EIK - Session 2 Part 6
Now, I'm going to say, take the tetrahedra and fasten each one to another tetrahedron, but with two of them touching a hinge between them. You find each one of these tetrahedra in here are touching another tetrahedron at two points. They are edge to edge with one another. Here's a tetrahedron in here, and it's edge to edge with this tetrahedron here. When you do that, when they are edge to edge, then it makes a fills all space this way, and seems to be very stable. This is exactly like the liquids. The liquids are non-compressible. They already are in the form of the closest packing, so they can't be compressed any further. But because they are hinged together, the hinges transmit loads, so liquids transmits any load, at any point, as in pneumatics, distributed to all of the tensile system.
Then we get to trivalent, then for the first time there is no hinging, no universal joint. They are absolutely rigid. They no longer distribute loads. Now these are the fundamental qualities the crystalline is absolutely rigid, does not distribute loads. The liquids distribute loads. And the gases distribute loads. But the gases are compressible and the liquids are not. This brings about a very important way to think.
But, I've got you now thinking about a tree as a set of tetrahedra coming out of tetrahedra, as basic structures. But also then you'll find that what makes a tree able to do what trees can do if you've ever tried to pick up any great weight let's say a 30 or 40 pound suitcase and you're trying to hold it out horizontally, and you'll just find that you can't do it. And yet you'll find a tree holding out a branch, and some of these branches if you weigh them, weigh up to as much as 5 tons. And to be able to hold out as much as five tons horizontally in a great wind, and yield to the wind and not break off it's a fantastic structural capability. Man has never done anything like it before. Well, it's done by a very simple way, because Nature then has in the crystalline you have a triple bond, and therefore you have the greatest tension. The liquid has two bonds, they are a little more viscous more tensile strength than the gases which have only one bond they come apart. So that the greatest tensile strength is accomplished by the crystalline. Therefore Nature ships in a seed the instructions for further crystal production, and what produces the crystals is really local waters and atmospheres and local chemistries. So these crystals grow, and the crystals then act as sacks for liquid, and so the tree is just filled with the liquid. And I gave you yesterday the tree also having to have roots so that it could not blow away when exposing all that leafage to take on the sun energy impoundment through photosynthesis. So that we have osmosis and the water goes only one way valving, pulling from the roots into the tree to fill all these sacks. So the tree is using the crystalline entirely in tension to enclose the liquids, and the liquids then completely distribute the loads throughout the tree. They valve it out in the sky just bit by bit to turn it into more rain to come back on more trees, so more of this process can go on elsewhere. But the water is entrapped in there, and therefore it will distribute its loads locally. So there is then, this absolutely non-compressibility of the liquids in distributing loads that makes that tree able to do this extraordinary task.
If we get an ice storm, off comes the branch. It can no longer it become crystalline, and it cannot distribute its load. Man has not built any buildings in that way. They have used entirely that crystalline continuity concept of compression on compression, so our building is incredibly inefficient. And so, I am now trying to understand a little about what goes on in tensegrity structures, and I will come then to the analogy with hydraulics and pneumatics of load distributing. Because we do have continuous tension and discontinuous compression.
I want you to think about what goes on inside a sphere when you blow it up. Let's say a basketball a balloon. You keep introducing more air. There are then, molecules of the gases, and you're getting them crowded in there. Now, all these gases are full of fundamental kinetics, and they are continually doing like this. With every action having its reaction and its resultant. So, every little molecule of gas that is going somewhere in there is doing it by shoving off from another molecule going the other way. Think about two swimmers. You've probably done swimming in a tank alright, and you dive and you get to the other end and you double up your knees and shove off from the wall, and you come out again. But two swimmers can meet in the middle of the tank, and shove off of each others feet. They double up and off they go, using the other one's inertia. This would be typical of the way that molecules are behaving in pneumatic structures.
Now, we find that the molecules, then, are not simply going they don't go to the center of the sphere and then explode outwardly. This would be a pulsative affair take time for them to get in and the thing would be vibrating like that. They're not doing that. They are ricocheting around inside. So each one is starting to go this way, another one goes that way, and the two hit the wall. And they can't go any further. They push the wall outwardly, and then they bounce, ricochet off, and hit the wall again, so they are acting like little chords inside the sphere.
Now, also, to introduce another principle, which is dealing in great circles and spheres, and the word GEODESIC. Geodesic means the most economical relationship between events between any two events. The great circles on spheres are geodesics. There is a shorter distance between any two points on a sphere on the great circle than there is on any of the lesser circles. A great circle is defined as a line formed on the sphere by a plane going through cutting through the center of the sphere. The equator is just such. Each of the planes of longitude go through the center of the sphere so those are great circles.
I want you to we have then on here also lesser circles. We have the latitudes. They are not great circles. We come up here to 80 degrees North Latitude. I'm going to take my dividers and open from the pole to the 80 degree North Latitude, and I strike this little circle. I've got my dividers fixed at that opening, and I go down to the equator, and put it on here, and I strike this same circle. So we have then the equator running like this, and the circle superimposed on it. Where the little circle, lesser circle, crosses the big circle at "a" and "b," and you'll find it a much shorter distance between "a" and "b" on than equator that it is going all the detour of 90 degrees and then coming back this way. I just want you to visualize quickly how great circles are the most economical between points on a sphere, and the chords of great circles are even more economical.
So, we find that the molecules bouncing around inside the sphere, will not go around in latitudes, or lesser circles. They just automatically have to get into bouncing in great circles. That becomes very exciting to discover. So, they're not just going around in layers. If they were going around in layers like this, this whole thing would flatten down really easily that way, and it has all this omni-directional stability due to the fact it is using the great circles.
Now, I get one great circle around here, and we find that every great circle crosses every other great circle at two points, so that this great circle of longitude crosses then the other longitudes at the North and South Pole always 180 degrees apart.
So I've got a great circle here, and another great circle there. Then I get suddenly a third great circle, the equator, and that makes a triangle. North Pole, equator, equator. Now we've found that two is unstable, and something I didn't say to you yesterday about the necklace and the triangle, that I would like to introduce right now, because it is very, very relevant to the understanding about that triangle.
I said, why and how did that necklace, consisting of three compression members, rigid and three flexible tension corners, how and why did it stabilize this pattern? I find that any two of them coming together are fastened one to the other like two knives of a pair of scissors, with a common fulcrum a lever. And the further you go out on the lever arm the more effective those shears are. Therefore, if we want to have a bolt cutter, you go way out on very long arms of good, strong steel. We find that each side of a triangle, compression member, is taking hold of the ends of two levers, and with minimum effort because it's on the ends of the lever, stabilizing the opposite angle. It gets really very exciting again to see how beautiful is this least effort that is being demonstrated by that necklace triangle.