Scalar Mathematics for Scalar Motion & Scalar Motion for Scalar Physics - Part IIa

Transcript

[Music] [Music] [Music] Well, uh, hello and welcome to the Honest Investigators Talk Shop Show. I'm your host, Doug Bundy, president of the Larsson Research Center, where we're unveiling the universe of motion. Now, today is the uh is Thursday, the uh January 21st uh 2016. We're uh redoing last Saturday's lecture, which was plagued with technical difficulties. And uh let me turn the volume down here a little bit.

got somewhat of an echo. Uh so uh they couldn't read the slides. Everything was a mess. Uh I was really embarrassed but due to circum personal circumstances I wasn't able to do anything about it until today. So uh here we go.

Once this show is over and recorded then the early one earlier one will be uh deleted and I apologize for that. But uh I tried a new technology where I could do a picturein picture uh kind of thing while I was presenting the slides and that didn't turn out so well. The colors didn't show up and all there was all kinds of ugly things uh that uh happened. So as a result we're trying to do better. We're just going to share our slides.

There won't be any picture and picture but we really don't need that anyway. So as I announced in that earlier show last week, I am presenting this lecture as the third lecture uh following the two that I presented nine years ago at the end of my lecture to then on the coming revolution of fundamental physics. I said I would present this one on scalar mathematics and then never got around to it. But uh so now we're trying to get that done. The videos of both lectures one and two that I presented back then are now available on our YouTube channel, the LRC Physics channel as we call it, as well as at our website lrcphysics.com.

You can just look uh in the menu on the left there and find lrcures and that has the actual slides synced with the video. So, um, even though I'm going to delete it, those for those of you that went there, you were able to see the slides, uh, plainly, but I'll, uh, post all of our YouTube videos on our website that way along with the slides so that it's a lot easier to follow than sometimes it is on the video. But uh I also explained then last week how we here at the Larsson Research Center or what we call the LRC refer to the Newtonianbased program that is the traditional mainstreambased program of theoretical physics as the legacy system of theory or the LST. And uh though that might seem to be a little presumptuous uh it's uh necessary a lot of times because we uh try to compare and contrast the difference between the two which is a lot of times very useful. But uh so we call that the LST and then the mathematics they use which are vector-based based on motion that moves from one location to another in one dimension at a time.

uh we call that the legacy system of mathematics or the LSM. So you have those two the or three LRC for the Larsson research center, LST for the legacy system of physical theory and then the LSM for the legacy system of mathematics. This uh not only helps us distinguish between our system of theoretical physics known as the reciprocal system of physical theory or the RST and our scalarbased system of mathematics known as the reciprocal system of mathematics or RSM. But it also makes it easier to refer to them in our speaking and in our writing. So, it's only five acronyms that you have to learn and they're real easy.

So, anyway, I wanted to get that out of the way right away. So in this part two then of our third le lecture scalar mathematics for scalar motion and scalar motion for scalar physics we begin the journey of unifying the LRC's RST that's reciprocal system of theorybased scalar motion theory of physics with its RSM reciprocal system of mathematics based scalar number theory of mathematics. So we want to uh uh begin then with our slides here and we'll try to make it a lot better. Hopefully this will work better than the other approach that we had and uh like I said we won't have a picturein picture but you'll know it's me talking. So we call this a multi-dimensional scalar number system and again the name of the program is scalar mathematics for scalar motion and scalar motion for scalar physics.

This is lecture three part two. So uh the thing that uh we want to understand is uh that it's based on the the the reciprocal system of theory. Of course, we can't go into it on every program, but there's plenty of resources on our uh website and uh actually here if you go back to those prior lectures that I gave nine years ago, there's there's a lot there on that as well. But you can then see that uh there are two postulates, fundamental postulates for the reciprocal system of theory. And uh the first one is uh is stated as follows.

The physical universe is composed entirely of one component motion existing in three dimensions in discrete units and with two reciprocal aspects space and time. Close quote. Well, this is uh these are from the this postulate in the uh second one which we touched on a little bit last time and we'll refer to more in the future. These two postulates make up the reciprocal system of physical theory that the author of which is Dewey B. Larson and he's the namesake of our research center here and uh so uh it's important to understand these that they constitute these two fundamental postulates uh uh const uh cont constitute the uh reciprocal system of physical theory.

Everything we do is deduced from these postulates. So, uh that's extremely important to understand. And from this first postulate, we've deduced the motion entities and combinations of them that uh form the observed particles of the standard model of particle particle physics. The LST uh what they call the uh standard model of particle physics. And it it includes quarks, the up and down quark, their anti, the anti- down quark and the anti-up quark.

