# On the work of Shlomo Jacobi & a cute more or less new Euler identity.

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.

Let me start with a link to the preprint archive:

On a novel 3D hypercomplex number system

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.

# Funny format/more pics needed & idiots at MIT observed?

Slowly but surely I am getting better at the GIMP (a free program for manupilating images). Right now I can place pictures in perspective while the GIMP als has a 3D picture manupilating tool I haven’t even used by now. Now one day I will have to end my usual way of formatting pictures, the biggest disadvantage is that you must always have a windows XP computer. May be it is possible to run a virtual XP on a windows 10 system but I never managed to get it properly at work. On the other hand computers in for example pin automats (money machines at the bank) still seem to work on XP. So likely in the future their will still be motherboards and CPU’s that allow for a fresh install of that mighty windows XP system.

Anyway with GIMP you can easily use the perspectives tool and place rectangular selections into a perspective like shown below:

No, the above format for publishing math does not work properly I guess. It is a screenshot from a post from earlier this year: Calculating the 3D exponential circle using first principles.

Now in another development I was also not very lucky. I found a few pictures of the creation of an electron-positron pair in a bubble chamber. Now if my view on electrons and positrons being magnetic monopoles is correct and because in a bubble chamber you have a magnetic field present, from the moment of creation they should start accelerate in opposite directions. And I thought all I needed was just one Google picture search but the results were a bit disappointing. Yes you can find some pictures but most of the time it is just one photo that is recycled over and over. Another disadvantage is that you see the electrons and positron bubble paths only in the direction of the magnetic field that is applied so that the electrons & positrons can do their typical circular movement due to the Lorentz force so it is abosolutely not possible to see the eventurental acceleration into the direction of the magnetic field lines… Well most of the time you find the next picture and yes it looks like the one particle is ‘going in’ and the other is ‘going out’ but that is all there is. No sideviews found at all and that is what I need. An interesting phenomenum that should occure is the next: Due to the bubbles there has to be some kind of drag on the electron and positron. So their velocities along the magnetic field lines should take on some limiting value. If that can be found that alone should be enough to validate that electrons canny magnetic charge and that all this ‘tiny magnet’ stuff is total bs.

And the last item for this post is the MIT people. Again it is blah blah blah because we now have stronger magnets we can make smaller nuclear fusion reactors. But if my view of electrons being magnetic monopoles in the end will be victorious, stronger magnetic fields do not solve the acceleration problem. Electrons get constantly accelerated and because there are two types of electrons namely the north and south charge they will get accelerated into opposite directions.

I have been saying this for years and years and still the university people keep on doing their retarded thing and not proves that electrons are actually magnetic dipoles. In the meantime those imcompetent shitholes keep on making promesis for a better future when it comes to energy for the population and blah blah this & blah blah that.

Remember the time that Lockheed Martin came out with the same kind of bullshit? By now we should have had the first mobile fusion reactors and of course they are nowhere to be found. And now we have exactly the same nonsense from MIT.

It’s not going to work, but try explaining that to a bunch of total incompetents! Here is a Youtube with the MIT stuff (about six minutes long):

We are dealing with a bunch of people too stupid to find out in centuries of time how 3D complex numbers should be found (or defined). And all I get is total neglect and they go on with their blah blah blah. Give us, the tax payer, finally some fucking proof that electrons are magnetic dipoles and that the structural instability of the plasma is not caused by accelerated electrons! Of course, as usual, there will be silence. Only the sound of silence combined with blah blah like ‘we now have stronger magnets’. Climate change is not going away in the meantime and it is charlatans like this that will make people going on with polluting the atmosphere more and more because there is some false hope nuclear fusion will save the day. Once more: Likely it is not going to happen. Look at the Lockheed Martin folks; they still have nothing to show for despite their past blah blah blah about having stronger magnets…

Ok, that was it for this post. The next post is about a math article from the preprint archive that is about 3D complex numbers. So keep tuned and see you next time.

