Let’s Destroy Internet Security!!!

Ok ok, I admit instantly that the title of this post is way over the top but for once I allow myself a catchy title that has only limited resemblance to what this post is about. In this post, if I write the word computer I always mean a classical computer so not a quantum version of it.

In the previous post there is a video in from the ‘Infinite Series’ that serves as an introduction to the Shor algorithm; if this algorithm could be implemented into a quantum computer that would likely break internet security for a short while. Beside the fact that large prime numbers are used in standard classical encryption, it can also be done with elliptic curves.

This post is about the principle of Jente, with a bit of luck you can find factors of large numbers using the principle of Jente. Counter intuitively the largest (prime) factor will be the easiest to find.
Now how did Jente find the principle of Jente?
Back in the time, end 1997 or begin 1998, we lived in a house without a garden and since I still smoked a lot of tobacco I always had a window open in my working room. Since this work room was next to the entry of the house, very often when the door to my room opened papers would fly from my desk because of wind going through the room.

There was this cute baby crawling around and one day she brought me back a piece of paper that had flown off my desk. And on that piece of paper was a little cute formula that read
m_{j+1}  = m_j – d_j. So that is how this got the name the principle of Jente.

Lately Jente turned 21 years of age, she now lives temporary in Australia, and I decided to write this old stuff down as a kind of present for her. The principle of Jente is extremely easy to understand, but as far as I know mathematical reality this principle has not been exhausted very much by the entire math community over centuries of time.

What is missing in this post is a way to converge fast with high speed to one of the factors of one of those huge composite numbers the software engineers use for internet security. My gut feeling says that it should not be that hard but until now I have never found it. It might very well be that inside things like Diophante equations somewhere the solution to this problem of fast finding the largest prime factor is solved without the person who has done that being aware of it…

I tried to keep this post as short as possible so I scrapped a whole lot of stuff but it is still 15 pictures long (picture size as usual 550 x 775 pixels). A feature that I like very much is that I am using so called Harry Potter beans in order to explain as why the Jente principle works. I feel a bit proud on that because it is so simple you could explain that to elementary pupils in their highest years.

For myself speaking I also like this approach to finding prime factors because it is so different from all other ways, yet it has that underlying undeniable thing in it named the Jente principle. The most important detail in this post is the table with the diagonals in it.
If you understand that table and, for example, you can find another algorithm for quantum computers that solves that problem, you have found an alternative to the Shor algorithm…

Have fun reading it, take your time because it is not meant to be grasped in five minutes or so.


I hope you understand the fundamental problem still open after almost two decades:

You start with some number j, calculate m_j = N mod j and d_j = N div j.
Having these, the Jente principle guarantees you can find (j + k) mod N for all k > 0.

But, how oh how, do you converge towards a solution of
m_{j+k} = 0 mod (j+k) ?????


The Shor algorithm: In the world of quantum computing we have the theoretical side where people just write down all kinds of elaborate scheme’s like the Shor algorithm and just as easy they throw in a lot of Hadamard gates that supposedly will bring a giant bunch of quantum bits into super position.

On the other hand you have people that actually try to build quantum computers.

As far as I know stuff, there is no way of bringing a lot of qbits into a nice super position or, for that matter, entangle them into a good initialization state in order to run your quantum software.

More info:

Hadamard transform

Shor’s famous algorithm: Shor’s algorithm

Elliptic Curve Cryptography: a gentle introduction


Ok, that was it. Don’f forget to pop open a few beers. Don’t believe all that nonsense that doctors are telling you like drinking less = good.
As far as I know reality, all people in my social environment that drink far too little beer always get killed in extremely violent events… 😉

Till updates.

Destroying Internet Security using the Jente principle, a teaser introduction.

A few months back suddenly there was a new video channel about math and it goes under the cute name Infinite Series. About two months back the channel posted a way to destroy internet security if you could only find that factorization of two giant prime numbers.

Most of present internet security hangs around the difficulty of observing a giant number N of, let’s say, one hundred digits and our incapability to factorize large numbers like that into their prime factor numbers.