The electron and the uh posetron which is its anti- uh particle and then the nutrino and the anti-utrino. Now they also have uh two other families of particles but these are the stable ones. The others are not stable. They only last for very short time before they decompose and we've chosen to not worry about that for now. And then over here you see is a mirror image of what's on the right.

Uh you've got the down quark here and uh it is the mirror image of the down quark over here. If you have the up quark here, it's a mirror image of this. And then uh the the posetron uh over here is mirrored as well and so on is with the bottom part. They're all mirrored except these two of course which are in the center. So and that's how uh the the uh standard model works there.

They call it chirality left and right-handedness of these particles and that's an important part. But what's uh more is that then there's also four Bzons they're called. And you can see they're in a different configuration and we'll talk more about that eventually. But this is the photon over here. And then you've got the W uh plus and minus Bzons and then an intermediate bzon that seems to be a composite of the two which is called the Zposon.

So uh that's important to understand. And these are all coming out of our ST uh uh combinations of motions. We have a suitor and a tutor which we call the suitor we call S. The tutor we call T. These are explained in our last lecture.

We'll explain them uh in more detail of course in future lectures. But for now just understand these as combinations of uh space and time. uh and uh we'll get into like I said how that works uh eventually. But if you'd like more information right now, you can go to our uh lecture of January 9th and uh that's also posted on our website as well as here in our LRC uh physics channel. So uh and then if you have any questions, of course, uh you're welcome to ask those.

And in fact, I guess I didn't turn it on, but normally I plan on at least we could do that maybe towards the end of the lecture when we'd have a question and answer period that you could Skype in and we can discuss these things. All right. Then so uh in the uh mathemat field of mathematics and physics, it's very interesting how the two go together. It's a mathematical uh advance that enables uh physicists to do the the major things that they've done. And last week in our program, Neil Turk, the president of the premier institute, I'm sorry, not the premier institute, the perimeter institute in Canada, explained uh the connection between calculus and algebra and geometry that came about through the most amazing formula in mathematics as he calls it and that's Oilers's formula e to the i pi + 1 is equal to zero.

Of course you exponentiate exponentiate the imaginary number i over pi and that will uh equal minus1. And that's the important thing that they came up with to uh uh uh to tell us how marvelous that was. And uh this they're tr it's that's true. They're right. But it's important to understand that it only takes us so far.

And it's uh going to be useful to understand that when uh we uh compare it with uh the u uh when we compare it with what we're doing uh in terms of the um uh scalar mathematics. So we want to understand that. So, I've edited and cut down quite a bit that uh same video we watched last week. So, let's watch this shortened version now. Now, I want to introduce a more bizarre mathematical character.

And it took people uh 2,000 years to make the next great leap in mathematics. Okay, geometry was pretty important. With Pythagoras theorem, you could build pyramids and structures and you know architects would wouldn't make a living without Pythagoras's theorem. Um but it took 2,000 years before the next huge leap forward in mathematics and that came about with this strange character I. So all of a sudden with this one extra character in the game, a problem that had seemed impossibly complicated and difficult because some equations seem to have solutions, some didn't have solutions.

Now all equations were on the same footing and they all had solutions. It's incredibly powerful simple idea. Once people had now it it relates to Pythagoras theorem uh as follows. Once you have the idea that you have this guy I now we are going to enlarge our space of numbers. We have a number x which could be any number from minus infinity to infinity an ordinary number.

And then we have another kind of number which is a multiple of i. So uh and we put the two things together. We say I'm going to allow numbers which are have a real part the x part and the imaginary part which is the multiple of i. Okay. So the dimension suddenly I've gone to numbers not being on a line they're now in two dimensions.

I can go along the line. I can also go in the i direction. And so I can go along x and up in y. and uh um and I get this number x + i y. Um so let's let's see it in action.

So here we are. we have this circle and um I'm uh the angle is the angle uh subended by this pointer and as the theta changes this e to the i theta is running around and you can see its real part is going backwards and forwards and backwards and forwards and so if I use that real part to model a wave which is traveling which is also traveling upwards as its amplitude is going back and forth. I get what we call a sinosoidal wave. So the wave is now following this function which came out of trigonometry through this construction. And it turns out this is how nature works.

Basically everything that goes back and forth in nature can be described in terms of functions which which look look like this. in particular. Okay. Uh we'll cut it off there. Uh but that is extremely important as he says that's the uh um this I if the invention of that and then Oilers's uh understanding of how when you exponentiate exponentiate that you get uh the square root of I which is minus one.

