number and make it for just one quadrant. One of the interesting things, this number is a very big number, I want you to take how many places there are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43 it would be 3 x 10 to the forty second power. It's a big number. This number is so big, it is interesting that Eddington at one time, no it was Sir James, James came out with this number as possibly the most adequate number in Universe.
If you'll take the using the diameter of the nucleus of the atom as length, and that is a very I can't remember what it is in relation to the diameter of the electron I'm talking about the nucleus versus the electron. But it's about, something like I think it's10,000 times to the electron, so it's a very small number. If I then, express the distance with the large radius of our observation, astronomically so far, which is 11.5 billion light years, and put that into miles, and then keep getting that down, I express, then, this largest measurement in the terms of diameter of the nucleus of the atom this number I can take it down to ten thousands of that size. It is that big. I just want you to realize what an extraordinarily accommodating number it is. And, we find then, as we get into the electron microscopes, we finally are getting into knowing something about when the first picture they ever took of atoms per se, where you could see them not one atom, but atoms, they had the pin-needle point, a tungsten needle point, and you could see it's shape alright. But it consisted of 'oranges' stacked up they were little spheres, and they would take it out and they would polish it, they would just rub it, and they would put it back again, and they just kept doing it, but it was always whole oranges. You could not, you can not fractionate one of the little spheres within closest packing. Nature always does it in whole numbers. She plays the game in whole numbers. And that's why your chemistry comes out that way.
So I felt you had to really find a comprehensive quotient that would permit everything to come out absolutely whole numbers, and this number is big enough to do that really. So I find it very exciting.
I'm giving you more and more evidence the way I try to look at things, where I must deal sum totally in my accountings and looking for the coordination of nature herself, and what are the tools we'd have to employ. And all of these things are in SYNERGETICS, and in very great depth, because there are 900 pages in SYNERGETICS so the kinds of things I've been talking about, we really get at, and we get at, and get at. And I'm hoping that we may be able to get some advanced copies for all of you so that you can really keep on, because I hope you'll like what we're talking about enough to want to go on and make models, and possibly, I would like, possibly, to improve our picture here, because I think we do really have a very important tool for our fellow man in this kind of a meeting that we're having, where I'm really checking with the young world. You have your experience and a lot of information. And, I'm quite confident that I'm not misleading you and that you're able to see how much that agrees with the experience you've had, and information you have, and find out whether this is reasonable. Because I really have been submitting to you a really different world from the way of accounting that human beings have been employing all the way through.
I find it very interesting again, going to Tobias Danzig's book on NUMBERS THE LANGUAGE OF SCIENCE , to note then the different languages and what they use for their, quite clearly, for their accounting system. And where they had a name for the number, they had a name for higher number than our 10. Where we have to say we say eleven and twelve though, that twelve thirteen is a 3 and 10 but twelve is a word by itself, so we could say the very word "zwoelf" these languages would have the name twelve, where people did include a three long ago. Thinking that would be better, so they got into dozens. You find the French getting up to sixteen, and they don't say and 7 until they get to dix-sept, seventeen.
So I find these are the cardinal numbers. Different languages have different magnitudes, and I thought very well of the French because 16 seems to be two octaves. Possibly a positive and negative octave. That seemed to me to be a very valid kind of a concept. But you can see that men were human beings were, way, way, back doing a lot of thinking, and these things are manifest in the world of the numbers which is a very revealing matter.
I'm now going to switch again. I want also to remind all of you that in making my plans for what I can see still has to be talked about, and I made a good inventory today having gone out 20 hours, I now can see exactly what I'm up against. I'm assuming that you're all going to be accumulating questions, and I thought on next Saturday would be the questions. I don't see any use in having questions until we really do submit so that you'll find many questions that you are prone to ask do get answered before you get to the question session. And so I think it would be better to have it the last day. So I'm assuming we're going to get quite a little time in next Saturday. We could do six hours. I will have something in reserve if we don't use that up, because I would like to be sure to get everything in and I don't think I can get everything in so I'm going to see what are the high priorities, and what is going to have to be left out. And Saturday we'll stuff those in if there is any time left over. So I'm not going to tend to answer questions people ask for questions, but.
I'm now going to switch over and open up about the chart I gave you. I'd like to get back more to the little human being. Really, so you can understand with me how I really happened to peel off it just was not noble, it was really just the only thing that could be done. I actually got to a moment where I was either going to do away with myself, or do something like this. And, I'd like to get into the strategies that I employ, for how the little individual can be effective. Certainly when the little individual tackles just in finding out about number these are very powerful tools, and you can understand that by looking at big patterns I get Synergetic effects that I would never be able to get if I went at things myopically. I saw our society with all it's specialization was just tending to exclude rather than to include, and the more I included the more chances I could see in the connections. Really, might really be that you could find something of very great power for man.
