This is another lightweight easy going summer update. It is about matrix representations and how to find the conjugate of a 3D complex or circular number. I use the case of the complex plane of 2D conplex numbers to show that conjugation is not some silly reflection just always but rather simple will always be the upper row of a proper matrix representation. As a matter of fact it is so easy to understand that even the biggest idiots on this planet could understand it if they wanted. Of course math professors don’t want to understand 3D numbers so also this new school year nothing will happen on that front…
Did you know that math professors study the periodic system? Yes they do, anyway in my home country the Netherlands they do because every year they get a pay rise and that pay rise is called a periodic. And as such they study the periodic system deep and hard…
I classified this post only under the categories ‘3D complex numbers’ and ‘matrix representations’ and left all stuff related to exponential circles out. Yet the exponential circle stuff is interesting; after reading this post try to find out if the numbers alpha (the midpoint of the exponential circles) are symmetrix (yes). And the two numbers tau (the log of the first imaginary unit on the circular and complex 3D space) are anti-symmetrix (yes).
This post is just over 7 pictures long. As the background picture I used the one I crafted for the general theorem of Pythagoras. (Never read that one? Use the search funtion for this website please!) All pictures are of the usual size namely 550×775 pixels.
It is a cute background picture, I remember it was relatively much work but the result was fine.
Ok, that was it for this update. Although it is so very simple (for years I did not want to write of just two simple planes that contain all the self-conjugate numbers) but why make it always so difficult? Come on it is summer time and in the summer almost all things are more important than math. For example goalkeeper cat is far more important compared to those stupid 3D numbers. So finally I repost a video about a cat and that makes me very similar to about 3 billion other people.
A lovely video was found where a guy from the Nottingham university is showing his workplace around. And they have that heavy equipment for making permanent magnets in just one blast. In the first five years of looking at magnetism I only told you about that slow process of heating up the material till above the Curie temperature, applying an external magnetic field, cool everything down slowly and voila: there are your permanent magnets! But you can do it in one blast too, all you need is a very strong applied magnetic field. For me that is nothing new because my father worked at the local electricity plant and decades back they too had the equipment to make a permanent magnet in one short blast. At an electricity plant they have plenty of electricity anyway so why waste that? (My father worked at the electric meter department and in those times they used permanent magnets in the electricity meters you had in your home or your business.)
Anyway, if my version of electron spin is true and electrons are not magnetic dipoles but come in two varieties carrying magnetic charge, in that case the ‘permanent’ in a permanent magnet arises from the fact that the unpaired electrons are shielded in the inner atomic orbitals. That is what makes them permanent… All that blah blah of electron spins aligning themselves to the applied magnetic field is pure nonsense, that blah blah does not explain why the magnetism is permanent. Of course professional physics professors will always point to the tiny detail that if you think you understand quantum mechancis, you don’t understand quantum mechanics… Now I too have a lot of things that I do not understand in quantum mechancis, but I think the electron being a magnetic dipole is 100% bullshit. They carry magnetic charge because that makes more sense and is a far more simple explanation of what we observe…
After having said that, if a permanent magnet always has it’s unpaired electrons that give rise to the emergent magnetism always in it’s inner orbitals, in that case if you blast them with a giant external magnetic field they should always heat up. They heat up because the unpaired electrons feels a relatively giant force from the applied magnetic field and as such are ripped out of those inner orbitals. And all ripped out electrons are replaced by electrons of the opposite magnetic charge… It’s as simple as it is.
Here is the video it is only 15 minutes long:
How do you prove electron bipolar magnetism?
Ok, let me end this post with a picture made from two screen shots from the video. In the top screen shot you see at the left those strips of metal. Wow man, those strips of metal are the wires that transport the 10 to 20 thousand Ampere blast. In the lower screen shot you see the blue machine where the magic seems to happen.
Ok that was it. If you make permanent magnets and they are not heated at the end, I am wrong about my electron idea’s… Only a professional physics professor will lamentate that applying a short energy burst of only 20 thousand amps will likely heat up everything.
This is a lazy easy going summer post, it does not have much mathematical depth. Let’s say the depth of a bird bath. But with most posts I write you also need a lot of knowledge about what was in previous posts and for the average person coming along that is often too time consuming… So we keep it simple today; quadratic forms on 3D space.
