Video: What happens to Fermat’s last theorem modulo a prime number p?

Last Fermat theorem

This year in January I started finding more and more counter examples to the last theorem of Pierre de Fermat. I started in the space of 3D complex numbers using the so called divisors of zero you can find there. Rather soon after that I found those very easy to understand counter examples using modular arithmetic modulo N where N was the product of two prime numbers. Along the way I found out there is also a cute improvement to make to the so called little theorem of Fermat, that was one of the many cute results of this year. Simple example:
Take 107^2, the old little theorem of Fermat says you must take it modulo 2 and you get the number 1. With the improved little theorem you do not take it mod 2 but mod 2*107 or mod 214. And voila: 107^2 mod 214 = 107.
So the problem of the little theorem of Fermat with small exponents is more or less solved in this way. It was a cute result for sure…:)

Yet since January I have been wondering if all counter examples must use some form of divisors of zero. If so there would be a small possibility to strongly improve on the result from Andrew Wiles. The video below shows a counter example using only integers modulo a prime number p. Since those number spaces modulo p do not have divisors of zero, actually these spaces are fields, I can now say that it is not needed to have divisors of zero. So that is why I decided to include this video in this post: it saves me a lot of time and funny enough this result goes back to at least the year 1917.

Lately there are much more math video’s on the usual video channels and a lot of them have these beautiful animations. A significant part of those new video’s can be traced back to the work of the guy that runs the 3Blue1Brown channel who more or less started to craft those beautiful animations. Somewhere this summer or may be spring he called for the public to make their own math video’s and even I thought about it a short time. But I have no video editing software, I have zero experience in using such software, I have no microphone and the only video camere I have is my photo camera that I never use to make video. So I decided not to try and make a video about 3D complex numbers, it was just too much work.
Here is how the small picture from the video looks on Youtube, it looks cute but likely it takes a lot of time to make such animations:

That graph sure looks cute!

Ok, back in the year 1917 a guy named I. Schur managed to find a counter example using the integers modulo a prime number. He himself in that old article cites another person so it is a bit vague how this all panned out. Anyway I do not have to be ashamed as not to find this result modulo p; it is based on the colorings of graphs like you see above. I do not know much about that so don’t blame me for missing these results. Besidew that, another cute result of this year was that I found out that my own 4D complex numbers form a field if you restrict them to the rational numbers. That simply disproves stupid but accepted theorems like the Hurwitz theorem that says that the only higher dimensional complex numbers are the quaternions and total garbage like the octonions. That whole fucking stupid theorem from Hurwitz is just not true and of course the mathematical community says nothing.
Anyway, the video is just 10 minutes of your time and my post is only two pictures long so have fun with it!

And now we go for the video:

The paper that was unpicked is written in German but don’t panic: It is not in that gothic font they used for a long time. You can find it here:
https://eudml.org/doc/145475.
So if you can read the German language you can try to unpick it for yourself… Ok, end of this post. Thanks for your attention.

What happens if an electron beam hits a magnetic field? Five easy calculations around magnetism.

Magnetism

It is just past midnight on a Saturday so why not start this new post? Two weeks ago all of a sudden I felt like doing a magnetics post once more and to be honest that is a tiny miscalculation because this is also post number 200. This should actually be about higher dimensional complex numbers or so but it is what it is so we are doing magnetics.
This year I stopped working on the magnetic pages on the other website, after more than five years and zero response I decided to classify the physics professors the same as the math professors: Just another bunch of incompetents that you better avoid being around. That policy stays in tact so although this post is very long you should not view this as an attempt to change the views physics professors have on magnetism in particular the idea that electrons must be magnetic monopoles because all other interpretations are not logical. To be honest I feel a bit more free now, now I can say you are a total idiot or a complete moron or a natural born imbecile instead of every time trying to come up with more reasons as why electrons cannot be magnetic dipoles.
This post contains five easy calculations around magnetism, to be a bit more precise: there are three forces that can act on an electron (Coulomb, Lorentz and say the Stern-Gerlach force) and the five easy calculations cover that. Ok, gravity also works on electrons but that is out of this story.
We will look at the speed and the acceleration of electrons and we will try to estimate how much of a gradient a magnetic field must have to explain the observed experimental results. I found a gradient of about 450 million Tesla/meter and that all in my living room… I cannot find a fault in it and of course a gradient so large is not realistic so I reject the way electron potential energy related to magnetism is incorperated into the standard model of particles.
Last week I found a perfect photo that can serve as a model of how physics professors are behaving in my view (a bunch of overpaid incompetents). The ‘blah blah blah’ can serve as my five easy calculations; for the idiots and imbeciles that the physics professors are, these calculations will be ‘blah blah blah’ material. Come on, next year 2022 it will be one 100 years since the Stern-Gerlach experiment was performed. If a collection of overpaid idiots have it wrong for one 100 years, the most logical thing is that they will keep it wrong for at least another 100 years.