# Is a weak planetary magnetic field dangerous for the atmosphere?

Today I came across a very interesting video from SciShow where they claim that computer models suggest that a weak magnetic field gives more leakage of the atmosphere compared to a situation where a planet like Mars has no magetic field at all…

The video is very interestig because it compares the earth versus some of the other planets in our solar system. It is not much of a secret that I think electrons carry magnetic charge and that is what makes them ‘move along magnetic field lines’. If electrons carry magnetic charge means they are magnetic monopoles and not the magnetic dipoles that is more or less included in the standard model of particle physics.

As usual we only apply the thing called ‘logic’ and we do not get emotional because the academic field does not respond year in year out. Ok ok, I am human too so let me allow a tiny amount of emotion: All those physics professors that think electrons are magnetic dipoles are just like math professors: incompetent to the bone because of groupthink. In the case of understanding magnetism the groupthink is easy to explain: it is the Gauss law for magnetism (magnetic monopoles do not exist) while there is zero experimental evidence for that Gauss law.

Why do particles with non zero spin move along magnetic field lines? I think that is because they carry net magnetic charge. The weirdo’s from the universities think that it is done because of the gradient of planetary magnetic fields. Of course it is never backed up by some calculations because: 1) Planetary magnetic fields are rather weak in the first place and because of that: 2) The gradient of such fields is completely neglectible. You see once more: All you need is a bit of the thing known as ‘logic’. Why the university people do not want to apply the thing known as logic is unknown to me. In my view it is far better to use logical reasoning if you want to make a bit of progress in understanding the stuff out there in the universe; but after talking like that for the last six years or so it has become clear university people just don’t want to think ‘logical’.

Let’s move on, why waste time on people that are mentally handicapped anyway? In the next picture you see a perfect accumulation of how not understanding electrons in a magnetic field leads to all kinds of weird representations of what actually is going on. Yes the earth magnetic fields acts as a ‘shield’ for the solar wind, but it is not that the particles that make up the solar wind ‘bounce off’ that shield. The next representation is rather retarded but that is what you get when humans just hold on the the Gauss law and hold on and hold on & just want to be retarded idiots.

Moving on, the video mentions computer simulations. But if you craft computer simulations where the electron is a magnetic dipole while the thing known as ‘logic’ say they cannot be magnetic dipoles, how can these computer models be a realistic representation of what is actually going on? Of course those computer models can’t do that, so these computer models must have some feature inside them that makes particles with non zero spin accelerate in magnetic fields.

Moving on, those computer models suggest leakage from the Mars atmosphere in the past if it had a rather weak planetary magnetic field. The reason I write this post is that they arrived at the conclusion that a weak planetary magnetic field leads to a situation where the magnetic field lines are not closed. They originate at the planet but never return to it.

Talking about idiots: That detail alone violates the Gauss law for magnetism (all magnetic fields always close in upon themselves).

But the insight of how a weak magnetic field could lead to more planetary atmosphere loss is brilliant.
All of my life I was too stupid to make it up:

At last here is the video that aroused my attention:

Let me close this post with two more ‘things’.

Thing 1: Almost by definition if the electron is a magnetic dipole it is neutral when it comes to magnetism. Just atomic hydrogen has one proton and one electron and as such it is neutral under the influence of electric fields. Let’s do a thought experiment: Suppose a planet as a whole has a strong electric charge either positive or negative of say a few million volts. Furthermore this planet has an atmosphere of atomic hydrogen (ok that is not very realistic but anyway). Now does the electric potential cause a dramatic atmospheric loss of the atomic hydrogen that is neutral in electric fields?

No of course not, because the atomic hydrogen is electrically neutral it has no net force acting on it. Hence a planetary size eletric potential should not lead to a loss of non-ionic atoms.

Thing 2: They once tried to figure out if the neutron was an electric dipole (or may be an electric tripole because after all the neutron seems to be composed of 3 quarks). They failed hard. But if we compare electron size to neutron size, likely the electron is orders of magnitude smaller than the neutron so why should the eletron not be neutral when it comes to magnetism?

Ok ok, the goodie old Stern Gerlach experiment says that electron is not neutral under magnetic fields hence elementary logic says the electron cannot be a magnetic dipole. As such all electrons must be magnetic monopoles…

As you see, when doing ‘scientific stuff’ it is always better to use logic and not silly emotions. Of course I get irritated nothing changes but why get overly emotional? And don’t forget: suppose somebody has done the perfect experiment that indeed validates electrons cannot be magnetic dipoles. Well such a person will be at the end of his or her career because no ‘respectable scientific journal’ will post such a result. That’s the way it is, so I don’t care about those journals.