If you have had one or two courses of linear algebra you likely have encountered quadratic forms. They are often denoted as Q(X) where the X is a column matrix and the quadratic form is defined as Q(X) = XT A X. Here XT is the transponent of X so that would be a matrix row. As you might guess, the X column matrix contains the variables while the constant square matrix A is the source of coefficients in the quadratic form Q(X). In most literature it is told the matrix A is symmetric, of course there is no reason at all for that; any square matrix will do. On the other hand it is easy to see or to show that if a square matrix is anti-symmetric the corresponding quadratic form will always be zero everywhere.
In this post we will take matrices that are always the matrix representation of 3D complex & circular numbers. Matrix representations are a complete category on this website so if you don’t know them you must look that up first. (Oh oh, here I go again: this was supposed to be easy but now the average reader must first try to understand matrix representations of higher dimensional multiplications…)
Compared to the previous update on the likely failure of all fusion reactors this post is far less dramatic. If in the future I am right and we will never have fusion power, that will be the difference between life and death of hundreds of millions of people in the long run… So in order to be a bit less depressing let’s lift the spirits by a lightweight new post on quadratic forms! Why not enjoy life as long as it lasts?
Ok, the actual post is seven pictures long, all in the usual size of 550×775 pixels.
As you see the math is only bird bath deep.
I have to admit that for me the use of the number alpha was important because that is at the center of the exponential circles in the 3D complex and circular spaces. So I have a legitimate reason to post this also under the category ´exponential circle´. And from the non-bird bath deep math, that is the big math ocean that is very deep, I like to classify as much posts under that category ´exponential circles´.
Ok, let´s leave it with that and try to upload this post. Till updates my dear reader.
To be precise: I am talking about all nuclear fusion reactor designs that use magnetic confinement for the fusion plasma. So these are the standard tokamak reactors that are build in a lot of places but also the stellarator fusion reactor from the Max Planck institute in Germany. Some years ago it came to my attention that the USA based company Lockheed Martin was also going into the fusion reactor thing and they were bragging about new technology and making mobile 100 Mega Watt nuclear fusion reactors. But their talk was a little bit strange, it was some CEO kind of guy that explained how their new technology would outbeat the tokamak design because with the new much stronger magnetic fields they could make, the magnetic field would be much stronger at the place of the fusion vessel wall. According to the Lockheed Martin CEO type of guy, plasma was diamagnetic and as such would stay away from the fusion reactor wall. Needless to say I had to laugh because in my view on physical reality electrons carry magnetic charge and will always make fusion plasma instable. In fusion reactions the protons (or the isotopes of hydrogen to be precise) need to fuse and that cannot be done if electrons constantly get accelerated to relativistic high speeds.
A few years back a lot of folks were bragging that by the year 2019 Lockheed Martin would have those mobile nuclear fusion reactors on large trailors, something like 100 Mega Watt per mobile unit. If they would have pulled that off, Lockheed Martin might be the first company to achieve a market capitalization of 10 trillion US$. That would be gigaenormous because after all 10 trillion = 10 thousand billion…
It was supposed to look like this:
Wow the first 10 trillion company!
As you see, the 2013 pipe dream is still not at the scene now in 2019. Why not? Well if plasma theorists keep on using the electron as a magnetic dipole, all of the advanced models they have for plasma behaviour will never depict an accurate picture of physical reality.
If in practice electrons come in two varieties, monopole north and south ones, in all of those fusion reactor designs they will move in opposite directions. It is more or less ‘along the magnetic field lines’ because all acceleration caused by the magnetic field makes the electrons accelerate in that direction. And this acceleration in two directions that will grow in a turbulent fashion and make the fusion plasma uncontrolable.
In this regard, I mean how turbulence arises, the density of the plasma is an important factor. In a low density plasma the electrons will have plenty of acceleration before they interact with other plasma particles. The denser the plasma is the shorter the length of those interaction free paths, that is obvious. In all present day plasma models, there is nothing that makes electrons accelerate along the magnetic field lines. That means all those models are wrong.