Of course, since the Infinity Channel is USA based, it is completely impossible that fresh math will come from that space. Here is the video and indeed only ancient math is around:

How to Break Cryptography | Infinite Series

The idea’s as expressed in the video are very interesting, but is just does not use the Jente principle that ensures you can find weakness in the integers surrounding the prime numbers that make up the factorization of the stuff you want to encrypt.

In the next two pictures you see that a prime number is extremely weak in avoiding detection using the Jente principle if you are close enough to that prime number.

And if a prime number is detected, in principle you could break down the security of the communication channel.


Let’s leave it with that, after all talking about a basin around a prime number that shouts out ‘the prime number is here’ is one hundred percent outlandish to those overpaid USA math professors…

End of this teaser post, I hope I have some more next week so see you around!

Some corrections and an addendum + a new way of taking Fourier transforms.

This post has many goals, for example in the previous post I talked about a ‘very rudimentary Fourier transform’. In this post it is a bit less rudimentary, a bit more satisfying definition is given but still I did not research all kinds of stuff like the existence of an inverse & lot’s more basic stuff.

For myself speaking I consider this ‘new Fourier transform’ more as some exotic bird that, if capable to fly a few meters, will only draw applause from specialists in Fourier analysis.
So for myself speaking I am far more happy we need a more advanced number tau and the mathematical miracles you can do with it in three dimensions.

Therefore I included two examples of exponential curves that go through the plus and minus of all three basis vectors in 3D space, after all this is one of my most remarkable math results…

In this post I also show you how to use the calculus of ‘opposite points, in three dimensions it works like a bullet train but the higher the dimensions become the harder it is to frame it in simple but efficient calculus ways like using opposite points on exponential circles.

Another thing to remark is that an exponential circle is always a circle; it is flat in the 2D sense and has a fixed radius to some center. When this is not the case I always use the words exponential curve

This post is nine pictures long, I truly hope you learn a bit from it.
You really do not need to grasp each and every detail, but it is not unwise to understand that what I name the numbers tau are higher dimensional versions of the number i from the complex plane.

Ok, here we go:

In these nine pictures I forget to remark you can also craft a new Cauchy formula for the representation of analytic functions. For myself speaking this was far more important compared to a new way of Fourier transform.

You still need that more advanced version of tau…

Can´t get enough of this stuff?
Ten more pictures dating back to 2014 at the next link:

From 18 Jan 2014: Cauchy integrals

A link to the Nov 2016 post on 2D split complex numbers that contains the disinformation about the sum of the coordinate functions:

The second hybrid: a 4D mix of the complex and the circular plane.

End of this post, likely the next post is about prime numbers and how to demolish the internet security we think we have using huge prime numbers…

So see you around!

Some very rudimentary Fourier stuff + a surprising way to do a particular integral.

Lately I was looking at some video’s about Fourier analysis and it dawned on me I had never tried if the coordinate functions of my precious exponential circles were ‘perpendicular’ to each other.

Now any person with a healthy brain would say: Of course they are perpendicular because the coordinate functions live on perpendicular coordinate axis but that is not what I mean:
Two functions as, for example, defined on the real line can also have an inner product. Often this is denoted as <f, g> and it is the integral over some domain of the product of the two functions f and g.

That is a meaningful way of generalizing the inner product of two vectors; this generalization allows you to view functions as vectors inside some vector space equipped with an inner product.

Anyway I think that most readers who are reading post number 62 on this website are familiar with definitions of inner product spaces that allow for functions to be viewed as vectors.


So I was looking at those video’s and I was highly critical if my coordinate functions would be perpendicular in the sense of such generalized inner product spaces. But indeed they are also perpendicular in this sense. Yet a bit more investigations soon gave the result you cannot build a completely new kind of Fourier analysis from this stuff.

Ok ok a few years back I already arrived at that insight because otherwise in previous posts you would have found stuff relating to that…

Generalized inner product spaces are often named Hilbert spaces, a horrible name of course because attaching a name like Hilbert to stuff you can also give the name Generalized Inner Product Space brings zero wisdom at the scene.
It is only an attempt to turn the science of math into a religion where the prophets like Mr. Hilbert are given special treatment over the followers who’s names soon will be forgotten after they die.

