This is Colin Power talking about the solution to infinity. And today we’re going to be talking about looking into the centre of infinity to find out exactly what is there. Sometimes we’ve talked about calculating the end of an infinite number. And some of the mathematics on some of the end of infinity can be a little bit tricky until we get used to the nuances of base 10. And then we actually find some of it’s quite useful, the vortex codes and all of that stuff, the number seven, we start to sort of get into a sort new mathematic there at the end of the infinite. But it’s, that’s it can be a little bit messy sometimes as well, we come times have to kind of feel our way around that a little bit. But one thing that’s for sure, is that the centre of infinity, it gets a little bit cleaner. Yeah, that’s right. So, so So the first question really is, what do I mean by the centre of infinity? Well, I mean, let’s say if I have a point between zero and one, and I know that actually there’s an infinite number of fractions that can exist between zero and one, even a number of numbers, and all of the whole numbers they can all exist between zero and one. So it’s an infinite infinity of infinities as double density infinity, in fact, just in that one space, and so what am I really doing I’m I’ve got this like quite dense number space. And into that number space. I’m, I’m able to fit an infinite number of numbers. Yeah. And somewhere in the middle of infinity is going to be the midpoint of infinity. And if I look at the number line, I think I know where that is. It’s going to be the number nought point five. That’s going to be the midpoint of infinity. But then what happens is, if I have a cross and I go from one and I move up to two, suddenly the midpoint of infinity becomes the number one. And then suddenly, if I move up to number three, the midpoint becomes a 1.5. If I move up to the number four, the midpoint becomes two. Ah, because it was happening, it’s the LF nought point five perfect as we say, you know, as we’re moving further and further into infinity, so the midpoint is getting further and further away from us. And so actually, as soon as the end of infinity it’s moving further and further away from a stamp. So what we need to do is we need to zoom in to the naught point five point and just to sort of see what’s there and the closer we get to it, all you find is is that actually we get a very strange thing way is like we get this one squared, and it’s got a square root of it’s got a square root of one across it, sorry, you got a square of one you got square root two going across it and then naught point five and then you got the square root is like is half is a quarter of that square. Isn’t it naught point five squared equals naught point two, five is a quarter. So that’s where we started to get a little bit confused. Oh, was that quarter thing again, isn’t it? Yep, that’s the one year transformation of dimensional space. That one yes, that’s what is. So all we can say is actually we can say we’ve divided the square of one into into four, haven’t we and the four quadrants, and those four quadrants, each will be the square root of naught point five. So the square root of one must exist somewhere between the square root of two and the square in all point five. But it’s a bit of a weird number as to where exactly that exists. Yes, strange, isn’t it? It seems to exist. Actually equal one, but obviously, square root of one does not equal one. And, and we know that so the same as the square root of minus one doesn’t equal one. We look at those as dimensional functions. So so so now we’ll understand a little bit about the squaring function. And we talked about a bit of square roots and things like that. And the power of square roots and this entity there. And we find this we mentioned about squaring that and we find the same the same density expression. So the question we need to ask them if we started from let’s say, we start with a binary Yeah, a binary code. We’ve got 010. And what you could say is, in a way, you’ve just got the one in the space of number, which is the one in the middle and you got zero to zero, either end at the end of the zero at the beginning, zero at the end of the number line, if you like, and that one in the middle represents a complete set of numbers space, isn’t it an infinite set of numbers space? And if you add three bits, isn’t it? Yeah, if you think about it as a zero, it’s a one is zero and a line. And that gives us an eight variations and so that makes a small cube, isn’t it of eight Yeah, so very good. So three bits make a cube very good. So we need to do now is only to say okay, let’s look in two dimensional space. If I was to extend now that to let’s say from zero now we’ve gone from the smallest, which is binary, isn’t it? Yeah, we’ve got 123 which is from infinity minus 01. Yep. So infinity minus two. And then basically, we managed to create a kind of little tiny micro infinity which we’re working with. Now we can extend that and say, really extend the noun right away to infinity. And what we find is at the end, it has to be actually the one in the middle has to be an odd number, if you like the ones that say 1111111 All the way they have to be odd number and the Zero has to be an even number. Now first, you might say well, how do I know that? Yeah, well, one was we’re talking about the doubling function where Yep, so everything has to be half of something. So and since we found there’s actually the halfing is naught point five, isn’t it? Yeah. Which is not number. Yep. And so if you double or vibing at one is not number. Yeah. So you see what I’m saying? Odd. Odd. Yeah. But that is contained within something. Oh, yeah. Now think about this as I if I, if I divide a number infinitely, or I multiply a number infinitely, we’re going into different directions. Aren’t we? Yeah. One is going