Oops; CERN did not find magnetic monopoles.

It has to be remarked that the physics folks are very persistant to keep on trying to find the so called Dirac monopole. How this has come to be is still a miracle to me. After all if the electron has one electric charge and for the rest it is a magnetic dipole, it would look naturally to look for a particle that is a magnetic monopole and an electric dipole at the same time…

But I have never heard about such an investigation, it is only the Dirac magnetic monople and that’s it.

Here is a quote from sciencenews dot org:

If even a single magnetic monopole were detected, the discovery would rejigger the foundations of physics. The equations governing electricity and magnetism are mirror images of one another, but there’s one major difference between the two phenomena. Protons and electrons carry positive and negative electric charges, respectively, but no known particle has a magnetic charge. A magnetic monopole would be the first, and if one were discovered, electricity and magnetism would finally be on equal footing.

Source:

Magnets with a single pole are still giving physicists the slip
https://www.sciencenews.org/article/magnetic-monopoles-single-pole-physics

Comment on the quote: Because in my view I consider the electrons having one electrical charge and one of two magnetic charges, I think we have a nice equal footing of electricity and magnetism… (End of the comment.)

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Back to CERN and stuff. Last month it came out that the MoEDAL experiment has failed in the sense that no magnetic monopoles were observed. Here is a small screenshot from the preprint archive stuff:

Comment: No idea what these people are talking about when they talk about 68.5 times the electric charge… Are they talking about electric charge or magnetic charge?
(End of comment)

Source of the content of the picture above:

detector in 2.11 fb−1 of 13 TeV proton-proton collisions at the LHC.

https://arxiv.org/pdf/1712.09849.pdf

After a bit of searching I found back this beautiful video, coming from CERN, explaining how to find magnetic monopoles. It is clear they never ever studied the electron.

Yeah yeah my dear average CERN related human; what exactly is a magnetic monopole?

Does it have electric charge too and why should that be?

In my view where the electrons carry both electric and magnetic charge, a magnetic monopole with zero electric charge just does not exist.

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Ok, let me bring this post to an end by observing that at CERN they were not capable in the year 2017 of detecting the magnetic monopole as it should exist following the lines of thinking like Paul Dirac once did.

So that is a good thing because after thinking about four years about magnetism it would be horrible for me to find that at CERN they had a major discovery about magnetic monopoles…

Sorry CERN folks, your failure to find magnetic monopoles your way does not prove that electrons are indeed carrying magnetic charge. It just makes it a little bit more plausible that they do…

So my dear CERN folks, thanks for publishing your failure because for me it is another tiny quantum move into the direction of accepting the electron as it is.

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End of this post.

More on the Majorana equation.

Yesterday I finally looked into the so called Majorana equation and it is easy to find where the Dutch universities have gone wrong. At the technical universities in Delft and Eindhoven they use electrons together with a hole that supposedly has a positive electrical charge so that the overall combination of electron and hole is electrically neutral.

And it is very easy to explain: If I am in the right and electrons also carry magnetic charge, the above constellation of an electron and a hole is not magnetically neutral like, for example, the Cooper pairs of electrons in super conductivity.

They want unpaired electrons because the Cooper pairs live there in the nano wire where the super conductivity is so they do not consider an electron pair together with two holes because that is both magnetic and electrically neutral…

No, I do not think that in Delft they found the elusive Majorana fermion. But time will tell because if this way of quantum computing will keep on failing or never get anywhere, I can use that as a future reason of why electrons cannot be magnetic dipoles.

Here is a wiki about the Majorana equation, already at equation number 2 I am lost in the woods because the mass m suddenly goes to the other term in the equation.

Majorana equation
https://en.wikipedia.org/wiki/Majorana_equation

And here is a short video from Youtube where the technical university of Eindhoven explains how they will try to prove the existence of the Majorana fermion as a quasi particle. The video is from 23 August 2017, that is only four and a half months ago.

From the wiki we have this information, what the differential operator with the ‘Feynman slash’ does is actually not important at all. The nice thing here is to understand what they try of find here:
A particle (or a collection of particles, the quasi particles) where all charge is compensated. Apperently the mass related to charge comes in with opposite charge and indeed if you can find solutions to such a wave equation you might hope to find it one day.

