Category Archives: Uncategorized

Comparison of the ‘Speed = the Square’ equation on 7 different spaces.

This post is very simlilar to a few back when we calculated the results on 4 different spaces. This time I hardly pen down any calculation but only give the results so we can compare them a little bit.
The way most professional math professors tell the story of complex numbers it goes a bit like this: We have the real number line, the complex plane and on top of that a genius named Hamilton found the quaternions. On top of that there are a bunch of so called Clifford algebra’s and oh we math professors are just so good. There is no comparison to us, we are the smartest professionals in the world!

Well that is very interesting because it is well known these so called ‘professionals’ could not find the 3D complex numbers for about 150 years. So how come they all say we have this and that (complex plane and quaternions) and that’s enough, we are just perfect! Why they keep on saying rubbish like that is the so called Dunning-Kruger effect. That’s something from psychology and it says that people who lack understanding of some complicated stuff also lack the insight that they are stupid to the bone when it comes to that particular complicated stuff. So the views of professional math professors is very interesting but can be neglected one 100 percent, it’s just Dunning-Kruger effect…

If you look at the seven results of the ‘Speed = the Square’ equations, the solutions form a strickt pattern that only depends of the number of dimensions and if it is the complex or the circular multiplication. So every time a math professor goes from the complex plane to the wonderful world of quaternions you now know you are listening to a weirdo.

I said I only give results but since I have never ever introduced the 4D circular numbers I just extrapolated the other six spaces to the solution that lives in that beautiful space. So the last example is a bit longer.

Anyway although the math depth of this post is not that very deep (solving a differential equation that wants the derivative to be the square of what you differentiate), it clearly demonstrates solutions of all 7 different spaces look strikingly similar.
But because of the Dunning-Kruger effect likely the math professors will keep on telling total crap when it comes to complex numbers. Why am I wasting my time on explaining math professor behaviour? Better go to the five pictures of our post. Here we go & bye bye math professors.

May be I should write some posts about general complex number theory on spaces of arbitrary dimension. On the other hand I found the 3D complex numbers back in the year 1990. So if after all those years I will once more try to write some general theory one thing will be clear: Math professors will keep on trying to convince you of the beauty of quaternions or that garbage from the Clifford algebra’s.

Why, as a society, do we keep on wating tax payer money on math professors? Ok, they do not everything wrong but all in all it is not a great science or so where the participants are capable of weeding the faults out and grow more of the good stuff.
Let me end this post and thank you for your attention.

Solving the ‘Speed = The Square’ equation on four different spaces.

With ‘speed = square’ I simply mean that the speed is a vector made up of the square of where you are. The four spaces are:
1) The real line,
2) The complex plane (2D complex numbers),
3) The 3D circular numbers and
4) The 3D complex numbers.

I will write the solutions always as dependend on time, so on the real line a solution is written as x(t), on the complex plane as z(t) and on both 3D number spaces as X(t). And because it looks rather compact I also use the Newtonian dot notation for the derivative with respect to time. It has to be remarked that Newton often used this notation for natural objects with some kind of speed (didn’t he name it flux or so?).
Anyway this post has nothing to do with physics, here we just perform an interesting mathematical ecercise: We look at what happens when points always have a speed that is the square of their position.

On every space I give only one solution, that is a curve with a specific initital value, mostly the first imaginary component on that space. Of course on the real line the initial condition must be a real number because it lacks imaginary stuff.

If you go through the seven pictures of this post, ask in the back of your mind question as why is this all working? Well that is because the time domains we are using are made of real numbers and, that is important, the real line is also a part of the complex and circular number systems.
The other way you can argue that the geometric series stuff we use can also be extended from the real line to the three other spaces. To be precise: we don’t use the geometric series but the fractional function that represents it.

Ok, lets go to the seven pictures:

That Newton dot notation just looks so cute…
The words ‘Analytic continuation’ are not completely correct…

Remark: This post is not deep mathematics or so. We start every time with a function we know that if you differentiate it you will get the square. After that we look at it’s coordinate functions and shout in bewilderment: Wow that gives the square, it is a God given miracle!

