The last Fermat theorem (positive version) versus the number 1.

Last Fermat theorem, Uncategorized

This is a short post; just over 3 pictures long. We make a few calculation on the ring of integers modulo 35. Of course that is a ring and not a field because 35 has two prime factors namely p = 5 and q = 7. These two prime factors form so called divisors of zero, that means that pq = 35 = 0 inside the ring of integers modulo 35.
Because the two prime factors have this property, that has all kinds of simplications when it comes to expanding (p + q)^n inside this ring. That is what I name the ‘positive version’ of the last theorem of Fermat: The ring of integers modulo 35 is a simple number space where the last theorem of Fermat is possible, here we again have 12^n = (5 + 7)^n = 5^n + 7^n.

In this post I use the fact that the prime numbers 5 and 7 are also relatively prime and as such you can make a linear combination of them to get the number 1. And once you have the number 1 you can use them as a basis for the entire ring of integers modulo 35. But if you have a healthy brain, likely you will remark that it is far more easy to just use the counting numbers 1, …, 35 or just 1 to craft such a basis… So I understand that you might think I am crazy to the bone. Of course I am crazy to the bone but there is a goal in this utter madness. Take for example 3*5 – 2*7 = 1, this is one possibility to form the number 1 as a linear combination of 5 and 7. Since both terms contain one of the pairs of divisors of zero as a factor, this linear combination allows for a positive last theorem of Fermat decomposition: For a natural numbers n we have that: (15 – 14)^n = 15^n + (-1)^n*14^n = 1.
Although such expressions are very cute looking, it has no significant math depth anyway. All in all this post it totally unimportant because it is all so simple. The post upon the 3D Gaussian integers is far more important because there it was possible to write the number 3 as a linear combination of two 3D Gaussian integers. As such for the first time in about 350 years it was the first serious counter example against the last theorem of Fermat because that number 3 was just on the line of integers. It was not something inside some modulo number space or so, that was the real deal for the first time in 350 years.

Will math professors react on such a finding? Of course not. For example they would reason before the finding that if you can’t use 3D complex numbers to find only one significant result in algebra or number theory, that proves 3D complex numbers are useless.
And after the counter example to the last fermat theorem? Well math professors are the most smart people on earth, they are higly agile and adeptable and now the reasoning will likely be something like: In the entire history of mathematics nobody has ever used 3D Gaussian integers. This all is so far fetched that this is not serious math…

Well that is how they are and there is no changing that kind of behavior I just guess. Anyway enough of the blah blah blah. The post is just over 3 pictures long, has no mathematical significance anyway and I hope you have some fun reading it.

For odd n you get a minus sign, for even n you get a plus sign.
It is not significant math, but it sure looks very cute!

It is now one hour after mdinight so it is time to hit that button named ‘Publish website’. Live well & think well my dear reader. See you in the next post or so.

Another counter example to Fermat’s last theorem using 4D complex numbers.

4D complex numbers, Last Fermat theorem

All in all I am not super satisfied with this post because the math result is not that deep. Ok ok the 4D complex numbers also contain non-invertible numbers, say P and Q, and these are divisors of zero. That means PQ = 0 while both P and Q are non-zero. And just like we did in the case of 3D circular and complex numbers because of the simple property PQ = 0 all mixed terms in (P + Q)^n become 0 and as such: (P + Q)^n = P^n + Q^n.

In the space of 4D complex numbers an important feature of the determinant det(Z) of a 4D complex number Z is that it is non-negative. As such there is not a clear defined layer between the part of the number space where the determinant is positive versus the negative part. During the writing of this post it dawned on me that Gaussian integers in the 4D complex space always have a non-zero determinant. As such the inverse of such a Gaussian exists although often this is not a Gaussian integer just like the inverse of say the number 5 is not an integer. A completely unexpected finding is that the 4D complex fractions form a field…

That made me laugh because the professional math professors always rejected higher dimensional complex numbers because they are not a field. For some strange reason math professors always accept or embrace stuff that forms a field while they go bonkers & beserk when some set or group or ring is not a field. This is a strange behavior because the counter examples that I found against Fermat his last theorem are only there because 3D and 4D numbers are not a field: there are always non zero numbers that you cannot invert.
As such a lot of math professors are often busy to make so called field extensions of the rational numbers. And oh oh oh that is just soo important and our perfumed princes ride high on that kind of stuff. And now those nasty 4D complex numbers from those unemployed plebs form a field too…
I had to smile softly because 150 years have gone since the last 4D field was discovered, that is known as the quaternions, and now there is that 4D field of rationals that are embedded into something the cheap plebs name ‘4D complex numbers’? How shall the professional math professors react on this because it is at the root of their own behavior over decades & centuries of time?