Yet in Delft and Eindhoven they hang on to the opinion that electrons are magnetic dipoles and as such they never had a need to put the ‘anti part’ of the magnetic dipole into the problem…

That was more or less what I had to say about the Majorana equation.
Of course I also wish you a happy new year! Till updates.

Prediction for 2018 and beyond: The Delft quantum computer attempts will fail.

Already for a few years the folks at the university of Delft are trying to make a quantum computer. They even teamed up with Microsoft and as memory serves the Dutch government is investing about 100 million € over the course of 10 years.

Only recently I dived into that Delft stuff and the spokeswoman from Microsoft was even talking about a Nobel prize for Leo Kouwenhoven because he seemed to have discovered so called Majorana fermions.

And I just felt sooooo proud that my fellow Dutch guy Leo who is sooooo ultrasmart would have a chance of winning such a prestigious prize like the Nobel prize. I will never get a Nobel prize for my stupid finding of the magnetic monopoles, come on that is not important because I am not a university person and Leo is a full blown physics professor.

After having said that it is nice to observe that the Delft team is trying to craft quantum computer with qubits made from Majorana fermions. So what are Majorana fermions because they have never been found since a guy named Ettore Majorana speculated about stuff like that in 1937? Well these are fermions that are their own anti particle.

It is well known that when you have a particle with a particular charge, the anti particle must have the opposite charge. Now our Leo Kouwenhoven genius from the Delft university is putting an electron into entanglement with an electron hole and as such it has no electrical charge if the electron hole has a positive electrical charge.

Furthermore since an electron entangled with a hole is only like half a fermion they cannot exist on their own so our genius folks from Delft figured out that two of those quasi particles would form a Majorana fermion.

Here is a Youtube video of about one hour long where our super hero Leo explains it all:

Majorana Fermions: Particle Physics on a Chip- Leo Kowenhoven – May 28 2015

Anyway, to make a long story short:

The Majorana particles as found by the heroic members of the Dutch university of Delft have a tiny problem: the electrons carry also magnetic charge beside the electrical charge. So a quasi particle made up of an electron and an electron hole cannot have the Majorana property of being it’s own anti particle…

So my estimation is rather simple: As long as the Delft hero’s keep on ignoring that electrons carry also magnetic charge, they will not succeed. On the contrary they will fail and very likely they will keep on failing because they are university people.

Too much money and too much titles & prestige, why should they change and get a more realistic view on quantum computing?

Before we split, here is a wiki on Majorana fermions. For me it is new that when a fermion is it’s own anti particle the wave function is real valued and not complex valued. As a take away you can also conclude that the Delft hero’s also got the wave function of the electron and electron hole completely wrong. Just like all those people in the science of chemistry who cannot model even the hydrogen molecule properly. So the chemistry people say ‘We need quantum computers’ and Leo Kouwenhoven says ‘I have great ideas in topological quantum computing!’

In my view these people are all crazy, but here is the wiki stuff on Majorana fermions:

Majorana fermions
https://en.wikipedia.org/wiki/Majorana_fermion

Till the next post.

Electron spin as explained by the Scientific American.

In a nice article there are three people explaining, for example, electron spin. The reason to post this here is because they are in climbing order of stupidity and explainer number three gives a total retarded explanation.

Recall once more that the name electron spin is one hundred percent misleading because of what we know of the size of the electron it should certainly be rotating much faster than the speed of light even if all electrical charge was concentrated on the equator of the electron.

I hope that by now my dear reader you know that I think electrons carry beside electrical charge also magnetic charge and as such they come in two flavours:
1) Electrons with a negative electrical charge and a north magnetic charge and;
2) Electrons with a negative electrical charge and a south magnetic charge.

Because particles with mass cannot mover faster than the speed of light, all explanations based on the electron spinning are wrong by definition. Therefore it is often said that electrons (and also protons and neutrons) have so called intrinsic spin so the rotation problem can be avoided.