So uh it's uh uh really uh an amazing fact but uh it troubles a lot of people because of the concepts involved. Uh they have you know understood it in terms of the vertical axis and so that makes a lot of sense when you get this this rotation but so you know science never looked back. It's an amazing thing that what happened as a result of that. We got an understanding of waves. We got an understanding of uh then you know electronics came about and so engineers were able to do that.

We understood light. Then we found out that there were uh that light was a both a wave and a particle. And so you know one thing led to another. But it was amazing how this uh advanced science. But that's not the end of the story.

It turns out that there are three properties of numbers and magnitudes. They both have these in common. Uh physical magnitudes have magnitude, the value of the magnitude. They also have dimension. And then they have this uh uh called direction or um what we call direction in quotes which is really a polarity.

And it's important to understand this. You look at the notation as we see here. We've got normally you don't put n in there which is the magnitude but that is really an implied unit. Then you have two directions which the two stands for directions and then you have the number of dimensions in the exponent. Now, that's really going to be important as we move on.

Um, and uh, we're going to see how that's not recognized that the two is not a magnitude in and of itself. It's actually the number of directions in which the magnitude is employed. Uh but this is really important because uh nature uh doesn't uh ex extend in uh in terms of numbers. They don't uh let me go back to that one. Uh they let me back up actually to to this one.

When we're talking about rotation, the biggest problem that we have is in solving this uh connection between a wave and a particle. Uh for the ancients, it was really a a difficult case when uh they realized that they couldn't find an exact magnitude of a circle that that matched the magnitude of a square. And so that was called squaring the circle. and it was impossible to do. But uh the uh other thing that happened as a as a result was that during way back in the days of uh Uklid when he would provide two proofs of his uh theorems, one for algebraic proof and the other a geometric proof.

Then uh uh also the same problem at about the same time with uh the Pythagorean cult. You know, they had lots of things that were dependent upon numbers. But when they when it was discovered that there was no number for the hypotenuse of the triangle, then that eventually brought down their cult. And this is that conflict that extends even today between algebra and geometry that this invention of the imaginary number i and the exponentiation of it over pi does not uh change. We still have this conflict between uh the uh quantum physics that has that are based on a fixed uh coordinate system and uh the discrete units of that and it has to have that fixed coordinate system and then the theory of gravity general relativity which uh is impossible to explain in terms of a fixed coordinate system.

So the two are totally incompatible and that incompatibility that conflict is at the heart of the trouble of physics today. We've talked about a lot about it on our website and you can go there and find lots of articles about that. But it's also a problem for us not just the legacy system. We uh have in our first assumption assumed that the uh universe consists of discrete units of motion. And so we've got to be able to explain gravity and and all the different interactions between the particles that we have discovered come out of our pos fundamental postulate.

We have to discover that and uh or discover how then to reconcile uh discrete magnitudes with continuous magnitudes along with all the rest of the world the modern world and the ancient world who've never been able to to solve it. So our approach is to approach the is to redefine really the number system itself. And now that gets us to this slide where we talk about the three properties of numbers that are actually the three properties of magnitudes and that is one the magnitude itself the dimension of the magnitude and the direction uh of the magnitude. Now we talk about there being two directions inherent in each dimension. So that's what the notation is shown here.

two to the 0ero, two to the first power is the first dimension. Uh two to the second power and two to the third power two cubed. So we got uh uh those numbers multiplied implied because it's not literally shown most times. We could put the n behind the two here or in front of it, but it's the multiplier. So the magnitude multiplied in two two directions actually no dimensions.

So that's null and void here. But in one dimension there would be two directions in which that magnitude would be manifest. And then here there would be four directions in two dimensions that that magnitude would be manifest. And here there would be actually eight two two cubed uh in which the direction number of directions in three magnitudes that would I mean in three dimensions excuse me that this magnitude n would be manifest in. So we explain that in terms of the binary expansion of the Greek tictacrris.

Um and we can see a correlary to the geometry and we'll see here in a minute how important it is. But re recall that the uh binary expansion follows the format if you will of the Greek tectras and that's used in many ways. Pascal's triangle it goes on and on it's called. But uh what's happened is that it actually represents uh zero dimensions uh the entities in zero dimensions and uh one dimension on the next level. If you go down this way you see on the right hand side that's a zero dimension that's one dimension this level.

The next level is two dimensions and this level is three dimensions. Of course, when you go to to another level, you don't cast away, for instance, a point. So, you've got a point in each one at each one of those levels. But here, it's a point in the middle of a line. Here, it's a point in the middle of a line in the middle of an area.

