This channel is of course not meant for political statements but this fucking war is a fucking distraction from doing math. While writing this post in small pieces I was constantly dissatisfied with the level of math (too simple, done too often in the past etc). But when I was finished and read it all over, all in all it was not bad. It is a short oversight of how to find shere-cone equations and once more how to find a conjugate. And once more: The math professors are doing it wrong when it comes to finding the conjugate for 32 years now & the clock keeps on ticking. On the one hand this is remarkable because if you do internet searches a lot of people understand that the Jacobian matrix should be the matrix representation for the derivative of a complex valued function in say three dimensional space. So that goes good, but when it comes to taking the conjugate for some strage reason they all keep on doing it wrong wrong and wrong again so they will never find serious math when it comes to number systems outside the complex plane or for that matter the quaternions.
The setup of this post is as next: 1) Explaining (once more) how to find the conjugate. 2) Calculating the two sphere-cone equations. 3) The solution of these S-C equations is the exponential circle that is, 4) parametrisized by three so called coordinate functions that we 5) substitute into both S-C equations in order to get 6) just one equation.
Basically this says that the complex and circular multiplication on our beloved three dimensional space are ‘very similar’. Just like that old problem of solving X^2 = -1 is impossible in these spaces while the cubic problem of X^3 = -1 has only trivial solutions like basis vectors. That too is ‘very similar’ behaviour.
Anyway this post is six pictures long.
That was it for this post on my beloved three dimensional complex numbers.
I know I know I have published stuff like this before and over again. But that was also years ago and now I do it again it is still not boring to me. After all the professional math professors still are not capable of finding those beautiful exponential circles and curves simply because they all imitate each other. And they imitate each other with how to use and find a so called conjugate. And if you use the conjugate only as some form of ‘flipping a number into the real axis’ all your calculation will turn into garbage. Anyway by sheer coincidence I came across two videos of math folks doing it all wrong. One of the videos is even about the 3D circular numbers although that guy names them triplex numbers.
You can do a lot with exponential circles and curves. A very basic thing is making new de Moivre identities. From a historical point of view these are important because the original de Moivre identity predates the first exponential circle from Euler by about 50 years. In that sense new de Moivre identities are very seldom so you might expect some interest of the professional math community…
Come on, give me a break, professional math professors do a lot of stuff but paying attention to new de Moivre identities is not among what they do. But that is well known so lets move on to the four pictures of our update. After that I will show you the two video’s.
Let us proceed with the two video’s. Below you see a picture from the first video that is about 3D circular numbers and of course the conjugate is done wrong because math folks can only do that detail wrong:
By all standards the above video is very good. Ok the conjugate is not correct and may be the logarithm is handled very sloppy because a good log is also a way to craft exponential circles. But hey: after 30 years I have learned not to complain that much…
The next video is from Michael Penn. He has lots of videos out and if you watch them you might think there is nothing wrong with that guy. And yes most of the time there is nothing wrong with him until he starts doing all kinds of algebra’s and of course doing the conjugate thing wrong. Michael is doing only two dimensional albebra’s in the next video but if you deviate from the complex plane very soon you must use the conjugate as it is supposed to be: The upper row of the matrix representation.
Here a screen shot with the content of the crimes commited:
Here is his vid:
Ok, that was it for this appendix to the previous post.