Before we go on with wrong mathematical models of plasma behaviour, sometimes the news upon nuclear fusion can be very funny. I just made an intenet search upon ‘Lockheed Martin nuclear fusion’ and I stumbled upon the next hilarious title from Yahoo finance:
As you see in this world there is just never a shortage of idiots; at Lockheed Martin they do not understand why the fusion plasma gets so instable but compared to the total idiots of Yahoo finance the Lockheed people look like pure Einsteinian human material… How stupid and 100% uninformed you must be to think that Lockheed is chasing cold fusion reactors…
Ok, a bit more on those math models they use to simulate plasma behaviour. It was in 2016 I came across that weird news from MIT, they simulated very large scale with lots of computer time how plasma should behave. There was actually an electron going round the entire plama vessel. Now my dear reader I was dumbfounded, if the electron is a magnetic dipole, how could it go round?
In my world where plasma electrons carry magnetic charge, the only thing the electrons want to do is going round and round… I never found how the model works that was used by the MIT smart asses, but here is a short video of the ‘result’ of the MIT plasma simulation:
Oh oh, that nasty turbulence…
In the video description there is a link where it even get more hilarious. Let me quote it:
A long-standing discrepancy between predictions and observed results in test reactors has been called “the great unsolved problem” in understanding the turbulence that leads to a loss of heat in fusion reactors. Solving this discrepancy is critical for predicting the performance of new fusion reactors such as the huge international collaborative project called ITER, under construction in France.
Comment: Don’t worry, ITER will never work if electrons carry magnetic charge. Plus the famous standard model says electrons are magnetic dipoles, so why worry that ITER will fail & fall flat on it’s stupid face? Link where you can find the quote:
Benford’s law is a statistical observation. If I remember the story more or less correct, Benford found at some point in time that those old logarithm tables had pages that were far more worn out compared to others. And it seems that people used those old (but at the time very important) tables much more for numbers starting with small digits like 1 or 2 and much less for high leading digits like 8 or 9. The observation was that the probability of a leading digit of d was given by log(1 + 1/d). I remember that during a train ride to the city of Utrecht about two decades ago I found a very simple distribution that gives the Benford law perfectly for numbers written in the usual base 10. Basically if you use a uniform distribution in the exponent, that more or less always gives rise to some approximation of Benford’s law.
Yet the way I did the stuff two decades back suggests that it is very hard to make a continuous distribution on such a large interval like 0 to infinity (the positive real line). So I decided to give a bunch of examples that all give Benford’s law perfectly. And I skipped studying the theorem at the end of the article of Kazifumi Ozawa. Yet that theorem of Suihara looks very interesting so may be that is something for a future post although this website is more or less dedicated to higher dimensional complex numbers of course.
The math in this post is more or less as basic as it gets: You need to know what the logarithm with base 10 is and it would be great you need the first course basics of probability theory. So it is handy you know about probability density functions p(x) and if you integrate them you get the probability for a particulat set. I guess all university introductionary courses in probability theory cover that for a lot of studies like math, physics, chemistry, biology and so on. Ok, it is handy if you can integrate such probability densities a bit but I have to admit I skipped all things related to that (so basic is this post). But I skipped a lot of things yet this post is still 10 pictures long. All pictures are of size 550 x 775.
That´s it for this post. Till updates my dear reader.
I am sitting on my couch watching Youtube videos while the dog is lying next to me. Is the dog always shaking from fear that I will beat her up? Come on, she is a dog and not a math professor! Anyway to my amazement there is a video from the David Pakman show with Sean Carroll, Sean is one of those television physics professors that you see relatively often on television or other media outlets. I get a warm feeling in my stomach because I can listen to the intelligent words of Sean, he truly is a high shot smart ass. So I play the video and everything looks fine but all of a sudden Harry Potter materializes behind the show presentator David Pakman and why does Harry Potter look so angry? Something to do with Brexit or so?
All of a sudden Harry Potter pulls his magic wand, points to to Sean Carroll and he shouts ‘Imbicilus Totalus!’. A sudden flash of lightning leaves the magic wand and enters the head of Sean. Slowly David Pakman is turning around to see what is behind him but Harry is much faster; out of a bag he pulls a short broom with a big handle and I can read the inscription on the broom. It is a SmartAss3000, fast and with a routine Harry sticks it in his ass and he flies away in the darkness of the night. Wow man that is totally different from what I remember from those Harry Potter movies! How life changes over time… May be those old Harry Potter movies are now in some parallel universe far far away.
