Curl, curl and more curl.

This post contains seven examples of the differential operator named curl. The motivation for this update lies in the fact that after my humble opinion inside the set of equations known as the Maxwell equations there is a tiny fault: Rather likely electrons carry at least a net magnetic charge.
And because they carry net magnetic charge they not only accelerated by electrical fields but also magnetic field.

If you have an old television set with one of those fancy tubes that contain one electron cannon for a black & white television and three electron cannons for a color television. With the help of a stack of these strong neodymium magnets it is easy to give experimental proof that the electrons indeed get accelerated… Why in the course of over one hundred years not one of the professional physics professors has done this is unknown to me; may be it is the separation of ‘theoretical professors’ versus ‘experimental ones’ a reason for this omission. May be it is the use of dogma (unproven things that live inside a belief system, in this case the belief system that magnetic monopoles do not exist).


Anyway the Maxwell equations contain a lot of the curl operator, that is not needed per sé but it makes the formulae look sleek and short. Originally Maxwell had a set of like 20 equations or so while at present day only four remain. But if you see those four equations for the first time it is very impressive, only over time you get used to it.

This post is 13 pictures long, size 550 x 775 pixels.
I start with examples that are as simple as possible and very slowly bring in a bit more abstraction.
Therefore I hope it is very readable, have fun with it!


















As far as I can remember, in the first year I opened these investigations into higher dimensional number systems again I calculated the curl for the complex multiplication in 3D space. In this post we only looked at the circular version of stuff.

But I can´t find it back so I cannot place a hyperlink to it.

Anyway, here is a nice wiki with the curl expressed as an integral (often much harder to calculate but nice to observe it can also be done that way):

Curl (mathematics)

And because this post was motivated by all that curl in the Maxwell equations, I tried to find back when I originally started writing about electrons having magnetic charge instead of being magnetic dipoles like they are tiny bar magnets. It was 29 April that inside the math pages I found the first update on that. Here it is:

From 29 April 2014 : Do electrons have spin?

Ok, that was it. Till updates my dear reader.


An important correction + Bad news from the Leiden university + updates on magnetism.

In the post on the factorization of the Laplacian from 5 August I made two rather stupid ‘cut and paste’ errors. But since this particular calculation is definitely inside my own list of top 10 magnificent calculations I decided to make the correction also a separate post.

That is only to show how important I rank this particular calculation; it should be posted flawless and not with stupid typo’s on stupid places…

Here is a picture showing the stupid ‘cut and paste’ typo’s and the corrected calculation as it should have been on 05 Aug of this year:

25sept2016-fault-plus-corrected-versionAs you see on inspection: Only the top line is wrong so in practice it is not a big deal.
But this particular calculation made me understand the importance of studying more and more of the sphere-cone equations so I want this to be tip top & as perfect as possible.


Next thing:

Bad news from the Dutch university of Leiden.

For the pictures on my website I rely on that so called WIMS collection of packages. I first found it at some French university but later it was found out it was also stored in my home country at the university of Leiden.

Yesterday when I needed just one new picture I found out the university of Leiden has removed this collection of math packages. Why they have done this I do not know but in my life from experience I know that by definition all university people are full of shit.

Now at date 25 Sept 2016 I once more understand I was stupid to rely on a service done by university people; in the end they will always fuck you in the ass. How could I have been as stupid as to be dependent for my graphics to depend on university people?????

Of course the university of Leiden offers me an alternative route: Go back to France where the whole thing is still online. Now just look at these perfect images as they come back from France (this is the equation for the top picture on this website on 3D complex numbers:

25sept2016-university-people-are-full-of-shitOnce more we observe: If it works at an university it is just so full of shit that you cannot measure the amount of shit in that particular person before or after a toilet visit… Back in the year 1992 I decided that a professional academic career was not my path of life, now 24 years later this is once more validated. Better avoid all contacts with weirdo’s like that…


Updates on magnetism:

Over on the other website I posted two more reasons as why electrons simply have to carry a net magnetic charge.