It has to be remarked once more that this is about the fourth year I am writing about electrons having magnetic charge and that as such they are the long sought magnetic monopoles, but until now I have zero reactions from only one of those professional physics professors… That abundantly shows how dumb they actually are and that there is little use in trying to write a real publication because it is still totally impossible to pass the so called ‘peer review barrier’. I mean; read the quotes I will post from these three people as found in the Scientific American and suppose they would be the ones that do the peer review of my article. What would happen?
Very simple: It will be rejected.

Let’s get started, here is the title and link to the small article in the Scientific American:

What exactly is the ‘spin’ of subatomic particles such as electrons and protons? Does it have any physical significance, analogous to the spin of a planet?
https://www.scientificamerican.com/article/what-exactly-is-the-spin/

The first quote is from Morton Tavel, quote:

“Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid ‘objects’ that can ‘rotate’ in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term ‘spin,’ however, still remains.”

Comment: From the macroscopic world we do not observe much ‘deflection’ of, let’s say, bar magnets in the presence of other magnets and magnetic fields. If electrons really were magnetic dipoles, because electrons are so small all magnetic forces would cancel out and we would never observe deflection.
And if Morton Tavel would have done some calculations or estimations, it is extremely hard for electrons to get deflected by non-constant magnetic fields. On the contrary, you need magnetic fields with a gradient of millions of Tesla’s per meter in order to accelerate the electron with only one meter per second squared…
No idea is smarthead Morton Tavel will ever read these words I write about him, but in reason number 50 I did such an estimation. Here is the link:

14 Oct 2017: Reason 50: A calculation on electron acceleration by a magnetic field.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#14Oct2017

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Let’s proceed with the second physics professional, his name is Kurt T. Bachmann and here is the quote from the wisdom he has to share:

“Starting in the 1920s, Otto Stern and Walther Gerlach of the University of Hamburg in Germany conducted a series of important atomic beam experiments. Knowing that all moving charges produce magnetic fields, they proposed to measure the magnetic fields produced by the electrons orbiting nuclei in atoms. Much to their surprise, however, the two physicists found that electrons themselves act as if they are spinning very rapidly, producing tiny magnetic fields independent of those from their orbital motions. Soon the terminology ‘spin’ was used to describe this apparent rotation of subatomic particles.

“Spin is a bizarre physical quantity. It is analogous to the spin of a planet in that it gives a particle angular momentum and a tiny magnetic field called a magnetic moment.

Comment: It is important to know that the original SG experiment was done with evaporated silver ions, this beam of silver ions was split in two parts by just a few unpaired electrons. If the professionals would do the calculations they would find this cannot be explained by inhomogeneous magnetic fields. The fact that no one says this makes clear they have never done the calculations needed…
That is the same as a carpenter that refuses to use the handsaw when needed or simply states: I do not need a screw driver, I just talk to these screws until the matter is resolved. Normally the carpenter would get fired but all those physics professors are glued to their seats living in ‘academic freedom’.

__________

The third person is truly 100% crazy, the term ‘intrinsic spin’ for the electron was used in order to avoid the problems with the spinning of an electron. And what does this weirdo named Victor J. Stenger make from this? Quoting this idiot:

“Spin is the total angular momentum, or intrinsic angular momentum, of a body. The spins of elementary particles are analogous to the spins of macroscopic bodies. In fact, the spin of a planet is the sum of the spins and the orbital angular momenta of all its elementary particles. So are the spins of other composite objects such as atoms, atomic nuclei and protons (which are made of quarks).

“In classical physics, angular momentum is a continuous variable. In quantum mechanics, angular momenta are discrete, quantized in units of Planck’s constant divided by 4 pi. Niels Bohr proposed that angular momentum is quantized in 1913 and used this to explain the line spectrum of hydrogen.

Comment: This is so utterly stupid it is hard to comment upon. By talking about intrinsic angular momentum he only shows that he thinks the electron is spinning. So he is a nutjob for sure.

 

Ok, end of this post without pictures but with three idiots as found in the Scientific American. Now some people might think I better be a little bit more diplomatic but from 1992 until 2012 I was very very diplomatic about higher dimensional number and thought that if you give people time enough that in the end they will do the right thing.