I need to calm the dog because the dog understands I am very agitated so I explain to her that not all humans do such weird stuff with a SmartAss3000. Loïs does not seem to understand what I am trying to say but since I am calm again she waggles her tail and soon she calms down again. Finally I started to watch the video while hoping that Harry Potter did not do too much damage with the Imbicilus Totales curse. My hopes were idle, after all Harry is a very good wizard, and after about 8.30 minutes Sean Carroll explains electron spin: “If you measure electron spin, the electron can only spin clockwise or counter clockwise” Sean explains… Oh oh, Harry Potter clearly succeeded with his curse because just a few posts ago we calculated that the electron needed to spin many times the speed of light in order to explain the magnetic properties the electron has. Say it needs to spin about 100 times the speed of light, in that case any electron spinning can account for at most 1% of it’s magnetic behaviour. No problem for Sean Carroll: it is spinning clockwise or counter clockwise and that is enough explanation for him…
Well not for me because I have a long list of problems with electrons being magnetic dipoles (the official version of an electron is that it is a magnetic dipole, of course we have zero experimental proof of that but who bothers?) The clockwise / anti clockwise spinning of an electron is nonsense because if it is a magnetic dipole, that vector can point into any direction. But as far as I see reality, all experiments point much more towards electrons having a magnetic charge. That is electrons are all magnetic monopoles and not magnetic dipoles.
But Sean is not the only to hang on the electron magnetic dipole thing, at CERN there are thousands of physics professors that actually think that electrons are pure point particles, that is they have no volume but are true points. If that were true, if the electron has no size, it would be completely impossible to accelerate electrons with a magnetic field like in the Stern Gerlach experiment. By the way, here is the video:
Ok, after having said that kind of stuff, the next post will be about Benford’s law. If I remember it correctly I worked a short time on that nice law back in the year 1999. One or two weeks back I made a search on the preprint archive and after a bit of thinking I decided to craft a post for this website out of it. It is very easy to find and craft all kinds of probability distributions that fit Benford’s law perfectly. Benford’s law is about numbers as we find them in nature and gives the probability distribution for the leading digit. Do an internet search if you never heard from it. Here is a teaser picture to get started for the next post:
I just finished brewing the 100-th batch of a beer under the names Dark Matter and Spin 1/2 beer. All in all that is an amazing amount of beer; in the past I brewed 35 liter per batch but now it is 40 liter per batch so all in all an amount of something between 3500 and 4000 liters… So ein prosit my dear reader.
The ‘new’ roots of unity aren’t that new, this post is a re-editing of something I posted on 05 Jan 2014 on the other website. Later that year I started this website. Actually these roots of unity are just over five years old. In mathematical terms that is still very young so in that sense they are still new.
Recall the roots of unity in the complex plane are solutions to z^n = 1 and as such these roots are found on the exponential circle (the complex exponential) in the complex plane. As you have found the exponential circle or exponential curve in some space, from that you can always make new roots of unity. That is hardly a mathematical achievement because it is so simple to do once you have found your exponential circle or curve. But in the diverse spaces these new roots of unity behave very different, for example in this post we will add them all up but unlike in the complex plane they do not add up to zero. That is caused by the fact that in the complex 3D space the number alpha is at the center of the exponential circle, as such if we add n roots of unity in 3D space the result is n times alpha. Last year we studied the space of 4D complex numbers and if you would craft new roots of unity in that space it will behave much more like those in the complex plane because in the 4D complex numbers we have 0 as the center of the exponential curve. (For dimensions above 3 the exponential curve always lies in a hyperplane so it can never be a circle.) It always amazes me that you have all those physics people who study string theory but as far as I know never use exponential curves…
Life is beautiful, because how can you do string theory without math like that? But in physics almost everything is beautiful, for example if they explain the outcome of the Stern-Gerlach experiment always 50% of unpaired electrons align with the applied magnetic field and the other 50% for some mysterious reason do the anti-align thing. And if one hour later the same physics professor explains how a permanent magnet can attract some piece of iron, all of a sudden 100% of the unpaired electrons align and all that talk of 50/50 suddenly is not observed… Life inside the science of physics is wonderful; all you have to do is a bit of blah blah blah and if people complain this is not logical at all you simply say: Quantum physics is such that if you think you understand it, you don’t understand it… How wonderful is the life of physics professors; talk some blah blah blah and if people complain you blame them for ‘not understanding quantum things’. For sure that is a beautiful form of life.