Do not worry my dear reader: They will stay the overpaid perfumed princes as they are. Field or no field, perfumed princes are not known to act as adult people.

After having said that, this post is only five pictures long all of the ususal size of 550×775 pixels. For myself speaking I like the situation on the 3D numbers more because there you can easily craft an infinite amount of counter examples against the last theorem of Fermat.
Ok, here we go:

Yes I have to smile softly: all this hysteria from overpaid math professors about stuff being a field or not. And now we are likely into a situation where the 4D complex numbers are not a field but the space of 4D complex rationals is a field…

Will the math professors act as adults? Of course not.
Ok, let’s end this post because you just like me will always have other things to do in the short time that we have on this pale blue dot known as planet earth. Till updates.

On plasma instability in nuclear fusion reactors.

Magnetism

The next post will be math again; more of the ‘positive’ last theorem of Fermat stuff. This time on the 4D complex numbers. In case you missed it, I found 3D Gaussian integers, say A and T and if we sum them up, say S = A + T, in that case S^n = A^n + T^n. The last theorem of Fermat says this is not possible for ordinary integers but in higher dimensional number systems it is not that hard to find.

Last week the UK Royal Institution had a new video out about nuclear fusion. At first I wanted to comment on it but it is more or less the same video as the one from four years back so I skipped that. Anyway in the UK they still have a workable nuclear fusion reactor and all those years I just thought they put it on just a few seconds every now and then because of the plasma instabilities. I was wrong, the latest video says it is because they do not have superconducting magnets, the magnets they use are made from ordinary copper wiring and that produces a lot of heat and that is the explanation for the short operational times.

But today I came across another video with news about nuclear fusion and there it was claimed that Korea succeeded into more than doubling the operational time of their fusion vessel! From 8 seconds to 20 seconds!
So I feel the need to once more explain how these plasma instabilities form using the simple idea that electrons are not magnetic dipoles but magnetic monopoles. I am well aware of the fact that people like Ian Chapman (he is in the UK video from the RI) start vomiting by the idea that electrons are magnetic monopoles, or may they consider it a funny joke from one of those dumb persons in the so called ‘general audience’. From my side of the story I will not poke fun about Ian Chapman because it is morally rejectable to poke fun at people who are mentally handicapped…;)

The Koreans used an Internal Transport Barrier…

In my view where electrons are magnetic monopoles there are two kinds of electrons: those with a ‘north pole’ magnetic charge and the ones with a south pole version of magnetic charge. Needless to say they have the same electric charge.
Ok, these electrons are in a plasma inside a torus shaped vessel of a fusion reactor and the magnetic field gets turned on. What will happen?

Very simple: The electrons get accelerated into the direction of the magnetic field lines. Therefore if the north pole charged electrons go say clockwise, the south pole charged electrons will go anti clockwise.

Since these electrons are constantly accelerated by the magnetic field that is supposed to contain them, they will cluster together in streams just like water going downhill. Water going downhill does not do that every water molecule on it’s own; it forms stream of water that accumulate in size until you get rivers… The electrons in the plasma simply do the same; if an individual electron finds itself back in an environment where there are lots of other electrons moving into the same direction, it will stay there and get more and more accelerated all of the time.

So over time there will be larger and larger streams or rivers of electrons and because there is a lot of kinetic energy in those streams, if the two streams interact it will be very violent.

That is the explanation in a nuttshell, I know that professional physics professors will laugh about me thinking I am the retarded one. I don’t care that much about that, after all they are too stupid to make use of 3D complex numbers so who is the retarded here at the end of the day?

Fantastic, this will save humanity from climate change…

An interesting detail in those plasma vessels that are shaped like a torus is that in the middle the magnetic field seems to be stronger. That would be an explanation as why the plasma does not blow into the wall at the very beginning. But if you would ask the plasma professors as why the walls are spared for a short time, those people likely have not a clue what soever.
The JET nuclear fusion vessel operates only for short amounts of time but already in these few seconds there are violent outbursts of the plasma against the walls of the vessel. Here is a screen shot from the video where Ian Chapman expains his wisdom at 20 minutes into that video.