Excluded the picture above, this post is 14 pictures long. And even then I skipped a lot of stuff like when talking about the solar wind I just assume all particles go with the same speed of say 750 km/sec. Of course that is an oversimpification; there are many different particles in the solar wind that all behave rather different.
I hope you don’t loose oversight and therefore I would like to explain how I arrived at that crazy magnetic gradient of 450 million Tesla/meter.
Here we go:

1) I estimate how fast electrons go in an old color television where I assume these electron have a kinetic energy of 40.000 eV. This is about 120 thousand km/sec or about one third the speed of light.

2) If you place a stack of those strong neodymium magnets at the television screen you see a black spot where no electrons land. I estimate the sideway acceleration the electrons make and that is a crazy huge number: about 4.5 times 10^15 m/sec.
That might sound very huge but it is just simple Newtonian mechanics: If the electron has a sideway acceleration this big for about 2 nanoseconds, the sideway displacement is about 1 cm. That is in line with what the photo of the television screen says..

3) I calculate the force on the electron for this sideway acceleration and plug this into the expression the professional physics professors use for the force related to inhomogeneous magnetic fields and voila: there is your gradient of only 450 million Tesla/meter.

All in all the five calculations are say advanced high school level / first year university level. Given the fact that physics professors keep on thinking that electrons are tiny magnets with a north and a south pole we can safely conclude that even a science like physics is much more some kind of social construct and not a hard ball science in itself.

Enough of the introductory talk, here are the 14 pictures:

Source of the in-picture screen shots: http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html

Ok, that was it for this post. Please remark that the polar aurora’s do exist for real while the blah blah blah of physics professors explaining this makes not much sense. For example they do not explain why the electrons go so fast that they ionize the air and most of all: These idiots are not aware they are missing something here.

At last I want to remark that for me it feels rather refreshing to talk about physics professors as idiots and imbeciles. That is much better as always being polite and respectful. Why should overpaid idiots and imbeciles also face a lot of completely misplaced respect?
See you in the next post & thanks for your attention because this post was a long reading for you.

De Padé approximations; why are they so good?

3D complex numbers

Already a few years back I wanted to write a post on the so called de Padé apprximations because they are so good at taking the logarithm of a matrix. For me the access to an internet application that calculated those logs from matrix representations was a very helpful thing to speed things up. It would have taken me much much longer to find the first exponential circle on the 3D complex numbers if I could not use such applets.
But in the year 2018 pure evil struck the internet: the last applets or websites having them disappeared to never come back. Ok by that time I had perfected my method of simply using matrix diagonalization for finding such logs of matrices. You can still find it easily if you do an internet search on ‘Calculation of the 7D number tau‘.
Yet in the beginning I only had such applets as found on the internet and I soon found out that using the so called de Padé approximation always gave much better results compared to say a Taylor approximation.
It is not very hard to understand how to perform such a de Padé approximation. Much harder to understand is how de Padé found them, after all it looks like a strike of genius if this works. The genius part is of course found in the stuff you can simply neglect in such approximations, at first it baffles the mind and later you just accept it that you are more stupid as de Padé was…;)
Anyway this week I stumbled upon a cute video and as such I decided to write a small post upon this de Padé stuff. (On the shelf are still a possible new way of making an antenna based on the 3D exponential circles and some updates on magnetism.)
So let us first take a look at the video, here we go:

As you see the basic idea is pretty simple: you use those two polynomials to ‘approximate’ that Taylor series and as a bonus you have a much better approximation of the original function. All in all this is amazing and it makes you wonder if there are methods out there that are even better compared to this de Padé approximation.

Now you can choose beforehand what degree polynomial you use in the nominator and denominator. There are plenty of situations where this brings a big benefit like in the video they point out the divergence problems of say the sine function that is bounded between +1 and -1 on the real axis. The Taylor approximations always go completely beserk outside some interval where they fit quite well. With the appropiate choice of the degrees of the polynomials in the de Padé approximation you can avoid this kind of stuff.
In my view the maker of the video should also have pointed out that a de Padé approximation can have it’s own troubles when you divide by zero. And when the original function never has such a pole at that point, the de Padé approximation also goes very bad. These de Padé approximations
are indeed much better compared to the average Taylor approximation but they are not from heaven. You still have to use your own brain and may be that is a good thing.

De Padé still rules in the year 2021, likely it was a good idea to start with.

In this post I did not cover the matrices and why a de Padé approximation of the logarithm of a matrix is good or bad. If you want to find exponential circles and curves for yourself, use those applets mostly on imaginary units who’s matrix representation has a determinant of +1. In case you want to find your very first exponential circle, solve the next problem:

Ok, it is late at night so let me hit that button ‘publish website’ and see you around.

