Sesamath 6 correction bit

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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 sesamath 6 correction bit 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, sesamath 6 correction bit 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 xin 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: Two years back in 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 sesamath 6 correction bit those sesamath 6 correction bit 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. That sesamath 6 correction bit 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: If you have never seen a matrix like that it is very hard to understand this post in only one reading….

Sesamath 6 correction bit 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.

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 problem with finding numbers tau becomes increasingly difficult as the number of dimensions rise. I remember back in the year 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: Yet back in the year I sesamath 6 correction bit 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. 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: Can you find the matrix M?

But with the logarithm comes a whole lot of subtle things sesamath 6 correction bit 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 sesamath 6 correction bit 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 sesamath 6 correction bit observed numerical values that are calculated via the above mentioned de Pade approximation. 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 Sesamath 6 correction bit 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 sesamath 6 correction bit never write stuff down like in a general dimension setting because that is so boring to read.

In part this post picks up where I left the stuff of the missing equations back in the year 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, sesamath 6 correction bit it be because these people will never change.

For example you can cut and paste the next five dimensional equations that represents a hypercone going through all the coordinate axis:. The above thing should give identical zero for all x. An important feature of exponential curves in sesamath 6 correction bit with an odd number of dimensions sesamath 6 correction bit 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:. At last the link to the original update from where I found sesamath 6 correction bit missing equations for the first time. But all I knew they were hidden inside the determinant. A few weeks ago Sesamath 6 correction bit decided to take a better look and the result is this post. From 14 July 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 sesamath 6 correction bit of sesamath 6 correction bit 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 sesamath 6 correction bit 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 dimensional number systemsall you have to do is factorize this determinant and from those factors you can craft the extra needed equations.

So in the next post I try to show you how sesamath 6 correction bit can have a very geometric approach to finding the higher sesamath 6 correction bit exponential sesamath 6 correction bit as the intersection of a sesamath 6 correction bit, a hyperplane, a bunch of cones and a bunch of cylinders. In my old notes I found a mysterious looking line sesamath 6 correction bit squares of cosines with their time lags.

That is this small post; it is about something that does not work. It is just 3 pictures long x 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. Tiny problem for the professionals: At the Jupiter site, regardless of inverted Sesamath 6 correction bit 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.

Basically tau-calculus is very easy to understand:. This is easy to understand but I could only do this sesamath 6 correction bit three and five dimensional space, seven or eleven dimensional space?

It is now 2. 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 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. 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 x pixels containing: Hope you can learn a bit from it, do not worry if you do not sesamath 6 correction bit all details because even compared to the 2D complex plane or the 3D complex numbers this website is about: 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 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 upon the missing equations is also worth a visit: This is what Sesamath 6 correction bit more or less had to say, have a nice life or try to get one.

See you in the next post. Via the so sesamath 6 correction bit 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. 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:

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In the previous post on 4D complex numbers I went a little bit philosophical with asking if these form of crafting a 4D number system is not some advanced way of fooling yourself because your new 4D thing is just a complex plane in disguise….

So from the viewpoint of differentiation and integration we are in a far better spot compared to the four dimensional quaternions from Hamilton.

And on the quaternions you cannot differentiate properly because they do not commute. So crafting Cauchy-Riemann equations can be done, but it does not solve the problem of may be you are fooling yourself in a complicated manner. Therefore I also included the four coordinate functions of the exponential 4D curve that we looked at in the previous post.

All math loving folks are invited to find the four coordinate functions for themselves, in the next post we will go through all details. And once you understand the details that say the 4D exponential curve is just a product of two exponential circles as found inside our 4D complex numbers, that will convince you much much more about the existence of our freshly unearthed 4D complex numbers. Of course the mathematical community will do once more in what they are best: After having said that, this post is partitioned into five parts and is 10 pictures long.

It is relatively basic and in case that for example you have never looked at matrix representations of complex numbers of any dimension, please give it a good thought. Because in my file I also encountered a few of those professional math professors that were rather surprised by just how a 3 by 3 matrix looks for 3D complex numbers.