No these are not God given miracles but I did an internet search on the next phrase of Latex code: \dot{z} = z^2. To my surprise nothing of interest popped up in the Google search results. So I wonder if this is just one more case of low hanging math fruits that are not plucked by math professors? Who knows?

End of this post, thanks for your attention.

Two more videos that explain electron spin wrong.

A happy new year by the way, it is now 3 Jan over here so it is not too late to wish you that. So be happy if you can ask a physics professor or teacher as why there is no experimental proof at all that electrons are tiny magnets. And if the answer is not satisfactory, just chop the head of while being happy…;)

But serious, I selected the first video because the guy from the Science Asylum channel gives are very tiny estimated upper bound for the possible size of the electron: 10 to the -18 power meter as diameter.
That is very very small, it is a nano nano meter.

Lets construct a so called ‘toy model’ for imitating in a simple manner how the electron is supposed to be a tiny magnet: Take two pointsize magnetic monopoles, a north and a south one and place them 10 to the power -18 meter apart. Lets name this distance d.
An important feature of such a dipole is that it’s magnetic field declines inversely with the third power of d.

Let me give you an example: Take a line through the north and south pole of our toy electron and go out a distance of say 10d above the north pole. So the distance of our point on that line is 10d to the north pole and 11d to the south pole. The magnetic forces or field strength if you want is now proportional to 1/10^2 and 1/11^2. But north and south pole have opposite workings so we are looking at the difference: 1/10^2 – 1/11^2 and that is something of the order 1/1000.

If the electron diameter is indeed at most this distance d, in that case the two overlapping magnetic fields cancel each other almost out. If all that tiny magnet stuff is true, in that case the electron should be magnetically neutral. In a constant magnetic field that does not vary in space, by definition this tiny magnet electron should be neutral (if it all was true).

Let me show you two screen shots from the video from the Science Asylum. The first simple shows you the claim the electron has at most this size d.

On a nano nano scale this should be magnetically neutral…

A long time ago I estimated the result in next picture too but I always used an electron diameter of 10 to the -16 power, so one hundred time as big as the Asylum guys claims. Anyway there is nothing spinning over there because it must rotate a huge multiple of the speed of light. Now we can honestly say that Albert Einstein did not understand much about electron spin, but we can safely conclude that electron spin is not related to rotation of a spherical charged body the size of d.

One million times the speed of light…

Ok, let me hang in the video where we have once more the implicit claim that magnetism is always a magnetic dipole without one iota of experimental proof for that claim:

In my view the most misleading name is spin, it sets your brain totally wrong.

In the next video you see a guy at work showing that the oxygen in the air you breathe is magnetic. The magnetic properties of oxygen are truly breathtaking because it has to do with a so called ‘non-binding’ electron pair. In chemistry a non-binding electron pair is a pair with the same electron spin. Weirdly enough the physics professors keep their mouth shut: All electron pairs obey the Pauli exclusion principle!
Until it doesn’t like in molecular oxygen.

But I digress, the reason I selected this video can be found at 3.40 minutes into it: The guy ‘explains’ the behavior of the oxygen by stating that the two electrons in the non-binding pair align their magnetic dipole to the applied magnetic field. The problem with this kind of ‘explanation’ is that it does not explain as why the electrons get accelerated. As said above; if electrons are tiny magnetic dipoles, they are basically magnetically neutral. And we are to believe that the oxygen molecules get accelerated by the applied magnetic field because two little electrons ‘align their dipole magnetic moment’. Give me a break: that is crap and the next stuff look much more logical and observable:
Electrons are not magnetic dipoles but magnetic monopoles.

Here is the second video:

The reason for posting this second video is that I often obverve people from physics thinking that the alignment or for that matter the anti-alignment explains the acceleration and forces involved.

After seven years into this stuff I only wonder:

Why do the physics professionals like teachers and professors not see they are telling utter crap? Why are they so fucking stupid all of the time?
End of this post. Once more: A happy new year.

Google’s quantum computer for chemistry: will it ever work? Nope, this is a disaster.