It is past midnight, this evening I brewed hopefully a lovely beer. It is late so let me keep the intro short. The last time I often lack stuff for new posts because most of the theory of 3D complex and circular numbers has been posted in this collection of 200+ posts. And you cannot keep it repeating over and over again, if all those years in the past the math professionals did just nothing, why would they change their behaviour in the future? Beside that I do not want have anything to do with them any more, it is and stays a collection of overpaid weirdo’s and there is nothing that can change that. On the other hand one of the most famous expressions in math is and stays the exponential circle in the complex plane. That stuff like e^it = cos t + isin t is what makes many hearts beat a tiny bit faster. So when someone comes along stating that he found an exponential circle in spaces like 3D complex numbers, you might expect some kind of attention. But no, once more the math professionals prove they are not very professional. Whatever happens over there I do not know. May be they think because they could not find this in about 350 years no one can so it must all be faulty. For me it was a big disappointment to get discriminated so much, on the other hand it validates that math professors just are not scientists. Ok they have their salary, their social standing, their list of publications and so on and so on. But putting lickstick on a pig does not make it a shining beauty, it stays a pig. So a math professor can have his or her prized title of professor, that does not make such a person a scientist of course. At best they show some form of imitating how a scientist should behave but again does such behaviour make these people scientists? Anyway a couple of days back at the end of a long day I typed in a search phrase in a website with the cute name duckduckgo.com. Sometimes I check if websites like that track this very website and I just searched for “3D complex numbers”. The first picture that emerged was indeed from this website and it was from the year 2017. I looked at it and yes deep in my brain it said I had seen it before but what was it about? Well it was the product of two coordinate functions of the exponential circle in 3D. It is a very cute graph, you can compare it to say the product of the sine and cosine function in the complex plane. So I want to avoid repeating all that has been written in the past of this website but why not one more post about the 3D exponential circles?
In the end I decided to show you how likely one of those deeply incompetent “professional” math professors would handle the concept of conjugation. Of course one hundred % of these idiots and imbeciles would do it as “This is just a flip in the real axis or in the x-axis” and totally spoil the shere-cone equation and only find weird garbage that indeed better cannot be published. After all our overpaid idiots still haven’t found the 3D complex numbers, I am still living on my tax payer unemployment benefit and life, well life will go on. But it is not only math, with physics there are similar problems and they all boil down to that often an idiot does not realize he or she is an idiot.
But let’s post the six pictures, may I will add an addendum in a few days, may be not. Here we go:
Ok, may be in will write one more appendix about how these kind of coordinate functions of exponential circles give rise to also new de Moivre identities. That is of interest because the original de Moivre identity predates the Euler exponential circle by about 50 years.
Yet once more: Likely there is just nothing that will wake up the branch of overpaid weirdo’s known as the math professors… So for today & late at night that was it. Thanks for your attention.
I finished the proof that was originally meant to be an appendix to the previous post. And I have two more or less small things I want to share with you so lets get started with the first thing:
Thing 1: Tibees comes up with a very cute program of graphing 3D surfaces. It’s name is surfer, the software is very simple to use and it has the giant benefit of making graphs from implicit equations like f(x, y, z) = 0. For example if you want the unit sphere in 3D space you must do x^2 + y^2 + z^2 – 1 = 0. Now for this website I always used an internet applet that uses ray tracing and by doing so over the years such graphs always look the same. But this surfer program has cute output too and it has the benefit you don’t need to be online. Here is how such a graph looks, it is the determinant in the space of 3D complex numbers, to be precise it shows the numbers with a determinant of 1:
By the way, the surface of this graph is a multiplicative group on it’s own in 3D space. I never do much group stuff but if you want it, here you have it. And for no reason at all I used GIMP to make one of those cubes from the above graph. It serves no reason beside looking cute:
The Tibees female had a video out last week where she discusses a lot of such surfaces in three dimensional space using that surfer software. And she is a pleasant thing to look at, it is not you are looking at all those extravert males drowning in self-importance only lamentating shallow thoughts. The problem posed in the video is an iteresting one, I don’t have a clue how to solve it. Title of the video: The Shape No One Thought was Possible. It is a funny title because if you start thinking about all the things that math professors thought were not possible you can wonder if there is enough paper in the entire universe to write that all out.. Link to the Surfer program in case you want to download & install it: https://www.imaginary.org/program/surfer.
Thing 2: The last weeks it is more and more dawning on me that all those centuries those idiots (the math professors) did not find counter examples to the last theorem of Fermat. Nor was there any improvement on the little theorem of Fermat. Only Euler did some stuff on the little theorem with his totient function, but for the rest it is not much… Well since Jan of this year I found many counter example to the last theorem of Fermat and in my view I made a serious improvement on the little theorem of Fermat. So is the improvement serious or not? Here is a picture that shows the change:
On a wiki with a lot of proofs for the little theorem of Fermat they start with a so called ‘simplification’. The simplification says that you must pick the number a between 0 and p. So if you have an odd prime, say a = 113, does the little theorem only make sense for exponents above 113? And can’t we say anything about let’s say the square 113^2?
With the new version of the little theorem we don’t have such problems any longer. Here is a screen shot from the start of that wiki, the upper part shows you the improvement:
If you follow that link you can also scroll down to the bottom of the wiki where you can find the notes they used. It is an impressive list of names like Dirichlet, André Weil, Hardy & Wright and so on and so on. All I want to remark is that non of them found counter examples to the last theorem nor did they improve on the little theorem of Fermat. Now I don’t want to be negative on Dirichlet because without his kernel I could never have crafted my modified Dirichlet kernel that is more or less the biggest math result I ever found. But the rest of these people it is just another batch of overpaid non performers. It’s just an opinion so you don’t have to agree with it, but why do so many people get boatloads of money while they contribute not that much?
End of thing 2.
Now we are finally ready to post the main dish in this post: the proof that the subset of four dimensional rational numbers form a field. Math professors always think it is ‘very important’ if something is a field while in my life I was never impressed that much by it. And now I am thinking about it a few weeks more, the less impressed I get by this new field of four dimensional complex numbers. Inside the theory of higher dimensional complex numbers the concept of ‘imitators of i‘ is important: these are higher dimensional numbers that if you square them they have at least some of the properties of the number i from the complex plane. They rotate everything by 90 degrees or even better they actually square to minus one. Well one of the imitators of i in the space of 4D complex number is dependent of the square root of 2. As such it is not a 4D rational complex number. That detail alone severely downsizes my enthousiasm. But anyway, the next pictures are also a repeat of old important knowledge like the eigenvalue functions. Instead of always trying to get the eigenvalues from some 4×4 matrix, with the eigenvalue functions with two fingers in your nose you can pump out the eigenvalues you need fast. This post is six pictures long each size 550×825 pixels. Here we go:
Yes that is the end of this post that like always grew longer than expected. If you haven’t fallen asleep by now, thanks for your attention and don’t forget to hunt the math professors until they are all dead! Well may be that is not a good idea, but never forget they are too stupid to improve on the little Fermat theorem and of course we will hear nothing from that line of the profession…
Man oh man, the previous post was from 12 Nov so time flies like crazy. Originally I wanted to write a post on a thing you can look up for yourself: the Dirac quantization condition. I have an old pdf about that and it says that it was related to the exponential circle on the complex plane. Although the pdf is from the preprint archive, it is badly written and contains a ton of typo’s and on top of it: the way the Dirac quantization is formulated is nowhere to be found back on the entire internet. In the exponent of the exponential circle there is iqg where q represents an elementary electric charge and g is the magnetic monopole charge according to Paul Dirac. Needless to say I was freaked out by this because I know a lot about exponential curves but all in all the pdf is written & composed so badly I decided not to use it.
After all when I say that electrons carry magnetic charge and do not have bipolar magnetic spin, the majority of professional physics professors will consider this a very good joke. And if I come along with a pdf with plenty of typo’s the professional professors will view that as a validation that I am the one who has cognitive problems and of course they are the fundamental wisecracks when it comes to understandig electron spin. Our Pauli and Dirac matrices are superior math, in the timespan of a hundred years nothing has come close to it they will say.
Here is a screen shot of what freaked me out:
Furthermore I was surprised that the so called professional physics professors have studied stuff like ‘dyons’. So not only a Dirac magnetic monopole (without an electric charge but only a magnetic charge), a dyon is a theoretical particle that has both electric and magnetic charge. But hey Reinko, isn’t that what you think of the electron? There are two kinds of electrons, all electrons have the same electric charge but the magnetic charge comes in two variants. There are so many problems with the idea that electrons are magnetic dipoles, but the profs if you give them a fat salary will talk nonsense like they are a banker in the year 2007.
So I decided to skip the whole Dirac quantization stuff and instead focus a bit on factorizing the Laplacian differential operator. I the past I have written about that a little bit, so why not throw in a Google search because after all I am so superior that without doubt my results will be found on page 1 of such a Google search! In reality it was all ‘Dirac this’ and ‘Dirac that’ when it comes to factorization of the Laplacian on page 1 of the Google search. So I understood the physics professors have a serious blockade in their brains because this Dirac factorization is only based on some weird matrices that anti-commute. These are the Pauli and Dirac matrices and it is cute math but has zero relation to physical reality like the electron pairs that keep your body together.
No more of the Dirac nonsense! I sat down and wrote the factorization of the Laplacian for 4D complex numbers on a sheet of paper. Let me skip all this nonsense of Dirac and those professional physics professors and bring some clarity into the factorization of the Laplacian. It took at most 10 minutes of time, it is just one sheet of paper with the factorization. I hope this is readable:
So that is what I have been doing since 12 April, since the last post on this website. I have worked my way through the 2D complex plane, the 3D complex numbers and finally I will write down what did cost me only 10 minutes of time a few weeks ago…
In a few days the post wil be ready, may be this week. If not next week & in the meantime you are invited to think about eletrons and why it is not possible that they are magnetic dipoles.
For a couple of years I have a few pdf files in my possession written by other people about the subject of higher dimensional complex and circular numbers. In the post we will take a look at the work of Shlomo Jacobi, the pdf is not written by him because Shlomo passed away before it was finished. It is about the 3D complex numbers so it is about the main subject of this website.
Link used: http://search.arxiv.org:8081/paper.jsp?r=1509.01459&qid=1603841443251ler_nCnN_1477984027&qs=Shlomo+Jacobi&in=math
Weirdly enough if you search for ‘3D hypercomplex number’ the above pdf does not pop up at all at the preprint archive. But via his name (Shlomo Jacobi) I could find it back. Over the years I have found three other people who have written about complex numbers beyond the 2D complex plane. I consider the work of Mr. Jacobi to be the best so I start with that one. So now we are with four; four people who have looked at stuff like 3D complex numbers. One thing is directly curious: None of them is a math professional, not even a high school teacher or something like that. I think that when you are a professional math professor and you start investigating higher dimensional complex numbers; you colleagues will laugh about it because ‘they do not exist’. And in that manner it are the universities themselves that ensure they are stupid and they stay stupid. There are some theorems out there that say a 3D complex field is not possible. That is easy to check, but the math professionals make the mistake that they think 3D complex numbers are not possible. But no, the 2-4-8 theorem of say Hurwitz say only a field is not possible or it says the extension of 2D to 3D is not possible. That’s all true but it never says 3D complex numbers are not possible…
Because Shlomo Jacobi passed away an unknown part of the pdf is written by someone else. So for me it is impossible to estimate what was found by Shlomo but is left out of the pdf. For example Shlomo did find the Cauchy-Riemann equations for the 3D complex numbers but it is only in an epilogue at the end of the pdf.
The content of the pdf can be used for a basic introduction into the 3D complex numbers. It’s content is more or less the ‘algebra approach’ to 3D complex numbers while I directly and instantly went into the ‘analysis approach’ bcause I do not like algebra that much. The pdf contains all the basic stuff: definition of a 3D complex number, the inverse, the matrix representation and stuff he names ‘invariant spaces’. Invariant spaces are the two sets of 3D complex numbers that make up all the non-invertible numbers. Mr. Jacobi understands the concept of divisors of zero (a typical algebra thing that I do like) and he correctly indentifies them in his system of ‘novel hypercomplex numbers’. There is a rudimentary approach towards analysis found in the pdf; Mr. Jacobi defines three power series named sin1, sin2 and sin3 . I remember I looked into stuff like that myself and somewhere on this website it must be filed under ‘curves of grace’.
A detail that is a bit strange is the next: Mr. Jacobi found the exponential circle too. He litarally names it ‘exponential circle’ just like I do. And circles always have a center, they have a midpoint and guess how he names that center? It is the number alpha…
Because Mr. Jacobi found the exponential circle I applaud him long and hard and because he named it’s center the number alpha, at the end I included a more or less new Euler identity based on a very simple property of the important number alpha: If you square alpha it does not change. Just like the square of 1 is 1 and the square of 0 is 0. Actually ‘new’ identity is about five years old, but in the science of math that is a fresh result.