More on Hilbert spaces: Hilbert space


This update is 11 pictures long, all size 550 by 775 pixels.
I kept the math as simple as possible and all three dimensional numbers used are the circular ones. So you even do not have to worry about j^3 = -1…

Have fun reading it:







I hope you like the alternative way of calculating that integral in picture number 11. It shows that 3D complex and circular numbers are simply an extension of mainstream math, it is not weird stuff like the surreal numbers that decade in decade out have zero applications.

May be in the next post I am going to show you a weakness in the RSA encryption system.
Or may be we are going to do something very different like posting a correction on a previous post.

Let´s wait and see, till updates.

New magnetic update + some pictures related to the post on the general theorem of Pythagoras.

I know I know I have not posted very much lately. There was plenty of material to craft new posts from but I skipped easily writing 10 posts or so because I am also wondering as why the so called ‘professional professors’ never make a move.

For the math professors this is 100% logical: If you are math stupid to the bone, you will never understand 3D complex number systems. But why the physics professors do not react in any way is completely unknown to me. Ok ok, for example their explanation of how permanent magnets work is very very strange. They formulate it often this way:

In a permanent magnet all spins align themselves.

That is a very stupid explanation and if you meet a physics professor and you whisper softly ‘quantum computer’ they start talking about atoms and electrons that can be in two places at the same time and that electrons can be in a so called super position of being spin up and spin down at the same time…

So in a permanent magnet the electrons and their spins are glued into place permanently while if those people need more funding all of a sudden even atoms can be in two places at the same time…

It is important to stress that the professional physics professors have a one 100% lousy explanation about how permanent magnets work. They completely miss the important fact permanent magnets have their magnetism because of the place of unpaired electrons inside the inner shells of those magnets… Here is my 04 Jan 2017 explanation of it on this very website:

How permanent magnets work, the official version against what I think of it.


On 19 March I posted reason number 46 as why electrons cannot be magnetic dipoles on the other website. It is about so called BCS theory that explains super conductivity using so called phonons.

It is a very very very strange theory because just one unpaired electron is capable of distorting a metal lattice at low temperatures to such an extend that another electron is attracted and as such super conductivity emerges…

It is an imbecile kind of theory, in my point of view it is a  basic thing is that the electron pair is magnetically neutral that gives rise to the emerging of super conductivity. And at that point we have the perfect collision with my views on magnetism and the professional view:

The professionals think that the electron is a magnetic dipole because about 150 years ago a guy named Gauss did write down some fancy math explaining flux conservation. I love that kind of math but it just does not go for the electron, furthermore there is zero experimental proof for the electron being a magnetic dipole.

Here is the link that replaces the official BCS theory by a model for super conductivity as I see it:

19 March 2017: Reason 46: BCS theory says electron pairs are bosons…

Don’t forget: It is not a theory but a model.
Yet it should cover all kinds of super conductivity materials from the old school stuff from 1911 by Heike Kamerling Onnes to the present day high temperature super conductors named cuprates.


After having said the above I am pleased to post five more pictures on the general theorem of Pythagoras. I know that in the last post I said this is the final post but then I was not capable of producing the pictures as shown below.

Here they are, only five pictures with very very simple math in it.

Have fun reading it!

Ok, that was it.

Have a nice life or try to get one.

And in case you are a professor in physics; why not cough up for the first time in you life that the electron is indeed a magnetic dipole???

Why not? A tiny bit of experimental proof would be great.

End of this post, till updates.

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

This week I finally did put in the last details of the proof for the general theorem of Pythagoras. Now a long long time ago somewhere like in 1993 or1994 when I found this proof I could only find a very different proof in the official literature.
That proof worked with a matrix, I do not remember how it worked but the important feature is that this proof that used a matrix did not need a special coordinate system.