It is important to know it gets unstable within a few seconds of operation…

These people chase a dream that is impossible. And at the same time when I demand proof that actually the electrons is a magnetic dipole those mentally handicapped people always stay silent. The silence proves the mentally handicapped thing and the video’s they spit out prove that they are severely overpaid and will never come to their senses.

No comment.

All that is left is to place the two video’s into this website. Because the video on fusion news is so short I place that first.

The Korean stuff is found at 5.30 minutes into the video

And here is the thing from the UK, by the way how is your Brexit going? The important details are at 23 to 25 minutes into that video.

Ok, that was it for this post. All those nuclear fusion plants will blow up but I just don’t care. See you in the next post.

Electrons can’t be magnetic dipoles; yet discontinuation of the magnetic pages…:(

Magnetism

After giving it a few months of thought I decided to discontinue the magnetic pages on the other website. For five years I collected reasons as why it is impossible that electrons are magnetic dipoles. Yet it never took off, if I do an internet search on ‘electrons cannot be magnetic dipoles’ weirdly enough it is a result from this website and just nothing from the files on magnetism.

As a comparison if you search for 3d complex numbers the results from the other website still pop up even dating back to the year 2012…

I had to conclude it just does not work and I better use my time for other hobby’s because there is little use in writing every month the stuff found down if nobody is reading it. That is a waste of time.

Of course from the get go five years back I understood it would be a hard sell to explain that it is impossible that electrons are magnetic dipoles to the community of physics. After all there is zero experimental evidence for the electron being a magnetic dipole so it must be some widespread belief not rooted into experimental proof.

There are more explanations possible as why the magnetic pages never took off; for example it could be that on average the physics professors are much more stupid compared to math professors. They are just too dumb or may be just too arrogant to give it a second thought.

Another possible reason for the failure of the internet search engines could be that in general people are just much more interested in math and not so much in physics. A clue to that could be the extreme popularity of a channel named ‘Numberphile’ on youtube. The guy that runs that channel has much more channels like stuff on physics but that seems to be far less popular.

Whatever it is, I have decided to put an end to it so no more updates in the magnetic pages forever. Here is the last update:

14 Jan  2021: Reason 87: There is ‘too much’ symmetry in the universe.

Yes, over a timespan of five years 87 reasons found while zero response in the internet search engines. In this last reason I quote some words from Gerard ‘t Hooft who is wondering why we only can measure two states for the electron. Well Gerard might have gotten his Nobel prize, but if he keeps on thinking the electron is a magnetic dipole without any fucking experimental proof for that he is a neglectable cognitive quantity.

Inside physics there are many more people that clearly are not very helpfull, take that arrogant piece of shit like a Edward Witten. Always 100% arrogant but just too stupid to understand it is plain impossible for the electron to be a magnetic dipole. How can a guy like Edward explain the results of the Stern-Gerlach experiment while the electron is a magnetic dipole? In my view this only shows that Edward Witten is a mathematical imcompetent person…

But hey I do not want to sound like a sour old man, after all it is with great pleasure but just a little smile on my face that I can write down words like ‘Edward Witten is a mathematical incompetent person’. Please do not think I am driven by hatred, I am not.

Ok, one more clue as why electrons cannot be magnetic dipoles. It is named the Stark effect and this effect is the application of an electric field and that seems to split the spectrum of the photons emmited. But it looks just like the shift in the spectrum of when a magnetic field is applied.
Here is a picture of the spectral shift under application of an electric field:

Oops, that looks just like magnetic splitting…

The above picture is a screen shot from a video source I will not link to.
If those physics people will never grow into adulthood, why take the time and trouble to place correct links and so. Arrogant weirdo’s like Edward Witten from the string theory crazies will only do their own overpaid nonsense…

In life it is important not to get consumed by hatred in the long run because always living in hatred is bad for your health. So you confine you deep hatred to only small attacks that make a bit of fun. After that you shake the hatred off like it is just some water.
And say for yourselve: The next picture shows my bike computer and it says 80 thousand kilometers done. I mean that’s life and listening to the words of Edward Witten is not much of a life…

Wow that is about twice circuling the earth if there would be a bicycle path around our beloved globe. In the next picture I made a cube from it:

And in the last picture also a cube about the results in the previous post where I found some cute results in 3D complex and circular numbers that can be classified as positive Fermat theorems. Now will a piece of shit like Edward Witten ever understand it? I do not care what that weirdo thinks.