And here, it's a point in the middle of three lines and three areas in one cube. So that's very interesting because the numbers correlate with the uh geometric understanding of points, lines, areas and volumes oriented orthogonally. So it turns out then that this is a unification of numbers and geometry. The numbers of the tic tacris actually correspond to a geometric magnitude of what we call Larson's cube. You can see it here on the right.

It's just a stack of two by two. See two this way, two into the depths and two high. So it's a stack of one unit cubes. Eight oneunit cubes stacked two by two by two. And uh each one of those then though corresponds to the dimensionality of the tectacris.

You see that you can talk about the point here by itself or you can talk about that point as an intersection of three lines or you can talk about it as a point in the intersection of three planes see seen here in the green. There's one oriented in each dimension and then here's the horizontal one. two verticals and a horizontal plane that's shown in the green there. And then finally there's one cube you see uh colored orange here that uh is uh contains them all and the point is the intersection for it as well. So if we looked at the three-dimensional figure here at the bottom, we see the point here in the middle, we see three blue lines oriented in uh uh or orthogonal dimensions and then the green indicating the three planes that are orthogonal and then the orange showing the unit cube itself when there's only one of those.

So that's an amazing correspondence and it's really important because this is mathematical and this is geometric. So with uh each instance here we're saying of a zer point we have three instances of a 1D line again three instances of a 2D plane and one instance of a 3D volume. very very important because two to the 0ero is equivalent to a point. Two to the one is two meaning a line with a point in the middle of it because it's uh a dimension or a magnitude one. Remember there's an implied one out here that we don't see.

So that was one magnitude in two dimensions of one dimension. So you can see that if you choose one of these that from the point you go in two opposite directions of the one uh D line and then when you have the plane choose one of these planes. Let's choose this one here. You see there's two uh there's four uh units in that plane. uh and uh if you draw from a line from the center point out to the diagonal of that plane which would be the square root of two because these are unit cubes.

So by Pythagorean theorem we know that that be the square root of two and uh and there's a point in the middle of that plane like I said and then uh when we look at the one cube we would have uh eight out to the uh eight diagonals eight diagonals out to the eight corners of the cube four at the top and four at the bottom. So that's a total of eight directions in the three-dimensional cube or 2 to the 3. So that's an amazing uh correspondence and it's something as far as I know, no one else has ever pointed it out. We've been talking about it and employing it and using it to study our reciprocal system of mathematics for years here at the LRC, but I as far as I can tell, we're the first and maybe even still today the only ones that are pointing it out. Uh now when we uh look at that though we we think of okay because it started if we go back here we think of starting with a point right in the tect tectactus we expand out in these uh three other dimensions.

Well here we could think of that as well. An expansion from the point would give us a line uh of two magnitudes in one dimension, four magnitudes in two dimensions, and then eight magnitudes in three dimensions. They're all part of that, but it expands out as a progression. So if we take that along time, we start with at t0 along a timeline and then at t1 we would expand in one unit of time to this figure here and then uh in uh in uh time two we would because this is a three-dimensional u progression we would expand to 64 which would be here you see it's 2 to the 3 then it's 4 to the 3r third because it's again two directions and so we add another uh magnitude in each direction. So so that's a this had a total of two.

So expanding out to the second unit of time that would be four and four cubed is 64 and 6 cubed is 216 and 8 cubed is uh 512. And if we were looking at the plane in there, you had four, but then four squared, that's two squared. Four squar is 16 and so on. It's 2 into the square to 2 n^2. And then of course for the uh dimensional one-dimensional line, it's two in each of the two opposite polarities.

And then the next unit of time, that's two more and then two more and two more. So it's two in the progression there. So uh we if we look at just a regular number pro progression we can we can go uh you know 1 2 3 and count up to infinity to any number n or we can count by twos if we wanted to 2 4 six which would be two n up to infinity and we could do that in threes we can do it in any numbers but as far as the numbers are concerned they don't care you know it doesn't matter we can have any uh progression that we want times uh infinity whatever. Uh so the numbers don't give us the st same constraints that the the uh tectacris and the three-dimensional expansion of Larsson's Q gives us. So that's important to understand and it's also important to understand that we don't we can't go any further than three dimensions as far as what can be observed.

String theory in the LST community uh string theorists want to go to 11 dimensions if you count time. They want to go to 10 dimensions and so they want to add seven more uh dimensions of space to these three dimensions. And of course they tried to do that but then they ran into horrible problems. But if they would have listened to a man by the name of Raul Bot BT he his theorem was proven that there are there is no physical phenomena beyond three dimensions. And that has to do with the number eight.

and it gets really complicated and maybe someday we'll explain a little bit about that but we have talked about it on our website. So if you want to go there and look more look into it more, you can do that. But here it's important to understand that if we're talking about multi-dimensional numerical expansions, we we would have to uh have them in one dimension, you've got to expand out in in both directions of that one dimension and two four directions in the uh in in a two-dimensional expansion. And then if you go to three dimensions, you have to start with eight directions. That's that's not a arbitrary decision.