A infinite list of counter examples to the last theorem of Pierre de Fermat.

Last Fermat theorem

This is a very simple post, all it contains is a list of the most simple counter examples to the last theorem of Fermat. You might wonder, if it is that simple, why take the trouble and post it? Well sometimes it is important to stress the obvious and say for yourself: there is not much reaction from the math professionals so although it is utterly simple it could be that even that is once more too difficult…

These most simple counter examples are all based on two (different) prime numbers and how they behave under exponentiation while taking that modulo the product of those two prime numbers. The most simple example is given by 2^n + 3^n = 5^n mod 6. For n you can only take natural numbers because inside the ring of integers modulo 6 the two prime numbers 2 & 3 do not have an inverse and as such 2^(-1) and the likes simply do not exist. Remark such counter example via some exponential orbit are always periodic, so each and every counter example to the last theorem of Fermat only adds a finite number of ‘actual’ counter examples. In the above example the period is 2 because for n = 3 we already have 2^3 + 3^3 = 5^3 = 5 mod 6.
I organized the list in a simple manner: We like at pairs of prime numbers say (p, q) and the q is always the plafond or maximum prime allowed.
For example the plafond q = 13 yields the following pairs: (2, 13), (3, 13),
(5, 13), (7, 13) and (11, 13).
The reason for doing so is that it is now very obvious it is a one dimensional list of counter examples to the last theorem of Fermat. You can now, if you wanted it, make a one to one correspondence between the set of natural numbers and the list of counter examples.

Another reason for writing this post was that I wanted to experiment a bit with other backgrounds in the pictures used. In the list of counter examples I used two of those beautiful photo’s from the Nikon small world contest. If you have never seen them, look it up on the internet. Althugh those Nikon photo’s are very beautiful I do not think they form a good background to the math as published in the futute so I stick to my old backgrounds I just guess. I always make my math pictures with a very old graphics program that only runs on windows XP. My graphics program is so old that when I save something as a jpg format picture, the program always informs me how long it will take to send it over 28kB telephone modem… Yes, not even a 56 kB modem but a 28 kind of modem. That shows more or less how old my graphics program is but making those kind of backgrounds with say a modern version of GIMP is extremely hard and very laborsome. I like GIMP too but that old program still has features that GIMP is bad at delivering.

Another problem is the picture size under use in a WordPress website. When I started this website about six years ago I could not use any longer my favorite size of 550×1100 pixels. It did not display properly. Anyway only now six years later I dived into that problem again and it seems that WordPress makes 3 pictures of every picture you upload:
1) A thumbnail,
2) A display picture that is not ‘too large’ and
3) Your original upload visible after clicking on the display picture.

There are all kinds of issues with that; if one of my original uploads contains an error and I correct it, that never shows up on the display pictures. So I repair a fault but it does not show up. Only when I rename my faulty picture the correction of the fault is there. But that is frustrating on a lot of levels because now the natural naming of my math pictures gets distorted for no reason at all. For example if a picture has the file name 11Aug2021=Frey_elliptic_curves_are_stupid05.jpg and I have to repair a fault that is in it, I have to make the name different from the other pictures and that is weird. You can only delete your original upload and not the extra pictures that WordPress generates. In that sense it is welcome to the Hotel California where you can checkout any time you like but you can never leave.
If my expectations are correct, the first picture will display properly while the second one is likely too small but if you click on it you will see the correct version of stuff:

This displays properly…
You see, it cannot handle a picture that is 1440 pixels high…

Why my version of WordPress does not show the larger picture is unknown to me. Likely I must change some settings but I do not have a clue. Luckily it is still readable so may be this is a good time to say goodbye and until the next post and so.

What happens to a Frey elliptic curve if we take it modulo 35?

Last Fermat theorem

Of course we have to take a Frey elliptic curve based on one of the counter examples to the last theorem of Pierre de Fermat for this ‘take it mod 35’ to be meaningful.
Welcome by the way!

A few months back I encountered this problem for the first time and the determinant of all of those Frey elliptic curves is always zero because it contains the factors that ensure it is a counter example to the last Fermat theorem. As such these two factors are always a pair of divisors of zero and as such if you multiply them you get zero. I did not give it a second thought, only remarked the determinant is zero and as such this likely spells some trouble for such a Frey elliptic curve. Recall that if the determinant is zero, there is at least one double zero to be found in your equation. Two weeks back I looked at it with a bit more detail and the result was rather surprising: The cubic part of such a Frey curve indeed gets some double zero, but all in all in the space of integers modulo 35 the thing has four zero’s! But all these Frey curves go like
y^2 = x(x + A)(x – B) so the ‘x-part’ is a degree 3 polynomial. And a 3 degree polynomial has at most 3 zero’s, or not?