But after 350 years of zero progress on the last Fermat theorem, I hope I made a tiny and very small contribution that will survive.

All that modulo stuff is hard to read. So read the previous post!

Ok we are at the end of this post. Till updates.

The last theorem of Fermat does not hold for the 3D so called Gaussian integers.

3D complex numbers, Last Fermat theorem

On the one hand it is a pity I have to remove the previous post from the top position. Never ever I would have thought that the Voyager probes would be a big help in my quest of proving that electrons are not magnetic dipoles. Electrons are magnetic monopoles, if your local physics professor thinks otherwise why not ask you local physics professor for the experimental evidence there is for the electron magnetism dipole stuff?

On the other hand this post is about Gaussian intergers for the 3D complex and circular numbers and it is with a bit of pride that I can say we have a bunch of beautiful results because the last theorem of Fermat does not hold in these spaces.

The last theorem of Fermat is a kind of negative result, it says that it is impossible for three integers x, y and z that x^n + y^n = z^n, this for integer values of n greater than 2 of course. (For n = 2 I think most readers know it is possible because those are the Pythagoras triples.)

Anyway I succeeded into writing the number 3 as the sum of two Gaussian 3D integers that are also divisors of zero. So this pair of integers, in this post I name them A and T because they are related to the famous 3D numbers alpha and tau, are divisors of zero so as such AT = 0. As such as a denial of the Fermat theorem, an important result as posted here is that A^n + T^n = 3^n. So on the 3D complex & circular numbers this result is possible while if you use only the 2D complex plane and the real line this is not possible…
But there are plenty of spaces where the Fermat conjecture or the last theorem does not hold. A very easy to understand space is the ring of integers modulo 15. In this ring there are numbers that do not have a multiplicative inverse, say 3 and 5. And if inside this ring you multiply 3 and 5 you get 15 and 15 = 0 in this ring… Hence inside this ring we have that 8^n = 3^n + 5^n (mod 15) also contradicting the Fermat stuff.

I did some internet searches like ‘Fermat last theorem and divisors of zero’ but weirdly enough nothing popped up. That was weird because I view the depth of the math results related to this divisor of zero as the depth of a bird bath. It is not a deep result or so, just a few centimeters deep. But sometimes just a few centimeters can bring a human mind into another world. For example a long time ago when I still was as green as grass back in the year 1986 I came across the next excercise: Calulate the rest of 103 raised to 103 and divided by 13. I was puzzled, after all 103^103 is a giant number so how can you find the rest after dividing it by 13? But if you give that cute problem a second thought, after all that is also bird bath deep because you can solve it with your human brain…

This post is 11 pictures long, all of the standard size of 550×775 pixels. Because I could not find anything useful about the last Fermat theorem combined with divisors of zero I included a small addendum so all in all this post is 12 pictures long.

After so much Gaussian integer stuff, there is only one addendum about the integers modulo 30. In that ring you can also find some contradictions to the standard way of presenting the last theorem of Fermat.

Ok, if you are still fresh after all that modulo 30 stuff, for reasons of trying to paint an overall picture let me show you a relatively good video on the Kummer stuff. Interesting in this video is that Kummer used the words `Ideal numbers´ and at present stuff like that is known as an ideal. For myself speaking I never use the word ´ideal´ for me these are ´multiplicative attractors´ because if a number of such an ideal multiplies a number outside that ideal, the result is always inside that ideal. Here is a relatively good video:

And now you are at the end of this post. Till updates.

Voyager probe says: Solar electrons accelerated to 670 times the initial speed…

Magnetism

In the first place I wish you all a happy new year & let’s hope for some improvement this year when it comes to the new corona virus.

It seems that the Voyager probes, who are now in interstellar space, have done a remarkable discovery when it comes to electron speeds coming from the sun. This was found when observing electron bursts that originate from solar bursts, first the electrons are detected while the plasma shock wave itself only arrived weeks later. This is a happy finding because it now is very hard to deny electrons get accelerated by magnetic fields because they are all magnetic monopoles. Of course 100% of the university people will deny that electrons are magnetic monopoles, this is a clear case of the law of conservation of retardness…;)
Anyway let me post a few quotes, the first quotes come from space.com. Here is a link: https://www.space.com/nasa-voyager-electron-bursts-interstellar-space. My comment is in a bold font.