Quantum computing looks like a good idea when it comes to simulation of quantum stuff like chemical reactions. But if your basic assumption of electrons being ‘tiny magnets’ it will all run from the rails if in the future it is found out that electrons are magnetic monopoles just like they are electric monopoles. Lately I have been joking that the only place in the universe where electron spin gets flipped is inside the heads of our professional physics professors.
I think there are two kinds of electrons, one with a magnetic north charge and the other with a magnetic south charge. For the time being I think this magnetic charge is permanent so there is no way or mechanism that turns a south charge electron in a north charged and vice versa.
Doing chemistry on a computer on the level of individual electrons and nuclei consumes an awful lot of computer resources. To focus the mind say you have a molecule with 100 to 150 electrons and some nuclei. The Coulomb forces alone are hard to simulate. But the way the magnetic forces must be done with the ‘tiny magnet’ model for electron spin is even much more horrible; in principle you have to calculate 100 to 150 vectors representing the bipolar magnetism of the electron. So this is all horribly complicated. Yet if electrons are magnetic monopoles, calculating a simulation for the magnetic forces should be of the same order of computer recourses as the Coulomb forces. That still is not very appealing but it is less worse as the Google engineers do it for the most simple atom there is in our universe: The hydrogen molecule made of two protons and one electron pair (the pair has opposite magnetic charges my dear reader, that is more logical as ‘opposite spins’ or for that matter ‘quantum numbers’).
The horror is that physics but also chemistry professors seem to think that in the electron pair every particle is in a super position of spin up and spin down. That is where that stuff like “If I separate the two quantum particles and I take one to the Andromeda galaxy and measure it’s spin in the vertical direction, instantantly the spin of the particle left behind will be the opposite“. And why don’t they never say that for a hydrogen atom? After all these are two quantum particles to but are these two particles that are both in a super position of their positive and negative electrical charges? Is the mass of both particles not defined but is either the proton mass or the electron mass? Most people will say that is mumbo jumbo.
The next picture is from a video I will show you below, likely all these Google people think that electrons are tiny magnets. So that is an amzing amount of salary costs wasted year in year out.

The |10> and |01> refer to the super position of magnetic states.

The Google view on electron magnetism is very different from mine where I like to keep it simple by stating electrons are magnetic monopoles. But they can make it much more complicated without any reason at all, in the next picture you see one of those singlet states and the chemistry folks have found out that an electron pair is ‘non binding’ if the two electrons have the same spin. If they have the same spin they don’t bond? And non of the chemistry weirdo’s remark that in a permanent magnet the spins must point in the same direction to make some magnetic bonding… Why does nobody see this is all not very logical and that this ‘tiny magnet’ stuff is just not true because it leads to all kinds of contradictions? Why are they so fucking stupid?

Let’s proceed with the second screen shot ensemble:

The thing with the minus sign is the anti-bonding pair. These people are crazy because a monopole magnetic charge is far more simple and much more logical.

Lets try to hang in the Google video.

So much money and so low in brain capacity.

So far for this Google stuff. Luckily IBM is also very good at donating a coin of quantum wisdom. Lately we had a Noble prize in physics for faster than light quantum teleportation of quantum properties like photon properties… I am not saying all this Bell inequality stuff is impossible, all I am saying is an electron cannot be in a superposition of spin up and spin down because electrons carry a permanent magnetic charge.

The IBM video was so bad that it became funny and some kind of parody.
Here is another superposition of screen shots.

I don’t know what to say.

The IBM video:

End of this post.

On the Frisch-Segrè experiment (a repeated SG experiment) from 1933.

Last week I finally found out after seven years that there is indeed at least one repeated Stern-Gerlach experiment. It is well known in quantum mechanics that the Pauli matrices can be used to calculate the probabilities for finding electrons into a particular spin state. And in a repeated SG-experiment, if you turn the magnetic field 90 degrees the Pauli stuff says it is 50/50 divided. If you example you first applied a vertical magnetic field and after that some horizontal magnetic field, you should get 50% of the electrons having spin left and 50% spin right.

But if you try to do a search on a term like “Experimental proof for the Pauli matrices” or just “Repeated Stern-Gerlach experiment” never ever serious popped up in the last seven years.