Let me leave it with that. See you in the next post.

# Impending Nobel prize & recycled Pythagoras theorem & it’s ‘inverse’.

Tomorrow is the new Noble prize in physics out, actually it is already past midnight as I type these words so it is actually today. But anyway. I am very curious if this year 2020 the Nobel prize in physics will once more go to what I name those ‘electron idiots’. An electron idiot is a person that just keeps on telling that electrons are magnetic dipoles because of something retarded like the Pauli matrices. May be idiot is a too harsh word, I think that a lot of that kind of behavior or ideas that can’t be true simply stay inside science because people want to belong to a group. In this case if you tell the official wisdom of electron spin you simply show that you belong to the group of physics people. And because people want to belong to a particular group they often show conformistic behavior, when it comes to that there is very little difference between a science like physics or your run of the mill religion.

In this post I would like to share a simple experiment that every body can do, it does not blow off one of your arms it is totally safe, and shows that those Pauli matrices are a very weird pipe dream. Here we go:

The official explanation of the Stren Gerlach experiment always contains the next: If electron spin is measured into a particular direction, say the vertical direction, if later you measure it again in a direction perpendicular on the vertical once more it has 50/50 probability. So if it is measured vertically and say it was spin up, if you after that measure it in say a horzontal manner once more the beam should split according to the 50/50 rule.

Ok, the above sound like highly IQ level based on lots of repeated laboratorium experiments. Or not? And what is a measurement? A measurement is simply the application of a magnetic field and look what the electron does; does it go this way or that way?

Electron pairs are always made up of electrons having opposite spins, in chemistry a pair of equal spins is named a non-bondig or an anti-bonding pair. Chemical bonds based on electron pairs cannot form if the electrons have the same spin.

Now grab a strong magnet, say one of those strong neodymium magnets and place it next to your arm. Quickly turn the magnet 90 degrees or turn your arm 90 degrees, what does happen? Of course ‘nothing happens’ but if electron spin would follow that 50/50 rule, in that case 50% of your electron pairs would become an anti bonding pair. As such your flesh and bones whould fly apart…

Now does that happen? Nope njet & nada. As far as I know it has never been observed that only one electron pair became an anti-bonding pair by a simply change of some applied external magnetic field…

As far as I know the above is the most easy day to day experiment that you can do in order to show that electrons simply do not change spin when a different magnetic field is applied…

I have been saying this for over five years but as usual when it comes to university people there is not much of a response. In that regard physics is just like the science of math: It has lost the self cleaning mechanisms that worked in the past but now in 2020 and further those self cleaning mechanisms do not work anymore. It is just nothing. It is just a bunch of people from blah blah land. So let’s wait & see if one of those ‘electron idiots’ will get the Nobel prize tomorrow.

Luckily I have a brain for myself. I am not claiming I am very smart, ok may be compared to other humans I do well but on the scale of things like understanding the universe I am rather humble. I know 24/7 that a human brain is a low IQ thing, but just like all other monkeys it is the only thing we have.

Very seldom the human brain flares up with a more or less bright idea that simplifies a lot of stuff. A long time ago I wanted to understand the general theorem of Pythagoras, I knew of some kind of proof but I did not understand that proof. It used matrices and indeed the proof worked towards an end conclusion but it was not written down in a transparent way and I just could not grasp what the fundamental idea’s were.

So I made a proof for myself, after all inside math the general theorem of Pythagoras is more or less the most imporatant theorem there is. I found a way to use natural induction. When using natural induction you must first prove that ‘something’ is true for some value for n, say n = 2 for the two dimensional theorem of Pythagoras. You must also prove that if it holds for a particular value of n, it is also true for n + 1. That is a rather powerful way to prove some kind of statement, like the general theorem of Pythagoras, holds for all n that is holds in all dimensions.

I crafted a few pictures about my old work, here they are.

It is from March 2018 when I wrote down the ‘inverse’ theorem of Pythagoras:

And from March 2017 when I wrote the last piece into the general theorem of Pythagoras:

Ok, let me leave it with that and in about 10 hours of time we can observe if another ‘electron idiot’ will win the 2020 Nobel prize in the science of physics. Till a future post my dear reader. Live well and think well.