Reason number 34 is about two more or less famous physics professors telling acute nonsense when it comes to electron stuff. You can find it in the next link:

13 Sept 2016: Reason 34: Two famous physics professors telling nonsense.

Reason number 35 is about explosive discharges in the field of nuclear plasma physics; professional plasma professors just do not understand their own line of work. Any idiot can find out that electrons are accelerated by magnetic fields but since all people working at universities are full of shit they are blind for the obvious facts of life.

New reasons for electrons carrying magnetic charge are in the making, here is a picture I will use in explaining the so called ‘bonkers force’:

25sept2016-the-bonkers-forceThe bonkers force is perpendicular to the Lorentz force.

You might wonder why this is named a ‘bonkers force’?

The answer is simple: It will make professional physics professors go bonkers.
And that my dear reader is a good thing, till the next post on the curl of vector fields.

Please be patient, a new post on the curl is coming…

I know I know, not posted much around here lately.
And on top of that I found some serious typo’s in the pictures from just two posts back: the post upon the factorization on the Laplacian operator.

These typo’s are rather serious; we just cannot have all those wrong and misleading differentiations going not repaired.

But reparation of old faults is time consuming.

On the other hand, the curl operator has a lot of fresh new insights in simple number systems like the 2D complex plane or my own hobby; the 3D complex number system.

For myself speaking I am still wondering as shall I include the ‘Theorem without Vodka’ in the new post or just leave it out? I do not know what I will do in the future but here is the Google translate version of the Theorem without Vodka:

24-09-2016theorem-without-vodkaMay be I just leave it out, after all this is supposed to be an update on the differential curl operator.

End of this post, till updates.

Teaser picture for a new update on differential equations.

I am going to make this update on the other website so in about one week you can check it out on page 4 of the 3D complex numbers. I admit I have been lazy the last month but now I have stopped smoking over three years my health is still improving so I am more exploring the environment with my bike while I can do that again…

Ha! At my worst about four years back I could only walk 100 to 125 steps and after that I needed to pause 3 to 4 minutes because I got camps in one of my legs. So it finally dawned on me I had to stop this nicotine addiction because the next phase would be a wheelchair combined with an oxygen mask and a tank of high pressured liquid oxygen on the back of my wheelchair.

Looking back I am glad I got so ill because without it I would never have managed to stop smoking those ridiculous amounts of cigarettes day in day out.

Sorry to bother you with my past health problems, this new teaser picture is rather funny and I hope also intriguing: I have crafted three coordinate functions x(t), y(t) and z(t) and if you differentiate them with respect to the time t you get a 3D square of the vector (x(t), y(t), z(t)).

So check it out for yourself; take the derivative of the three coordinate functions and see if you can get the three equations as on the bottom of the teaser picture…

The new update (on the other website) is ten pages long meaning it is 10 pictures of size 550 x 1100. Click on the teaser picture to land on the new update:

03-Sept-2016-teaser-pic-for-differential-equationsFor me it is just so cute: If you differentiate to time you get the square of the position you are in the 3D complex number system.

For use in the science of physics I do not think it is that important because real physical problems never rely on the coordinate system you use, but you never know…
For use in the science of math it is also not important because professional math professors still have not developed the cognitive capabilities of understanding 3D complex numbers.

I also made a teaser picture for use on the other website, it is the same solution to the simple differential equation as above but this time I solved it inside the complex plane. Of course I could not use that on this website as the first teaser picture given the face we more or less always try to focus on the 3D complex & circular number systems…


Ok, end of this post.
And life, as usual life will go on.

Till updates.

Wirtinger derivatives and the factorization of the Laplacian.

This post could have many titles, for example ‘Factorization of the Laplacian using second order Cauchy-Riemann equations’ would also cover what we will read in the next seven pictures.

The calculation as shown below is, as far as I am concerned, definitely in the top ten of results relating to all things 3D complex numbers. Only when I stumbled on this a few years back I finally understood the importance of the so called sphere-cone equation.

The calculation below is basically what you do when writing out the sphere-cone equation only now it is not with variables like x, y and z but with the partial differential operators with respect to x, y and z. In simplifying the expressions we get I use so called second order Cauchy-Riemann equations, if you understand the standard CR equations these second order equations are relatively easy to digest.

Have fun reading it.