Two decades of diplomacy are gone, now I know that when confronted with idiots you better explain why they are idiots…

See you in the next post my dear reader.

On reason number 51 and 52 as why electrons cannot be magnetic dipoles.

This week I posted reason number 51 and 52 on the other website in the magnetic pages , page 1 contains 41 reasons and is from 2015 & 2016. Page 2 is covering what I wrote this year on the subject.

Very often when professional physics professors start explaining electron spin they do blah blah blah like the earth is spinning around it’s axis and also spinning around the sun. This is a retarded explanation because the strength of the magnetic stuff related to the electron cannot be explained by the electron spinning around it’s axis.

Now I was watching a few video’s from Microsoft where they explain the subject of topological quantum bits. The Dutch based university of Delft is also participating in that project of making topological quantum bits and the researchers from Delft are thinking they have found a quasi particle named the Majorana particle. This Majorana particle seems to be it’s own anti-particle and according to Leo Kouwenhoven such a quasi particle is comprised of a hole and an electron…

The fact they claim this stuff is it’s own anti particle struck me as odd, it is well known that if a particle meets it’s anti particle the result is a violent annihilation of both particles and it is very very hard to imagine that if two holes and two electrons meet there will be violence…

Anyway this made me think of what actually happens when in those high energy particle physics experiments like in CERN we observe the creation of an electron and a positron. The positron is the anti particle of the electron.

And even in such an elementary thing it makes no sense the electron is a magnetic dipole. It might look logical that if one particle has spin up the other created particle must have spin down.
But if we assume there is spinning around an axis, both the electron and the positron must rotate into the same direction, this is a direct violation of the principle of conservation of angular momentum.

So if electron spin is spinning around some axis and we want to preserve the total amount of angular momentum, they should be spinning in opposite directions but that would create two equal magnetic spins and that is also nonsense.

But if you assume that electrons and positrons carry beside electric charge also magnetic charge, all of a sudden the creation of the electron-positron pair becomes much more logical:
If the freshly created electron has north pole magnetic charge, the positron will have south pole magnetic charge…

That makes sense while the professional physics standard explanation does not make sense. Here is a link to the stuff involved in reason number 51:

17 Dec 2017: Reason 51: Spin properties of the positron.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#17Dec2017

Reason number 52 covers the fact that the Juno probe around Jupiter has observed that in the aurora’s on Jupiter the electrons also seem to be coming from the atmosphere of Jupiter. That would not be a problem if there were some electrical fields to move the electrons, tiny problem is those electrical fields seem to be missing often.

So all those so called professional physics professors have it straight in their face: how do those electrons get accelerated. I think it is the magnetic fields from Jupiter that do this, just like on the sun and so but before our precious ppp’s will arrive at the same conclusion we will be many centuries later… (Or not?)

In the next picture you can see how this was told in the news as you can find it on Youtube channels like Scishow (often more show than science but anyway they serve some part of the public).

Oh oh Catlin Hofmeister, they are not pulled up but expelled by the magnetic field of Jupiter… Reason number 52:

19 Dec 2017: Reason 52: Jupiter aurora’s without the electrical field acceleration.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#19Dec2017

Ok let’s say goodbye for the moment, till updates in the next post!

An important calculation of the 7D number tau (circular version).

I really took the time to compose this post; basically it is not extremely difficult to understand. Everybody who once has done matrix diagonalization and is still familiar with the diverse concepts and ideas around that can understand what we are doing here.

It is the fact that it is seven dimensional that makes it hard to write down the calculations in a transparent manner. I think I have succeeded in that detail of transparency because at the end we have to multiply three of those large seven by seven matrices with each other and mostly that is asking for loosing oversight.

Luckily one of those matrices is a diagonal matrix and with a tiny trick we can avoid the bulk of the matrix calculations by calculating the conjugate of the number tau.

Just like in the complex plane where the conjugate of the number i equals -i, for tau goes the same.

Basically the numbers tau are always the logarithm of the first imaginary component. But check if the determinant is one because you can use the tau to craft an exponential curve that will go through all basis vectors with determinant one.

