EIK - Session 2 Part 9
We'll learn a little later on that this is very important this precessional association, the way things comes together rotatively like that. Now, I'm going to also then come back to something I did talk a little about yesterday. The six edges of the tetrahedron as acting the six represented one unit of quantum these six vectors. And, I made an experiment with my own personal body in relation to degrees of freedom. Being brought up in a good community, I went to a good school, and I learned considerable about physics and so forth chemistry. I was very intrigued by the concept of the interattractiveness of the masses and so forth. And I said (also as I got into Navigation in the Navy), if I'm looking at something like the Pleiades or Andromeda, it's approximately just one little point, but you learn that that's a whole constellation. You're looking at incredible numbers of stars. But they are so far away that they appear to be one star. And thinking, then, about mass interattraction and so forth, I said, if they are pulling me, I don't think each of those stars separately a million billion stars in there, are pulling on me separately. They really would be, they are so far away that parallax sets in and they really in effect are only one pull. We do have then in astronomy this phenomena of parallax, and it is continually operative, where things do pair together. So I said, "I wonder how many lines are pulling on me in the Universe." It's always pulling on our earth a little more so, but "I wonder how many are pulling on me, or how many are pulling on our earth?" Are each one of those stars there pulling separately, or do they group up possibly into pulls? And due to the fact that they are non-simultaneous, possibly the interpullings do integrate in some extraordinary kind of timing way of coming from different periods of time. So I said, let me think about I'm going to look at those stars and I look out and I see a hole in those stars, and some place where it looked like I might accelerate, I might go out and get away from all the stars, and I go further and further away from all the stars, and I find that it gets to where it all looks just like one. But there still would be mass interattraction, so I would be very much as if, like a ball on a string. We call it a tether ball. We have a mast and a string and a tennis ball on there, and you can hit it. And that ball can go all kinds of ways. But the one thing it can't do is get away from the Universe. So there is just one restraint on it. But you can find it can make all kinds of shapes spheres, all kind of it can describe anything there.
Now, I'm going to say, I don't think, experience suggests to me that we really will find a hole thru those stars till I finally get thru a billion times 100 billion stars that surround us, that we now know of already. If I were to take the numbers of atoms in this room surrounding me here, and in those pretty thick walls, I'd get into that kind of number. So that I probably wouldn't find any hole out in the stars. It's much more likely that I might be able to take all the stars in the heavens and divide it by looking there is the milky way and take two halves of all the stars, and sort of divide them into two teams so they pulled on me, kind of evenly.
So, I took my ball that had a string on it, and I put another string on it, and I fastened I got you to take a hold of one end and I take the other end. So the ball is in the middle. It's like a ball that's in the middle of a violin string. It can still move, but it can only move in a plane. It can make figures of 8 and clover leaves, etc., but only in a plane.
So, I said, I don't think I really can divide the stars up, even in that way. More probably I'll have to get more teams. I'm going to take three pulls on me. So I took a third string on this ball in the middle between you and I. I took a third string and pulled it, and you pulled it over there. And I now see that it can still move, but it is like a ball in the middle of a drum head. It can oscillate only in a line. That interested me. One restraint allowed me to have sphericity. Two restraints made me a plane. And three restrainings produces a line. So then I said, I'm going to pull the drum head one way. I put a fourth line on the ball and pulled it vertically, and it suddenly seems to be immobilized, as if I muted the drum by pulling the skin just one direction. But I made a model where I made a steel tetrahedron with four corners, and had four thin, steel rods come into a central ball at the center of gravity of the tetrahedron. And the steel ball, and I pulled those rods tight. They were very thin so the slenderness ratio, and I found that the ball, if I put a plumber's Stillson wrench on that ball I could rotate it in place. I could not move it away from any of the four corners, but locally it could rotate. In fact put it on several ways and it kept rotating, so it was locally rotatable. Why? Because you found that any two of these rods were coming into the surface of the sphere. They were not coming to the center of the sphere you couldn't get to the center of the sphere. You're bound, as long as there is any sphere there at all. There's one coming in here, and one in here like that, so it makes a trapezoid there was a distance between where they hit the sphere. And a trapezoid is unstable. It's a four-side figure. So I found that in order to stop it from doing any rotating like that locally, I had to take each of the four rods that came in and turn each one into three rods from four corners. And each one had to come in, the three came in tangentially, making in effect four tetrahedra coming in tangentially, and then, for the first time, it could not move. And so, sum totally, I found that 12 rods were necessary to completely, to eliminate all degrees of freedom.