05aug2016_factorization_of_the_laplacian05 05aug2016_factorization_of_the_laplacian06


05Aug2016_factorization_of_the_Laplacian07This post is also categorized under Quantum Mechanics, the reason for that is that the wave equation contains the Laplacian operator and the more you know about that rather abstract thing the better it is in my view.

I would like to close with a link to a wiki on Wirtinger derivatives, originally they come from theory with several complex variables. That explains why in the wiki the Wirtinger derivatives are written as partial derivatives while above we can use the straight d´s for our differential of f.

Here is the wiki: Wirtinger derivatives

Till updates.

How I found the first modified Dirichlet kernel in 5D numbers.

Back in Jan 2014 I was able to solve the circular and complex 5D numbers systems using the so called ‘tau-calculus’. Basically tau-calculus is very easy to understand:

  1. Find a basis vector (from an imaginary number) that has determinant +1.
  2. Craft analytical expressions that you cannot solve but use internet applets for numerical answers. Or, equivalent:
  3. Use an applet to calculate the logarithm of your basis vector once you have put it on a matrix representation.
  4. Start thinking long and hard until you have solved the math analysis…

This is easy to understand but I could only do this in three and five dimensional space, seven or eleven dimensional space? It is now 2.5 years later and I still have no clue whatsoever.

Anyway back in the time it was a great victory to find the exponential curves in 5D space. May be some people with insect like minds think that the Euler identity is the greatest formula ever found but let me tell you:
The more of those exponential circles and curves you find, the more boring the complex plane becomes…

In the months after Jan 2014 I wanted to understand the behavior of the coordinate functions that come along those two exponential curves. But the problem kept elusive until I realized I had one more round of internet applets waiting for me.
I had to feed this internet applet for the log of a matrix over 50 matrices and write down the answers it gave me; that was a lot of work because every matrix had 25 entries.

Originally I planned for ‘digesting’ 10 matrices a day so it would be a five day project, but when I finally started somewhere in June 2014 after two days I was ready to sketch my strongly desired coordinate function of the very first coordinate in 5D space.

I still remember sitting at my table and do the drawing and when finished it was so fast that I realized the next: This is a Dirichlet kernel.

And the way I used it, it was so more simple to write down this kernel and if you think how those exponential curves in higher dimensional spaces work with their starting coordinate function and all the time lags that follow… This finding will forever be in the top ten of most perfect math found by your writer Reinko Venema…


Ok, what is in this new post?
Nine pictures of size 550 x 775 pixels containing:
Basic definitions upon 5D complex and circular number &
Tau calculus for the exponential curve &
Explaining how I found the graph of the first modified Dirichlet kernel &
A small quantum physics example related to probability amplitudes &
Some cute integrals that are easy to crack now.

Hope you can learn a bit from it, do not worry if you do not understand all details because even compared to the 2D complex plane or the 3D complex numbers this website is about:
The 5D realm is a space on it’s own!

Have fun reading & thinking upon it:










A few links of interest are the next:

You need a good applet for the log of a matrix representation if you want, for example, crack the open problem in tau calculus for the 7D complex numbers:

My original update on the other website about the 5D number systems from Jan 2014:

If you are more interested in those kind of weird looking integrals suddenly easy to solve if you use a proper combination of geometry and analysis, the update from July 2015 upon the missing equations is also worth a visit:
The missing equations.


This is what I more or less had to say, have a nice life or try to get one.
See you in the next post.

Modified Dirichlet kernels for low dimensions.

What the hydrogen bomb is in the average nuclear arsenal, that is what modified Dirichlet kernels are for higher dimensional complex & circular number systems.
Via the so called tau calculus I was able to achieve results in 3 and 5 dimensional number systems and I really had no hope in making more progress in that way because it gets so extremely hardcore that all hope was lost.

Yet about two years ago I discovered a very neat, clean and very beautiful formula that is strongly related to the Dirichlet kernel known from Fourier analysis. The formula I found was a dressed down version of the original Dirichlet kernel therefore I named it ‘modified Dirichlet kernel’.

This modified kernel is your basic coordinate function, depending on the dimension of the space you are working in you make some time lags and voila: There is your parametrization of your higher dimensional exponential (periodic) curve (only in 2D and 3D space it is a circle).