The Voyager mission has detected a new type of “electron burst,” which will provide insights into the mechanisms of flaring stars, a new study reports.

 
“The idea that shock waves accelerate particles is not new,” corresponding author Don Gurnett, professor emeritus in physics and astronomy at the University of Iowa, said in a statement.

“Physicists believe these electrons in the interstellar medium are reflected off of a strengthened magnetic field at the edge of the shock wave, and subsequently accelerated by the motion of the shock wave,” the University of Iowa said in the same release. “The reflected electrons then spiral along interstellar magnetic field lines, gaining speed as the distance between them and the shock increases.”

Comment: The above is retarded nonsense that shows university people think that electrons cannot be accelerated by magnetic fields and as such you get all that blah blah blah about shockwaves that can accelerate particles. If memory serves these are Alvén waves, but it is straight in your face: 670 times as fast and that is far out of the realm any Alvén wave can do.

Since it is a joyful day, why not include some fictional pictures representing what likely is one of the Voyager probes in space:

From a website under the name extremetech.com I found the next cute quote. A CME is a solar coronal mass ejection while the ISM is the inter stellar medium:

Each time one of these big CMEs reaches the ISM, the researchers have noted an electron burst in advance — the shockwave itself didn’t arrive until 13 to 30 days after the high-energy cosmic ray electrons. It’s counterintuitive to see this signal showing up ahead of the shockwave, but the team says this is all thanks to the properties of magnetic field lines in the ionized gas of the ISM, which are apparently almost perfectly straight. Large CMEs punch through the heliopause and interact with these field lines, causing some of the electrons inside to accelerate along the magnetic straightaways. They can reach relativistic speeds, about 670 times faster than the shockwave that originally delivered them to the edge of the solar system. That’s why Voyager 1 and 2 see the electron burst before the CME shockwave.
Scientists have never seen electrons accelerated ahead of a shockwave like this. It’s an entirely new mechanism and one that could help us better understand the ISM.

Comment: Just another example of how retarded all those explanations are. It has nothing to do with the ISM but only with electrons getting accelerated by magnetic fields because electrons are magnetic monopoles. It serves as another example of a law from the social sciences namely the conservation of retardness inside academic organizations.


Link from the quote:

Ok, that was it for this update. Once again a happy new year and thanks for your attention.

05 Jan 2021: Correction & addendum: May be I should have included a link to the ‘scientific article’ the whole stuff was based on. Here is a link to that: https://iopscience.iop.org/article/10.3847/1538-3881/abc337

Anyway you have to pay if you want to read that article so I won’t do that.

Yet in my line of thinking where electrons are always magnetic monopoles, they come in two different kinds like the south pole and north pole magnetically charged electrons. Also they are never in a mixed state of ‘spin up’ and ‘spin down’. Just like in the hydrogen atom the proton and electron never get confused what particle carries the electric charge…

But hey, let’s ask the professional physics community once more to bring forward some experimental proof that the electron is actually a magnetic dipole… Of course they do not have such experimental proof or at least some kind of validation, so they will keep on talking weird stuff when it comes to electron spin.

End of the Correction & addendum thing.

Another tiny victory for electrons being magnetic monopoles? Solar corona temperature ‘explained’.

Magnetism

Since the official version of the electron is that it is a magnetic dipole, as such it cannot be accelerated by magnetic fields. But often people do not understand why but if I explain it via atomic hydrogen all of a sudden everybody thinks ‘hey that is logical’.
Explanation via atomic hydrogen:
Atomic hydrogen is made from one proton and one electron and as such it cannot be accelerated by electrical fields.
End of the explanation.

Ok ok the electric field can be so strong that the hydrogen atoms get ripped apart but as long as that is not the case it can’t be accelerated by any electric field. Now if electrons are truly magnetic dipoles, if that were true they cannot be accelerated by magnetic fields.

Tiny problem: Every idiot looking at those beautiful video’s from the sun can see with their own eyes that the plasma gets accelerated by magnetic fields… And there are more problems; the surface temperature of the sun is far below that of the solar atmosphere or the solar corona.