But enough of the talking, somewhere in the next seven pictures I did forget to insert a graph of the determinant. Yet I showed you the structure of the non-invertible numbers so often, I think I post it with that fault included. After all why should life be perfect? If life would be perfect you would have no way of improvement and likely that is the moment you die: no more possibility of improvement. As usual the pictures are 550×775 pixels but I had to make the first one a tiny bit longer. Good luck with digesting it & have a bit of fun in the process.
End of the pictures.
For myself speaking it was fun to read my own two proof for the rain theorem again after five years. Please do not forget that new roots of unity on other spaces can be very different in behavior, after all they are always part of the exponential circle or curve in that space so they will derive their math properties from that. Till updates.
At first I wanted the next post to be about the so called Bell experiment because with this experiment comes the so called Bell inequalities and weirdly enough these are a perfect for the determinant of 4D complex numbers. Everything just looked perfect: the Bell inequality has maximum breaching when a bunch of correlations takes on the value of two time the square root of two. But that value of two time the square root of two is also what makes a 4D complex number on the unit sphere in 4D space noninvertible… So everything looked perfect but in the end it did not work because I could only find solutions with correlations above 1 (or below -1) and we all know that is not possible.
So let’s put the stuff on the shelf and wait a few years… The Bell experiment is one of those crazy quantum experiments and I am very interested in it because the original proposition as done by Mr. Bell was done with electrons and positrons. Yet results with electrons and positrons have never been published, all there is are experiments with photons and all those experiments seem to violate the Bell inequality…
Anyway a few days back I came across some old work I had written and that contained stuff like the anihilation theorem and the rain theorem, I did absolutely not remember what it all was about. And oh yes, it was that time that I wrote about a new set of so called roots of unity. And I remembered that I more or less hoped all those years ago about some kind of reaction from the math professionals. Of course there was zero reaction one more year; in those long lost years I still had to learn that university math professors are all shit. That is a uniform property of those people; they are all perfumed princes in relatively high paid permanent jobs. And perfumed princes do what the average perfumed prince think is important: we do perfumed prince stuff like the Langlands program and oh oh oh how smart we are. Luckily we have no dealings with those dirty peasants that live in the mud and cannot afford our exclusive perfumes. Tax payers should be happy they can finance us because what is a modern economy without smart math professors?
Once more I was stupid to the bone: The fact that you can easily find 10 videos with math professionals stating that the roots of unity are so very wonderful does not mean if you throw in a new set of unity roots there will be a healthy response…
I will leave the new post more or less like the old one, I only change the title and will do some editing to make it more readable. For example in the past I used the matrix environment for multi-line calculations while at present day I use the align command in the Latex typesetting program.
Here is the old file from five years back:
The Song of Omega Reloaded http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff02.htm#05Jan2014
Ok, a small screen shot of the new roots of unity. Actually they are already five years old but the perfumed math professors have of course better things to do. They are so smart…
As you see it could use a bit typo improvement, in the meantime let it rain perfume.
End of the intro to the rain theorem.
Ok, I have done editing and decided to make a very simple teaser picture containing a simple calculation that indeed shows that if you square the opposite point of 1 on the exponential circle you get +1. As such we have three solutions to the equation X^2 = 1 in the complex 3D space: the usual X = +1 and -1 and the third solutions lies on the exponential circle. Here is the teaser picture and likely later this week I will hang in the rest on this website.
Ok, it is not an advanced & fancy calculation but it is still 1.