For myself speaking: this result of finding the modified Dirichlet kernel is for sure in my own top 10 list of most important results found. Not often do I mention other mathematicians, but I would like to mention the name of Floris Takens and without knowing how Floris thought about taking a sample of a time series and after that craft time lags on that, rather likely I would not have found this suburb and very beautiful math…


I haven’t decided what the next post will be about.
It could be stuff like:

  • How I found the first modified Dirichlet kernel, or
  • Wirtinger derivatives for 3D number systems, or
  • Wow man, can you factorize the Laplacian operator form Quantum Mechanics???

But factoring the Laplacian requires understanding 3D Wirtinger derivatives so likely I will show you how I found the very first modified Dirichlet kernel.


This update contains six jpg pictures each about 550 x 775 pixels and two old fashioned animated gif pictures. I tried to keep the math as simple as possible and by doing that I learned some nice lessons myself… Here we go:



This is the animated gif using z = 0 in 3D while this picture is showing the Euler exponential circle:




Here is an animated gif of how this coordinate function looks when you combine it with the two time lags for the y(t) and z(t) coordinates. Does it surprise you that you get a flat circle?
If it does not surprise you, you do not understand how much math is missing in our human world…





In case you are interested in the ‘time lag’ idea as Floris used it, here is a nice Youtube video that gives a perfect explanation. If you apply this time lag idea for example is a 17 dimensional real vector space you get a 17D exponential curve with all of it’s magnificent properties…

Takens’ theorem in action for the Lorenz chaotic attractor

Yes, end of this post. See ya around & have a nice life or try to get one.

More proof for electrons being magnetic monopoles.

This post is another advertisement for the magnetic page on the other website with the funny name:

A primer on the electrons that are the long sought magnetic monopoles. Author: Reinko Venema.

Ok, in the previous post I said the next one would be on the modified Dirichlet kernels but I did not update the magnetic page for over one month so I had to rearrange priorities.

When riding my noble iron horse through the local landscape I was thinking about how professional physics professors would waive away my insights with just a little hand waive while mumbling ‘Lorentz force’.
Just like they do when explaining the electron spin, they say stuff like: It is spinning and when an electrical charge is spinning it creates a magnetic dipole moment (in the meantime they also shrug their shoulders a little bit and move on with the lesson).

Now while riding my noble iron horse (a 269 € bicycle) I suddenly thought:
What would happen if I cut my stack of strong neodymium magnets into two pieces and use that???

And hurray: It was a big success; there was some strong asymmetry observed and I think this might be a manifestation of the Lorentz force. This is not rock solid proof because I do not know how strong the magnets are and as such I have no clue about the radius induced by the Lorentz force.
But this looks very promising.

Here is the first photo, on the black spot no electrons slam into the television screen:


Under the assumption electrons are magnetic monopoles and as such carry a magnetic charge just like they carry an electric charge, the next is observed/happening:

  1. The color television has three electron cannons, each electron is attracted or repelled by the strong neodymium magnets.
  2. As such the electrons slamming into the screen in between the two stacks of strong magnets are the attracted ones while those that are repelled are found on the outside of the black region.
  3. In the dark region no electrons land on the screen, a feature that cannot be explained by any of the Maxwell equations or the Lorentz force.

In the next photo you see that I am trying to make the region of attraction horizontal, but for that to happen I have to place the magnet stacks more or less diagonal:

0025_12June2016_new_photos02The costs of this experiment are below 50 €, the television was only 6 € and the magnets about 40 € included shipping and handling. This is a very important detail because over at CERN they always burn an extreme amount of money before they get any kind of result.

It is also important because high schools in my country often have lousy budget for physics experiments so for 50 € you have a perfect thing to show to the pupils/students…

All in all this is reason number 30 as why electrons carry magnetic charge (aka they are the long sought magnetic monopoles):

12 June 2016: Reason 30: New photo’s from a television experiment

Ok, thanks for your attention and till updates!

Three centuries after de Moivre finally some new baby steps.

I am a little bit late with this post but after the previous post I took some time to enjoy it because not every day you can craft a brand new coordinate system…

Also I was a bit in doubt about this post, shall I finally start with those modified Ditichlet kernels or work out a simple de Moivre example in 3D? It became the latter so likely in the next post I will do some first things with modified Dirichlet kernels.

