The directional derivative (for 3D & 4D complex numbers).

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

A couple of days ago all of a sudden while riding my bicycle I calculated what the so called directional derivative is for 3D & 4D complex numbers. And it is a cute calculation but I decided not to write a post about it. After all rather likely I had done stuff like that many years ago.

Anyway a day later I came across a few Youtube video’s about the directional derivative and all those two guys came up with was an inner product of the gradient and a vector. Ok ok that is not wrong or so, but that is only the case for scalar valued functions on say 3D space. A scalar field as physics people would say it. The first video was from the Kahn academy and the guy from 3Blue1Brown has been working over there lately. It is amazing that just one guy can lift such a channel up in a significant manner. The second video was from some professional math professor who went on talking a full 2.5 hour about the directional derivative of just a scalar field. I could not stand it; how can you talk so long about something that is so easy to explain? Now I do not blame that math professor, may be he was working in the USA and had to teach first year math students. Now in the USA fresh students are horrible at math because in the USA the education before the universities is relatively retarded.

Furthermore I tried to remember when I should have done the directional derivative. I could not remember it and in order to get rid of my annoyance I decided to write a small post about it. Within two hours I was finished resulting in four pictures of the usual 550×775 pixel size. So when I work hard I can produce say 3 to 4 pictures in two hours of time. I did not know that because most of the time I do not work that fast or hard. After all this is supposed to be a hobby so most of my writing is done in a relaxed way without any hurry. I have to say that may be I should have taken a bit more time at the end where the so called Cauchy-Riemann equations come into play. I only gave the example for the identiy function and after that jumped to the case of a general function. May be for the majority of professional math professors that is way to fast, but hey just the simple 3D complex numbers are ‘way to fast’ for those turtles in the last two centuries…

Anyway, here is the short post of only 4 pictures:

Should I have made the explanation longer? After all so often during the last years I have explained that the usual derivative f'(X) is found by differentiating into the direction of the real numbers. At some point in time I have the right to stop explaining that 1 + 1 = 2.

Also I found a better video from the Kahn academy that starts with a formal definition of the directional derivative:

At last let me remark that this stuff easily works for vector valued functions because in the above limit you only have to subtract two vectors and that is always allowed in any vector space. And only if you hang in a suitable multiplication like the complex multiplication of 3D or 4D real space you can tweak it like in the form of picture number 4 above.

That was all I had for you today, this is post number 166 already so I am wondering if this website is may be becoming too big? If people find something, can they find what they are searching for or do they get lost in the woods? So see you in another post, take care of yourself & till the next post.

What is one-way light speed? + A plasma lamp in a magnetic field.

Magnetism, Uncategorized

Lately the Veritasium guy from the Youtube channel with that name came out with a video that made me think. It seems that the only way light speed has been measured experimentally is by using a mirror and as such you always measure a so called ‘two-way light speed’ average. It is possible that in this universe light has some preferred direction and in that derection it goes faster compared to say the opposite way.

You might wonder as why that is but that is the old problem Mr. Einstein faced & solved: It is very hard to get two clocks synchronized when they are apart. Vertitasium explains that if light has a preferred direction, in that case it all gets even harder and rather complicated.

Anyway to make a long story short, he also claims there has never been such a ‘one-way’ experiment. That made me think about it and I think that I have found a solution that does not depend on the nasty synchronization problem. All you need is two atomic clocks that are always a fixed distance apart. It gets more complicated compared to where there is perfect sync but if the universe has a preferred direction for light to go in, from the data you collect you should be able to find it.

First let me show you via a screen shot from the video what the usual way is to experimentally measure the speed of light:

Here you send out and receive light at the same spot in space.

Please first look at the video so you understand the problem here:

In the next six pictures I try to explain that using two atomic clocks on two satellites can pull the trick off. Both satellites have a laser or for that matter any em radiation would do like normal radio waves. And on both satellites there is perfect registration of the local time of the times a laser signal was put out or received. Both satellites should be in the same strength of the local gravity field so that their atomic clocks run at equal speeds. Every day both satellites send out one laser pulse on a fixed time and on a daily basis these send & receiving times are recorded.

So far for the first video.

We proceed with a video from the Brainiac channel. On Youtube there are more than one Brainac channels, I mean the guy with the big magnets. And with big I really mean big, the most heavy ones are a staggering 13 kg. A couple of years ago I wondered if I should buy a plasma lamp in order to study how my own set of small neodymium magnets should influence the plasma. These lamps cost only 20€ so that was not the problem. But I have already plenty of lamps so I decided not to do it. After all the photo’s from how an old television set reacts on the neodymium magnets should be enough.