This post is a continuation of the 01 May post on magnetism where we estimated that it is totally impossible that actual spinning of the electron would cause it’s magnetic properties. In the 01 May post I told you I had never seen how in physics they think electrons get accelerated in an inhomogeneous (and constant in time) magnetic fields. But when I finally tried to do some internet searching it was terrible easy to find. The offcial view is that they have an expression for the potential energy and the force is simply the gradient of the potential energy. But in order to explain the splitting in a beam in two in the Stern-Gerlach experiment something very strange has to happen: half of the electrons go into a somewhat lower energy and the other half in a somewhat higher state.
By all standards this is strange. Compare it for example to the next: You are standing on top of a building or a mountain and you start throwing rocks. Half of those rocks start falling to the ground as as such they are lowering their potential energy. The other half start flying up and as such gain potential energy like they feel anti-gravity. By all standards this is strange…
In my version of electrons where they are not magnetic dipoles but carry magnetic charge, you do not have this strange energy behavior because all electrons simply will follow their magnetic charge and as such all will go to lower energy levels.
And if the official version was true, that is half of the unpaired electrons turn into a lower energy and the other half in a higher energy spin state, that instantly brings problems when it comes to explaining permanent magnet behavior. If I grab a permanent magnet and stick it to a piece of iron, if half of the unpaired electrons would have spin up and the other half spin down, the magnet would never stick… Basically the official version of explaining the SG experiment is that you get those separation in unpaired electron spin states while when you stick a permanent magnet to a piece of iron all unpaired electrons will align to the magnetic field of the permanent magnet… That is highly contradictionary!
When just over five years back I found out the results of the SG experiment for the first time, my understanding of using an inhomogeneous magnetic field has always been that the electron feels tiny different forces with it’s north and south pole by the applied extermal magnetic field. And because the electron is so tiny, how could one unpaired electron pull an entire silver atom in two different directions?
Anyway this post is 8 pictures long, I had to made two of the a larger the rest is of the usual 550×775 pixel size.
Oh oh am I now shaking in fear because of the above photo as found on the preprint archive? If true, that would smash my idea of electrons carrying magnetic charge because if they carry magnetic charge it would not make much of a difference if the applied external magnetic field is inhomogeneous or not. A constant magnetic field simply would do. Ok, for the time being is this the end of this post.
I got the idea for this post already a couple of years back but I shelved it because I would like to have some application for it. But I still haven’t found a killer application yet anyway I decided to write this rather simple post about the projections you get when you multiply any 3D complex and circular numbers with the number alpha. If you need a refreshment on the importance of the number alpha (or what it actually is) please use the search function of this website and search for ‘Seven properties of the number alpha’.
Now two months back I observed some guy in a video explaining the math you need for quantum physics (yes I have a very boring life) and he was explaining you also need projectors P such that P^2 = P meaning that if P is some measuring operator, if you measure it twice you get the same result. And ha, now I write this post down I realize I did not prove that for both operators in the pictures below so that is something you can do for yourself if you want that.
Basically it goes as next: Pick any 3D number X, circular or complex, and multiply it by the number alpha. The result is a number on the main axis of non-invertible numbers (and as such an entire 2D plane gets projected on each of the main axis non invertible numbers). The other operator is (1 – alpha) and if you multiply any 3D number X by that, it gets projected on the plane of non-invertible numbers (and as such a line gets projected on a point of that plane).
All in all it is very basic, but ha ha ha I am doing this stuff now for years on a row and may be for the average reader it is all not so basic. This post is easier to grasp if you understand the shape of the non-invertible numbers: it is a plane and perpendicular on that plane the main axis and both the plane and main axis go through zero. In this post I skipped all things eigenvalue, but in 3D space we have 3 eigenvalues per capita number so unlike in 4D space we cannot have eigenvalue pairs only. In 3D space it has to be different and that explains more or less the shape of the non-invertible numbers.
This post is five pictures long, as usual all 550×775 pixels and I really hope it is not that hardcore this time.
That is caused by the eigenvalues of a number.
Before we split, on the other website I posted reason number 73 as why electrons cannot be magnetic dipoles. I was that lucky to come across an old 1971 translation of some stuff of the Goudsmit & Uhlenbeck guys. I always suspected there had been some very sloppy physics going on back in the time at the local Leiden university. The translation confirms that more or less (anyway in my view it does). Even after reading the 1971 translation for a third time I kept on falling from one amazement into the other. Have fun reading it, here is a link:
