Okay, this is Colin Power from in2infinity. And this lesson is all this broadcast is all about the bounce point. Oh, yes. Bouncing numbers over the one, like cracking an egg. Yeah, into a frying pan so you can see what’s going on inside. Yeah. But you got to do it gently so you don’t break the oak. That’s the that’s the key to finding the bounce point. What we’re going to be talking about is the bounce point of numbers. This is a new concept, or fourth dimensional mathematics that allows us to find the real values of numbers, as opposed to the algebra the algebraic numbers, which into infinity, once we move into the infinity of fourth dimensional mathematics, fail to create any mathematical result whatsoever. So in order to overcome that we need to learn how to crack the egg as it were. Now, when I say bounce point, what I really mean is actually every number has a kind of reciprocal value. And some of those reciprocal values in a sense, play play a special role. When when when interfacing with their real with their with the whole partner. So the classic example, that we’re going to look at first is the square root of two. And the square root of two is what they call a poly nominal equation, isn’t it? They call it in an irrational, an irrational number. We don’t we get into infinity in the infinity of fourth dimensional mathematics. Actually the square root two is very, very rational. So to call it irrational is a little bit of a funny terminology. What it is it’s a in our world, it’s it’s a geometric constant. So geometric constants appear irrational because of base systems. That’s all it is. They’re actually quite rational. Once you untangled the base system function and work to base infinity, and then it becomes very, very rational, in fact, so but the square of two generally you can see it, what it looks like is a diagonal across the square of one. So it’s actually what we could say a ratio function of infinite density really, and in our case the square root two is the is the expansion function, if you like, of the squaring function that actually creates what we can call the compression of number spaces are kind of mean between the compressions. But we can talk more about that the function of square root of two and things later, but let’s first just use it as an example because it the reason it does this thing to numerical space is because of its reciprocal partner, which if you if you minus one of the square root of two, you get square root two minus one and if you plus the one to the square to get the square root two plus one, and the square root two minus one, and the square root of plus root two plus one are actually what we call reciprocal partners. So in other words, we can find out that actually, if we go one over the square root of two minus one, he actually equals the square root of two plus plus one. Got it? Does that make any sense? Let’s have a look at it on the number line instead. Maybe it make more sense. So let’s say we had a number line and got zero here. We got one. Yeah, I’m in between the space of one we’ve also got a space here too. And so actually in the space between zero and one, there’s a reciprocal value of the square root of two is called the square root of 9.5. So what’s going to happen is, is that if we’re going to add one to the square root, we’re going to take the on the other side of the square root to the same place. Yeah. And if we’re going to take the number one, and then so you can just imagine we’re going to take that number and we’re going to minus one off of it. Yep. And what’s going to happen is that the value is going to reduce, and it’s going to get, it’s actually smaller than the square root of naught point five is one minus naught point 4411 foot 124 and four, so normally 414. So what happens then is that we’ve actually, we’ve gone under the square root function. But actually now on the other side, if we were to plus the number one on to the square root of two, we find that these two reset the reciprocal and its whole room perfect balance. And one of the reasons that is is something to do with these, what we call the square, the reciprocal number law, whereby if you want to take a reciprocal number, and you want to find the whole version, you need to take the find the whole version, and you need to square it in order to divide. Yeah, that’s right in order and then you multiply that by the reciprocal. And so there’s a squaring function in other words, you can because the square root of two falls across the diagonal of the square. The reciprocal number law law that actually produces moves numbers from reciprocal space to hold space, as found in equilibrium with the number one. So that’s, that’s what we call a bounce point. You know, that’s a bounce point for the number two. The square of two would be the number one, and it creates something we call the silver mean. And the silver mean is related to the octagon, so you can check out some of that stuff. If we move up the scale a little bit, we’ve got another one called the square root of five, which has got a sort of plus or minus one we normally say is plus or minus a half. Normally actually what we do is we divide the square root five into two and then we plus or minus we plus or minus one, two square and five, and then we divided by two, so once again to the square root of two there, so you can see what’s happening. We’re moving up through the means. And as we are we’re moving through. There’s there’s one for the square root of three. And the bounce point for that is something we call universal scaling. And we often use universal scaling as a replacement for a i The number I partly because in a fourth dimensional sense, what it kind of represents is the the distance of the diagonal vector. In a four dimensional hypercube. That’s all Yeah, so there’s that kind of thing. But anyway, we can sometimes sort of look at these sort of things as sort of splitting the number over the number one in such a way that when we do we just find a perfect balance of, of Recipro pools and that’s when we’ll we want to we want the things are balanced perfectly. So that actually, you know, we can get this dysfunction happening. Now, what is happening then with the number pi, yeah, and the bounce point of pi. Actually pi does have also a bounce point. And here’s what’s quite interesting about the bounce point of pi is that it actually is the reciprocal of pi itself. So in other words, where we had plus or