Now, I've given you this the grand strategies of great navies, the grand strategies of the old city state, and that is replaced by the line of supply and then this gets into the goes from the water into the air. Now the water had limits of continents, but the air had no limits. And so, that, we're in an era where the game of the power structures and of ignorance that it has to be you or me, are being played in a very big way, and they buy the capability to do that with their military mandate that it has to be you or me, therefore we've got to get the very best weapons and tools. And, so what are you and I as little individuals, going to be able to do that really will bring this to a halt. Obviously if you go out and stand in front of the railroad train, you don't stop the railroad train. Protesting means nothing to me. Activism, I'd simply say it is part of a political game of psychological warfare playing on one side by the other to upset the other guy's economy. But as far as it stopping anything, I don't think it stops anything.
I do think it is educational, and everything that goes on in Universe I figure is the way it ought to be, so I think that these things happen, and I credit everything that happens I'm glad that it happened that's the way it did. But I don't think it gets positive effects. It may stop negatives, but it doesn't make positives.
I was deeply impressed with Mahatma Gandhi's passive resistance, but while it could then really break down the enemies offensive side, it could not really "feed" and so forth. It didn't solve the problems of the poverty. So, this is why, I'm sure Nehru became very interested, I think I told you about meeting with Mr. Nehru. Did I tell you that? In 1958 I was speaking in New Delhi, and I spoke three times in the same day. First at the School of Architects, then to Engineers, and then I think artists was the third group in the evening. And to all three sessions, Mrs. Indira Gandhi.
And at the last session, I'd been introduced to her in the first of the morning session. I was tremendously impressed that she appeared three times that day and I gave her a little tensegrity structure to take home, and she said "Would it be possible for you to come on Saturday, to meet my father Mr. Nehru." I had been planning to go to see the Taj Majal on that day, and I said that I had been planning to go to the Taj, but I'll just not do that. And she said "Well, don't tell my father that you did that, because he doesn't like people to come to India and don't go see the Taj," and I said I'll see it another time so it makes up for the deficiency. At any rate, we did meet, and I minus well tell you a little bit about this, because I talked about the meeting with Einstein, and these people are very fascinating to meet.
Mr. Einstein had an extraordinary quality about him. I still don't know how much was psychological within me, but I really felt very much in a presence, in the aura of the man.
Mr. Nehru, came home from the Parliament to see me. I talked to Mrs. Ghandi all morning, I had my maps and we had them out on the floor of the parlor floor there. And then he finally came, and he came into the doorway and she introduced him to me. And he never came any further than the threshold of the main door of the parlor there. And she said, "Please explain your philosophy to my father," and so I said "I have a strategy which is other than political, and I know how extraordinarily well informed you are in the world of politics. " And I explained that I had a policy where, instead of trying to solve problems by political reforms or laws, any reform of man, I was interested in reforming the environment, because the environment itself is continually reforming itself, and I said there are options and I can participate in it, and if I can bring about a favorable environment by virtue of producing artifacts I must never use words, I must actually find a tool that solves the problem makes what is going on obsolete.
As for instance I gave you the other day a bridge over roaring gorge and the people need something on the other side instead of having to keep risking their lives crossing through the roaring gorge, they all spontaneously use a bridge and less people die, and they get what they need more readily.
So that, I said, "This is my strategy," and I felt that it was the objective side of the Nehru's coping with the negative the subjective side. And I talked to him possibly something like 20 minutes or something like that 20 or 25 minutes. I didn't have my watch out so I can't tell you, but it seemed to be kind of that magnitude. And he stood all that time, like this, facing absolutely straight ahead. Not looking at me. There was no way for me to get anything from his eyes. It was very strange to talk to a man standing like that. He was in his beautiful white kurta, and finally, I said, "I think I've said it all." So he just went out. And, I met him of course later on again, but I was told by other engineers and scientists that he had done that with them I've not heard of him doing it with other people. But apparently, when he really wanted to hear you, really cared, this was his discipline of his body. He was absolutely listening. He made it clear to me further that he hadn't missed one iota of one word that I said. He had absolutely straight, clear it was amazing. This man coming from the Parliament with all that going on all kinds of political messes of that kind of a life, to suddenly give himself like this, he really addressed himself to me.
In years, after this Mrs. Ghandi said, whenever you come to India, particularly New Delhi, where their house is, be sure to telephone right away and let us know you're here. And I have done so ever since. And there came a time, there was one meeting that we had with Nehru, at Lake Kashmir, a beautiful place in the Vale of Kashmir, and he had gone there to rest, and I had a number of things I had written with me. When I talked to him that day, I said you just have words, words, words, and you're hear to rest I'd better stop talking. And he said "I like your words." He was a man of very few words, but what he said, you really felt them. And when I was leaving he took me out, we were way out on a hillside in the car, and he took me into the house because Krishna Menon was coming to call and then he introduced me to him. But on the way out, I had these things with me, reprints of magazines and so forth, I said "I have with me a number of things that I have written, but I don't believe you have time to read them..." He said "I read every word of yours I can get a hold of." Now, I say, very few times did he speak to me, but when he did say something it was just like that.
