And another of those “We cannot find the 3D complex numbers” video’s.

3D complex numbers

This is one of those videos based in large part on that old theorem of Frobenius that says there are no 3D fields containing the complex numbers from the complex plane. There is another similar proof out, also rather old, that says the same.
Well there is nothing new about that, after all there is nothing in the 3D complex numbers that squares up to -1. (See a few posts back when I wrote the first so called general theory where I show that in all odd-dimensional number systems you cannot solve for X^2 = -1).
It is also not much of a secret that beside 0 there are much more non-invertible numbers in 3D real space. So no, it is not a field but I knew that for over 30 years my dear reader.
Over the years I have joked at many occasions that the only thing math professors are good at is at saying “We cannot find the 3D complex numbers”. And that is so deep ingrained for some strange reason that actually they can’t. Ok ok there is also the question of competence into doing new math research. As a matter of fact most math professors are relatively bad at doing researh on new math stuff. Math professors are rather good at reproducing the good math from the past, in such a comparison they are much more like a classical orchestra that plays old works of music from Bach or any other long dead composer. But most professional musicians do not compose very music for themselves, it is their job to repeat the old music from the past and that’s it. Math professors are just like that often, now that is not only negative or so. For example the proof of the prime number theorem (how much primes are there asymptotically under a given magnitude?) was hard to find and it is long. If you can repeat that proof in front of a class, that is for sure a highly cognitive thing to do. I am not saying all math professors are dumb.

But as far as I know it most of them have a strong tendency for shallow thought, better fast than accurate and much slower. For example in 30 years of time every now and then some folks discover the 3D complex numbers again and oh oh what exiting it is to find the conjugate! They do it all wrong, yes one 100% take the wrong kind of conjugate and after that all calculations fade into total nonsense and as such they too conclude there is not much going on with 3D complex numbers. I have never seen anyone finding the 3D complex exponential, that is what I mean with shallow thinking. People just project on the new stuff things they know from the old stuff and the new stuff ‘must’ for some strange reason obey the old stuff and when that does not happen they begin to cry like the crybabies they are.
I did that too on a few occasions but after doing stupid twice I understood what I was doing wrong: I just was not open minded about how the new stuff actually worked.

Now when I viewed the video for the first time a few weeks back I was relatively annoyed, not only because of the dumb content but also because of the title (3D complex numbers do not exist). But the days after when this new post came to my mind I just felt so tired. Why is it always so fucking stupid and shallow? Why is that year in year out why are all those math professors never evolving, why is it always fucking stupid and no oversight at all?
So I did not have a good feeling about it and because the video is so stupid I could easily write 20 different posts and that made me feel even more tired and exhausted because these people just don’t improve.
Anyway I decided to keep it short and simple and only point out that the two most important new numbers in the 3D complex numbers are the number tau and alpha that are related to the 3D complex exponential. These two numbers if you multiply them that gives zero, the property that non-zero numbers can multiply to zero is called divisors of zero.

And guess what, the video from Michael Penn begins with a small list of the properties that 3D numbers have to obey in case you will have something meaningful or so as Michael says it. Well in his small list is indeed it must be a field and also it does not have divisors of zero. Furthermore Michael did not figure it out himself but uses the work of another person so we have everything combined: Shallow thinking combined with repeating the work of other people.

Here is the video:

If you want impossible properties, you will find not much…

Left is placing the two pictures that compose this post here below. And I have an extra pdf with that Frobenius stuff in it, it is hard to read and is precisely the kind of math I avoid to write down. You can find the Forbenius classification from page 26 of the pdf.

The pdf from Ray E. Artz:

Oa_Frobenius_theoremDownload

For myself speaking: I consider this pdf a disaster to read. It is all overly complicated formulated with not much math content to it. But it contains a bit of the old school Frobenius stuff so it has some value although it has weird notation that is hard to grasp…

Over time I have come to understand that the 3D complex numbers are an expansion from the real line just like the complex plane is. For example: multiplication in the 3D complex numbers is ruled by the imaginary unit j who’s third power equals minus one: j^3 = -1.
But if you have seen only the complex plane your entire life, in that case you are likely tempted to try and think of it as e to some imaginary power like on the complex plane. But you cannot do that because the number i from the complex plane does not live inside the 3D complex numbers. So for me they have equal right to exist or to study, they are very different but at least you can do complex analysis on the 3D complex numbers and you can’t do that on the famous quaternions.