Seven years ago I arrived at the conclusion that it is impossible that electrons are “tiny magnets” or for that matter have a bipolar magnetic field. A lot of things can be explained much better and more logical compared to mystifications like the Pauli exclusion principle. If electrons are magnetic monopoles, in that case it is logical that if they form pairs they must have opposite magnetic charges.
And with the electron pair we already have a detail where the ususal model of electrons as “tiny magnets” fails; two macroscopic magnets are attracking only if their magnetic fields are aligned. If two macro magnets are anti-aligned, they repel. So how the hell is it possible that two electrons only form a pair if they have opposite spins, only if they anti-align?
What I still don’t understand is why people like Pauli, Einstein, Feynman etc etc never remarked that it is nonsense to suppose that electrons are tiny magnets. Remark there is zero experimental proof for the assumption that electrons are tiny magnets. They just projected the Gauss law for magnetism on electrons without ever remarking you must have some fucking experimental proof.
In the next picture you can see the experimental setup; you see two Stern-Gerlach experiments and in the middle is a inner rotation chamber where they try to flip the spin of the electrons.

Einstein proposed the use of the hot wire…

So Einstein must have given it a thought, this SG-experiment and never realized the impossibility of the Gauss law for magnetism for electrons.

Last week I found a nice pdf upon the Frisch-Segrè experiment and I would like to quote a few hilarious things from it:

“The physical mechanism responsible for the alignment of the silver atoms remained and remains a mystery” and quoting Feynman, “… instead of trying to give you a theoretical explanation, we will just say that you are stuck with the result of this experiment … ”

This is also the first time that I see this ‘problem’ actually stated; how is it possible that a tiny thing like an electron anti-aligns it’s spin with the applied external magnetic field? That is very very strange, for example water molecules are tiny electric dipoles and if they meet an electric field the only thing they want to do is to align themselves with that electric field. Why do electrons gain potential energy in a magnetic field?

To understand how crazy this is: If you go outside and throw away a bunch of rocks, do half of those fall to earth and the other half flies into space? Nope, in the end all rocks try to get at the state of minimal potential energy.

But if you view electrons as magnetic monopoles this weird detail of climbing in potential energy is’n there any longer: an electron with say a north pole magnetic charge will always go from the north pole to the south pole of a macroscopic magnetic field. And vice versa for an electron with a south pole magnetic charge. The weird energy problem isn’t there any longer.
You can compare that to a bunch of electrons and protons entering an electric field; they feel opposite forces and that is how they both lower their potential energy.

At last let me give you the pdf. This pdf is not very useful because it is written by one of those weirdo’s that keep on believing that electrons are tiny magnets…

Once more I want to remark that if you see a physics professor doing his or her blah blah blah thing on electron spin, they just don’t have any serious experimental proof that electrons actually have two magnetic poles.
Furthermore, none of them has a problem with that.
So why are we funding these weirdo’s with tax payer money?

Ok, that was it for this post. Thanks for your attention.

3 Video’s to kill the time & Unzicker’s horror on the quaternions…

To be honest I like the Unzicker guy; he is from Germany I believe and he alsways attacks the standard model for particles. According to him there are zillions of problems with the standard model and likely he is right with that. But he fully buys the crap that electrons must be magnetic dipoles without any experimental confirmation at all.
So that I post a video of him talking weird stuff about electrons is not a way to rediculize him. On the contrary, because he always tries to attack the idea’s inside the stadard model he in itself is a perfect example as why the physics community swallows all those weird explanations upon electron spin.

For myself speaking I think that electrons don’t have their spins ‘up’ or ‘down’. I don’t think that they are tiny magnets with two magnetic poles but in itself they are magnetic monopoles that come with only one magnetic charge… My estimate is that this magnetic charge is a permanent charge, that means there is no such thing as spin flip of an individual electron.