That's uh that's something that comes out of nature itself. And so we need to understand though that uh nature of course doesn't expand that way. It doesn't expand by numbers the way we can expand numbers. uh if we start with that 2x twox two cube though there's something wonderful that happens we find out that there along with the expansion of the of the uh uh 2 n to the3 uh numbers that what we call p uh p to the 3 or p cub make up these things uh p cubed or piece sub3 cubed here I've written it as a 3D progression uh that we get uh you know that that number of cubes we have eight and then we've got a stack of 64 and then we have a stack of 216 and we have a stack of 24 but it turns out that we can define balls uh volumes in that just fit as a ball with a radius one inside that stack So a stack of the as we start off with a stack of eight in one unit of time we have a ball with the radius of one which is a square root of one if we want to use Pythagorean theorem. uh we've got uh we can explain that in more detail later.

But then we have in uh using the radius of the from the distance of the from the center point to the two-dimensional corner which is square root of two starting off and then of course it doubles as we go on to 64 and triples as we go on to 216 and so on. But in the stack of three-dimensional cubes described perfectly by three-dimensional numbers, we have these three radi. One is equal to the square root of one. The other is equal to the square root of two. You can see it over here.

It was hard for me to try to put all this together in one. So I separated this one out. And then of course the third one is this blue ball here which I tried to see. See you would have the radius is square root of three. By Pythagorean theorem, you go from the center point out diagonally to that corner which would define the radius of this ball.

So we have three balls. one uh within the stack that's the square root radius of the square root of one and then one with the radius of square of two and one with the radius of square of three that are automatically defined if you will by the expansion uh numerical expansion of 2 n to the3. So we could label these uh we could label this the first progression cube pro progression which would be the 3D progression of the inner unit ball which is what we called out black one there. And then we have P sub2 cubed which would be the 3D progression of the middle unit ball which uh you see we've depicted here with radius uh square root of two and and we've colored red and then of course we have the blue one which we would call P sub3 cubed which is the 3D progression of the outer unit ball. The outer unit being again the square root of three, the middle unit being the square root of two and the inner unit being the square root of one which is equal to one of course.

So that's amazing thing. Now, so we've we've we've taken what we already know about numbers and uh geometry and we found some amazing things and lo and behold, one of those amazing things is that we've got continuous magnitudes associated with the discrete magnitudes which should give us a clue because this is the greatest mystery of all time in science and mathematics. So if we look at the interval scalar progression with square root of one then in time that time zero I mean time one time zero is just a point in time one then it's this ball of radius square root of one and then in time two it's two times the uh one which is two square of one which is two three times that which is three four times that which is four. And that will always just fit inside the stack beginning with eight, but then the next one is 64 and the next one is 216 and the next one is 512. 2 n cubed when n is 4 is equal to 512 and right on up to infinity.

Right? So that's amazing that we can specify within this these different cubes of the two end uh cubed progression this continuous progression as well. And then the same with the outer ball that is that fits that the cube fits into. Again it's it's h a little difficult for me to show everything at once. So I'm trying to show them separately but understand that this is called the inner ball because it fits inside the stack and this would be the outer ball because it fits just or the stack just fits into it. So we have then uh a radius that goes out to the from the center point to the eight corners of the cube.

Four on top and four on bottom. But each one of those is equal to by Pythagorean theorem the square root of three. So then when we go to time uh t2 that's expanded and uh the stack now is 8 by8 not this four cubed. Uh so we've got 64 and the ball that it just fits into will have a um a radius of twice this one. And this one would have one that's three times that the original one and this one four times.

So uh then we have the middle uh ball that is uh defined by the two-dimensional uh radius which is a square root of two. And so as the progression proceeds then the radius increases as well doubling two * the square of two three time which is what square of 8 then this is the square root of of 18 and this is square root of 32 and so on. So I mean there there's no getting around it. This is not uh constructed. This is this is just an observation of how nature works.