Wrong! A 3 degree polynomial has at most 3 zero’s (or precisely 3 zero’s if you count with multiplicity) but in spaces with divisors of zero it is possible to get extra zero’s. On the spaces of 3D complex and circular numbers it is easy to find a parabola with 3 zero’s. Take p(x) = x^2 – x. If you solve for p(x) = 0 you basically try to find numbers that are their own square. After all if a number is it’s own square, there is no denying that
x^2 – x = 0. Of course x = 0 and x = 1 are their own square, but on the three dimensional complex and circular numbers the center of the exponential circle has also that impotant propery. The center is usually denoted as the number alpha and yes that is a zero too. Yet you cannot use such an extra zero in a factorization of such a parabola. The factorization is and stays
x(x – 1) and if we substitute alpha in we get alpha(alpha – 1). But ha ha ha these last two factors are a pair of divisors of zero and that is why it’s zero…

I also found a cute applet that you can use for making graphs of elliptic curves modulo a single prime number. Most of the time I needed modulo 35 or anything with two prime numbers in it and the applet tries to warn me every time when I do that. I also made a few graphs from counter examples to the last theorem of Pierre de Fermat with it. That was relatively funny and made me decide to write this post. Of course we do not need some applet to validate my counter examples to the last theorem because there is plenty of proof. But it was funny anyway.

Links to the two relevant applets:
Elliptic curves over finite fields, and
Curves over finite fields. With the last applet you can make those counter examples to the last theorem of Pierre de Fermat because it allows you to use exponential expressions. It has to be remarked that the applet is not so good at exponential series so already at the stuff modulo 35 it runs awry and returns gibberish instead of a nice flat zero.

This post grew longer as planned before hand, but that is with most posts I write. You always think ‘ah that is simple to explain in just a few words’ but if you try that and also estimate the math content of the average math loving person, I always need more and more words to explain the stuff involved… Well so be it.

This post is 9 pictures long in the format or size I use lately: 550×825 pixels.

From modulo 35 and higher the applet starts disfunctioning.

Ok, let’s hope there are no unseen typo’s in the above. I always hate when later I read stuff already published to the internet and find out there are typo’s in it…
The next post is likely an infinite list of counter examples to the last theorem of Pierre de Fermat or it will be about a cute antenna design based on the 3D exponential circles. This cute antenna should produce circular radiation and as far as I know this design is not used anywhere. (I do not know if it is better compared to what we have at present date, after all antenna design is a well developed technical field.)

Ok, that was it for this post.

Three video’s to kill the time in case you are bored to the bone…

3D complex numbers, Last Fermat theorem, Magnetism

A couple of days ago I started on a new post, it is mostly about elliptic curves and we will go and see what exactly happens if you plug in one of those counter examples to the last theorem of Pierre de Fermat. There is all kinds of weird stuff going on if you plug such counter example in such a ‘Frey elliptic curve’. I hope next week it will be finished.

In this post I would like to show you three video’s so let’s start that: In the first video a relatively good introduction to the last theorem of Fermat is given. One of the important details of that long proof is the relation between elliptic curves and so called modular forms. And now I understand a bit better as why math professors go bezerk on taking such an elliptic curve modulo a prime number; the number of solutions is related to a coefficient of such an associated modular form. It boggles the mind because what do those other coefficients mean? As always just around the corner is a new ocean of math waiting to get explored.

Anyway, I think that I can define such modular forms on the 3D complex and circular numbers too so may be that is stuff for a bunch of future posts. On the other hand the academic community is never ever interested in my work whatsoever so may be I will skip that whole thing too. As always it is better to do what you want and not what you think other people would like to see. The more or less crazy result is shown in the picture below and after that you can see the first video.

Yet it might be this does not work on the 3D complex numbers…

Next video: At MIT they love to make a fundamental fool of themselves by claiming that their version of a nuclear fusion reactor will be the first that puts power on the electricity grid… Ok ok, after five or six years I have terminated the magnetic pages on the other website because it dawned on me that the university people just don’t want to read my work. I have explained many many times that it is just impossible that electrons are magnetic dipoles but as usual nothing happens.
Oops, wasn’t it some years ago that Lockheed Martin came bragging out they would make mobile nuclear fusion reactors and by now (the year 2021) there would be many made already? Of course I would never work properly because at Lockheed Martin they to refuse to check if the idea’s of electron spin are actually correct. If electrons are magnetic monopoles all fusion reactors based on magnetic confinement will never work. Just look at Lockheed Martin: So much bragging but after all those years just nothing to show. Empty headed arrogant idiots is whart they are.

And now MIT thinks it is their time to brag because they have mastered much stronger magnetic fields with their new high temperature superconducting magnets. Yes well you can be smart on details like super conducting magnets but if you year in year out refuse to take a look at electron spin and is that Pauli matrix nonsense really true in experiments? If you refuse that year in year out, you are nothing but a full blown arrogant overpaid idiot. And you truly deserve the future failure that will be there: A stronger magnetic field only makes the plasma more turbulent faster. And your fantasies of being the first to put electricity on the grid? At best you are a pathetic joke.