Anyway that is what I thought: Given the fact the audience is composed of scientists, simply communicating the facts should be enough. And applying a bit of logic simply says electrons are not magnetic dipoles but in order to explain the behavior on an old television set is far better explained by electrons being magnetic monopoles. Of course now we are five or six years further down the timeline all I observed is that university people are still very good at just one thing: being important. And no no no, of course we do not talk about that. Electrons magnetic monopoles? Great minds from physics, also people who were very important, said it ain’t so. So no no no, we are important and those crazy people from outside science should shut up and pay the taxes we need for being so important.

Yet now a few years later the video from the Brainiac guy shows that the plasma in the plasma lamp does not react at all as you might expect from a bunch of magnetic monopoles. On the contrary: If he applies one of those 13 kg neodymium magnets, the plasma lamp stops working. So I am glad I never bought one of those lamps because that would make me doubt my own insights that were derived from the electron cannons in the old television set… But the Brainiac guy has much more electronic equipment and he soon found out that the plasma in a plasma lamp is steered by and alternating electric current. So the plasma shakes hin und her with a high frequency and it is not streaming in one direction or so…

Furthermore he explains perfectly why the lamp stops working: the applied magnetic field from the 13 kg magnet stops the transformator in the plasma lamp from working properly. And that explains why the lamp stops working… By the way, if electrons were really magnetic dipoles, the 13 kg magnet would never hinder the functioning of a transformator because a magnetic dipole the size of an electron is by definition neutral for external magnetic fields.

Well here is the perfect video if you want to understand a bit of nature and in case you are one of those fake scientist only occupied with the importance of self, why not walk to a mirror so you can look at yourself?

It’s a great video!

This post is getting far to long for the attention span people have in the present media environment. But I want to show you also a part that the Brainiac guy does not understand: the next screen shot from his video shows only electrons that are repelled by the giant magnet he uses. If he would have used an other direction you could have seen also the electrons that are attracted by the magnet. All of this stuff nicely confirming year in year out that it is impossible for electrons to be magnetic dipoles…

Ok, end of this far too long post. See you in the next post & thanks for having a long enough attention span for reading these very words.

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

3D complex numbers, CR equations, Exponential circle, Matrix representation

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.

Yes all you need is that alpha is it’s own square.

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?

Magnetism, Uncategorized

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:

This is the original as found near my birth village.

I have no clue if this is readable. At 1440 pixels I could read it but now…

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.

This is one of the miracles of the universe.

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):

One more proof university people are incompetent.

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?

Magnetism

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.

This is absolutely not what is going on. How can the earth have aurora’s this way?

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:

Why do electrons get accelerated by planetary magnetic fields?

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’.

Magnetism, Pythagoras stuff, Quantum mechanics

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.

Waiting, just waiting. Will another electron idiot get it?

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 that form of a normal vector I am still proud of many years later.
This is a basic step in the proof of the so called ‘inverse Pythagoras theorem’.
And the same two ‘math cubes’ but now with a black edge.

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

What is the inverse Pythagoras theorem?

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

The general theorem of Pythagoras (second and final post).

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.

Magnetism, Uncategorized

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.

If you accept the magnetic monopole of the electron, stuff like this becomes logical…

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:

In the name of Ramajujan: Why not turn existing math professors into bio diesel?

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?

Part 22: The eigenvalues of the 4D complex number tau.

4D complex numbers, Exponential circle, Exponential curves, Matrix representation

This post took me a long time to write, not that it was so very difficult or so but lately I am learning that graphics program named GIMP. And that absorbs a lot of time and because I am only sitting behind my computer a few hours a day, doing GIMP goes at the expense of writing math…

I always make my pictures with an old graphics program named Picture Publisher 10. It is so old that on most windows 7 and windows 10 it does not run but it has all kinds of features that even the modern expensive graphics programs simply still don’t have. Silently I was hoping that I could use GIMP for my math texts and yes that could be done but in that case I have to use old background pictures forever. Or I have to craft a ‘new style’ for making the background in the math pictures that can last at least one decade.

But let’s not nag at what GIMP cannot do, if you install just one large addon you have about 500 filters extra and my old program PP10 comes from an era when the word ‘addon’ was not a word used ever. Before we jump to the math, let me show you a nice picture you can make with the tiling filter inside GIMP. It is about my total bicycle distance since I bought this bicycle computer, it says 77 thousand km so the Tour the France racers can suck a tip on that:

Just one tile already looks nice.
And this is how four of these tiles look.

Ok, let us look at the math of this post. This is part 22 in the introduction to the 4D complex numbers. The 4D complex numbers have three imaginary units, l, l^2 and l^3. And the stuff that makes it ‘complex’ is the fact that l^4 = -1, you can compare that to the complex plane where the square of the imaginary unit equals -1.

On the complex plane, if you know what the logarithm of i is, you can use that to find the exponential circle also known as the complex exponential. This is what the number tau always is in all kinds of spaces: It is always the logarithm of the first imaginary unit that has a determinant of +1. In this post we will calculate the eigenvalues of this important number tau. That will be done with two methods. In the first method we simply use the eigenvalue functions, plug in the number tau and voila: out come the four eigenvalues. In the second method we first calculate the four eigenvalues of the imaginary unit l and ‘simply’ take the logarithm of those four eigenvalues.

It is not much of a secret that my style of work is rather sloppy, I never order my work in theorems, lemma’s or corrolaries. It is not only that such an approach if too much a straight jacket for me, it also frees me from a lot of planning. I simply take some subject, like in this case the eigenvalues of the number tau and start working on explaining that. While writing that out there always comes more stuff around that I could include yes or no. In this post what came around was that only after writing down the four eigenvalues I realized that you can use them to prove that the exponential curve (the 4D complex exponential) has a determinant of 1 for all points on that curve. That was an important result or an important idea so I included it because that makes proving that the determinant is 1 much more easy.

Now a few posts back with that video from that German physics guy Alexander Unzicker I said that he (and of course all other physics professionals) could always use the 4D complex exponential curve for the ‘phase shifts’ that those physics people always do. But for doing such 4D ‘phase shifts’ or unitary transformations in general, you need of course some kind of proof that determinant values are always +1. Well Alexander, likely you will never read this post but below you can find that very proof.

The previous post was from the end of August and now I think about it: Have I done so little math during the last four weeks? Yes there were no results simply left out, it was only penning down these eigenvalues of tau and the idea you can use these eigenvalues for proving the 4D exponential curve always has a determinant of 1. It is amazing that GIMP can hinder the creation of fresh math… 😉

The math pictures are seven in number, all in the usual size of 550×775 pixels. I hope you like it and see you in the next post.

So these are the four eigenvalues of the number tau and based on that the four eigenvalues of the 4D complex exponential for a values of time.

That’s it for this post. See you in a future post.

Added on 27 Sept 2020: This proceeds the two pictures made with GIMP that started this post. I just made the whole stuff on a cube (actually it is a beam because the starting picture is not a square). It is amazing how good such filters in GIMP are:

That does not look bad at all!

Ok, you are now at the real ending of this post.

Part 21: More on the structue of non-invertible 4D complex numbers.

4D complex numbers, Exponential curves

Finally I have some time left to update this website. I would like to proceed with another part into the introduction to the four dimensional complex numbers. The previous part 20 dates back to 02 Feb 2019 and that too was about this structure of the non-invertible numbers in four dimensional complex space.

When I was reading back a few of my own old writings like part 20 from 02 Feb it struck me that those non-invertible numbers are all just linear combinations of the so called imitators of i. Imitators of i live always in dimensions higher than 2 and they mimic the behaviour of the number i from the complex plane. For example in the spaces of the 3D complex and circular numbers those imitators are not capable of squaring to minus one but they do a pretty good job at rotating stuff by 90 degrees if you multiply by them. In the 4D complex space there are two of such imitators and they do square up to minus one. Of course this is related to the fact you can find two copies of the 2D complex plane in the 4D complex space. So in that regard the 4D complex numbers are a bit different compared to the 4D quaternions that exist of 3 copies of the complex plane (but those do not commute and as such you cannot differentiate or integrate stuff).

Another interesting detail is that in the 4D complex number system the set on non-invertible numbers consists of just two lines that are perpendicular to each other. That is very different from the 3D situation where the set of non-invertibles is always a plane combined with a perpendicular line through zero. The reason that in 4D complex space the set is so small lies of course in the matrix representation and the determinant. On the 4D complex space the determinant is non-negative, just like the determinant is non-negative on the complex plane. Every 4D complex number has four eigenvalues and they come in conjugate pairs, so the product of these four eigenvalues gives the determinant hence the determinant cannot be a negative real number.

And say for yourself: aren’t the eigenvalue functions a very handy thing? If you want to find the eigenvalues of let’s say the 4D complex number Z = 1 + 2l + 3l^2 + 4l^3, that is often a horrible mathematical exercise. But once you have these four eigenvalue functions, you simply plug in any Z and voila: there are your 4 eigenvalues.
This post is seven pictures long, as usual in the 550×775 pixel size.

Remark det(Z) = 0 does not show up in a ray tracing method.
Oops, did I forget the eigenvalues of the number tau?

Ok, that was it for this post. Till updates my dear reader.

Why does 21 cm astronomy work? Why does it not get absorbed?