There came a day when I came to New Delhi, and I called the Secretary of Mrs. Ghandi, and the secretary called back in just a couple of minutes and said would I please come right over, and I went over to their the Prime Minister's House, and they have a number of little ante-rooms, I find myself in different rooms as I come into those houses, and she came in very quickly and her eyes were in tears really, and she said "My father has just had a stroke." And, I was very moved that she wanted me to come, but it wasn't as if I really knew her well enough to, but on the other hand she really didn't have, I want you to think about how she had been brought up. Her father in prison most of the time, a political prisoner and some of the time she was in prison. And all of her education, he did all of her education from the prison. His book on World History, a very great work on World History, but it was the book he wrote from putting together letters he wrote to his daughter. She was brought up by him, by his extraordinary writing, and she had been Mahatma Ghandi's flower girl, but she had been in the world of politics all of her life, and she really didn't have anybody too close in there. She was married, had two sons, her husband died.
So, I said, trying to think of what'd you'd say to a lady who's father had just had a stroke a great man. I said, if your father were not to recover, or if he were even to die, would you try to carry on his political work. She said "Oh, No, I would not think of doing so. I really have no aptitude, I really couldn't be more familiar with that world. That's not my world. I'm at my best to be my father's companion, and to carry on in that kind of way, but as for taking any political initiative, I don't have it in me at all." This was a very important thing to hear from her, under those circumstances. I don't think the question had ever come up. Because later on when he did recover for a while, he did get back in Parliament then later on he did die. But when he did die, the Congress Party which he and the others had put together which was an extraordinary accomplishment, because England left them, and I gave you "divide and conquer" nothing could have been more divided than India so it was an extraordinary thing to get a party that would really hold together. And he had great genius there.
When he died his political opponents and other ambitious men there would like to take over, so they thought they could carry on fine, but they found they couldn't. Things became quite clear that the Congress Party was really going to break up completely, the only thing that could hold it together would be just the name, so they asked Indira if she would be willing pro tempore to be acting Prime Minister till they had the next election something to hold things together, so she said she was willing. When I heard that she had done that, I thought about what I'd heard her say under those extraordinary conditions, that I was possibly the only person in the world who knew that she wasn't going in there for any political ambition. She was going in absolutely for dedication to her father, and Mahatma Ghandi and their philosophy. So she went in as a housekeeper, and she has been in there that way ever since.
Every time I go to India I see her. She usually gives me, at least she likes having me around about an hour or so. And I sat with her as the Pakistani had their first air attack on India at that time. I've been at some very critical moments there. So she'd like to have me there, and she'd like me really to talk about other things.
And, now, I was asked to give the third Nehru memorial lecture, and I can't remember what year it was, now, certainly half a dozen years ago, and maybe eight years ago. And, I've had very interesting experiences in India.
Now, that came about, my talking about that because I was talking to you about my grand strategy and the idea about developing artifacts. I saw that there was nothing to stop the little individual from developing artifacts, and particularly if you are really going to see what some of the big problems are and one of the big problems was quite clearly I had become excited by my navy experience, and realizing that we were doing more with less and the more with less of the navy was what we called "high secret," this was the most highly classified information in the world. What you could do more with the same or more with less, when it came to contact, and I realized the more with less you could get where the little airplane, then was sinking big battle ships "It could be, I said that, "Malthus was really wrong. He didn't know that foods would be preserved." I spoke to you about that the other day. So I also, then saw, that on the there was the possibility of doing so much with so little that we might be able to take care of everybody. And the whole raison d'etre of politics themselves, war, weapons would actually be obsolete. This seemed to be something to really shoot for the little individual, because I saw that it was full of soft spots because nobody had ever really taken, what they call there is "weaponry" and I invented the word called "livingry" nobody is trying to see what would happen if we took care of "livingry," because they said there is never going to be enough to go around, so money just doesn't get spent that way it's just useless it only gets spent in this negative way.
Nobody has really said, "What do you need for human beings?" Nobody has ever spelled it out. So this, particularly came then, to the weights that I knew of buildings. I saw that man was using incredible amounts of material, and that there was no science in it it was beautiful skilled craftsmen, but the architect had designed the building in various shapes and he had to be fairly well informed, something about corbling and so forth, but he did not have to lay the bricks, the craftsmen made the thing work out there, following his shape. And he was doing shapes that a client says he wants this way. Very, very much. And, so I said, "It is a possibility, in the direction of "livingry" and particularly in the environment controlling, the shells and the equipment that goes in and takes care of our various chemical processes, and energy needs. There is possibility that this could be cut down quite far, and so you can understand then, by great luck, carrying out of the navy which had taught me so much there. First, before W.W.I, I had been also, I went to Harvard, and I was looking forward tremendously to going, and when it all happened, I got into a social nonsense of coming from an expensive preparatory school with very rich boys my family was not rich at all. My mother and I, my father was dead, was really just able to get me there just pay the tuition and rent and a very small allowance. And I found myself not being able to join clubs and things there but at any rate, for one reason or another a love affair that didn't go right, and this and that. I