Now I don’t want to sound as a sour old man, after all this post was not very funny to write but on the scale of things it is just a luxery problem. Let me end this post with thanking you for your attention.

Remarks on a pdf about a generalized form of the cross product. (Author: Peter Lewintan.)

Pythagoras stuff

I have this pdf about a year now. Last year when I was doing that matrix form of the theorem of Pythagoras I came across this pdf and I saved it for another day.
Last year when working on that matrix Pyth stuff you always get a large bunch of those determinants of those minor matrices. And I thought like “Hey you can put them in an array and in that case the length of that array is the volume of that parallelepipid”. Well in this pdf Peter is just doing that: He does not use a nxd matrix but only two columns because the goal is to make a product.
Last year after say an hour of thinking I decided to skip that line of math investigation and instead concentrate more on if it would be possible to make that none square nxd matrix into a square nxn matrix.

Another reson to save this pdf for a later day was the detail it was also about differential operators. Not that I am very deep into that but the curl is a beautiful operator and as you likely know can be expressed with the help of the usual cross product in three dimensions. To be honest I considered this part of the pdf a bit underwhelming. I really tried to make some edible cake from that form of differential operators but I could not give a meaning to it. May be I am wrong so if you want you can try for yourself.

The pdf contains much more as the above, a lot of cute old identies and also some rather technical math that I skipped because sometimes I am good at being lazy…;)

My comments are four pictures long and after that I will try to hand the dpf from Peter into it.

What is it that makes those present day picture generators so bad at things having five fingers? I think those genrative ai machines don’t count on their fingers.

But serious, here is the pdf:

Lew_cross_product_in_N_dimensions_preprintDownload

I posted this in the category Pythagoras stuff because it is vaguely related to that matrix version of the Pythagoras theorem.
Ok that was it for the time being. May be the next post is from some nutty professor who claims in a video that 3D complex numbers don’t exist. Or something completely different. Who knows where our emotions bring us?

Spin selection rules and the permanency of magnetic charge of the electron.

Magnetism

The official version aka the standard model of particle physics says there is only one kind of electron, all electrons are the same, and their magnetic properties like spin are only a matter of alignment cq anti-alignment with the magnetic field. The standar model treats electrons as tiny magnets.
I think that electrons are magnetic monopoles and as such there are two kinds; a north pole and a south pole kind. But can electrons flip their spin? After all a lot of quantum computing is based on the idea that indeed electrons can flip their spin even stronger: the electron can be in a super position of spin un and down.
Over the years I slowly evolved to the position that the magnetic charge of electrons is permanent. And if the magnetic charge is permanent in that case in the electron cloud of an atom or a molecule, al lot of transitions cannot be done. During those transitions the spin of an electron cannot flip simply because it’s charge is just like the electric charge: permanent.

Now I did not know it but inside a lot of chemistry files you can find a thing known as ‘Spin selection rules’ that give a good description of how an electron can jump up and down the diverse orbitals when it comes to it’s spin. You can also find it under ‘Forbidden transitions’ but also stuff like radioactive decay has forbidden transitions.

An important feature of a forbidden jump in electron transitions is that ther assiciated energy can be observed but that is always on a longer timescale. My impression is that the chemical people don’t understand very good as why this is: Well an electron in some atom or molecule can only ‘flip’ it’s spin as it gets replaced by another electron.

Example: The 21 cm radio frequency in radio astronomy. Photons with a wavelength of 21 cm come from atomic hydrogen that undergoes a spin flip to it’s lowest potential energy configuration when it comes to magentism.
But if that can only be done by other electrons bumping into that hydrogen atom, that says something about the electron streams in vacuum from where the 21 cm radiation is coming.

Here a simple picture of what is allowed and what not:

Basically it says: Spin flip is not allowed.

It is very well known inside the science of chemistry that energy states like those singlet and triplet stuff above are very close to each other. So how it is possible that just some thermal shaking or good old molecular vibrations do never flip the spin of an electron?

If all that mumbo jumbo about electrons was true, why can’t some heat or some vibrations make that sole electron flip it’s spin? Do we get that nonsense like “If you think you understand quantum mechancis, in that case you don’t understand quantum mechanics” one more time?