In the Unzicker video Alexander asks for help about differentiation on the quaternions or so. Well have I done my utmost best to craft all kinds of spaces where you can integate and differentiate, stuff like 3D complex numbers, 4D complex numbers etc, comes a weirdo along asking about the quaternions… On quaternions differentiating is a true horror and that is caused by the property that in general the quaternions don’t commute. I wrote a one picture long explanation for that. The problem is that differentiation on say the square function on the quaternions destroys information. That is why there is no so called ‘Complex analysis on the quaternions’, it just doesn’t exist.
Ok, lets go to the first video. It is not that very good because he constantly throws in a lot of terms like SO2 and SO3, but for an audience like physics people that is allowed of course.

Because it is still the year 2022, it is still one hundred years back that the Stern-Gerlach experiment was done. The next short video is relatively good in it’s kind; there are a lot of videos’s out there about the SG experiment and most are worse. In this video from some German at least there are some more explanation like it is not the Lorentz force because these are silver atoms. But as always in all explanations out there it misses as why exactly electrons do anti-align themselves with the applied external magnetic field.
For example water molecules are a tiny electric dipole, if you apply an electric field to clean water, all these tiny electric dipoles for 100% align with the electric field. So why do electrons not do that?

As always: electrons being magnetic monopoles is a far better explanation for what we observe. But all these physics people, one hundred percent of them have no problem at all when there is no experimental evidence that electrons are indeed ‘tiny magnets’. That is what I still don’t understand: Why don’t they see that their official explanations are not very logical when you start thinking on these explanations? Why this weird behavior?

Ok, lets hang in why differentiation on the quaternions is a total horror.

Hasta la vista baby!

The last video is a short interview with John Wheeler where he explains the concept of positrons being electrons that travel back in time. At some point John talks about an electron and positron meeting and anihilate each other. Well it has to be remarked that this doesn’t always happen. They can scatter too and why could that be? Well it fits with my simple model as electrons being magnetic monopoles. Positrons and electrons only kill each other if they have also the opposite magnetic charge…

Ok, that was it for this post. Thanks for your attention.

An old unsolved problem regarding the exponential function f(x) = e^x.

This is a problem I found about thirty years ago and I was never ever able to solve it. The problem as I formulate it is about finding a so called ‘composition root’ to the exponential function. Just keep it simple, say the composition ‘square root’. If we denote that as r(x) what I mean is that this function if composed with itself gives the good old exponential function: r(r(x) = f(x) = e^x.
There are many interesting aspects to this problem. For example take a piece of paper and a pencil and draw the graph of the exponential function and the identity function. It is now very easy for every point on your graph of the exponential function to find the graph of the double composition f(f(x) = e^(e^x)). But, as far as I know, you cannot go back and given the function f(x) find it’s composition root r(x).
It is very well possible that this problem is solved in the theory of dynamical systems. If memory serves we once had a lesson in when a family of functions could be interpolated but that was 30 years back and what I want is explicit expressions and formula’s and not only a vague existencial proof without a way to find an explicit answer.

Back in time before the logarithm was invented, the people of those long lost centuries had a similar problem understanding what exponential behaviour was. And you can go a long way in understanding exponential behaviour but say for yourself; without knowledge of the logarithm that kind of knowledge is far from being optimized.

In this post I only talk about the composition square root but of course any n-th root should be possible and as such giving rise to the idea that you can iterate or compose the exponential function also a real number amount of times. I have to admit I also have no proofs for the solution to this all being unique, but you should be able to differentiate all stuff found and it should still be coherent so my gut feeling says the solution is unique. My guess is there is only one ‘composition square root’ r(x) that is as smooth as f(x) itself…

This post is only two pictures long so here we go:

And it is also the end of this post. Give it a thought and if you are able to make some inroads on this that would be great. But all in all I think we do not have the math tools to crack this old old problem.

See you around in the next post.

Two videos so bad they are actually funny & a PERFECT gif found.