In the proof that I found I need the origin in the place where all lines, planes, hyper planes etc meet perpendicular so it is pretty natural to use the natural basis in n-dimensional real vector space.
The simplicity of this proof hangs on the construction of a normal vector to a hyper-plane and although I know this result for over two decades once more I was stunned about how easy this normal vector is to find and how easy it is to use the properties of this normal vector in proving the general theorem of Pythagoras.

Because after all; if you are given n + 1 points in n-dimensional space and you must prove something about the convex span of those n + 1 points, most of the time you just scratch your chin a bit, think a bit about it & never make any progress at all…
But using this easy to construct normal vector, instead of a difficult fog you have crystal clear skies over math paradise, what more should a reasonable person want???

In the year 2017 we have a much much better developed internet compared to the times when I originally did find my own version of a proof, but I did not research any of the outlets we have today like, for example, Google books.
If I can find a few good links I will update this post later.

This post is an additional 7 pictures to the previous post, each picture is as usual 550 x 775 pixels.
If you haven’t read the first post containing the first five pictures, please go here.

Once more: The surprising result is how easy to construct this normal vector is…


For myself speaking I am a little bit dissatisfied by notations like O with a hat and a + in the exponent, but I could not find a more easy notation so you simply must swallow that:

O hat lives in n-dimensional space while
O hat with the plus in the exponent lives in (n + 1)-dimensional space…

Ok, this is what I had more or less to say. If I can find a few good links I will post these later and if not see you around & try to get a nice life in case you don’t already have such a kind of life.

General Pythagoras theorem part 1: The 3D case.

A long time ago I found a very simple proof for the general theorem Pythagoras. At the time the general public had almost zero access to internet resources and in those long lost years I could not find out if my proof was found yes or no.

As memory serves, Descartes was the one that gave a proof for the 3D version of the Pythagorean theorem… (But I never did read the proof of Descartes.)

Two weeks back I was cleaning out my book closet so I could store more bottles of beer for the ripening process and I came across that old but never perfectly finished proof.

And it entered my mind again because it is fascinating that just by constructing that perfect normal vector, you make it of unit length, calculate a few higher dimensional volumes and voila:
There is you proof of the general theorem of Pythagoras.

In this post we only look at the 3D example for the theorem of Pythagoras. But already here we use a normal vector together with the 2D theorem of Pythagoras in order to prove the result for 3D space.
Basically this is also precisely the way the proof works in all higher dimensions, ok ok the notations and ways of writing the stuff down is a bit more technical but if you understand the proof in this post you will immediately understand how the general proof works.

The general proof is based on the principle of natural induction, likely the reader is familiar with natural or mathematical induction because beside it’s elegance it is also easy to explain to first year students in exact sciences. Basically you prove some stuff for low values of n, say n = 2 or 3 for 2D and 3D space and after that you do the so called ‘induction step’ where you must show that if it holds for a particular value of n, the stuff you want to prove is also true for n + 1.

Here is a wiki on the subject: Mathematical induction


This post is five pictures long (size 550 x 775 as usual) so have fun reading it:






In the last line of the proof it is important to remark that both the length of XY is done with the 2D version of Pythagoras, but the height h of triangle XYZ is also done with the 2D version of Pythagoras. And so you get the 3D version of the famous Pythagoras theorem.

See you in the next post where it is all a bit more abstract and not slammed down to just two or three dimensions. Have a nice life or try to get one.

CERN stuff on super conductivity and a primer on the general theorem of Pythagoras.

A few weeks back while cleaning out my book closet I came across that unfinished proof of the generalized theorem of Pythagoras that uses n-dimensional pyramids. (May be these are called simplexes and not pyramids, I still have to figure that out).

On the CERN stuff I can tell you I used a picture of CERN to explain a bit about super conductivity because at CERN they also run an experiment where they try to find magnetic monopoles…

It is now year number four where I constantly keep on telling that electrons are the long sought magnetic monopoles; electrons carry electrical charge, that is known in the scientific community, but they also carry two different magnetic charges.

As such electrons are much more like quarks that also carry electrical charge but also color charge, the fact that the electron carries only two magnetic  charges is the main explanation as why we only have electron pairs. If the official version of physics were a true description of reality, so electrons are truly magnetic dipoles, why only have electron pairs???