This post is just 4 pictures long (size 550 x 775 pixels) and to be honest it contains no serious math whatsoever. I was only driven by curiosity about how difficult a simple example of the new 3D versions of it would be.
Now it is not 100% trivial but it is also not a very deep result, at best you can say it is a bit technical because you constantly have to apply those sum and difference formulae for the cos and sine functions.

The real deep math work was crafting those exponential circles in 3D in the first place and later finding the coordinate functions belonging to that. That was the deep math because once you have those, the new de Moivre formulae are a piece of cake (make sure it is gluten free!).

In this update I also would like to make an advertisement for a long update I started about one year ago on the other website; all in all it is 37 pictures long (size 550 x 1100) and it took about 3 weeks to write it. It has the title The Missing Equations because with those modified Dirichlet kernel I knew I had solved a terrible hard problem but the higher in the dimensions I got the more missing equations I had for my wonderful solution… Here is the link:

From 14 July 2015: The missing equations.


After this small advertisement here are the four pictures of this update:





Once more: This is not a deep mathematical result or so.
I was just curious of how difficult it would be to get one of the most simple 3D new de Moivre formula results using only the 3 century old stuff from about 50 years before Euler entered the scene…

The most important lesson you can learn from this is that instead of focusing on all kinds of details like n = 2 and only the real part and so on is a waste of time and energy.
After all using the exponential circle is what brings peace to the heart; it is simple, it covers all powers at the same time and you have all coordinate functions at once…


Now you have to wait a few minutes more because I would like to pop up a fresh home brew and after that I will hit the ‘publish post’ button…

Thanks for the waiting 😉 Now I will hit the publish button and see you next time around!

The new 3D coordinate system; [a, r, t] coordinates.

About a full week late all is now finished. Also there was that problem of the hacked webpage; the third update on the Schrödinger equation was loaded and loaded with all kinds of weird comments. But if you did read those comments you could see the overwhelming majority was not written by humans but were posted by bots.

Anyway in the end even advertisements for online sales of viagra and stuff surfaced so I took an evening to see if this could be repaired. For the time being it is not possible to post comments although before it was also impossible but that was due to an unknown technical fault…


In this update we dive into the [a, r, t] coordinate system and this is very similar to using polar coordinates in the complex plane only in 3D we are moving a half-cone along a line and as such sweep through the entire 3D space. In short it goes like this:

With a we control how far the cone is moved from the origin,
with r we denote the distance from a particular point X to the top of the cone and finally,
with t we figure out how much we need to rotate stuff using an applet for the log of a matrix.

I also give once more the coordinate functions of the exponential circle so that you are able to find coordinates on the main cone (that has the origin as it’s top) for yourself.

Without prove I also give a new de Moivre formula, the original de Moivre formula is from about 50 years before Euler so after 3 centuries there is a bit of moving forward on that detail.

I also give a rather strange looking sum of squares of cosine functions that add up to 1.5; the three cosine functions all differ by 120 degrees or 2pi/3 if you want.

It is important to remark I did my best to keep it as simple as possible so I also concentrate on a few worked examples so it is not just theory but also how to find these new coordinates. In relation to other posts like the Schrödinger equations posts, I think this new coordinate system is definitely of interest to people from quantum physics and chemistry that try to calculate those atomic and molecular orbitals.

This update is relatively long: 14 pictures of size 550 x 775 pixels and for the first time I use unshrunk jpg pictures because year in year out the bandwidth of internet connections is still rising fast so why remove fine detail from jpg pictures any longer?


I hope you learn something new, here are the pics:
















0024_23May2016_the_art_coordinates14Ok, that was it. For myself speaking I more or less expect everything to be the same:
Professional math professors from around the globe will keep on talking about their own research and just how important it is to use complex numbers from the complex plane.

A few useful links:

De Moivre’s formula’s_formula

And a good applet for the logarithm of matrix representations is also handy:

And last but not least is a proof for the latest formula above: the circular multiplication on the [a, r, t] coordinates can be found on the other website:

From 06 May 2016 : On the length of the product of two 3D numbers.

Let’s leave it with that. Till updates.