Now if we take those then we've got uh we can call it the zd if we count that normally we don't that's just a point of no extent and no direction no dimensions so it's it's uh all zero so by pythagorean theorem it would be the square root of zero which makes no sense but we have the 1D 2D and 3D numbers then in three dimensions inside this progression that we have just seen that we're talking about the two ncube progression and if we then took that as the uh r the u uh square root of zero then of course all these terms are zero and doesn't make any sense but when we go to 1d you see we in the pythagorean theorem of three dimensions we have three terms but in one dimension there's only one term that's populated so that becomes our n So n squared the square root of n squared since n^2 here is one the square root of one is the answer. So onedimensional uh Pythagorean theorem would be the square root of one and we can plug that in here. The point again is is uh just the point. But when we plug that in as the implied multiplier of the two directions in our in our uh binary expansion of the tectacris, we're multiplying by the square root of one, which of course is just one. So 2 to the 1 is two.

Two to the uh 2 * the square of 1 squared is 4. And 2 * the square t of 1 is two. and that's cubed is equal to 8. So that's that is nothing more than a different uh way of writing our familiar uh binary expansion down this way. But uh now when we go to to the 2D case again we're in three dimensions.

So now we have two dimensions of n in the two dimension in the three terms. We've got one that's not populated but two that are. And so 1^2 is 1 + 1^2 is 1. That's a total of two. And uh 2^2 then is the answer.

And we plug that in and as our implied unit and we've got two times uh for the one dimension. We've got two directions where that is manifest that that magnitude is manifest. Here we have four directions. 2 ^2 is four directions in which that is manifest. And this would be then uh 2 * the square of 2 cubed.

And that's the manifestation of 8 units of square root of two. So you see how that works. And the same thing with on the 3D where we populate all three terms of Pythagor of the Pythagorean theorem and that gives us a square root of three and we plug that into our equations and we get the results there numerically. So you see while over here we have these balls defined we also see that we can define them in the numbers of the titactus as well. So now we've got the one 0D point.

We've got the three orthogonal 1D numbers, the three 1D intersected lines there, the three orthogonal 2D uh planes, and uh one 3D number volume, which would be the orange cube. And those all then correspond. But now we've got some uh continuous um magnitudes associated with both our tic tactric and our Larsson's cube which we'll call RLC the 2x two by two stack of eight unit cubes. All right. Well then we people say well but you got three you know and that's we don't see that but so you can understand that that there's actually 14 units if we ignore we call it a generic unit maybe where we ignore the dimen the difference in the dimensions we actually have 14 units of magnitude in the 14 directions of the LC normally when our unit is the square root of one or or one and we can see this that there are 14 because we can we can easily see in the orange cube here that there are two to the three or eight three-dimensional directions as I said from the point in the center out to each diag each from the point in the center diagonally out to each corner of the cube four at the top and four at the bottom so we have eight directions that are three-dimensional directions then if we collect collapse that.

Let's say, it doesn't matter how we collapse it, but we let's say from top to bottom, we just push it down here to the bottom uh plane or push them both up both uh from the top and the bottom. So, we get the middle plane here or we can push it from forward to back or we can collapse it or push it from le uh push left and right together. But in any way we collapse the 3D um figure to a 2D figure and that gives us then the four two-dimensional directions. We can go from the point out to the diagonal which is a square root of two and that would give us then four of those. And uh so uh the same thing then we can collapse the two dimensions down to one dimension.

Now we have two magnitudes where we before we had four one two three four now we have two. So we started with eight then we got four. Now if we collapse this down we get it a line that has two in each two magnitudes in each or two directions in opposite directions opposite polarity. And uh then if we collapse the line to a point by pushing the two ends together we come to a point that has no magnitude. So uh in total then we have 8 + 4 + 2 + 0 is equal to 14 directions of magnitude that's in this tctrris and it's also in I mean in this LC in this Larsson's cube this 2x 2x two stack geometrically stacked uh unit that corresponds to our two two uh n cubed progression or it's the initial value of our two uh NQ progression.

So, and the same thing is in the tetactas, but the important thing is is that we normally when we think of the two NQ progression, it's just the we're only counting the directions that are three-dimensional. We're leaving out the two-dimensional directions in the onedimensional direction. So if we don't do that and we say well we've got eight directions in in three dimensions four directions in two and two dimensions in two um I mean two magn two directions in one dimension uh then the total directions in it in the LC itself is 2 + 4 + 8 is equal to 14. So, the LC's progression is actually a composite progression, and I'm stomping the floor here if I were teaching a class, consisting of three progressions. The 2ned one-dimensional progression, the 2n square two-dimensional progression, and the 2n cubed three-dimensional progression.

Now, that's important to understand. We've never noticed it before. I try then to capture it in this graph by showing the multiple units of of uh the LC's. So if we progress in our two n cub progression, we start with eight and then the next thing we go to is 64. But see it looks like well you would combine these two.