This post is 10 pictures long (size 550 x 775), in the beginning I use an applet for the numerical calculation of the matrix representation of the first imaginary unit in 7D space, here is the link:

Matrix logarithm calculator
http://calculator.vhex.net/calculator/linear-algebra/matrix-logarithm

Two years back in 2015 after I found the five dimensional numbers tau every now and then I typed in a higher dimensional imaginary unit and after that only staring at the screen of the computer: How to find those numbers as the log applet says…

The method as shown here can be applied in all dimensions and you now have a standard way of crafting exponential curves in all spaces you want. This method together with the modified Dirichlet kernels that provide always a parametrization of the exponential curve form a complete description.
Ok ok those modified Dirichlet kernels always have period pi while this way to calculation the log of the first imaginary unit is always related to the dimension (recall that the 7D first imaginary unit l has the property l^7 while for the complex multiplication in 7D space we have l^7 = -1), but it is very easy to fix the Dirichlet kernels to the proper period in the time domain you want.

The most difficult part of this post is in understanding the subtle choice for the eigenvalues of tau = log l, or better; choosing the eigenvalues of the matrix representation involved. That makes or breaks this method, if done wrong you end up with a giant pile of nonsense…

Have fun reading it and if this is your first time you encounter those matrices with all these roots of unity in them, take your time and once more: take your time.
If you have never seen a matrix like that it is very hard to understand this post in only one reading…

I am glad all that staring to those numerical values is over and we have the onset of analytical understanding of how they are in terms of the angle 2 pi over 7.
The result is far from trivial; with the three or five dimensional case you can use other ways but the higher the dimension becomes the harder it gets.

This method that strongly relies on finding the correct diagonal matrix only becomes more difficult because the size of the matrices grows. So only the execution of the calculation becomes more cumbersome, the basic idea stays the same.

__________

I have no idea what the next post is going to be, may be a bit of magnetism because a few days back I got some good idea in explaining the behaviour of solar plasma included all those giant rings that shoot up and land in another spot of the sun.

And we also have those results from the Juno mission to Jupiter where the electrons also come from Jupiter itself without the guidance of electrical fields. But in the preprint archive I still cannot find only one work about it, that might be logical because often people do not write about stuff they don’t understand…

Ok, that was it. I hope you liked it & see ya around.

Intro to the calculation of the seven dimensional number tau (circular version).

All details will be in the next post but I succeeded into using matrix diagonalization in order to find this seven dimensional number tau.
For people who do not understand what a number tau is, this is always the logarithm of an imaginary unit. Think for example at the complex plane and her imaginary unit i. The number tau for the complex plane is log i = i pi/2.

The problem with finding numbers tau becomes increasingly difficult as the number of dimensions rise. I remember back in the year 2015 just staring at all those matrices popping up using internet applets like the next one:

Matrix logarithm calculator (it uses the de Pade approximation)
http://calculator.vhex.net/calculator/linear-algebra/matrix-logarithm

Yet back in the year 2015 I was riding on my noble iron horse (a cheap bicycle) through the swamps surrounding the village of Haren and suddenly I had a good idea. Coming home I tried the idea of matrix diagonalization out in 3 dimensions and it worked.

I even wrote a post about it on 23 Nov 2015:

Integral calculus done with matrix diagonalization.

Now I think that most readers who visit this website are familiar with the concept of finding a diagonal matrix D containing all eigenvalues of a given matrix M. Once you have the eigenvalues you can calculate the eigenvectors and as such craft your matrix C containing all eigenvectors.
You can write the stuff as next: D = C^-1 M C.

Suppose you don’t know what M is but I give you the matrices D, C and the inverse of C. Can you find the matrix M?

Yes that is a beerwalk, all you have to do is calculate M = C D C^-1 and you are good to go.

But with the logarithm comes a whole lot of subtle things for making the right choice for the eigenvalues that you place inside the diagonal matrix D. It turns out you only get the desired result if you use arguments in the complex plane between minus and plus pi.
This is caused by the fact that you always need to make a cut in the complex plane if you want to work with the complex logarithm; but it is a bit surprising that only the cut where you leave out all real negative numbers (and zero of course) makes the calculation go perfect and in all other cases it ends in utter and total disaster.