Super conductivity is caused by electron pairs, not by free electrons. A material can only become in a super conductivity state if first the so called Cooper electron pairs are formed.
If the official version is true and electrons are magnetic dipoles, in that case any applied magnetic field would have zero point zero influence on the formation of electron pairs.

That is crystal clear because all forces on the north pole of the electron would be canceled out by the forces on the south pole of the electron. Yet in practice, as not only CERN but the entire community of super conductivity research is telling us: In the presence of a too high magnetic field the material just not enters the state of super conductivity…

So you can cool your ass off, if magnetic fields are too high electron pair formation just does not set in. The next picture from CERN shows a bit of state space as where in super conductivity materials should get their super conductivity properties:

18Feb2017_critical_magnetic_field_and_super_conductivityLet me not put salt on every snail observed but the title should be ‘State space diagram of superconductors’ because ‘phase’ is related to 2D complex number stuff.

At last I would like to remark that although CERN is on a very expensive hunt for magnetic monopoles, they failed all of the time.
Now do CERN people talk about electrons being carriers of magnetic charge?
Come on; CERN people will fail all of the time.

On the other website we have reason number 45 as why electrons cannot be magnetic dipoles, as you have guessed it is about the above picture from CERN:

Reason 45: The critical magnetic threshold in super conductivity. 


After having said my views on fantastic organizations like CERN, why not do some elementary math like for example the 3D theorem of Pythagoras?

As memory serves the math ideas in the picture below were found centuries ago, but I have to say I do not know much historical development of the math ideas involved.

But I do know that I found a very simple proof to the most general theorem of Pythagoras and that is what will be in the next post and may one more extra post to finish it off.

Here is the teaser picture for the next post (or may be two posts on this subject of generalizing the theorem of Pythagoras):


The good thing about the last line of calculations is:

We need the millennia old 2D theorem of Pythagoras in order to prove the century old 3D theorem of Pythagoras…

I don’t know how far I will push this detail but if I find it back in my book closet may be I will write a tiny bit more. End of this post, see you around and try to get a nice life in case you never understood those electrons in the first place.

Till updates.

Debunking the most successful relation between theory and experiment in physics using electron magnetic charge.

May be it is best that you first take a look at the video given below, think about it for some time and, hopefully, arrive at the conclusion that at Fermilabs they have a lot of shallow thinkers.

With QED the physics people use that as an abbreviation for quantum electro dynamics, inside theories like that they sometimes use a so called ‘coupling constant’. The physics professors think they have found a perfect relation between the theoretical value of this coupling constant and experimental evidence.

This coupling constant relates the magnetic properties of the electron to the so called Bohr magneton. The Bohr magneton is related to the mass of the electron pair and as such is related to a magnetic dipole.

Anyway the video showing a guy named Dr. Don Lincoln has all the hallmarks for ‘shallow and easy thinking’ that is so pregnant through all of physics; just do some bla bla bla before an audience and actually come away with it. Here it is:

QED: Experimental evidence.

Now from the get go of the discovery of electron spin it was known that the large magnetic properties of the electron could not be explained via a spinning electron; even if all electrical charge was concentrated on the equator of the electron it should spin with a large multiple of the speed of light.

An important conclusion we can draw from that is: the actual spinning of an electron is more or less insignificant.

Now the measurement of the magnetic dipole moment of the electron was not done via a measurement of the magnetic dipole moment of an electron but only via year on year making many measurements of the frequency that those electrons did send out as electro-magnetic radiation.

It is well known that electrons send em-radiation when they get accelerated, this is a very general principle on all levels of the em-spectrum. Electrons always behave the same whatever frequency they oscillate.

So if electron magnetic properties cannot be explained via the actual rotation of an electron, why do the shallow thinkers as Don Lincoln always portrait it this way? Here is what the idiots show the public:


Yes they compare it to a gyroscope…

Now congratulations with your stupidity my dear Fermilab Dr. Don Loncoln; usually electrons do not spin faster than the speed of light.