The content of this post is seven pictures long, please read the pdf first and I hope that the mathematical parts of your brain have fun digesting it all. Most pictures are of the standard size of 550×775 pixels.
Ok ok, may be you need to turn this into exponential circles first in order to craft the proof that a human brain could understand. And I am rolling from laughter from one side of the room to the other side; how likely is it that professional math professors will find just one exponential circle let alone higher dimensional curves?
I have to laugh hard; that is a very unlikely thing.
End of this post, see you around & see if I can get the above stuff online.
This post took me a long time to write, not that it was so very difficult or so but lately I am learning that graphics program named GIMP. And that absorbs a lot of time and because I am only sitting behind my computer a few hours a day, doing GIMP goes at the expense of writing math…
I always make my pictures with an old graphics program named Picture Publisher 10. It is so old that on most windows 7 and windows 10 it does not run but it has all kinds of features that even the modern expensive graphics programs simply still don’t have. Silently I was hoping that I could use GIMP for my math texts and yes that could be done but in that case I have to use old background pictures forever. Or I have to craft a ‘new style’ for making the background in the math pictures that can last at least one decade.
But let’s not nag at what GIMP cannot do, if you install just one large addon you have about 500 filters extra and my old program PP10 comes from an era when the word ‘addon’ was not a word used ever. Before we jump to the math, let me show you a nice picture you can make with the tiling filter inside GIMP. It is about my total bicycle distance since I bought this bicycle computer, it says 77 thousand km so the Tour the France racers can suck a tip on that:
Ok, let us look at the math of this post. This is part 22 in the introduction to the 4D complex numbers. The 4D complex numbers have three imaginary units, l, l^2 and l^3. And the stuff that makes it ‘complex’ is the fact that l^4 = -1, you can compare that to the complex plane where the square of the imaginary unit equals -1.
On the complex plane, if you know what the logarithm of i is, you can use that to find the exponential circle also known as the complex exponential. This is what the number tau always is in all kinds of spaces: It is always the logarithm of the first imaginary unit that has a determinant of +1. In this post we will calculate the eigenvalues of this important number tau. That will be done with two methods. In the first method we simply use the eigenvalue functions, plug in the number tau and voila: out come the four eigenvalues. In the second method we first calculate the four eigenvalues of the imaginary unit l and ‘simply’ take the logarithm of those four eigenvalues.
It is not much of a secret that my style of work is rather sloppy, I never order my work in theorems, lemma’s or corrolaries. It is not only that such an approach if too much a straight jacket for me, it also frees me from a lot of planning. I simply take some subject, like in this case the eigenvalues of the number tau and start working on explaining that. While writing that out there always comes more stuff around that I could include yes or no. In this post what came around was that only after writing down the four eigenvalues I realized that you can use them to prove that the exponential curve (the 4D complex exponential) has a determinant of 1 for all points on that curve. That was an important result or an important idea so I included it because that makes proving that the determinant is 1 much more easy.
Now a few posts back with that video from that German physics guy Alexander Unzicker I said that he (and of course all other physics professionals) could always use the 4D complex exponential curve for the ‘phase shifts’ that those physics people always do. But for doing such 4D ‘phase shifts’ or unitary transformations in general, you need of course some kind of proof that determinant values are always +1. Well Alexander, likely you will never read this post but below you can find that very proof.
The previous post was from the end of August and now I think about it: Have I done so little math during the last four weeks? Yes there were no results simply left out, it was only penning down these eigenvalues of tau and the idea you can use these eigenvalues for proving the 4D exponential curve always has a determinant of 1. It is amazing that GIMP can hinder the creation of fresh math… 😉
The math pictures are seven in number, all in the usual size of 550×775 pixels. I hope you like it and see you in the next post.
So these are the four eigenvalues of the number tau and based on that the four eigenvalues of the 4D complex exponential for a values of time.