In the next three pictures I show you some screen shots with numerical values of matrix representations and the logarithm of those matrix representations.

The goal is to find mathematical expressions for the observed numerical values that are calculated via the above mentioned de Pade approximation. We don’t want only numerical approximations but also catch the stuff in a mathematical formulation.

At the end of the third picture you see the end result.

So it took some time to find this result, I wasted an entire week using the wrong cut in the complex plane. And that was stupid because I had forgotten my own idea when riding my noble iron horse through the Harener swamps…

The result for the seven dimensional number tau (circular version) as calculated in the next post is a blue print for any dimension although I will never write stuff down like in a general dimension setting because that is so boring to read.

Ok, see you around my dear reader.

On a way to find more equations so that the 1D existence of exponential curves in all possible dimensions is assured.

In part this post picks up where I left the stuff of the missing equations back in the year 2015. The missing equations are found inside the determinant equation; for this to succeed we must factorize determinant of the matrix representations of higher dimensional numbers. A well known result from linear algebra is that the determinant is also the product of the eigen values; so we need to craft the eigen value functions that for every X in our higher dimensional number space give the eigen values.

These eigenvalue functions are also the discrete Fourier transform of our beloved higher dimensional numbers and these functions come in conjugate pairs. Such a pair form two factors of the determinant and if we multiply them we can get rid of all complex coefficients from the complex plane.

A rather surprising result is the fact that if we subtract a cone equation from a sphere equation we get a cylinder…

This post is also a way of viewing the exponential circles and curves as an intersection of all kinds of geometric objects like the unit sphere, (hyper) cones, (hyper) planes and (hyper cylinders. Usually I represent it all as some analysis but you can take a very geometric approach too.

I have no idea if the shape of the higher dimensional curves is studied as a geometrical object; I suspect this is not the case since the use of complex numbers outside the complex plane is very seldom observed. The professionals just want their tiny fishing bowl (the complex plane) and declare it an Olympic swimming pool…
Well, let it be because these people will never change.

All in all this post is 20 pictures long (size 550 x 775) so it is a relatively long read.

                                     

The pictures of the graphs were all made with an applet named Animated drawing, here is a link and there you can find it under ´Online calculators and function plotters´±

https://wims.sesamath.net/wims.cgi

For example you can cut and paste the next five dimensional equations that represents a hypercone going through all the coordinate axis:

((1/5)*sin(5*x)/sin(x))*((1/5)*sin(5*(x-2*pi/5))/sin(x-2*pi/5)) +
((1/5)*sin(5*(x-2*pi/5))/sin(x-2*pi/5))*((1/5)*sin(5*(x-4*pi/5))/sin(x-4*pi/5)) +
((1/5)*sin(5*(x-4*pi/5))/sin(x-4*pi/5))*((1/5)*sin(5*(x-pi/5))/sin(x-pi/5)) +
((1/5)*sin(5*(x-pi/5))/sin(x-pi/5))*((1/5)*sin(5*(x-3*pi/5))/sin(x-3*pi/5)) +
((1/5)*sin(5*(x-3*pi/5))/sin(x-3*pi/5))*((1/5)*sin(5*x)/sin(x))

The above thing should give identical zero for all x.
An important feature of exponential curves in spaces with an odd number of dimensions is that they all are inside a hyperplane. The hyperplane says the sum of the coordinates is always 1. If you cut and past the next sum of the five coordinate functions you see that you always get one for all x:

((1/5)*sin(5*x)/sin(x)) +
((1/5)*sin(5*(x-pi/5))/sin(x-pi/5)) +
((1/5)*sin(5*(x-2*pi/5))/sin(x-2*pi/5)) +
((1/5)*sin(5*(x-3*pi/5))/sin(x-3*pi/5)) +
((1/5)*sin(5*(x-4*pi/5))/sin(x-4*pi/5))

At last the link to the original update from 2015 where I found the missing equations for the first time. But all I knew they were hidden inside the determinant. A few weeks ago I decided to take a better look and the result is this post.