If you come up with explanations like this, it is very clear you do not understand how electro-magnetic radiation is crafted in the first place. It has to do with both an electrical charge and a magnetic charge getting accelerated. The important thing to notice is the localization of both charges on the electron itself…

All that talk of electrons being magnetic dipoles is nonsense.


From the viewpoint of psychology, the idea that physics professors have about the accuracy of the magnetic dipole moment of the electron is of course a big big hinder for accepting that electrons carry two possible magnetic charges: a north charge and a south charge.

Here is the source of their smirks, laughs and arrogant behavior:

13-02-2017_just_a_coupling_constantBut this measurement is only based on measuring frequencies of em-radiation.

Yet electrical fields can also accelerate electrons and oscillating electrical fields can also produce em-radiation from the electrons…

For the time being lets leave it with that; imbeciles that bring up stuff spinning above the speed of light while waiving away reality are classified as shallow or pseudo scientists.

And at Fermilabs, USA based, they have plenty of those people.
Till updates.

Simple statistics on the video of the oversight of the Stern-Gerlach experiment + Dwave qubits (quantum bits) explained.

Exactly one month ago I posted the update about the historical oversight on the Stern-Gerlach experiment from 1921. This experiment is just so confusing; how can a magnetic field split a beam of electrons in two parts?
If electrons are really magnetic dipoles, this should hot happen.
But it happens, hence I jumped to the conclusion electrons are beside electric monopoles also magnetic monopoles. As such they carry two magnetic charges known as north and south.

The video with the historical oversight had 1222 views on 03 Jan 2017, that would amount for about 9 views a day. This is very little if you compare that, for example, if Miley Cyrus brings out another ass shaking video but hey this was about an experiment in physics done about one century ago.

Right now the video has 1702 views and that means it has about 19 to 20 views a day since 03 Jan.
So the daily number of views has doubled but it is only 10 views extra a day.

But ok ok, I still accept it would be a long long battle; if there are truly about 100 thousand physics professors really thinking that electrons are magnetic dipoles because some fancy math says it is so, stuff has turned into dogma.
When I found the magnetic charge solution for myself I strongly remember asking myself:

And there are some problems with the official version: The only thing that says electrons are magnetic dipoles is the Gauss law for magnetism. Tiny problem: electrons were discovered much time later…

Anyway I still advertise viewing the Stern-Gerlach experiment oversight because it is a treasure trove of not only historical facts but it also rings home that people like Albert Einstein, Niels Bohr, Erwin Schrödinger, Wolfgang Pauli etc etc just had NO CLUE WHATSOEVER on the fundamental importance of the outcome of the Stern-Gerlach experiment.

So once more the video:

The Stern-Gerlach Experiment And The Discovery Of Electron Spin – Sandip Pakvasa [2016]

The great thing about electrons having two magnetic charges it that you understand so much stuff from nature on a far deeper level. That is very rewarding and you can compare that for example to the discovery of the nucleus of the atom.

Now the title of this post says ‘Dwave qubits explained’ but if I would do that I would have to keep up a long story as why the formation electron pairs are needed for super conductivity (electron pairs are a north and a south charge together more or less magnetically neutral ensuring the super conductivity) while unpaired electrons are not neutral in the magnetic sense.

And so on and so on.

No, let me only post a picture from Nature, the famous Nature scientific outlet is somewhere I can never publish because they have so called ‘peer review’. Of course ‘peer review’ will never allow for crazy ideas that say electrons carry two different magnetic charges…

That is why university people and me will never be friends; we just do not speak the same language.

Here is the picture from the Nature outlet:


Picture source:
Figure 1: Superconducting flux qubit.

Dwave qubits are macroscopic objects, they are not small quantum systems but as you see in the picture above the folks from Dwave computer have succeeded into generating two electrical currents that go in opposite directions.

Ok ok, let me share just one simple to understand detail:

The two currents are unpaired electrons, although Dwave computers use super conductivity unpaired electrons do not follow the stream of super conductivity…

So after initialization, the two currents will die out.
I wonder if the people at Dwave are aware of this line of reasoning.

Let’s leave it with that, have a nice life or try to get one & till updates.