MIT & me, are we mutual jokes to each other?
Just like ITER and the Wendelstein 7X this will not work!

It is very difficult to make a working nuclear fusion reactor on earth if you just don’t want to study the magnetic properties of electrons while you try to contain the plasma with magnetic fields. Oh the physics imbeciles and idiots think they understand plasma? They even do not understand why the solar corona is so hot and if year in year out I say that magnetic fields accelerate particles with a net magnetic charge, the idiots and imbeciles just neglect it because they are idiots and imbeciles.

The third video is about a truly Hercules task: Making a realistic model of the sun so that can run in computer simulations… If humanity is still around 10 thousand years from now may be they have figured it out but the sun is such a complicated thing it just cannot be understood in a couple of decades. There is so much about the sun that is hard to understand. For example a number of years ago using the idea that electrons are magnetic monopoles, it thought that rotating plasma like in some tornado kind of structure is all you need to get extremely strong magnetic fields. But I never ever wrote down only one word in that direction. Anyway about a full year later I learned about the rotational differential for the sun: at the equator it spins much faster as it does on the poles. And that would definitely give rise to a lot of those tornade like structurs that must be below the sun spots.
Of course nothing happens because of ‘university people’ and at present day I do not give a shit any longer. I am 100% through with idiots and imbeciles like that. For me it only counts that I know, that I have figured out something and trying to communicate that to a bunch of overpaid highly absorbed in their giant ego’s idiots and imbeciles is a thing I just stopped doing. If it is MIT, ITER or Max Planck idiots and imbeciles, why should I care?

Ok, that was it for this post. If you are not related to a university or academia thanks for your attention. And to the university shitholes: please go fuck yourselves somewhere we don’t have to watch it.

On a beautiful identity related to the new little theorem of Pierre de Fermat.

Last Fermat theorem

Just a few minutes ago I thought that may be the next title to this new post would also be funny: WTF! Doing math research with the help of a Google search suggestion??? And yes, if you think about that it is rather weird but it is true. How come I have fallen so deep?
Well a couple of weeks back I did a Google internet search by typing in one of my counter examples to the last theorem of Pierre de Fermat. In the normal html search results nothing popped up but when I looked in the pictures to my surprise every time there was only one picture of my website. And indeed that picture contained the search phrase I had just typed in… So at present date & year the Google search algorithm can translate a phrase like 5^n + 7^n = 12^n mod 35 to the actual content of a picture on this website. By all standards this is amazing. Here are the two search phrases I did put in and if you do that yourself you can find back in the pictures from Google search the actual picture on this website that the search phrase is about. Here are the two pictures explaining the stuff a little bit:

This is amazing!

When I started this website in 2015 in the second post I explained how this website was set up: The math will be mostly in the pictures I create so it is a pity that internet search engines cannot read that. Well now almost six years later as a matter of routine the Google search engine can indeed a bit of the math content as found in my pictures.
Here is the second search string or search phrase:

To be honest I was amazed at the results. So later I decided to check what would pop up on Google if I would search for my new little theorem of Pierre de Fermat. So my search phrase was p^q = p mod pq and yes Google can find that content in my pictures too.
But the Google search engine also popped up an alternative search phrase also containing the mod pq stuff. And for a few seconds of time I started to panic like ‘Oh oh have the math professional professors already found the new little theorem of Fermat and am I only an idiot doing weird stuff that is known to science for centuries????‘ But very soon I calmed down, ok they might have proven that identity that Google search suggests, but they are still overpaid weirdo’s never ever able to connect this particular identity to the new little theorem of Fermat. Compare it to the Cauchy-Riemann equation that rule differentiation in the Complex plane; despite having those 2D equations the math professors just cannot bring those same ideas to 3D space. And not for just a few years or so, no they cannot do that century in century out. Even if there is a dedicated website out like this website doing a lot of 3D complex number theory, the overpaid & incompetent math professors keep on being silent year in year out and likely also century in and century out.

But let’s not get emotional about how stupid this all is, after the indentity found is very beautiful and all in all very much like my new little theorem of Pierre de Fermat. And may be it is a bit unwise from me to view the collective of math professors as ‘utterly stupid’ After all they have some kind of proof for it and most of those proofs use the CRT or the Chinese remainder theorem. And that made me pause for a moment, the remainder theorem is very old so how the hell did China industrial spionage in other parts of the world in those long lost centuries? Did they find the CRT without stealing intellectual property? Wow!