You got eight here and eight here. That's a total of 16. But see, these are not physical entities that we're combining. And so as a result, what we see here is a change in the number n. So this then would be two n because since these are units of of motion, they would combine.

And so if we drew them as one, then the these two units would become one unit with a point. I mean these two lines here would become four units with a point in the middle. And uh these four 2D uh uh magnitudes would become uh four in each direction. So 16 you see and so on. So it's not actually the way we normally think in terms of of physical entities where this would be one and we add one we get two and we add one we get three and we add one we get four.

No, what we're really doing is changing the n here. So we got n equal to one, n equal to two, three and four and so on. So that's why in our progression we go 864 216 and 512. So if we look at that we can see that the progression of the LC is actually a multi-dimensional composite progression of magnitudes who we over here on the left we have in a in the 3D case we've got eight directions and when one when n is one excuse me 1 cubed is one so 8 * 1 is equal to 8 here we've got four directions and when n is 1 1^2 is 1, 4 * 1 is 4 and so on with 2. 2 * 1 is 2.

So we have 14 directions that then give us 14 magnitudes. But when n changes to two, then 2 cubed is 8. So 8 * 8 is 64. 2^2 is 4. 4 * 4 is 16.

2^ 2ar is two. And or not two squared but two to the first power is two. 2 * 2 is equal to four. So now we still have 14 directions but we have 84 magnitudes and in this case uh 258 magnitudes and here 584 magnitudes of multiple dimensions in our composite progression. Now, I know that's a little bizarre, but uh if you think about it, you'll see that that's the only way that we're just too used to using the one-dimensional numbers that this is a taken as a one-dimensional number cubed.

And so, as we go on, we don't we don't have a gem. Normally, we don't think of a geometric uh equivalent, but if we did, it would be uh one here with 64. area would be 4x4 by 4 deep uh which would be 4 cubed would give us 64 cubes not 16 and so on with the rest of them. So that's important to understand as we go on here. But now uh what we so so now we're understanding a little bit more about the actual discrete progression and the units that are involved in it.

But then we also have the continuous progressions that we just saw with the square root of of one square root of uh of three of two and the square root of three. And so uh those are all cubes and cub because they're volumes. So we're talking about a a number in the exponent of three. But see we can write it differently. We can write uh that same thing two directions times one but now we're thinking of the one as the square root of one which is the radius of the inner ball right cubed.

Well that's really important. So that gives us the square root of 64 which of course is eight. So it's the same thing as 2 to the 3 = 8, but it's written in a way that corresponds to the next level, which we we substitute the implied unit multiplier of the two directions with the square root of two and cube that and we get the square root of 512. and the and do the same thing by substituting the square root of three for our unit implied unit multiplier and cube that and we get a 1,728 cubic units. Well, it's when we start looking at how these are related.

For instance, we divide the 2d1 by the 1D1, we find that that's related by the square root of eight. that goes into 1D goes into 2D the square of 8 times uh 3D divided by 1D the square of 27. So that then gives us some one two and threedimensional relations that we haven't used before. Uh trying to express them here two uh times the implied multiplier two directions times one magnitude cubed is equal to eight. That's the same thing as we just showed up here.

If we substitute the unit one by the square root of one, we get the square root of 64. And that is the same thing as as the one above. They're they're identical. It's just a different way of expressing them. But then we come down here in the second dimension and we substitute our multiplier with the square root of two and we get the square root of fi of 512.

But that's the same as if we took the square the the square root of one multiplier and uh and multiplied it by the square root of eight. If we do that, we're going to get the second d the in other words, if we took the first dimension, multiply it by the square root of eight, we'll get the second dimension. And and the square root of 8, of course, is a square root of two to the 2 cubed, and then we take uh the square root of 3 cubed and multiply it by the one dimension, and it gives us the third dimension. So now we have, you know, you got to understand, I don't know, I may be nuts because I'm not a professional, right? And a lot of times they call us cranks and things. So somebody could uh really correct my understanding here.

I'm just being honest, an honest investigator trying to talk shop here. But this is amazing. Uh this is just like uh you know if you multiply uh a number two to the 3 uh times two uh times well let's take two because we always using that 2 to the 3* 2 to the 1 is 2 to the 4th because you have to add exponents. uh but uh if there's no such thing in uh in in uh our uh physical reality because we don't have four dimensions. So we can see this disconnect between geometry that has the three dimensions that we observe and numbers which doesn't have that constraint except in the tic tacris when the dimensional and the directional information is taken into account.