towards the zero, and one is going up to infinity. So as I divide, we’re going to get closer and closer and closer to zero. And as we multiply and we’re going to get further and further and infinity. And we can see that’s the case. That’s what’s actually happening as we as we move towards zero. That actually the knob that’s that’s the end of the of the square root or that of the halfing. Even if the feeling about dividing into two dividing into two dividing into two sorry, is the end of the halfing function. Yeah. And, and it just goes all the way down to there. And like we said, it’s not square root to the squaring function. So dividing, and in the squaring function, if begins reciprocals raise you’re in the squaring function, you’re going to go down towards zero as well. So you can you see whether I’m timesing or whether I’m dividing. It doesn’t really matter. What originally right here actually, when you wrap your head around it is whether the two numbers that we’re working with, are being in the same space or in opposite spaces, if they’re in are both in reciprocal space, we can square them and start to produce or multiply them together and they will produce smaller numbers. If one of them exists in the whole space at the number two for dividing into two the whole number, then it will just drift right away down to zero. So you’re going to go the other way around. So that’s how that kind of works. But still, it’s quite a curiosity. And it was that it was that phenomena that first drove me to understand the Avon finishes number line and develop fourth dimensional mathematics based on that concept, or that understanding to say so what we’re going to say then if zero isn’t, is an even number one is an odd number. And one needs to be encapsulated by zero like we saw with the binary code 010. We’re gonna say the infinity is an even number. And actually, it kind of makes sense, isn’t it? Zero and then we had naught point nine No, no, no, no, no, no. No, no, no, no, no, no, no, no, just before the one which is an odd number. Isn’t it as an odd number? Yeah, that’s right. And so technically speaking, there must be an even number. That means that one particular one must be an even version of one if you think of just a sort of mess with your mathematical brain there for a second. Maybe that’s why we never reach it. Anyway, that’s another story. But before we go, in more of a sense, what we can say is, infinity isn’t even number. And why that is important. If we if we think about even number and we divide it in we look at its centre point yeah, let’s say it’s gonna have a centre point. And whether it’s an even number or whether it’s not number will it will change the type of centre point that it has. I mean, are you going to have something which has a centre point which has an even number, ie Are you gonna have one with the centre point which is not number set? Yeah. And so it doesn’t actually matter which way round you do it but we we like to say that zeros the positive. And so what happens is that produces a particular type of square it’s produces a particular type of square. When we see this, what we can say is we can we can put a square and divide it into four for example, and then we’ll have a cross over that over the four. Yeah, we’re gonna divide it into four smaller squares. And there’s zero point Yep, is zero squared. Everybody, that’s the one Yeah. And what I can also do is I can put a square at the halfway point. So that we have a square same orientation square. Now set and its corners will define the centre point of all of the other four squares. And the corner of the define that were all of the other four squares. Join the centre zero will be at the centre of that one. Yep, that’s what we call the one squared over the one. So that’s a tapestry of something. It’s more than just an anomaly. It’s actually something which is saying something about space. You see how like the centre point is being defined by the corner points of one square and the corners of the one of the corners out of the four for all of the other four squares is now defining the centre of a square of one. And that pattern is the pattern that you will see at the centre of a number line. or so is a numerical number space, particularly when we think of something such as the square root of two so let’s just have a think about this, right? If I have, let’s say, let’s say go across, three. Yep. And I can divide the square in half. Can I? Yeah, I can divide the square in half, and I can go 123456 and then I’ll go 123456 square of nine isn’t as that what? Oh, that’s because on one side, it appears that there’s slightly less squares than on the other side, and the side that the one that runs up the middle is the one that sort of offsets everything, so I need to colour that in a different colour. And now I’ve got 123 on one side, 123 on the other side and 123 that run up the diagonal like a Noughts and Crosses. And if I extend that again into the next one, which is for the situation changes slightly, because in the square of four now I’ve got a 16 you can see what’s happened to the centre part now formed a dot which where there was once a square with a square of nine. If I overlaid them, yep. And what we can see is actually that that zero line is now being offset. So in two half steps, and it’s that half step where we’re talking about about dividing infinity into two. And so what we can see is, is if we extrapolate to infinity, that pattern will remain intact. It doesn’t matter how large or what number numbers you use, at the centre of that square will still be the same thing. And as the root to run through the centre of the square. That’s going to be right bang at the centre of root two. And why we want to know that is because we want understand route two from another perspective other than just this calculative reiteration of the you know, the silver