But let’s get serious, this post is five pictures long and all about that search suggestion as done by Google. Before we start I once more want to show you that the new little theorem of Fermat is indeed an improvement. For those who already know that, just skip it if you want.
The old theorem of Fermat says that a^p = a mod p, here p is a prime number and p should not be a factor of a. So a and p must be relatively prime to each other. But if p is a small number, it does not work that well. Take for example a = 105 and p = 2. Well 105^2 mod 2 = 1 but everybody already knows that the square of an odd number is odd.

The new little theorem of Fermat says a^p = a mod ap and because ap is always greater than a, this also returns a when p is small. For example now we have 105^2 mod 210 = 105. So I think this is a small improvement.

Ok, let us go to the five pictures:

Yes it is the end of this post but I would like to remark that if you look at the banner of this website it says ‘Math as you have never seen it before’. Of course that is not a goal an sich but a natural by product of the things I like to study. My math all hang together in ways that are often not obvious. For example the new little theorem of Fermat is not a stand alone result, it emerges directly from when I studied the exponential orbits during all those counter examples to the last theorem of Fermat. In return all those counter examples started with the first ones I found in my own 3D complex numbers. So this all hangs together while understanding this new little Fermat theorem can also be understood using just plain old math without any 3D complex numbers or so.
The professional math professors never found this new little Fermat theorem because they do not want to walk the path from 3D complex numbers to where we are now. They only want the 2D complex plane and ok may be the cute quaternions and that’s it. Of course that is not forbidden, but if in 3.5 centuries of time you even cannot find the new Fermat little theorem, might it be time to scratch the head a little bit and do some rethinking?

Of course not my dear reader, the math professors will never change.

See you in the next post & thanks for your attention.

The new little theorem of Fermat: Checking it out with Pari.

Last Fermat theorem

This week the first blue berries were ripe so it is that time of the year again: Beer with blue berry juice! Lovely; it is a very smart way to get a bit of vitamins…;)
It is not much of a secret that every now and then I have some tiny forms of criticism against the professional math people. It really is minor and tiny; calling somebody an inverted asshole is often even a compliment compared to what they actually deserve. This day it is different, I came across a computer program named Pari and it is actually very good. I think or estimate this program started before we had computers with a so called GUI (=graphical user interface, you know the click stuff with a mouse). So you have to type in commando’s and press enter.
There are two versions of the program; a 32 and a 64 bit version. On my old computer the 32 version does not work properly (it does not work at all but that is more my computer to blame and not the program). The 64 bit version runs perfectly so that’s fine.
Pari seems to be used a lot by number theorists, I do not know much about number theory so that is why I never heard of the program. Pari is from France so if you speak that language will you can even install the french version of it all. For myself speaking I am glad I now finally have some program that does not limit me to the say 12 digits of a Casio hand held calculator. Not that you need so many digits very often but it is good to have that capability.

One of the other reasons for posting this is that when you do a Google search for ‘The new little theorem of Fermat’ my relevant posts from earlier this year just do not pop up on page one, two or three of the search results. On the one hand that is logical: a lot of people and websites with large traffic volumes have been writing about the little theorem of Pierre de Fermat. I would like to let it pop up a bit higher in the search results so you readers must all massively do a search every day on Google for the new little theorem of Fermat…;)
I remember that when I started this website, if I searched for 3D complex numbers you always had that stuff known as Alan’s pages (or may be Allen’s pages) popping up above me. Just always. That guy had only one page on 3D complex numbers and everything you could do wrong, Alan did it wrong. So for me it was kind of frustrating; why does that idiot pop up above me year in year out? It was only later that I realized a lot of people click on that kind of fake science because those people likely did everything wrong themselves. Likely they are professional math people who are trying to expand the complex plane to 3D space, that is something that does not work at all. If you do not base it on an imaginary unit, say j, with the property j^3 = -1, all your work will be in vain. Anyway after some time I finally popped up above that stupid Alan page and since that time it has always been higher. The lesson is you must not hurry; math is a long term thing and with this new little theorem of Pierre de Fermat it will take some time before it will be valued properly.

The Pari program is very good at doing the modulo thing, if you want to calculate a mod b in Pari you must enter the command Mod(a, b).

This post contains four written pictures about the new little theorem of Fermat, I left the proof out because I already wrote two proofs, after that just a few screen shots from the program Pari. And of course a few links for the downloading stuff although the Pari program is easy to find on the internet. Let me start with four pictures in the size 550×825 pixels:

This website is a WordPress website and as such it is horribly bad at handling larger image files. So I hope and pray that the screen shots that are about 850 pixels wide will display properly. Here we go, this is the opening screen of Pari and you see it is just like a DOS window:

As you see it does not display properly; it looks like it is 550 pixels wide so likely that is how I ended with those math pictures all 550 pixels wide…

A detail not to be missed is that you can get moral support and all you have to do is type the command ?17. That is very handy, so the next time you feel frustrated you do not need to go out and slaughter and kill at least 20 children and babies in order to get rid of your frustration. No, all you have to do is type ?17. It is amazing! No more baby killing, just type ?17.
Ok, next screenshot that will not display at 850 pixels wide:

Beside moral support, this is how you can get help.