But here we're multiplying uh the the uh uh onedimensional unit up here by the square root of 3 cubed and we get the three-dimensional unit. And here we're multiplying the the unit ball that we'll call it. It's a volume. See, because it has the exponent of three. It's a volume, but we're multiplying it times the square root of 8, and we're getting a two-dimensional volume, if we can put it that way, you know, meaning it's got a radius of the square root of two, but it's Yeah, I hope I can.

It's hard to make that clear, but think of that two-dimensional frame uh defining that red ball. It's identified with two dimensions. that ball and this one's divided or identified with the one-dimensional black ball. So, and this one with the one dimens or uh with the uh blue ball. They're all three-dimensional volume units, but uh it's identified with that color blue.

And here we we're getting it by multiplying the unit ball by the square root of 3 cubed. So that's really important I think to understand. Now I may be corrected and shown to be really dumb and all of this but uh there it is. We'll see now. So in putting it in words then uh we can say this about discrete and continuous identities at least in this 2n cubed progression we can say that it can be demonstrated that the LC composite progression of discrete magnitudes is equivalent to a corresponding LC composite progression of continuous magnitudes if the implied unit multiplier of the two directions in each dimension is replaced with the appropriate radius unit and then multiplied by the appropriate constant, the square root of 2 cubed or 3 cubed.

Now, that might be that that's up for challenge. Somebody can point out my fallacy here, and it wouldn't be the first time. I make some stupid mistakes, but I'd rather make stupid mistakes that get me to the next uh level than not to do anything at all. So anyway, this is where we're at with this scalar um new scalar mathematics. And so we present then the new what we would call I guess LC algebra.

the LC's N, that's the N and the LC in its three dimensions is distributive because no matter how we add up the numbers for N, whether it's A time B + C or A * B plus A time C for instance, it will still come out right. And same way it doesn't matter the order of of u of the operations in when we're subtracting a * b minus c is also equal to a * b minus a * c. See we can distribute these numbers in any way and I might point out at this point that we lose this in the imaginary number and the rotation of the waves that property is lost uh this distributive property because uh you don't have a point that you can call you arbitrarily can choose one but in the numbers there are there is no zero anywhere along the circumference of the circle can be the starting point and then you can go around 360 degrees and return to it. Uh so the distribution here the order if you will uh is not implied in the complex numbers. So we lose this distributive property in the complex numbers.

Then if we move up to the uh uh quatronians, we lose this commutative property where it if you have a + minus b equal to uh minus b or if you want it to be equal to minus b plus a where you reverse the order of the of the terms both in multiplication and addition. It's doesn't work. you lose this commutative uh capability. There there is a lecture by uh John Bayz that's on our website under LRC well I think it's on the LRC physics YouTube channel as well. uh Phil you really need to watch that because it really explains how then when you go to the octonians which is the three-dimensional uh level of vector algebra the normal algebra you lose this associative power that we don't lose in other words for us it doesn't matter if you take a plus b plus c it's going to equal the same thing as a plus b plus c when you group uh b and c together instead of a and B together.

But that's not true for the uh Octtonians. They lose the associative power and they've lost the commun commutative power at the two-dimensional level with octonians. I mean with the quatronians and with the complex numbers which is the uh uh uh the the uh we might call it the one-dimensional it's they change the meaning of the word dimensions but you can see that this would be one-dimensional if you look at it in geometric terms uh the complex numbers the quatronians are two-dimensional and the LC's are three-dimensional and so you lose these properties with them but you do not with us with this scalar algebra. In other words, the last bullet here, the LC algebra is completely distributive, commutative and associative. So that's really important to understand and that's the end of our presentation of scalar mathematics.

And I hope it's uh made sense to you. Um there's a lot more to say about it. This is an introduction only of course and we will have this up on our website and then next week I don't know if I'll be able to do it this Saturday because of some other commitments that I have but if I can I will and we will uh take it to the next step. But uh feel free to uh comment and uh in the section below, comment section below or on our website or uh however you'd like to comment. But uh and point out anything that you might see here that is out of order.

But uh in uh in this we are uh planning on being able to um analyze our uh equivalent to the standard model particles here. So that we can see how for instance of the these two the posetron and the electron if I move electron here and the posetron um interact and why the proton which is made up of two of these and one of the downs which is you know chair is in the way but anyway right the uh all the interactions of these particles we need to explain But we need to explain them not as the LST community has in terms of vector algebra where uh things are moving whether they're moving around the circumference of the unit circle or whether they're moving in some other way. Their idea of motion is a change of location. Our idea of motion is a change of size or change of scale, an oscillation of a volume if you will. And uh that's going to require a whole different algebra.

And hopefully this is going to be at least the beginning of that. But uh there it is for what it's worth. And uh I hope it uh has been worthwhile. And so I'll bid you adue uh until the next time.