got myself quite unhappy, and I got perfectly good marks no trouble at all. But I was really feeling I was there for athletics and fellowship and things. I had not gone there, really, with the idea of getting education. Because I have already made it fairly clear to you my feelings about the mathematics for instance, while I was still in the preparatory school, and I was working those afternoons when I had to stay in I had really gotten through quite far into college and university mathematics. When I got to Harvard I didn't take mathematics at all, because I, by this time I had really caught onto a lot of patterns, and I was pretty sure that I could just read my own mathematics I didn't really have to go and, I assumed that I didn't take the things that I knew a lot about. I took the things that I didn't know about. So I took musical composition and things like that. At any rate, I took government. I really wasn't interested in, I had never been interested in government, but I took government because I thought it was a good idea but at any rate, in no time at all I found myself in pain, and I cut all my mid-year exams, so they had to expel me. It was just like a little bit of non-sense in here. I had been quarterback on my football team in my preparatory school, and the quarterback just before me became the Harvard quarterback, and the quarterback before him became the Harvard quarterback, so I had a good chance, I thought, of being the quarterback. And I busted my knee and everything went all to pieces on that, I didn't have that to go on. And many other things seemed to keep coming up. I certainly wasn't going to be taken into any clubs, and I certainly didn't want to be outdone by my friends, and my sister had been married the year that I went to Harvard, and she'd gone on her honeymoon. She had a beautiful Russian Wolfhound and she asked me to take care of it in Cambridge instead of a kennel, and I found I could do something wonderful. I could take my Russian Wolfhound and go to the theater where there was some very popular actress, and I could stay outside the theater door with my Russian Wolfhound, and she would always stop and I could get to talking with her, and we'd get somewhere. (the whole audience breaks out in giggles). So, I'd take Mitzi and I went to the stage door of "The Passing Show" in l9l2. And there was a very attractive girl who was called the premier dancer, and her name was Marilyn Miller. She was unknown at that time. And so, I used to take her out, and her hired mother and Mitzi, we'd go with the Russian Wolfhound and her hired mother so we'd have dinner. Not a very cozy affair, but at any rate. Her play had tried out in Boston and it was a success and they were going off to New York, so, this is where the Millers came along, so I simply went down to New York with them and I took my whole second half year's allowance, and I invited the whole chorus at Winter Garden out to dinner. And I didn't know what to do with these girls, I assure you, but at least I had them there, and I could at least say to my classmates, "I'm really outplaying you altogether here." One-upmanship. I say nothing could have been more childish and stupid in a sense, but I was really extraordinarily young and naive at that point in my life.
However, this then got me out and got me in learning to be a millwright. I was sent to Canada to work in the cotton mill with some Lancastershire Englishmen who were putting up the cotton mill machinery for a brand new factory cotton mill. And it was a fascinating experience. And I learned to put up one of each of the cotton mill machines myself, and I kept notebooks and so forth, and everybody said this boy has done so well, Harvard invited me to come back again, so I did go back. And I went through the same thing again, and got out, and went down, this time I worked for the packing house I told you about Armour and Company in New York. I worked in 28 branch houses of Armour and Company, where their markets opened at 3 in the morning and you worked to maybe 5 or 6 at night. It was a very long day. And, I had this experience of pre-morning New York at all the different you know, going way up in Westchester everywhere there were 28 different branch houses all over Jersey City. And I really got to knowing New York and what feeds it, so it was a very extraordinary experience.
And then W.W.I came along and I went off in the war, off to the Navy. Then when the war was over, by then I was regular United States Navy. But then our first child was born just the last year of the war. Just at the time of the armistice and she caught flu and then infantile paralysis and then spinal meningitis and we had a long battle till she died just before her fourth birthday. And, this was a very you can imagine how we felt about this. And, she had been all the more endearing she couldn't move around, her little mind and brain not damaged at all, but unable to move like other children. And she asked we found her demonstrating this extraordinary capability, because she couldn't get out to touch things with her own hands, as every other child wants to, she had to get her information about things through other human beings in the room. And there were we had two trained nurses, first one and then the other, and my wife, one of us would be on duty all the time, and very often two of us were in the room together. And this little child was so sensitive to us that we'd be about to say something to each other that would be to do with our grown up things, not really to do with this little child, and just as you had the words all formed on your lips and she'd say it. And we'd look with astonishment. And I began to really realize that all human beings have something in them, that once and a while you say the only way I can explain that is telepathy. We all have those experiences. But we've also learned to shun things you can't explain, and that's not scientifically accredited, so it's not well looked upon. But I felt, that quite clearly nature has what we can call "fail safe" alternate circuits, all kinds of alternate capabilities so when this thing doesn't work so we all have this telepathic, but don't usually use it very much. But this little child had nothing else to get her information so it was highly developed.
At any rate, this made me accredit telepathy as being something probably in due course to be known exactly as ultra-high frequency electromagnetics. But for the moment it is inexplicable it is said. At any rate my feelings about this little child were incredible. My wife was the oldest of ten children. Her mother died the same year our child died, and one of her brothers was killed. It was a very sad year. She then stayed at home with them looking after, and I went on with an activity I had started in the building world. And both in New York where she was, but mostly I was away, and I had a big operation in Chicago and Boston and Washington and other places.