In the above screen shot you see why I like this Pari computer program: You can fill in calculations like 8269^9973 for the a in Mod(a, b) and 8269*9973 for the b in Mod(a, b). Remark that 8269 to the power 9973 is a very huge number, yet Pari gives the correct answer in a split of a second.

Let’s look at the last screen shot:

In the above screen shot you see a numerical validation of the new little theorem of Pierre de Fermat. Of course we do not need such validations because I already gave two proofs for the new little theorem. But it is nice to observe that a standard computer can handle giant numbers like 8269^9973 with easy. So my compliments go to the French math community for this perfect computer program!

Here is a link to the Pari homepage: https://pari.math.u-bordeaux.fr/
Do not skip the documentation, it’s all not bad.

Ok, let me try to find that button known as ‘Publish website’ and see you around in a new post.

How does nature flip electron spin in atomic hydrogen?

Magnetism

The so called ‘spin flip’ in atomic hydrogen is relatively important in astronomy. There is a tiny difference in energy levels of the electron in atomic hydrogen, when the spins of the nucleus and electron are the same it is said to be in the higher energy level. And with opposite spins the lower energy level is there. The difference between the two energy levels is such that a photon has a wavelength of 21 cm if this energy is released by a hydrogen atom when it’s ‘spin flips’.

In astronomy the study of this 21 cm wavelength is rather important; in our galaxy there is so much dust and clouds of all kinds of material that a lot of the visible light is blocked. But using the 21 cm radiation astronomers were able to prove the existance of the invisible spirals of our galaxy. So understanding a bit more about how the spin in atomic hydrogen flips could be important you might think.

It is not much of a secret that about 100% of physics professors think that the magnetic properties of say an electron or a proton are bipolar. So each and every electron and proton in our universe has a north and a south pole, that is the so called ‘tiny magnet’ model for elementary particles.

It is also not much of a secret that for over five years I am thinking the professors are all crazy because that bipolar stuff is just not logical on all kinds of levels. I think all electrons and protons carry magnetic charge just like they carry electric charge.

In this post we are going to take a detailed look as what happens when in atomic hydrogen the electron goes round and round the proton that is the nucleus and how the energy levels behave. As usual, if you follow that standard knowledge of bipolar ‘tiny magnets’ magnetism you only find a big mountain of total nonsense.
My choice went for atomic hydrogen because that is the most simple atom there is and by using elementary logic there is only one orbit for the electron that could explain the 21 cm wavelength as observed in astronomy.

If it is true that magnetism is always a ‘tiny magnet’ when it comes to elementary particles, in that case it is very hard to explain why the frequency emitted is precise 21 cm and nothing else. We will do a very simple thought experiment and from that we can conclude that there is only one orbit possible that gives always the 21 cm radiation.

These kind of very small energy level differences are known as hyperfine spectral shifts. They also occure in large molecules, that is why I did choose atomic hydrogen because if the explanation fails there it should also fail in large molecules. With ‘failure’ I mean the bipolar idea’s of magnetism that the professional physics professors have all of the time.

I wrote seven pictures about the energy levels in atomic hydrogen, if you base it on electrons and protons being bipolar magnets instantly you run into all kinds of trouble. After these seven pictures I show you a few video’s that make clear that 100% of professional physics people simply do not have a clue what electron spin is. As such they have a tendency to talk out of their neck, that means what they say is not thought through in any meaningful manner. Here we go:

Remark there are trillions of molecules in such samples.

In my view the conclusions are clear: All reasoning based on electrons and protons having two magnetic poles always leads to nonsense fast. Just like here where we found orbits that have the same oscillating energy levels for both spin directions. Of course that is 100% nonsense.

This is about the sixth year I am researching electron spin. If now I do an internet search about “How to flip electron spin” and I hardly get any results I know instantly that likely it is not possible to flip the magnetism of an electron. Do such an internet search for yourself, nowhere is there any person that can explain how you can do that.

It is time for the video’s about this subject. Here is the first video, it does not contain hundreds of faults only a few minor ones like the Zeeman effect is not interaction between the electron and it’s orbit.

It’s comedy: Wavelength in eV and that is 1/10 of the Zeeman effect…

The guy from the video (Michel van Biezen) has an amazing 737K subscribers, so he makes plenty of money via the Youtube advertising scheme I just guess. In the next video you can observe the full “talking out of their neck” habit that so many physics people have. Michel tries to explain why there is an energy difference between the spin states in atomic hydrogen. He just talks from his neck by ‘explaining’ this as two currents that are repelling or atracting (like in the old experiments from the Ampere guy in the 19-th century). View it as comedy and not something serious:

It is hard to pack so much comedy in the first 60 seconds only…

I even made a screen shot from the last video. It can serve as a fundamental proof that on average physics people are very good at talking out of their neck. How you can see this as some good explanation is beyond me. At best it is comedy, at worst you understand why I will never ever try to publish something in a ‘professional journal’. These people they are all idiots and imbeciles.