I wanted to confirm that in another way so I then began to think about a bicycle, and a bicycle wheel. Bicycle wheels are fascinating because bicycle wheels manifest man getting into tensegrity in his structures. The old fashioned solid wooden wheel, just a number of plates boarded together like that for one thing. Then we got into what you called the artillery wheel, and they found you could put holes in the solid wheel instead of having just holes, you could deliberately have columns, a series of columns running between the outer rim and the hub. And the columns had to be, then, what you call a stout column, or a short column, so you would not get into the critical slenderness ratio or they would bend.
So each one of them is a pole, like pole vaulting, as you go over the bar, they give you another bar, and they keep going along on these columns. Then we came to the wire wheel, and the wire wheel is very different because the load is the wagon, and the wagon, then, goes out to it has its spindles here and the hubs. And you want to support them at the hub the wheel is there to do that. So in a wire wheel, you hang the load by a thin wire, which otherwise would bend with any compression on it. But you hang the load from the top of the wheel down to the hub. So, if there was just one spoke as the wheel went along, then suddenly the whole thing would crash.
We find then, if you want to have your bicycle wheel worthwhile light, you have an awfully lot of weight to pump as you pump your own bicycle, so you'd like to have the wheel weigh as little as possible. So you'd like to have the rim good and thin. And the rim is a mast, it is over a bent mast going round and coming back to itself, so that what I want to do is shorten up the unsupported length of the rim. So I'm going to have a hub and one tension down from the top to the hub, and then go 120 degrees on the wheel and have another spoke over here, and another here, so I've got three spokes now. They are just wire spokes to the hub. Well, I find they act like that drum head. They'll oscillate, the whole thing will oscillate in the wheel, and be completely unstable and unsteerable. So that won't do. I want to see what I can do if I had two skins on the drum head, and I put a spacer in between the two, then you muted it by putting a positive and a negative. So I could have six spokes now, and three come from one side of the rim into the hub, and three from the other side. So there are three emanating from the end of the hub. Instead of having them like this, have them turned like that. They then have shorter sections of unsupported rim to stabilize it.
But I found that didn't work, because as the six came into the hub, again they came in where, again, I've shown you this circle before. They came in forming a trapezoid. So there is a little section here where the hub could torque locally. I found that I had to take each of the six came in there, and break each one into two and have each one come in the pairs tangentially, one taking care of the rotation this way, and one taking care of the rotation that way.
Now it is perfectly possible to put of those six, that I could only take two of them and cross them to take care of this torque you say, but then you find if you do, that you unbalance the wheel has to have symmetry of structuring all the way thru, and if you have an oddity like just one pair across the top then you'll find that she's going to wobble like that. She'll have what you call, dynamic instability. So that it takes a minimum of twelve spokes for a wire wheel. It took a minimum of twelve restraints to immobilize me in Universe. So I find then, these seem to be the six positive and the six negative of the same of our old friend the tetrahedron. The tetrahedron, then, as we saw yesterday, can turn itself inside out, and so then this is the positive and negative side of the same tetrahedron.
I gave you yesterday the dimpling in, that the tetrahedron can turn itself inside out if it has rubber legs. I just move one vertex, just one vertex had to move and if the legs are rubbery it will do that. Then, we looked at the octahedron, and found that the octahedron simply one half of it nested back into the other half. And in the icosahedron there is a local dimpling.
As we get to the even larger numbers of a (could I have that sphere please) as we get to higher and higher frequency of triangular subdivision, going beyond the icosahedron, which this does, then you find, this gets to be what I call local dimpling, and the higher the frequency the more local the dimpling. So you begin to understand then, the tetrahedron turns itself completely inside out, and here we're going to have less and less effect as you get the positive and negative here of the dimpling.
Now, I want you to think in largest possible context of our Universe, and our Universe, which is continually transforming everywhere, but everywhere transforming at different rates; and I gave you the importing-exporting of energies, of the Boltzmann effect, where energy is given off by this beginning to form new, and they begin to be new local systems in Universe new stars and then they begin to gradually get to the point where instead of being, I use the word "syntropic" in contradistinction to the great second law of thermodynamics, "entropic", where they're giving off energies, they are a place where energy is being imported, and not only imported but sorted and being put into increasing order.