At any rate, we were five years of this and then, suddenly, our second child was born in 1927, and we had been entrusted with a new life. It was a very extraordinary moment. During those interim years, I drank a lot. I worked fantastically hard on what I was doing, but I lived a very rough life, and I got to know Al Capone, just through stopping at his I had a factory in Joliet, Illinois and I used to go out there everyday from Chicago, and he had a big bar on the way in from Joliet. So I used to stop there. But I did I've had some very extraordinary experiences in my life, and when this new child was born, all this sort of negative, I'd really been trying to bury hurt and feelings and I'd gotten really where I'd gotten, I had quite a lot of people who loved me, and really a lot of rich young friends who wanted to back me when I went into the building world in 1920 when I came out of the I had to resign from the navy because of the imminent death of my first child, and went back in Armour and Company, and at Armour and Company I became Assistant Export Manager for Armour and Company. And that was a very beautiful big pattern experience.
And, incidentally, in the navy I had had this big pattern experience where I had become after a quick short course at the Naval Academy, I became Aide to Admiral Glease who was in command of the Cruise and Transport Full Operation I think I mentioned that 130 ships moving across the Atlantic, but the pattern handling big patterns was very, very important. I'll also connect that with you the fact that I was born very cross eyed. And I mentioned to you the other night about well not, nobody knew why the cross eyed. But they said, we mustn't fool around with eyes, they are very, very delicate. We have to wait till the child is 4 and then there's no chance that the muscle will be strong enough to straighten his eyes out. And so at a little after 4 I was taken to the eye doctor for the first time and they found I was very, very far sighted, and therefore I got my glasses. So I mentioned that to you the other day, that I had 2 almost second birth of seeing with a new set of seeing capability. It was such a high order compared to the first three which I also made clear to you the other day. That is a very, very big jump. And I'm sure that had a lot to do with my life.
At any rate, my father also died when I was very young. And I'm sure that had a lot to do with my life because I was brought up then by my mother and people who would give advise, and all these people saying "Never mind what you think, really listen this is the way the game goes, and everybody saying I'd got to learn to play the game, not to do my own thinking. So we have this moment when, after I, just at the time of the death of our little child I was still at Armour and Company and I, my father in-law had invented a very interesting method of building he was an architect, a very good architect, and I thought this ought to be nobody was producing it, and I felt strongly about doing so, so a lot of my friends backed me going into this building business. And then I did get up I did get five factories going in different parts of the Unites States in those years between 1922 and 1927 when the first child died and the second child was born, and I did get up 240 buildings. They were large residences, small and it might be a very large commercial garage or something relatively small buildings but 240 of them and all through the eastern United States. Nothing west of the Mississippi, but it gave me enormous experience in the building world, and I'd like to talk about that for a minute.
We are going a little late tonight, but I want to get in enough time, so I'm going to finish some of this particular thinking about why I did what I did, and how I organized myself.
In the building world, I found then, in the first place, the method of building we had was very attractive, and absolutely novel, and I might as well tell you what it was. It was a method of making first place I had to develop the manufacturing way to do it. We made fibrous blocks. And these fibrous blocks are used wood excelsior. You've seen packing excelsior. And we, I had an enormous rotating machine and shredder and so forth, and we covered it with a very evenly spreading on the fibers ever so like pulling spaghetti out of a pile or throwing hay up with a hay fork, wetting each of these pieces with what you call magnesium oxychloride cement. And this we'd get all of this just beautifully wetted on the surface, and then I blew them together and felted them together in a mold. And made a block form 16 inches long, 8 inches thick and 4 inches high, with two four-inch holes on eight inch centers. So that when you put a block to the other end the next hole would be eight inches away from the end hole of this block. So the holes, they were four inch holes quite large in an eight inch block. So there was about a two inch wall between the hole and the outer side.
These magnesium oxychloride treated fibers then firmed up and became very, very very rigid, and gradually, they literally petrified. But their very interesting behavior was that they were very light. They might they weighed somewhere between 2 1/2 and 3 pounds each. They were so light and strong like a felt had that you could throw them up to the scaffolding to be laid. And they were laid end to end, and then we had, using wires formed something like croquet wickets, a croquet wicket, but when you came to the foot it went out about 3/4 of an inch. And these croquet wickets were 16 inches this way and four inches across the top of the wicket. These croquet they would go down through the holes joining blocks, but you put them in upside down the other way transversely to the wall so we had four wires, two going longitudinally in the wall and two cross wise like that, and they were put in and then we mixed a very fine concrete with fine gravel and poured the column up to leaving one block open. We laid, we laid every time four courses, but you'd leave one course open so that we laid three courses and the wickets were four courses deep, and so they overlapped at the course below, so the wickets then we left the last top unpoured, then we put the three more blocks, and the wicket from above would lap down into the wicket from below before you poured so that at every the wickets overlapped each other four inches. I found that this was equivalent, the bond of it was equivalent to being continuous wire, so I had reinforcing both in the wall and longitudinally in the wall; and then we didn't, we didn't when we laid up the blocks you didn't put any cement in between them. They were just laid up dry, and then where we poured concrete, when we came to a window we had girth blocks and we poured a beam to cap the columns, and then we had beams above the windows and we had beams above the openings, and then every floor height is a continuous beam heading all the columns. This is another kind of pouring block. And we could lay these up so fast you would lay up a whole floor of a house in a day, and sometime a whole house in a day, and we put a the cement is wet, so we had wooden bracing and so forth so the wall would not move while it was setting up. Then when it was set up, we then plastered the inside and we stuccoed the outside, so that this fibrous block became a beautiful bond for stucco or plaster and the interior plaster and the exterior stucco were only united by completely flexible fibers so the expansion and contraction inside and outside were very different, so the wall didn't tend to crack, it tended to be a very beautiful wall, and we found that the blocks had they were equivalent to 4 inches of cork in their insulation value.
And you could put roll tops on it and all it could do, it would just char away, absolutely just a red top, as I said, gradually these blocks petrified. And I've been to some of the houses in recent years, and it's absolutely just pure stone fibers. So it was a beautiful fireproof, beautiful insulation, a wonderful bond for the plaster and so forth, and you could build very fast. And they were relatively low cost. And so my friends were excited by it, and they all thought they could make lots of money by backing me. And my father was always a prominent architect, and many architects, very great architects thought it was very beautiful. So it did get into a great many very special residences of very rich people, and they made very good houses.
But when I, then, when the architects say I'm going to use your material and the owner said he liked it fine, I would then have to go around to the architects office and show them how they designed their walls, and give them that kind of service. Then came the time when the house was all designed and the architect would then put the drawings out for bids to the contractors, and the contractors would see this, and say, I could lay this up in brick very easily and so forth, I never saw this thing before and I'm just going to lose money on it. And I know how to do this better. So, they didn't like it at all. I would have to go out to probably be five contractors be bidding I'd have to go out to their place and go to the estimators and go over what it would cost, and an extraordinary service you had to give there. And I had to practically promise the contractor I would go out and lay it up for him when the time came to be sure if he ever bid favorably, so sure enough, we got to where now we're going to build it. Alright, the contractor has given his bid.
Then came problems with insurance companies, so I had to go to them. Then came to problems there was no code that allowed it in that town so not a town in America that would allow it. I would have to, then, find a rather prominent client, an architect, and they would be able to get me somebody they knew in the town council, so they'd let me have a hearing in the town council. I'd have to appear there. And then they would say we will give you a special permit provided you have tests made at our particular University. So I'd have to make up a test wall and let that cure, and we'd test at the University, and sure enough it would have the strength we said it had, and so finally came to you're going to build.
And so they gave me an order for two or three truckloads of this. It wasn't really worth very much. By this time you had used up any possible profit you could make in an incredible overhead, so then I found that we got to the job and the carpenters said this was form work therefore it belongs to us. The masons said, obviously these are blocks, this is masonry. So if the masons put it up the carpenters went and pulled it down, and if the carpenters put it up the masons pulled it down. And the lathers said, "It's lathe." So they didn't like it. So there was nothing but jurisdictional disputes. This used up more money. Out of the 240 buildings that I was able to get up, I assure you that I just couldn't make money, and when it was all over, I had to have special insurance, and I had to have special the banks didn't like it for mortgages and things when it was all over I had to start all over again there was absolutely no momentum from the thing you'd done before. There was none.
I said, "This particular building world is just incredibly out of gear with the Universe, and everything man has learned to do technologically everything is backward, and everybody doubts it, and the only thing that is any good is "my grandfather built it that way, that's the way to build it." So that really tore me after the 240 buildings, just about the time that our second child was born. I had really made a mess of this, and the company sold out the operation to Celotex Company who liked the material and my method of manufacturing, because I was delivering by air and so forth, and you probably have seen in buildings.
Oh, incidentally, because it looked so inflammable, this white the oxychloride cement did not give the wood color it just looked kind of wood, it looked like it was just any bale of packing excelsior that was going to burn up like that. So I used a carbon black powder and it made it gray, made it look like concrete blocks. At any rate, the Celotex Company bought it, and there has never been anything that is quite so good as a sound absorbent. So there is a material called Soundex that you'll see many places, where you'll see those fibers matted that's the material I developed for that building. So I at least see my stuff around. And I sold out to Celotex, and I was really out and I was penniless, and my friends did not think well of me, the people at least who tried to make money a friend is a friend, so there were some friends left alright, but I was in anything but high repute as a businessman. And here was this new child.
So, I'll tell you and I had been doing all this drinking and everything like that and suddenly it was an entirely new kind of life. And, I really felt at that moment, that I had had really by good luck of getting out of Harvard, I had had an acceleration of experience. I really had much more experience than my contemporaries. I however felt that I had made such a mess of things that I didn't really like to try to make money anyway, I wanted to build a good wall. I liked to make a good material. I wasn't really interested in the money side. And I was having to play very much of a game there and I was not good at that.
So, I said, "I am just quite clearly a mess," and, I thought, then, that maybe my mother I say she was not well off she was well off for just a single woman, and I said my wife's family and my mother might be able to take better care of my wife and my daughter than I could. I just seemed to be a mess. I really felt tremendously "messy" I assure you. And, so I really contemplated very much suicide not contemplated, I started out to do so. And I got into the thoughts about "What is a human being, what are we?" If you're going to do away with this what are you doing away with? I said.
One of the things I would be doing away with would be a very great deal of experience. And I really learned an enormous amount with my experience, I assure you. And the fact that I didn't make money didn't mean that I hadn't learned my technology superbly. And I learned enormous pattern of how people get things done, and I had been through in getting those five factories going in five different cities and people putting up money, enormous amounts of legal work and patent work and so forth very familiar with those kinds of things, and I was very familiar with the business world's way of looking at things.
So, I said, "Well, each one of us is some kind of an inventory of experience, and I said "I do not really think that we own ourselves, that we are here by virtue of others, and I said "It could be that my experiences could be of value to man. So I said, "there is only one condition for you not getting rid of you, as far as you for you goes, you've got to get rid of you for you. You can only you are only entitled to stay alive if you really commit yourself and all your experiences to other human beings in a very really complete out and out way. I told you how much impressed I was with principles, so this idea of precessionally going off at 90 degrees did not seem to be illogical to me. In fact it seemed very logical. But it had never been tried, and so all my contemporaries were tied up with "have to earn a living" and I said I think this is just what we ought not to be doing. We ought to be saying "What do my experiences teach me needs to be done, which if not done will find world society in great trouble, and which if attended to will find them in advantage? And what will I need to know over and above what I now know that made me see that that is so, what more would I need to know to do something effective about it? I said, those are the kinds of question I think we ought to be doing. I then, also, then, came to asking myself a number of other questions. And I said, then, "The only condition of your staying is that you are committed to others, and that number one you have to do your own thinking. Everything that has happened to you really relates very much to your accepting other people's thinking, trying to play games that you didn't have your heart really in, so that this is going to be a very new kind of discipline. And you're going to have to be absolutely trustworthy that you really are committing yourself to other people. There's no cheating on this you're not just where you arrange not to kill yourself now, and then you're going to start cheating on this. You're going to have to have absolute conviction that you will be able to carry through for your full lifetime."
Well, I asked myself quite a number of things, and number one I said, "Alright you've experienced an enormous number of human beings who are deeply moved by their religions that they have been taught by their families, and they belong to very large great religions have great fervor." And I said, "Alright, I've got the number one question, you're going to have to ask yourself is, 'if you're going to do your own thinking, and this means giving up all belief.'" And I'd been taught to believe various things and I accepted them more or less whole-heartedly, I said "I'm going to have to give up all of those things. I'm going to have to start absolutely from experience. Experiential base." So I said "Do you have any personal experiences which give you reason to have to assume some greater intellect operating in Universe other then that of man?"
I said "I'm just overwhelmed by the evidence of that." These generalized principles themselves which can only be intellectually detected, and they are utterly intellectual. They are weightless, a generalized case is absolutely intellectual. And there is an integrity all these principles are all inter-accommodative so that I'm overwhelmed by an a priori greater intellect operative.
I'm going to talk more about this on Friday, but I just wanted that was one of the important questions right at the outset, so I said, "Then I'm going to assume, in doing my own thinking, I'm going to try to understand I am, really whether a Great Intellect thinks it is worthwhile for me to carry on. And what would be the requirements of a comprehensive integrity of our Universe. Whether it is looking out for all humanity, or looking out for Universe, why do we have these generalized principles? What is Universe itself trying to do? I said, I'm going to have to learn to ask myself some very big questions. I'm going to have to answer them myself from experience.
Now, certainly, one little human being going to see what absolutely penniless, dependent wife and child and trying to commit himself in such a big program as that, and everybody saying you've got to earn money I assure you that my family and my wife's family and all of our friends just thought I was being really very treacherous to do such a thing. And it was not easy to carry on there was nobody to tell you what to do, nobody to mark your paper. you had to really set out you've got a commitment of how to solve problems by artifacts and what are the first artifacts that have to be done. Luckily there had been that navy experience, there had been the "doing more with less" of the sea there had been the "doing even more with less" of the sky. And then getting into this building world where everybody was doing everything just absolutely opposite, the heavier and bigger, heavier and higher the more secure.
And that's the way the people were thinking. I saw incredible ignorance that was dominant in that world. Therefore the artifacts that would have to be produced, would be how do you then give man such high performance. And I have particularly said, "I'm going to surround and commit myself primarily to the young life, to the new born where there are no conditioned reflexes trying to arrange the environment controls so it would make it possible for that young life to be well protected, but be able to get all the information it really needs to be able to carry on in a very logical way to employ it's brain so to coordinate the feeling of its senses information with its senses. So, you can begin to see how the grand strategy began to shape up. Certainly I said I've heard people always trying to talk to other people and persuade them to do this and that. I must never from now on, I have so little time, if I ask people to listen to me they're not going to listen, and your life will be gone. You must not talk to anybody unless they ask you to talk to them that's a very prime principle; and you must not talk about your artifact that you think will work until you literally have designed it, actually made it, tested it and find out whether it works. Then if people say, "What is that", then I have the obligation to tell them what it is, and then if people ask me I must give them my best, I must not have just a short moment.
We are now really coming to time to stop tonight, and I will have to say some more about this grand strategy in that moment, but I don't want to have to come back to that moment very much more. But, I want you to understand why it really was enough to be a real turnaround. It had to be an absolute turn around.
I've often said about friends of mine that I'm very, very fond of, that have been brought up with money and wealth, and really charming human beings and very loving and lovable. And yet drinking and wasting and so forth, and I often said, if they could get in enough trouble to really hit bottom, then they might really get somewhere. But it is pretty difficult to get in enough trouble just to do that, or not just to stay in trouble or so forth.
Anyway I represented that the world was in a state evolutionary where certain things had to be done, and there would be a Mr. X or a Mr. Y to come along in certain moments to do certain things like that. I simply happened to fit into a Mr. X position, an average healthy human being, and nothing else he did not want genius, except that we are all genius. But somebody that could some how or other be so committed that we would, then, be able to recapture the sensitivities we had. So, I apparently, just about qualified through getting into enough mess to be, to be, to be Mr. X. But for all times there, you have to keep being testing, and at my age, I assure you, I continually have to keep at myself about the disciplines to be sure it is really, really out for everybody and not getting to the moment where you say it's sort of fun, because there are a lot of friends, people around who say I like you, or I this must not have anything to do with it. And absolutely I'm thinking you can really feel with me being with me these few days how much I really do feel then the outgo and the commitment to you. And I do not enjoy I really do feel quite badly when I'm being introduced, and being made "Mr. Big." And I have to deflate that as rapidly as I can on the platform, because that is not the way I feel.
I was deeply impressed, just reading my history, where time and again such people as the Julius Caesar's and so forth beautiful Shakespeare's Julius Caesar and so forth. The individual who really built some great roads, and did make some very important advances for humanity in the counting systems in one way or another. Then suddenly, going "Mr. Big" I am something special and therefore I'm emperor and I'm something of God, I am something different. I said, you know enough of those things, so you'll not go in if you do what you're doing, it's going to probably open up some very great treasures. But those don't belong to you. I've done I've conducted then a great many kinds of projects, as you will see, and I've done things to protect them as operations, but not as possessions.
I would end this patent business, because this comes up from time to time and I'd like to get it out of the way. I've taken a great, great many patents. I've taken them because here I was demonstrating what a little individual could do that great corporations couldn't do and great states couldn't do but with great states and great corporations throwing their influence around very, very powerfully. As for instance, when I developed the geodesic domes and I had very extraordinary patents the same patent attorney I told you, who got for me the patent on the projection, because the statement had been that it was pure invention. The same man, then, took out the geodesic patents he wrote very good claims. Patents are only as good as the claims written by a patent attorney.
And when the geodesic domes came into great need for the radar programs and many other of the government uses, but particularly the radar programs where they were going to spend hundreds of millions of dollars on it, they found that I had already made a structure. They tried everything else out and nothing else would work, and the President of MIT there was a physicist in charge of the project of the getting ready the microwaves and the radar system for the early warning system the DEW line, the Defense Early Warning system. And Weissner, then, asked me to produce one of my domes, and I did, and he put it around one of his radars. And if he hadn't done that we just wouldn't have gotten anywhere, but at any rate, they hadn't found anything else that did work, and when Weissner bought my geodesic dome polyester fiberglass dome, and put it up around his radar up on the Lincoln Project roof, the MIT structural engineers, then, calculated according to the most favorable analysis for, it's called Chemcheko, for spherical structures. And they found that this structure would disintegrate in a fourteen mile an hour wind, so they advised the physicist that he had made a very great mistake in acquiring this dome. And luckily, Hurricane Carol came along that year 1953, and they had wind gusts up to 120 miles an hour, and it was just getting on fine. So the physicist called up the engineers and said, you'd better look out there, and see that it is not coming apart in these very high winds. So the engineers said they obviously didn't understand this, so they needed to know more about it, so they moved that particular dome to the top of Mount Washington where they have the highest winds in the United States. And no structure has ever stayed on top of Mount Washington until they put that dome up, and it stayed there for two years. The Air Force has a platform up there, and they put structures on it with a stopwatch to see how many minutes before it blows away. It was just regularly.
And so, suddenly, the domes were in and all the big corporations wanted to be in, so the Air Force has said, I had agreed that I didn't have any money, no capital to produce the domes, so I would license any reputable corporation. So they said, you've behaved so well we'll protect your patents too. So on all the drawings that went out from the Air Force they always had, then, to get the patent license from me.
We had, really, the largest corporations in America all wanting to get into this program so that my patent attorney would have the patent attorney of a great corporation coming to see him in New York. And my patent attorney told me that out of the over a hundred patent attorneys for major corporations came to see him to talk about licenses, that at lunch time or sometime during the day long meeting, they'd say, you know, "the first thing my client had me do was to try to get around your patent. The only reason I've come to you is because your claims are so well written, we had to take your license. This is simply to say to you, if I had not taken out patents you would never have heard of me, because I only got to be known through the geodesic dome. And I simply knew I would be absolutely steam rollered. I was working out of this was a big corporation any kid who wanted to get a license, I just gave him a license, but the corporation really had to pay royalty. All of those royalties got spent in more research and so forth. But, I do want you to know why I've taken out patents. And I tell other kids, please don't spend your money because it is very, very expensive. I've spent over $300,000 in patents to try to protect these things. I felt this is part of the responsibility of the job I am doing, and not a matter of possessions.
So, we've come to the end of today. Thank you.