In the last five years I have given plenty of explanations of how those solar loops and stuff likely work. It is very likely that below all those sun spots the plasma is actually rotating, spitting out the electrons that are getting much more accelerated compared to the protons and as such we have a giant dynamo made from rotating plasma.
Well nobody talks about that because university people only talk about the stuff you find in expensive journals like Nature or Science. And of course I am not going to waste my money on journals that are too expensive anyway & read only by overpaid perfumed princes from the universities…

But let’s go to the video stuff from Anton Petrov. He talks about Eugene Parker and Mr. Parker is the guy who’s name is used in the Parker solar probe. Already in the 1970-ties Eugene explained how the solar corona could be so hot compared to the surface of the sun. According to Anton he explained it via mini flares coming from the surface heathing the atmosphere of the sun. With such an explanation Eugene Parker avoided being a pariah by stating that this is only possible if electrons and protons are not magnetic dipoles but are all magnetic monopoles and as such carry magnetic charge. My estimate is that both Eugene and Anton do not have any fucking clue as why the plasma gets accelerated, if you keep on hanging to that retarded Gauss law for magnetism it is very hard to explain stuff like that.
Anyway, here is the video and the title is:
We Finally Know Why Sun’s Corona Is So Extremely Hot
I would add: No you don’t, observation is not explanation.

Observing solar plasma acceleration by magnetic fields is not an explanation if your belief system is the standard model of physics in general and the Gauss law for magnetism in particular.

Anyway, Anton rightly remarkes that those mini solar loops & flares are only observed on a tiny part of the sun this does not prove the overall temperature of the solar corona…

He is right with that, Let me end this post with two pictures and after that we will split and say goodbye until the next year 2021.

Once more: if electrons are magnetic dipoles, why do they get accelerated?

And the last picture, it is not a mini-loop but one of those giant loops:

Ok, that was it for the last post of the year.
See you in the next year.

The total differential for the complex plane & the 3D and 4D complex numbers.

3D complex numbers, 4D complex numbers, CR equations

I am rather satisfied with the approach of doing the same stuff on the diverse complex spaces. In this case the 2D complex plane and the 3D & 4D complex number systems. By doing it this way it is right in your face: a lot of stuff from the complex plane can easily be copied to higher dimensional complex numbers. Without doubt if you would ask a professional math professor about 3D or higher dimensional complex numbers likely you get a giant batagalization process to swallow; 3D complex numbers are so far fetched and/or exotic that it falls outside the realm of standard mathematics. “Otherwise we would have used them since centuries and we don’t”. Or words of similar phrasing that dimishes any possible importance.

But I have done the directional derivative, the factorization of the Laplacian with Wirtinger derivatives and now we are going to do the total differential precisely as you should expect from an expansion of the century old complex plane. There is nothing exotic or ‘weird’ about it, the only thing that is weird are the professional math professors. But I have given up upon those people years ago, so why talk about them?

In the day to day practice it is a common convention to use so called straight d‘s to denote differentiation if you have only one variable. Like in a real valued function f(x) on the real line, you can write df/dx for the derivative of such a function. If there are more then one variable the convention is to use those curly d’s to denote it is partial differentiation with respect to a particular variable. So for example on the complex plane the complex variable z = x + iy and as such df/dz is the accepted notation while for differentiation with respect to x and y you are supposed to write it with the curly d notation. This practice is only there when it comes to differentiation, the opposite thing is integration and there only straight d‘s are used. If in the complex plane you are integrating with respect to the real component x you are supposed to use the dx notation and not the curly stuff.
Well I thought I had all of the notation stuff perfectly figured out, oh oh how ultrasmart I was… Am I writing down the stuff for the 4D complex numbers and I came across the odd expression of dd. I hope it does not confuse you, in the 4D complex number system I always write the four dimensional numbers as Z = a + bl + cl^2 + dl^3 (the fourth power of the imaginary unit l must be -1, that is l^4 = -1, because that defines the behavior of the 4D complex numbers) so inside Z there is a real variable denoted as d. I hope this lifts the possible confusion when you read dd…