If you start commenting on bad videos you will have a busy hobby for the rest of your life. But there are also reasons to take a look at these videos, for example the math video is horrible but the path of calculation shown is rather beautiful. The other video is about magnetism and when I viewed it for the first time it was really late at night and only after a good night sleep I realized how horribly bad that video was.
But it was the magnetism video that made me look up the average size of the so called magnetic domains and that was when I found that PERFECT gif. So I cannot say it was all a waste of time, that perfect gif is made with something that is named a Kerr microscope and with such a device you can make magnetic domains visible.
Years ago, if memory serves it was Feb 2017, I was studying so called ‘racetrack memory’ that was under development by IBM. That IBM project failed because they kept on hanging to electrons being ‘tiny magnets’ with two magnetic poles, because that is likely not true all their work failed. Anyway they came up with the fact that you cannot move magnetic domains with magnetic fields and I totally freaked out. Late at night I realized that within my broader development of understanding magnetism at the electron level, the IBM findings were logical if magnetic domains in say Iron or so, always have a surplus of either north pole monopole electrons or south pole monopole electrons. Domain walls separate the two kinds of magnetic domains. Itis a pity that about five years back I never heard of those Kerr microscopes.
Again I want to highlight that I do not want to convince anybody that electrons are the long sought magnetic monopoles. I have done that for six or seven years and it was only in this year 2021 that I arrived at the conclusion that physics professors are just as stupid as the average math professor. It is a pile of garbage so it is not much of a miracle that six or seven years of trying to apply logic did not work at all. So from this year on going into the future the physics professors have the same status as the math professors: A pile of rotten garbage that you must avoid at all times at all costs needed.

After having said that, this post is five pictures long where I comment on the two horrible videos. Below that I will post the two videos so you can see for yourself (or may be you want to see them first). And at the end you can see that perfect gif where magnetic domains change in size due to the application of an external magnetic field. Also back in 2017 I more or less figured out how magnetic domains will change if you approach a piece of iron with a permanent magnet. What you see in the gif is more or less precisely that: Some domains grow while domains next to that shrink.

Ok, here we go:

Now we can go to the first video, the math one:

I found the magnetics video by doing an internet seach on ‘The Stern-Gerlach experiment for iron’. It is disappointing that almost no significant results are there. Some of stuff out of the 2030-ties of the last century but that was all behind pay walls. Very high in the rankings came the next video that uses iron filings to mimic or imitate the Stern-Gerlach experiment. The video guy should have used magnets on only one side, if that resulted into attraction & repulsion of the iron filings he would have gotten a standing ovation from me. Without any insult; the way he executed this experiment is a true disaster only showing he does not understand why the SG experiment is so important.
And by the way: If my idea of electrons being magnetic monopoles is in fact correct, you do not have to use inhomogeneous magnetic fields. Everything will do; even the most constant magnetic field in space and in time will do. But again after so many years of talking to deaf ears from stupid physics people, I have lost my desire to convince anybody any longer..

With magnets on two sides; of course it will spread out! This is stupid!!!!!

Ok, I have never hung any animated gif into this WordPress website so let’s check it out if it works properly:

As you see: Some domains grow while adjecent ones shrink.

I found this animated gif in a wiki: Magnetic domain.
That was it for this post. Thanks for your attention.

Counter examples to the last theorem of Fermat using the number 210.

Ok ok one more post upon the easy to find counter examples to the last theorem of Fermat. In this post we will take a look at the real integers modulo 15 and modulo 210. It still amazes me how easy it is to find counter examples to the last Fermat theorem using the integers modulo n where n has at least two prime factors. From my own education I remember that the integers modulo n are studied in math mostly via additive groups and multiplicative groups. For some strange reason it is not commonly studied via rings where you have the benefit of addition and multiplication inside one simple to understand structure of numbers… Inside professional math there is always that tendency to study fields only, of course there a legitimate reasons for that like it makes math life often more simple. But rings are not fields, rings allow for non zero numbers that are non-invertible anyway. As such you can always find plenty of pairs of so called ‘divisors of zero’ and once you have stuff like that it is always a piece of cake to find counter examples to the last theorem of Fermat.

Yet I tried a few times to find some counter examples on the internet but all I got was boatload after boatload of total nonsense like the weird stuff paraded in the previous post. Could it be that math professors tried to find counter examples to the last theorem of Fermat while they never dipped into the power of the divisors of zero? That’s crazy because the Fermat theorem was open for about 350 years. I think many people have found the easy to understand results in this post before I did but if they tried to get the stuff out they were blocked by the scientists of those days and as such in the year 2021 it is hard to find something back.