# Two video’s to kill the time.

Two very different subjects: the earth magnetic field and the standupmath guy has a great video about the perimeter of an ellips.

Video 1) From the Youtube channel Scishow a video with the title
‘Satellite Squad Goals: The Cluster Mission to the Magnetic Field’.
For me that video contains relatively much completely new stuff, the fact that there are 4 satellites out there constantly monitoring the earth magnetic field was unknown to me.
And the presenter of the video claims that after the so called ‘magnetic reconnection’ the charged particles from the solar wind slam into the north & south pole of the earth with a staggering 10 thousand km/sec. I did not know it was that fast…
The official explanation for the acceleration of for example single electrons is that you must have an inhomogeneous magnetic field. After all these folks think that electrons have two magnetic poles and if the electron goes through a magnetic field that varies in space the two forces on the north and south pole of the electron do not cancel out and there is a net force responsible for the acceleration. There is only one problem: they simply multiply the electron magnetic moment against the gradient of the magnetic field and voila: that’s it. But if the acceleration is explained as a difference in opposing forces, should you not take into consideration the size of the electron? Yes of course, but since physics professors are so terribly smart why don’t they do this? Well if you take the size of the electron into your calculations, there is no acceleration or better it is basically zero.

Now years ago I tried to estimate how stong a magnetic field had to be to accelerate one of those dipole electrons with a acceleration of only 1 meter per second squared. If memory serves I used an ‘electron size’ of 10 to the power -15 meter (in reality it is even much smaller) and again if memory serves you needed magnetic fields with a gradient of over 100 thousand Tesla per meter.
And if you think about that estimation it makes a lot of sense: electrons are very small and as such have an extreme density given their size and mass. Say it is in the order of the density of a neutron star. And if you try something with the density of a neutron star to accelerate with the difference of a magnetic field, likely you won’t go far…

Ok, suppose for the moment that the electrons are the long sought magnetic monopoles. So they are not magnetic dipoles but the electrons themselves are magnetic monopoles just like they are electric monopoles.
Now look at the picture below: it is about when the magnetic reconnetion just closed. Just before the closing along the magnetic field lines emergin from the earth north & south pole, the particles were expelled because they carry the wrong magnetic charge. But when reconnection takes place, the particles that were expelled by say the earth south pole find themselves back on a trajectory going to the earth north pole. And as such they will get accelerated into that direction.

Yet a couple of years ago when I published those estimations that show you need crazy gradients for all that shit to be true, of course nobody reacted. All those university professors in physics, when you tell them that extra ordinary claims like the electron being a magnetic dipole also needs extra ordinary proof, all of a sudden they are deaf deaf deaf.
These people they don’t have any experimental proof that the electron is a magnetic dipole. And worst of all: They don’t even think about it…
Finally, here is the SciShow video:

Video 2) From the Standupmath guy a video about the perimeter of an ellipse. Weirdly enough it is not possible to find a more or less simple expression for the perimeter of an ellipse. Of course a long long time ago I tried to find an expression myself but using the standard stuff like arc length brings very fast a lot of headache. With the present day of math tools it is completely not possible to derive a good expression for the perimeter of an ellipse.
What I did not know is that there is a world of approximation stuff out there for estimation such ellipse perimeters. And of course in itself this has it’s own logic: after all an ellipse is more or less completely defined by saying what it’s two half axes a and b are. You can always fix one of those axis to 1 say b = 1 and study the perimeter problem as a function of the variable a. You do some curve estimation, you drink a few pints of beer and later when you are sober again you drink some green tea.
And you conclude some curve estimation is relatively good but that all in all the ellipse perimeter problem is just too large for our human brains that in general are not good at doing math.
There is only one exeception; Ramanujan.
In the next picture you see one of those Ramanujan approximations and once more you see how the human mind should work if we were living in a better world:

The video is here, 21 minutes long but worth the time:

Ok, that was it for this post. Think well, live healty and try to make some bio fuel from the basic ingredient known as ‘math professor’.
In that case we will find ourselves back in a better world, or not?