More on the common convention: In the post on the factorization of the Laplacian with Wirtinger derivatives I said nothing about it. But in case you never heard about the Wirtinger stuff and looked it up in some wiki’s or whatever what, Wirtinger derivatives are often denoted with the curly d‘s so why is that? That is because Wirtinger derivatives are often used in the study of multi-variable complex analysis. And once more that is just standard common convention: only if there is one variable you can use a straight d. If there are more variable you are supposed to write it with the curly version…

At last I want to remark that the post on the factorization of the Laplacian got a bit long: in the end I needed 15 pictures to publish the text and I worried a bit that it was just too long for the attention span of the average human. In the present years there is just so much stuff to follow, for most people it is a strange thing to concentrate on a piece of math for let’s say three hours. But learning new math is not an easy thing: in your brain all kind of new connections need to be formed and beside a few hours of time that also needs sleep to consolidate those new formed connections. Learning math is not a thing of just spending half an hour, often you need days or weeks or even longer.

This post is seven pictures long, have fun reading it and if you get to tired and need a bit of sleep please notice that is only natural: the newly formed connetions in your brain need a good night sleep.

Here we go with the seven pictures:

Yes, that’s it for this post. Sleep well and think well & see you in the next post. (And oh oh oh a professional math professor for the first time in his or her life they calculate the square Z^2 of a four dimensional complex number; how many hours of sleep they need to recover from that expericence?)
See ya in the next post.

Majorana particles gone? How significant is this?

Magnetism, Quantum mechanics

It is no secret that over the years I have made a few rather bald predictions when it comes to magnetism. I think each and every electron is in fact a magnetic monopole and not a ‘tiny magnet’ like the professional professors think. As such I have predicted that all nuclear fusion reactors based on the magnetic confinement design will never work because if you turn such a machine on it will accelerate the electrons to crazy speeds creating tons of instability and turbulence in the plasma. And if I say ‘hey where is your experimental proof that electrons are actually magnetic dipoles’ of course nothing happens. You must never forget that all these physics professors are extremetly important persons and they will never mingle with inferior shit like people who are unemployed for almost 20 years now… No no no, we are not going to react on some crazy stuff like electrons are not magnetic dipoles. If we start doing that, the next day a homeless person will come along saying if we heal the electrons from their trauma’s you get better beer. No no no, incompetent people aren’t unemployed for no reason at all. We will neglect weirdo’s like that, after all we are the physics professors and we are on the edge of becoming masters of the universe once we have our quantum computers up and running!
I also predicted a few years back that the approach of the Delft university combined with Microsoft will not work because the Majorana particles they are based upon do not exist. It is very simple: a Majorana particle is it’s own anti particle, physics professors thought that if you combine an electron with a hole (the absense of an electron) you have a structure that is it’s own anti particle. But if you combine an electron with a hole, what mechanism is there to ensure the hole and the electron also carry opposite magnetic charges? Just like the electron and the positron carry opposite electric charges the same should go for the magnetic charges after my lazy unemployed insights.

A couple of days back when reading the news on Google news I made an internet search for ‘quantum computing’ and to my surprise there was an article from last May in the local newpaper De Volkskrant stating there was ‘bad luck’ for the heroes at Delft university. Oopsy toopsy, the Delft heroes had to withdraw an article published in Nature where the existance of Majorana particles was claimed. The fact that Nature published this bullshit in the first place is also interesting, likely the peer review mechanism works perfectly for getting the best of science into that outlet of articles. Today I checked what the publication fees are for Nature, it is only 5000€ or so (I more or less expected it to be at least 10000€) so today I learned something too… Those fees are of course a fundamental root cause as you will never find my name Reinko Venema in such overpaid shit publications. Why should I lay out 5000€ for something that will never ever pass the peer review hurdle? Since I am not an overpaid person, most of the time I try to spend my money wise.

I am sorry that the news article is in Dutch, but here is a link:
Tegenslag voor Nederlandse pionier van de quantumcomputer.

Anyway I consider this a very small success, of course the main success I am hunting for is that plasma instability in fusion reactors is caused by the acceleration of the applied magnetic fields and as such we cannot halt climate change with fusion reactors. But we have to do with overpaid university shitholes, so the waiting will be long. The combination of being overpaid while at the same time you are to stupid to ‘do the math’ often does not give a good outcome. As an example for that, look at the last financial crises that started in 2008: all those overpaid bankers and the troubles they created.