minus, plus or minus one, yeah, for the square root of two. What happens is we get plus or minus pi, or one over pi, should we say and so what happens is we start to have this, this thing where we can where we can now devolve pi through through by cracking over the one if you like. And when we do, we find that we get the four pi constants, we’re able to devolve four pi constants and these are types of infinite number. But they do have the they do hold a number of significance. There is like an infinite number. And the two pairs of infinite numbers are exactly the same, but one is assigned to 01 starts with one. The other ones start other pair starts with two and goes to three. So they are so so that basically those are the PI coordinate numbers we do we do a quad bounce on PI, in order to understand that it is that’s what the major difference is between the and the square root of two and all the other things is that it’s not a single bounce. It’s a it’s a bounce of pi itself. This way, the infinity of pi meets itself. But that’s why the bounce point of fire is really interesting, because obviously it’s the point of unification between number one and pi is pi itself. And so what we look at then is that is pi transcendent well you can’t if you’re looking from the perspective of old mathematics that also calls the square to irrational and all of that stuff. But when you move into fourth dimensional mathematics, you’re just looking at what what happens with the bounce points. So in that case, we can identify with a bounce point is and we do that through the signatures the week write the Infinity signatures, which we’ll talk about some point shortly. And by looking at and comparing those signatures on a grid, that is actually proportional normally a grid of nine now simply because we want to absorb the square root function of three we can do that with 993 squared isn’t not three square root three squared, and square again, you get the 90. And so the square root of three is used in the cubic dimension for the cube and was the square root two collapses into two dimensions. So that means we can collapse by you know, putting on a root of nine we really can collapse like the cube into us into into a flat plane. And that allows us to make a lot gives us a kind of backdrop if you like of number space, and then we just drop the degeneration wave of fire as it bounces and the bounce point will cross at a certain point from the from the reciprocal over and it’s not the number one. What it is it’s the is the PI constant. And the PI constant is one above itself. So we flipped everything around now so that actually now we’ve got the PI constant plus or minus one. And what’s more is that we can take that pi constant and we can break it over the one again, and we get another blank constant. This is plus or minus, again, plus or minus two this time to plus or minus. Yep. So you can see what’s happening. We can carry on bouncing by on to infinity, so that creates the five numbers. But after but after the thing, the second bounce at the moment, it appears that phi loses its resonance with that stuff. So so what we have what we have here then is basically a way of now calculating something else which is if it’s if we have four numbers for example, we can understand how much something is moving away from the one centre point Yeah, because each one will come closer to the one on a curvature. And so we can measure that curvature. And by understanding that curvature, we can understand the offset of the of the PI function, which actually maintains the density of infinite number space as it rotates through 90 degree axis. So So that’s the kind of where we are with the fourth dimensional mathematics on bounce numbers and bounce points. You can see we’ve included the documentation for and the you know the Excel sheet, which shows you the bounce point for five Pi it’s very simple. And and that kind of proves that PI has a bounce point and we can find them for pretty much any number as well. So every number does have a bounce point. And when we bounce it through that point. What tends to happen is that we get what’s called the real number. And it doesn’t matter what happens you can try and change the you can try and change the number. No algebra will have any effect you put pi in there to always equal the same number. So that’s why we call them the real numbers. Because they’re like rock solid, you can’t do it. You can’t make algebra have any effect on them whatsoever, but you can perform calculations with them. So and they do produce mathematical results. So so basically by going down to this these will be called through the dimensional levels. What we’re looking at is a new new system of number that actually can appear by cracking open numbers using the number one as a kind of opening device and appear inside those numbers and create a sequence of number which although looks chaotic, actually does have a pattern because it can be reversed as well. So we can reverse it to digit right the way back to the original number. So because it can be reversed it means you can move up and down the number line like would plus an ad. And then what we can do is we can run different types of calculations by plotting and adding on different number lines and then combining those totals to produce new numbers and the new kind of mathematical as we call it, fourth dimension. And it does not work upon the foundations of algebra, Algebra does not work. So we have to work with bump bounce points. And that’s one of the key technologies for fourth dimensional mathematics. And as we discover more and more of the bounce points we’ll be able to map them more and more with more detailed computer technology. Because it’s such a new discovery that we’re just pioneering right now, we have only mapped the major constants and the whole numbers. But we’ve we can be pretty sure that every single kind of fraction will also produce an infinite bounce point which means we have an infinity of infinities. And indices. Now we’ve extended the number of availability to include extra and infinite numbers. So that’s all good news on the on the nature of infinity as we open up number space and peer into its murky depths to see what secrets it can reveal. That’s all for us this week. Join us again soon and we’ll have more on bounce points and the nature of number infinities coming away shortly. This is calling power from into infinity. Thank you for listening