Derivation of the number tau for the circular 3D number system.

There are lot’s of reasons for this update; one reason is that the actual calculation is mega über ultra cool. Another important reason is that this collection of plain imitation of how the value for the number i in the complex plane was found serves as a proof in itself that this way of crafting 3D complex and circular numbers is the only way it works.

Don’t forget that on the scale of things the Irish guy Hamilton tried for about a decade to find the 3D numbers but he failed. Yet Halmilton was not some lightweight, the present foundation of Quantum Mechanics via the use of the Hamilton operator is done so via the work of Hamilton…
Wether the professional math professors like it or not; that is the scale of things.

During the writing of this post I also got lucky because I found a very cute formula related to the so called Borwein-Borwein function. I have no clue whatsoever if it has any relevance to my own work on this website but because it is so cute I just had to post it too…

Furthermore I used two completely different numerical applets, one for integration and the other for evaluating the log of a matrix, only to show you that these kind of extensions of the complex plane to three dimensional space is the way to go and all other approaches based on X^2 = -1 fail for the full 100%.


This post is ten pictures long, size 550 x 775 pixels.

At the end I will make a few more remarks and give you enough links for further use in case you want to know more about this subject. Have fun reading it.










22oct2016-calculation-of-the-circular-tau10The applet for the logarithm of a matrix can be found in this nice collection of linear algebra applets:

Linear algebra

In this update you might think that via the pull back principle you observed some proof for the value of the integrals we derived, but an important detail is missing:
In 3D space the exponential circle should be run at a constant speed.
As a matter of fact this speed is the length of the number tau, you can find more insight on that in the theorem named ‘To shrink or to grow that is the question’ at:

On the length of the product of two 3D numbers.

A bit more hardcore is my second proof of the value of the integrals as derived in this post. On 15 Nov 2015 I published the second proof that I found while riding on my bicycle through the swamps near a local village named Haren. It is kinda subtle but you can use matrix diagonalization to get the correct answer.
The reaction from the ‘professional community of math professors’ was the usual: Zero point zero reaction. These people live in a world so far away from me: overpaid and ultra stupid…

Integral calculus done with matrix diagonalization.

A link to the online encyclopedia of integer sequences is the next link.
Remark that by writing the stuff as on-line instead of online reflects the fact this website must be from the stone age of the internet. That is why it can have this strange knowledge…

The On-Line Encyclopedia of Integer Sequences (Just fill in 1, 2, 0, 9, 9, 5, 7 in order to land on my lucky day).

The last link is one of those pages that try to explain as why 3D complex numbers cannot exist, the content of this page is 100% math crap written by a person with 0% math in his brain. But it lands very high in the Google ranking if you make a search for ‘3D complex numbers’.
So there must be many people out there thinking this nonsense is actually true…


Ok, this is what I had to say. Let me close this post, hit the button ‘update website’ and pop up a fresh beer… Till updates.

Too little time left so only a second teaser picture on the next post on the details of the 3D tau calculus.

Originally I planned to upload tonight the new post on the integrals related to the number tau for the circular multiplication. But I found this very cute result from some other math professors, I believe these are two brothers Borwein & Borwein.

Beside that I also had more time to spend on a very important hobby: Brewing beer…;)

Four years back when I for the first time derived integrals like this with the cosine and sine stuff to the power three in it, I just had no clue whatsoever how to find analytical stuff for their value. These kind of integrals cannot be solved by throwing in some simple primitive or so.

At present I have two independent proofs for their value.
Back in the time I knew there was some internet website that contains a whole lot of integer sequences so if I could find that I would have at least some analytical clue about that nasty problem. Only a long time later I found that website, but is said ‘we do not know’.
Or ‘unknown integer sequence’ or whatever what.

But yesterday when I tried more or less to get a negative result my luck changed for the better: the website with the integer sequences in it actually returned an answer.

And for my few pounds of human brain tissue the answer was completely crazy.
Therefore I decided to put the result of this Borwein function on top in the teaser picture and my own idea’s at the bottom. Here it is:

20-10-2016-borwein-borwein-teaser-pictureI have absolutely no clue as why these two things should be the same, but four years back I had absolutely no clue as what this numerical value like 1.2092 actually meant…

The link to what might be the Borwein & Borwein function

A248897 Decimal expansion of Sum_{i >= 0} (i!)^2/(2*i+1)!.

Let’s leave it with that, see ya in the next post.

Three new magnetics updates + Intro to a new post about calculation of the number tau.

On the other website I posted reason number 37, 38 and 39 about why it is impossible for electrons to be magnetic dipoles. Let me give you the links and short descriptions about their content.

05 Oct 2016: Reason 37: Old and new experiments upon the bonkers force.

Once more the importance of repeatable experiments is stressed; my own simple experiments with that old color television is explained once more. Furthermore I am proposing a few other experiments that I cannot do here myself because, for example, they should be done is a space without magnetic or electrical fields.

The thing ‘bonkers force’ is acting along the magnetic field lines and makes electrons (and protons etc) accelerate. So it is perpendicular to the Lorentz force.

10 Oct 2016: Reason 38: The Hendrik Casimir effect and the vacuum catastrophe.

The Nobel prize in physics went this year to three men who studied two dimensional structures of electrons. So with just 50 to 70 minutes of labor I managed to do the same and explain as why the experiment of Hendrik Casimir has a wrong experimental set up because there they use the idea that electrons are magnetic dipoles. En passant using this wrong set up of Hendrik Casimir I can explain the root cause of the so called ‘vacuum catastrophe’.
The theoretical value of the so called zero-point energy of one cubic centimeter of space should be 10 to the power 112 erg of energy, yet at present day the best value found is about 10 to the power -8.

That is off the mark by just a factor of 10 to the power 120…

14 Oct 2016: Reason 39: The acceleration of the solar wind.

This is just one of the many things you cannot explain with electrons and protons being magnetic dipoles; despite gravity and or the influence of electrical fields the solar wind does not go down in speed. The professional physics professors cannot explain this nasty detail because they keep on holding on to the Gauss law for magnetism that says magnetic monopoles do not exist…

For the electron pair the Gauss law is valid but not for loose electrons.
As far as I know the winners of the Nobel prize from this year also believe electrons are magnetic dipoles so the Nobel committee has done a great disservice to the progress in physics.

So from the vacuum catastrophe to the properties of the solar wind: the professional physics professors will not find an explanation century in century out because you must not think that by writing down how stuff likely works they will change their ways.

But, ha ha ha my dear but incompetent and coward physics professors: My experiment with an old television can be repeated by any person and you, you fxckheads, cannot explain it…


Ok, we proceed with math: The next post will be about how to find the number tau that you must use for crafting exponential circles and curves in dimensions above 3.

In order to focus the mind I would like to repeat a rather famous calculation from the complex plane: the calculation of the logarithm of the imaginary number i.
It is a beautiful calculation and it says that log i = i*pi/2.

Three teaser pictures to ram home to the brains of professional physics professors that I know plenty of complex numbers and that in my view using only 2D complex numbers simply shows what kind of brain matter you folks are made of:




At the closing of this small update I would like to remark that in the next post we are going to try and find logarithm values for imaginary numbers from 3D space.

And if in the future the Nobel committee would select Nobel prize winners that can actually think deeply and not all this shallow stuff, that would be great!

See you around my dear reader, till updates.

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.