Magnetism

I estimate that most of my readers are familiar with emission and absorbtion spectra as used in astronomy. Light is produced when electrons fall in to a lower energy state in atoms, but that same light (the photons so to say) can also exite another electron in another atom and as such the photon gets absorbed.

Another example: why is glass transparent? Well the photons in the visible range have energies that do not interfere with the electrons in the glass. That is why these photons simply pass through and we can use stuff like glass for the windows in our homes.

So an element, say atomic hydrogen, is capable of emitting light at particular frequencies and at the same time that atomic hydrogen can absorb the same frequencies.

Now we go to the famous 21 cm wavelength: the standard explanation for the source of this em radiation is that in atomic hydrogen you find that both the proton and the electron have the same spin. The spins are aligned so to say and that state has a tiny bit more energy compared to the situation where the electron spins are not aligned. If the spins are aligned (that can be both up or both a down spin) there is a tiny probability that the electron spin flips. That releases a photon of 21 cm wavelength. It is never explained as why it is the electron spin that should flip, after all if the proton spin would flip this should give rise to the emission of a 21 cm photon also…

It is not much of a secret that I think that electrons are not magnetic dipoles but magnetic monopoles. Electrons get accelerated into the direction of the applied magnetic field, but if electrons were magnetic dipoles they would be neutral to external magnetic fields. Ok ok, professional physics professors come up with non homeogenous magnetic fields that should do the acceleration but if I do an easy estimate I find crazy gradients are needed. Something like 100 thousand Tesla per meter or so. It is important to remark that all those people doing the blah blah thing about inhomeogenous magnetic fields only do the blah blah thing: they never show a calculation that supports the blah blah. And yes, they also have a Hamiltonian kind of thing, but in the Hamiltonian the size of the electron is not incorperated. But the smaller in size a magnetic dipole is, the less it will get accelerated by such magnetic fields.

Another example that is hard to believe is the deflection of the solar wind by the earth magnetic field. Not only is the earth magnetic field very weak out there in space, it is hard to believe it has a serious gradient there in outer space. It must be very constant. Yet the solar wind gets deflected by the weak magnetic field of the earth. In my view this can only be done if electrons and protons are magnetic monopoles.

Here is an old ‘picture of the day’ from December 18, 1996 ‘A sky full of hydrogen’.

Why doesn’t the 21 cm radiation get absorbed?

The spin flip that ’causes’ the 21 cm radiation seems to be a seldom thing; about once in 10 million years. And it is always mentioned that it is spontaneous. In the next picture from a wiki you see how this supposedly works. Link: Hydrogen line https://en.wikipedia.org/wiki/Hydrogen_line

Again: Why no absorbtion?

Ok, what is my version of events? Very simple: Suppose there is an hydrogen atom in outer space that has it’s proton and electron carry the same magnetic charge. So both proton and electron have a north or a south magnetic charge. Suppose it is a north hydrogen atom. This atom simply bumps into a single electron having the south charge. Under the right conditions (bump not to slow and not to fast) this leads to a hydrogen atom with a north proton and a south electron. The north electron gets ejected because like magnetic charges repel. And the radiation emmited simply has wavelength of about 21 cm.

The 21 cm em radiation is also used in atomic clocks like those in the EU Galileo global satellite positioning system. In an apparatus named maser the hydrogen atoms get separated due to their magnetic charge and released in a resonance chamber. The point I want to make is that such a resonance chamber must have a very special coating on the inside otherwise the hydrogen atoms all ‘spin flip’ much to fast. So the coating must be a material without any unpaired electrons in it’s outer shell and of course it can’t be a metal because metals often have an electron sea that just sloshes around. From the ESA, here is a scetch of a hydrogen maser:

This was more or less what I had to say on this magnetic subject. If you start thinking about if it is possible that electrons are magnetic dipoles always you will find it is not logical. For example if it is true that the electron goes round the proton in atomic hydrogen, why the hell would the stuff get anti-aligned? If magnetism is just a vector pointing into some direction, if the electron goes round and round the up & down state would lead to precisely the same hydrogen atom…

All you need is a bit of logic.

Ok, we are at the end of this post. All I want to share with you is a teaser picture for the next post. The math of the next post is more or less finished but I still have to turn the stuff into the standard jpg pictures. The next post is more or less Part 21 into the basic introduction to the 4D complex numbers. I stopped those intro files back in Feb 2019, at this point in time I do not know if I will proceed but at least in a couple of days I will add post number 21 into that 4D number system. It is mainly about the so called ‘imitators of i‘, these imitators mimic the number i from the complex plane. Here is the teaser picture:

Here is an internal link to Part 20 intro to the basics of the 4D complex numbers:

Part 20: On the structure of non-invertible 4D complex numbers.

That was it, thanks for your attention & in a few days the new post will be ready to publish. So see you around my dear reader.