mean, yeah, we need another way to understand it. And we can read to understand it through two dimensional space, which means that we’re going to have to go more into fractal geometry and actually, what we see here with that overlaid, is what we call the silver mean, actually, you take the centre square and you just rotate that centre square within the other square, and you start to create a slightly larger, a larger square, the square suddenly clicks into place doesn’t ever you start to rotate it, it starts to form the circle. And that circle itself has a kind of ratio to the other circle that surrounds the larger square. So we’ve got these ratio two circles. And if you can imagine we can just keep that ratio expanding our infinitely duh, right the way through infinity always maintaining that ratio through the uniformity of number space. And so what we’re seeing there is that that pie function then, is really a relationship between the rotation of that square at the very centre which causes that explosion of number space. Now, when we look into fourth dimensional space, what we see is the square actually is reflected in the four parts of, of zero squared, zero squared makes the cross and we’ve got the four sections of number space, and when we draw the root two, we actually do create the silver the Silver ratio is there. They’ve got the root twos the square the die. The diagonal, and then we just rotating that square and we’re going to create the golden ratio. So the Silver ratio, the silver mean, and that will actually will now define a square in the centre of zero and a square at the corners and that can be compressed number space. And each one of those corners can flip out. And so we’ve still got that a co relation between space to space for each one of them. And if you look at the space that they’re flipping over, it’s actually that ark curvature. And what the Ark curvature is, it’s like opened up that square root of two and we’re looking inside of that square root of two now, that function is now curved one way over one way with the pie function, and where the pie function is curved underneath on the other way. Now there is a gap and the square that fills that gap just happens to be the same surface area as the two squares that are just reflecting either side. So in other words, if we were going to take space between one and zero we can now say that exactly exists in that square. And actually, we have another set of number squares which combined will equal the same space, which will be an n identity, won’t it have yet that’s right, and if naught point five, it’s right there in front of your eyes, yeah, that one corner, but what we realised is now that when we take the whole of number space into account in the fourth dimension, that is actually reflected in another three locations. And now we didn’t know that there was obviously a negative space but obviously mathematics have been banned negative square numbers from the the axioms of mathematic have lost a large portion of the negative number space. And then there’s the other two negative numbers negative and positive numbers basis, which don’t actually even appear in the current mathematic we are using. But actually, we can only perform four dimensional mathematics on the whole if we look at the whole space, otherwise, we can find we can find we won’t even ever work in symmetry, which is fine, but it doesn’t allow us to provide an ordinal system of timespace Yeah, because everything will always happen in symmetry, there’ll be no difference between one space or the other. But as soon as we do make a difference, the reflected the changes can reflect in the other in various different inadvertent proportions. And if we offset those differences from a start point, then actually they will converge in a certain way, which will create a certain signature. So only by having those four points. Can we map for example, the PI function, you know, we’ve got these two, the two sets of pi constants that we mentioned previously. And you know, those two pi constants can also be mapped into onto those two number spaces. And we can then start to work out you know more about pie and things like that. So so what we’re doing is we’re introducing the missing numbers, and we’d like to point out but the time could 03 which is actually the proper three dimensional space, it gets even more bizarre, because we’re not missing. We’re just we’re only counting for two out of the eight number spaces. So that means we’re actually missing six number spaces. And something about the square root of six there, don’t worry guys, and then and then basically those numbers are very important because that’s how we calculate fourth dimensional rotation of the hypercube and so you can imagine if mathematics doesn’t have those numbers, there is no way that it can communicate or even possibly understand fourth dimensional rotation, because it doesn’t have the number set doesn’t have the axioms. And as we’ve already discussed, because algebra cannot solve infinite equations, it just ends up being infinity equals x, you know, whatever you do, therefore, we have to use a different system. And that’s where we use the ordinal number system or the ordinal number system of time. And we have to keep track of the spatial cardinal numbers in order to maintain a four dimensional number space in intact so and that’s what that system does, system of numbers. So there we are a little bit there on some of the structures of numbers and all that business. So I hope that cleared things up a little bit. And if there are any more questions, do feel free to drop us a line on we’ll try to answer them as soon as we can. My name has been Colin power. This has been a broadcast from into infinity where we’ve been solving the solutions to some of the most challenging mathematical problems such as pi infinity and even the Riemann hypothesis.