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?