That’s it for this post. See you in a future post.
Added on 27 Sept 2020: This proceeds the two pictures made with GIMP that started this post. I just made the whole stuff on a cube (actually it is a beam because the starting picture is not a square). It is amazing how good such filters in GIMP are:
I want to start with a bit of caution: In this post you can find the definition of the 4D Fourier series. It looks a lot like the definition as on the complex plane. But I still did not prove all those convergence questions. And I also do not remember very much from the time when I had that stuff as a student (that was about 30 years ago). So I don’t know if I will be able to make such proofs about convergence and what kind of functions you can use to make a Fourier series from etc etc.
Yet in this post I define a set of possible signals that I name ‘pure tones’ and these clearly have a 4D Fourier expansion because by definition they have a finite number of non-zero Fourier coefficients. Of course when you only have a finite amount of non-zero coefficients, you don’t have any kind of convergence problem. So for the time the convergence problems are avoided.
In this post, number 154 already, I hope I demenstrated enough that the basis functions used in the definition are all perpendicular to each other. After all that was a nasty hurdle we met when it was tried with just the four coordinate functions of the 4D exponential curve as our basis vectors. So we do not meet that problem again using the exponential curve as a whole. If I denote the exponential curve as f(t), the basis functions we use are basically f(nt) where n is a whole number. Just like in the previous posts I always use the notation f(t) when the period is related to the dimension and g(t) when the period is different. Here I use of course a period of two pi because that is convenient and it makes the coordinate functions more easy to write out: the first one is now cos(t)cos(2t) and the other three are just time lags of the first one. But if you want to write g(t) as an exponential, because of the period it now looks a bit more difficult compared to just e to the power tau times t.
For myself speaking I have no idea at all if crafting a Fourier series like this has any benefits of using just the definition as on the complex plane. After all I only have more or less basic knowledge about the use of Fourier series, so I just don’t know if it is ‘better’ in some regards and ‘worse’ in others.
At last without doubt under my readers there will be a significant fraction that wonder if those 4D complex number system is not some silly form of just the complex plane? After all if that 4D space is based on some imaginary unit l with the property that now the fourth power l^4 = -1, how can that be different from the complex plane? The answer to that lies in the logarithm of the first imaginary unit l. If this 4D space was just some silly extension of the complex plane, this log of l should be nicely bound to i pi/4 where i is of course the imaginary unit from the complex plane. But log(l) is the famous number tau because with that you can make the exponential curve f(t) = e^(tau t). Basically the main insight is that i pi/4 makes the complex exponential go round with a period of four because i^4 = 1 and the 4D number tau makes the exponential curve go round with a period of 8 because l^8 = 1.
This post is six pictures long, all 550×775 pixels in size.
As usual I skipped a lot of stuff. For example, how did Fourier do it? After all at the time all this stuff with inner products was poorly developed or understood. That alone would be a cute post to write about. Yet the line of reasoning offered by Joseph Fourier was truly brilliant. In case you are lazy or you want to avoid Google tracking you, here is a link to that cute symbolab stuff: symbolab.com Link used: https://www.symbolab.com/solver/fourier-series-calculator
Ok, that is what I had to say for this tiny math update.
Oh oh, this is one of those posts where I only calculate in the 3D circular numbers while I classify it as 3D complex numbers. In the past when I made those categories on this website I did not want to have too many categories so that is why I only have 3D complex numbers as a category.
All in all this post (number 146 already) is not extremely important because over the years I have given many proofs that the parametrization for the exponential circle indeed fulfills all those equations like the sphere-cone equation of the fact the determinant is always one. On the other hand, if you have an important mathematical object like the exponential circles, it is always good to have as many proofs as possible. Just like there are many proofs for the theorem of Pythagoras, it would be strange if we only had one proof and nobody cares about more proofs to that theorem that more or less the central to a giant mountain of math.
What do I mean with ‘first principles’? Very simple: that is the summation formula for the exponent of a linear operator or the matrix exponential if you want. In this post I use a somehow slightly different number tau; I use a number tau that gives a period of 2 pi for the exponential circle. The reason is simple: that makes the long calculation much more readable.
