Monthly Archives: August 2021

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.