Wow, the wisdom is not measureable I just guess.

Another very funny detail that often comes along when you figured out that electrons are likely magnetic monopoles is the lack of magnetic monopoles there is in our present universe according to overpaid physics professors. In astronomy they figured out that in the beginning of our universe there should have been an awful lot of magnetic monopoles. Well yes that is true, every electron is one of those things. But the overpaid idiots and imbeciles known as physics professors think otherwise and if you think electrons and protons and even quarks are always magnetic dipoles, you have a hard time finding the missing magnetic monopoles. That is why these people, retarded as they are, claim that it ‘is enough’ there is only one magnetic monopole in an entire galaxy and ‘therefore they are that hard to find’. It is another form of comedy: where are all the missing magnetic monopoles???

At last a few words on that TOE (theory of everything) and GUT (grand unifying theory) stuff: If only one detail like understanding electron spin is wrong, automatically the entire GUT or TOE will be wrong.

But yet, as I am in the sixth year of investigations into electron spin, the physics community still does not find it nessecary to prove their stupid claims on electron spin via any experiment whatsoever. Is there ever done an experiment that proves electrons have two magnetic poles? Nope! Have they any plans in doing so? Nope!

All in all I am expecting no different behavior is say the next six years: The only thing that will not be different is that physics people will keep on talking from their neck without realizing how stupid they are.

Oversight of all counter examples to the last theorem of Pierre de Fermat, Part 3.

3D complex numbers, Last Fermat theorem, Matrix representation

It is late at night, my computer clock says it is 1.01 on a Sunday night. But I am all alone so why not post this update? This post does not have much mathematical depth, it is all very easy to understand if you know what split complex numbers are.
In the language of this website, the split complex numbers are the 2D circular numbers, In the past I named a particular set of numbers complex or circular. I did choose for circular because the matrix representations of circular numbers are the so called circulant matrices. It is always better to give mathematical stuff some kind of functional name so people can make sense of what the stuff is about. For me no silly names like ‘3D Venema positive numbers’ or ‘3D Venema complex numbers’. In math the objects should have names that describe them, the name of a person should not be hanged on such an object. For example the Cayley-Hamilton theorem is a total stupid name, the names of the humans who wrote it out are not relevant at all. Further reading on circulant matrices: Circulant matrix.
I also have a wiki on split complex numbers for you, but like all common sources they have the conjugate completely wrong. Professional math professors always think that taking a conjugate is just replacing a + by a – but that is just too simplistic. That’s one of the many reasons they never found 3D complex numbers for themselves, if you do that conjugate thing in the silly way all your 3D complex math does not amount to much…
Link: Split-complex number.

This is the last part on this oversight of counter examples to the last theorem of Pierre de Fermat and it contains only the two dimensional split complex numbers. When I wrote the previous post I realized that I had completely forgetten about the 2D split numbers. And indeed the math results as found in this post are not very deep, it’s importance lies in the fact that the counter examples now are unbounded. All counter examples based on modular arithmetic are always bounded, periodic to be precise, so professional math professors could use that as a reason to declare that all a bunch of nonsense because the real integers are unbounded. And my other counter examples that are unbounded are only on 3D complex & circular number spaces and the 4D complex numbers so that will be neglected and talked into insignificance because ‘That is not serious math’ or whatever kind of nonsense those shitholes come up with.

All in all despite the lack of mathematical depth I am very satisfied with this very short update. The 2D split numbers have a history of say 170 years so all those smart math assholes can think a bit about why they never formulated such simple counter examples to the last theorem of Fermat… May be the simplicity of the math results posted is a good thing in the long run: compare it to just the natural numbers or the counting numbers. That is a set of numbers that is very simple too, but they contain prime numbers and all of a sudden you can ask thousands and thousands of complicated and difficult questions about natural numbers. So I am not ashamed at all by the lack of math depth in this post, I only point to the fact that over the course of 170 years all those professional math professors never found counter examples on that space.

This post is just 3 pictures long although I had to enlarge the lastest one a little bit. The first two pictures are 550×825 pixels and the last one is 550×975 pixels. Here we go:

That was it for this post, one of the details as why this post is significant is the use of those projector numbers. You will find that nowhere on the entire internet just like the use of 3D complex numbers is totally zero. Let’s leave it with that, likely the next post is about magnetism and guess what? The physics professors still think there is no need at all to give experimental proof to their idea of the electron having two magnetic poles. So it are not only the math professors that are the overpaid idiots in this little world of monkeys that think they are the masters of the planet.