From 14 July 2015: The missing equations.
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#14July2015

Ok, that is what I had to say. Till updates.

On an old idea that did not work…

Recently I am working on a relatively long post where I try to take a much more geometric approach to finding exponential circles and exponential curves. That post is also going forward from a few years back when I was searching for the so called missing equations.

The problem of the missing equations does not arise until you start working in five dimensions or higher; the equations as generated by the sphere-cone equations are just not enough to end up with a one dimensional curve.
Back in the time I simply took a few weeks until I had found the answer: The missing equations can be found inside the determinant!

For example if you have a 17 by 17 matrix in 17 variables (the so called matrix representations of 17-dimensional number systems), all you have to do is factorize this determinant and from those factors you can craft the extra needed equations.

Weirdly enough you find a hyper plane and a bunch of hyper-cylinders.

So in the next post I try to show you how you can have a very geometric approach to finding the higher dimensional exponential curves as the intersection of a sphere, a hyperplane, a bunch of cones and a bunch of cylinders.

__________

In my old notes I found a mysterious looking line of squares of cosines with their time lags. That was from before I solved the problem and this ‘solution’ has all kinds of faults in it.

That is this small post; it is about something that does not work.
It is just 3 pictures long (550 x 775 pixels):

It was just over two years back I wrote that long update on the other website about the missing equations, I was glad I took those weeks to solve this problem because it is crucial for the development of general higher dimensional theory on this detail.

Here is a link to that old update±

From 14 July 2015: The missing equations.

I hope next week I am ready with the new long post, after that I will likely pick up magnetism again because I finally found out what the professionals mean when talking about ´inverted V-s’; that means there is also an electric field accelerating the particles in the aurora’s of earth and Jupiter.

Tiny problem for the professionals: At the Jupiter site, regardless of inverted V-s yes or no, the plasma particles get accelerated anyway…
So that looks like one more victory for Reinko Venema and one more silence from the professional professors.

See ya around!

On the derivative and integral of the inverse function.

After all that magnetism stuff it is about time to throw in a tiny bit of simple math around how to find the derivative and primitive (the integral) of the inverse of a function.

In most (introductory) textbooks on calculus you will find a nice way of finding the derivative of the inverse of a given function f(x) defined on the real line. For integration where you need to find the anti-derivative there is also a very elegant way of calculating those, but in my life I have never ever seen it in print on paper in an actual existing book.

Now last week I came across a video where another guy claimed that finding the primitive in this way was completely new but within 60 seconds with the help of the Google search engine you can find this is not the case.

According to a wiki on the subject of integration of the inverse of a function, the first know results date back to 1905. This is a remarkably short time ago and for myself speaking I think that many folks found this way too but for some strange reasons it never popped up to the surface. It is strange to observe that for example the method of the calculation of variations was invented included those fine differential equations that form the way to find for example the path of least action or minimal time but somehow those people never found the way to integrate the inverse of a function…

On the other hand, I have seen it myself that there can easily be a complete vacuum in mathematics; in my first year at the university I invented the so called product integral. Normally when you calculate an integral you can view that as adding up all the area under the graph of a certain function, with a product integral you do the same but you do not add it up but you multiply all stuff.
And in it’s most natural setting you do that with raising a function f(x) to the power dx.
That was my invention but although product integration has been studied for over a century, nobody had ever taken a function to the power dx…

Now enough of the blah blah blah done, this post is four pictures long and the wiki stating this cute formula was found in the year 1905 is the next:

Integral of inverse functions
https://en.wikipedia.org/wiki/Integral_of_inverse_functions

This post is four pictures (550 x 775 pixels), here they are:

So that was it for this post, see ya around my dear reader.

Updated on 16 Oct 2017:
Today I found that video back where some guy made those unsubstantial claims that this result was never ever found in the entire history of mathematics. That is not true but it is strange that the derivative is in every introductory course or book while the integral version is always absent.
We can safely jump to the conclusion that the integral version is not widespread known and this causes authors of those books not to include it.

The video goes under the title:
Rare Integration Strategy – You won’t learn this in Calculus.

So that was it for this update on this post, see ya around my dear reader.