Compare it to electron spin; it is hard to swallow that I am the very first person in history that claims electrons cannot be magnetic dipoles because it is just not logical for hundreds of reasons. Yet in the daily practice of how science is done at the universities, it is a no show that electrons are magnetic monopoles. What happened to all those other persons that understood that electrons cannot be magnetic dipoles? Well at least they got neglected and university life just went on with electrons being a magnetic dipole because ‘we are so smart’ and ‘the standard model explains almost everything’. And more of that nonsense…

This post is 8 pictures long, all of the usual size of 550X775 pixels.
Since it is about counter examples to the last Fermat theorem I expect it will not make much headlines in the news for another 3500 years.
After all the only thing university people are good at is being incompetent…;)
Here we go:

At last I found a more or less readable article about near misses of the last Fermat theorem. It was found inside old work from Ramanujan so that is always interesting. Most of the time when I looked for counter example to the last Fermat theorem I only find piles of garbage but this time I tried it with Duckduckgo and something readable comes floating up:
Ramanujan surprises again.

Ok that was it for this post. Thanks for your attention.

Why can’t I find counter examples to Fermat’s last theorem on the internet?

After a few weeks it is finally dawning on me that it might very well be possible that the professional math people just do not have a clue about how easy it is to find counter examples to the FLT. (FLT = Fermat’s Last Theorem.) That is hard to digest because it is so utterly simple to do and understand on those rings of integers modulo n.
But I did not search long and deep and I skipped places like the preprint archive and only used a bit of the Google thing. And if you use the Google thing of course you get more results from extravert people. That skews the results of course because for extraverts talking is much more important compared to the content of what you are talking or communicating. That is the problem with extraverts; they might be highly social but they pay a severe price for that: their thinking will always be shallow and never some stuff deeply thought through…

As far as I know rings of the integers modulo n are not studied very much. Of course the additive groups modulo n are studied and the multiplicative groups modulo n are studied but when it comes to rings all of a sudden it is silent always everywhere. And now I am looking at it myself I am surprised how much similarity there is between those kind of rings and the 3D complex & circular numbers. Of course they are very different objects of study but you can all chop them in two parts: The numbers that are invertible versus the set of non-invertibles. For example in the ring of integers modulo 15 the prime factors of 15 are 3 and 5. And those prime factors are the non-invertibles inside this ring. This has all kinds of interesting math results, for example take the (exponential) orbit of 3. That is the sequence of powers of 3 like in: 3, 3^2 = 9, 3^3 = 27 = 12 (mod 15), 3^4 = 36 = 6 (mod 15) and 3^5 = 18 = 3. As you see this orbit avoids the number 1 because if it would pass through 1 you would have found an inverse of 3 inside our ring and that is not possible because 3 is a non invertible number…

Likely my next post will be about such stuff, I am still a bit hesitant about it because it is all so utterly simple but you must never underestimate how dumb the overpaid math professors can be: Just neglecting rings modulo n could very well be a common thing over there while in the meantime they try to act as a high IQ person by stating ‘We are doing the Langlands program’ & and more of that advanced blah blah blah.
Anyway it is getting late at night so from all that nonsense weird stuff you can find on Google by searching for counter examples to the last theorem of Fermat I crafted 3 pictures. Here is the first one:

I found this retarded question on quora. For me it is hard to process what the person asking this question was actually thinking. Why would the 2.999…. be important? What is this person thinking? Does he have integer solutions to say 2.9 and 2.99 and is this person wondering what would happen if you apply those integer solutions to 2.99999999…..???????

It is retarded, or shallow, on all levels possible. So to honor the math skills of the average human let’s make a new picture of this nonsense:

We will never be intimidated by the stupidity of such questions and simply observe these are our fellow human beings. And if ok, if you are a human being running into tons of problems, in the end you can always wonder ‘Am I a problem myself because I am so stupid?’

If you have figured out that question, you are getting more solid & you look more like a little cube:

I want to end this post on a positive note: Once you understand how stupid humans are you must not view that as a negative. On the contrary, that shows there is room for improvement.