How can you find that they asked, but it is fucking elementary linear algebra and sometimes I think these people do not understand what is in their own curriculum…. And may be I am coming a bit too hard on the professional math professors. After all they must give lectures, they must attend meetings where all kinds of important stuff has to be discussed until everybody is exhausted, they must be available for students with the questions and problems they have, they must do this and must do that.

At the end of the day, or at the end of the working week, how much hours could they do in free thinking? Not that much I just guess…. Lately I have been working on the next post about the basics of the 4D complex numbers.

You simply need those basics like matrix representations because later on when you throw in some 4D Cauchy-Riemann equations, it is very handy to have a good matrix representation for the stuff involved. This tau in any higher dimensional number system or a differential algebra in case you precious snowflake can only handle the complex plane and the quaternions is always important to find.

Informally said, the number tau is the logarithm of the very first imaginary component that has a determinant of 1. For example on the complex plane we have only 1 imaginary component usually denoted as i. Complex numbers can also be written as 2 by 2 matrices and as such the matrix representation of i has a determinant of 1. Anytime they talk about a phase shift they always use this in the context of multiplication in the complex plane by some number from the unit circle in the complex plane.

In this post, for the very first time after being extremely hesitant in using dimensions that are not a prime number, we go to 4D real space. Remark that 4 is not a prime number because it has a prime factorization of 2 times 2. Why is that making me hesitant? That is simple to explain: If you can find the number i from the complex plane into my freshly crafted 4D complex number system, it could very well be this breaks down to only the complex plane.

In that case you have made a fake generalization of the 2D complex numbers. So I have always been very hesitant but I have overcome this hesitation a little bit in the last weeks because it is almost impossible using the complex plane only to calculate the number tau in the four dimensional complex space…. May be in a future post we can look a bit deeper in this danger; if also Cauchy-Riemann equations are satisfied in four real variables, that would bring a bit more courage to further study of the 4D complex number system.

After the introduction blah blah words I can say the 4D tau looks very beautiful. That alone brings some piece of mind. I avoided all mathematical rigor, no ant fucking but just use numerical results and turn them into analytical stuff.

That is justified by the fact that Gerard is a physics professor and as we know from experience math rigor is not very high on the list or priorities over there…. That is forgiven of course because the human brain and putting mathematical rigor on the first place is the perfect way of making no progress at all. In other sciences math should be used as a tool coming from a toolbox of reliable math tools.

This post is seven pictures long, all are by pixels in size except for the last one that I had to make a little bit longer because otherwise you could not see that cute baby tau in the 4D complex space. It is very very hard to stay inside the complex plane, of course the use of 4 by 4 matrices is also forbidden, and still find this result…. I am still hesitant about using dimensions that are not prime numbers, but this is a first result that is not bad.

I can prove that because it is on video. Yes you already told that into the statements you made after arrest by the police. So we took the freedom and ask Mr. But judge, it is not Hermitian, that is only a trick. Do you think we get complex analysis in law school?

After this somewhat strange introduction I repeat I was innocent. I was just looking at a video of a guy that is just like me old and boring. That is what this post is about; Three punches in the face as delivered by Gerard.

It is the very first time I observe professional physics professors using the number tau while claiming the stuff has to be Hermitian to make any sense. I was devastated because in my little world of mathematics it had to be anti Hermitian so at a first glimpse it looks like a simple shootout between Gerard and me: Only one can be right….

Let me also temper the enthousiasm a little bit because at present date 26 Feb in the year I only know of one example where three quantum states are rotated into each other: That is the transport of the color charges as it is found on the quarks inside the proton and neutron…. Here is the video, after that the nine pictures that make up the mathematical core of this new post:.

Let me spare you a discussion on the entire video but only look at what you can find on the very introduction as shown above because all of the three punches at my face are already found there. 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.

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 x , 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:.

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. 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: 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. 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 problem with finding numbers tau becomes increasingly difficult as the number of dimensions rise. I remember back in the year 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: Yet back in the year 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.

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: Can you find the matrix M? 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. 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….

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