We close this post with a few pictures. The copyright of the content goes to Sam Rentmeester who likely made the photo from that extremely important Delft based physics professor:

Wow wow wow, do electrons carry magnetic charge?

Ok, that was it for this post. The next post is about math and we will dive into the total differential for 2D, 3D and 4D comples numbers.

Factorization of the Laplacian (for 2D, 3D and 4D complex numbers).

3D complex numbers, 4D complex numbers, CR equations, Laplacian, Magnetism, Quantum mechanics

Originally I wanted to make an oversight of all ways the so called Dirac quantization condition is represented. That is why in the beginning of this post below you can find some stuff on the Dirac equation and the four solutions that come with that equation. Anyway, Paul Dirac once managed to factorize the Laplacian operator, that was needed because the Laplacian is part of the Schrödinger equation that gives the desired wave functions in quantum mechanics. Well I had done that too once upon a time in a long long past and I remembered that the outcome was highly surprising. As a matter of fact I consider this one of the deeper secrets of the higher dimensional complex numbers. Now I use a so called Wirtinger derivative; for example on the space of 3D complex numbers you take the partial derivatives into the x, y and z direction and from those three partial derivatives you make the derivative. And once you have that, if you feed it a function you simply get the derivative of such a function.

Now such a Wirtinger derivative also has a conjugate and the surprising result is that if you multiply such a Wirtinger derivative against it’s conjugate you always get either the Laplacian or in the case of the 3D complex numbers you get the Laplacian multiplied by the famous number alpha.

That is a surprising result because if you multiply an ordinary 3D number X against it’s conjugate you get the equation of a sphere and a cone like thing. But if you do it with parital differential operators you can always rewrite it into pure Laplacians so there the cones and spheres are the same things…

In the past I only had it done on the space of 3D numbers so I checked it for the 4D complex numbers and in about 10 minutes of time I found out it also works on the space of 4D complex numbers. So I started writing this post and since I wanted to build it slowly up from 2D to 4D complex numbers it grew longer than expected. All in all this post is 15 pictures long and given the fact that people at present day do not have those long timespan of attention anymore, may be it is too long. I too have this fault, if you hang out on the preprint archive there is just so much material that often after only five minutes of reading you already go to another article. If the article is lucky, at best it gets saved to my hard disk and if the article has more luck in some future date I will read it again. For example in the year 2015 I saved an article that gave an oversight about the Dirac quantization condition and only now in 2020 I looked at it again…

The structure of this post is utterly simple: On every complex space (2D, 3D and 4D) I just give three examples. The examples are named example 1, 2 and not surprising I hope, example 3. These example are the same, only the underlying space of complex numbers varies. In each example number 1 I define the Wirtinger derivative, in example 2 I take the conjugate while in the third example on each space I multiply these two operators and rewrite the stuff into Laplacians. The reason this post is 15 pictures long lies in the fact that the more dimensions you have in your complex numbers the longer the calculations get. So it goes from rather short in the complex plane (the 2D complex numbers) to rather lengthy in the space of 4D complex numbers.

At last I would like to remark that those four simultanious solutions to the Dirac equation it once more shouts at your face: electrons carry magnetic charge and they are ot magnetic dipoles! All that stuff like the Pauli matrices where Dirac did build his stuff upon is sheer difficult nonsense: the interaction of electron spin with a magnetic field does not go that way. The only reason people in the 21-th century think it has some merits is because it is so complicated and people just loose oversight and do not see that it is bogus shit from the beginning till the end. Just like the math professors that neatly keep themselves stupid by not willing to talk about 3D complex numbers. Well we live in a free world and there are no laws against being stupid I just guess.

Enough of the blah blah blah, below are the 15 pictures. And in case you have never ever heard about a thing known as the Wirtinger derivative, try to understand it and may be come back in five or ten years so you can learn a bit more…
As usual all pictures are 550×775 pixels in size.

Oh oh the human mind and learning new things. If a human brain learns new things like Cauchy-Riemann equations or the above factoriztion of the Laplacian, a lot of chages happen in the brain tissue. And it makes you tired and you need to sleep…
And when you wake up, a lot of people look at their phone and may be it says: Wanna see those new pictures of Miley Cyrus showing her titties? And all your new learned things turn into insignificance because in the morning what is more important compared to Miley her titties?

Ok my dear reader, you are at the end of this post. See you in the next post.