Another thing I want to mention is that the long calculation is nine lines long. For myself when I read the works of other people I do not like it if calculations go on and on and on. I always try to avoid too long calculations or I just don’t write posts about them. Almost nobody reads the stuff it it’s too long and gets too complicated so most of the time I simply skip that. Beside that there is always 0% feedback from the mathematical community, so although I always year in year out try to keep it so simple that even math professors can understand it, nothing happens. Just nothing, so after all those years it is not much of a miracle I don’t want to engage with these overpaid weirdo’s at all. Likely if you are born stupid you will die stupid & I have nothing to do with that. Mathematics is not a science that is capable of cleaning itself up, the weirdo’s keep on hanging to their fantastic quaternions and their retarded ideas of what numbers & complex numbers are. Too much money and too much academic titles have not lead to a situation where the science of math is capable of cleaning itself when needed.
Enough of the blah blah blah, after all the physics professors have the same with their electron spin: where is your experimental proof that the electron is a magnetic dipole? For over five years nothing happens except a lot of weird stuff like quantum computers based on electron spin…
This post is five pictures long, for me it was cute to see how those three cosine functions slowly rise from the start of the long calculation. Also of importance is to notice that I had to use the simple formula for cos(a + b) = cos(a)cos(b) – sin(a)sin(b) that comes from the exponential circle in the complex plane. Just once more showing that 3D complex & circular numbers are indeed emerging from the 2D complex plane. Not that the math professional will react, but anyway…
Let’s go to the five pictures:
Again, this is not a ´very important´ post. Given all those results and proofs from the past it is logical such a long calculation has to exist. It´s relevance lies in the fact you simply cannot have enough proofs for the calculation of parametrizations of the 3D exponential circle.
Let me leave it with that. See you in the next post.
This time a somewhat different post, just 3 video’s I thought are interesting to share for their own reasons. In the first video the American television physics professor Brian Greene goes beserk on the beauty of the exponential circle in the complex plane… Brian, like so many others, do not know what they are missing. So many spaces have exponential circles and curves and indeed they are beautiful.
The second video is about a question that is often asked: Is math invented or is it a discovery? I think this is a false way of looking at math, if you replace the word ‘math’ by ‘food’ you already understand this is a weird question: Is food invented or is it discovered? In my view that often goes hand in hand but opinions vary wildly on this subject. The video is an interview with the UK math professor Roger Penrose. I included this video because back in the 80-ties of the previous century Roger had written some books on the things known as spinors. A lot of so called scientists think that spinors have something to do with electron spin, there are even weirdo’s that think after the electron has encircled the nucleus once it’s spin state is altered so that after two rounds the electron has it’s original spin back… Oh oh for people like Roger and those others it will be a long way in understanding the electron cannot be a magnetic dipole. In all ways possible that is not logical. For example the unpaired electron is not magnetically neutral while the electron pair is. And there are a whole lot more examples to be given showing electrons simply can’t be magnetic dipoles. And you only have to use the thing called logic for that; no weird quantum mechanical stuff but just a magnetic charge on the electron gives much better results if you use the thing called logic.
The third video is about a weird line of reasoning that I have observed in many video’s. It is about explaining how those jets form that emerge from black holes and their accredion disks. The reasoning is that the plasma in the accretion disk goes around the black hole and if a charge goes round it produces a magnetic field & that is all explanation given always. That is nonsense of course, even spinning metals like when you are drilling a hole with your drill machine never produces a magnetic field because for every electron that goes round on average also a proton goes round and all in all there is no overall magnetic field created. But if the electrons are magnetic monopoles, they will have much more acceleration compared to the far more heavy protons and as such an accretion disk around a black hole should be positively charged all of the time and that explains why the magnetic fields are so strong over there.
Ok, I crafted 8 pictures from the stuff. For example I made a 4D generalization of the 3D outer product while explaining such math is an invention and not a discovery. After the 8 pictures I will post the three video’s that aroused my attention for one reason or another. Have fun reading it.