And I admit that too: If you are that stupid to view the electron as a tiny magnet, yes indeed the science of particle physics but also chemistry becomes very hard to understand. It’s loaded with weird stuff all over the place. In chemical bonding the electrons in a pair must always have opposite spins but in permanent magnets the spins must always be aligned.

May be it is time to split my dear reader. See you in the next post.

Proof that Z^2 = -1 cannot be solved on real spaces with an odd dimension. (General theory part 1.)

3D complex numbers, 4D complex numbers, 5D complex numbers, Matrix representation

Finally after all those years something of a more general approach to multiplication in higher dimensions? Yes but at the same time I remark you should not learn or study higher dimensional numbers that way. You better pick a particular space like 3D complex numbers and find a lot out about them and then move on to say 4D or 5D complex numbers and repeat that process.
Problem with a more general approach is that those spaces are just too different from each other so it is hard to find some stuff all of those spaces have. It is like making theory for the complex plane and the split complex numbers at the same time: It is not a good idea because they behave very differently.
The math in this post is utterly simple, basically I use only that the square of a real number, this time a determinant, cannot be negative. The most complicated thing I use of the rule that says the determinant of a square is the square of the determinant like in det(Z^2) = det(Z)^2.

This post is only 3.5 pictures long so I added some extra stuff like the number tau for the 4D complex numbers and my old proof from 2015 that on the space of 3D complex numbers you can’t solve X^2 = -1.

I hope it’s all a bit readable so here we go:

Oops, this is the circular multiplication… Well replace j^3 = 1 by
j^3 = -1 and do it yourself if you want to.

So all in all my goal was to use the impossibility of x^2 being negative on the real line to the more general setting of n-dimensional numbers. As such the math in this post is not very deep, it is as shallow as possible. Ok ok may be that 4D tau is some stuff that makes math professors see water burning because they only have the complex plane.
Let me end this post with thanking you to make it till the end, you have endured weird looking robots without getting mentally ill! Congratulations!
At the end a link to that old file from 2015:

Another proof the complex number i does not live in three dimensions…

Video ‘proof’ that all chemistry professors are nutjobs.

Magnetism

Over the years I have written about the weird fact that according to the official theory the electron pair is a binding element in chemistry if they have opposite spins. That is very strange because that means the two electrons must be anti-aligned so the binding must happen via a north pole to north pole binding or a south pole to south pole binding.
But if you formulate it that way, instantly everybody understands you are crazy because a magnetic north pole is repelling against another magnetic north pole.
That is why they always talk about the Pauli exclusion principle and that you must use quantum numbers and more of that blah blah blah that is only there to masquerade that the binding is 100% crazy if the official theory upon electron spin was true.
It has to be remarked that if it is true that electrons are tiny magnets (they are not!), in that case it is logical that the binding must be done via equal magnetic charges. So north pole against north pole and the same for the south pole stuff.
Haven’t chemistry professors never heard of the elementary thing about magnetism and electricity: Like charges repel and different charges attrack?

Lets look at electricity first: Suppose you have two metal balls and one is strongly negatively charges so it has a surplus of electrons and the other is very positively charges so it has a deficit of electrons compared to the protons there are in the ball.
It is well known that these two metal balls now feel an attractive force between them. There is even a name for that: These are Coulomb forces. We find this behaviour back on every scale, the smallest example is the most simple atom there is, the hydrogen atom where one proton and one electron behave the same as macroscopic things like metal balls.

Now we look at magnetism: If you have two macroscopic magnets the lowest energy state is when north pole meets south pole. Why is this the lowest energy state? Simply because it costs energy to remove the two magnets. But according to the physics professors and the chemistry professors, in the electron pair the spins are not aligned and as such they are anti aligned.

And nobody remarks this is crazy, on the contrary they rejoice in all that stuff by stating things like “If you think you understand quantum mechanics, you don’t understand quantum mechanics”.

All that weird stuff is based on the idea that magnetic monopoles do not exist and as such even small point like particles must be a tiny magnet. And the idiots fool themselves by believing that the so called magnetic moment of the electron is measured with 12 decimal places exactly. These people are dumb to the bone: they have zero experimental evidence that electrons are tiny magnets while the 12 decimal places thing was done via measuring frequencies. Why do those people get tax payer money for their salaries?

Anyway the simple solution to this all is that electrons are not tiny magnets and as such they are magnetic monopoles. Only in that case we have that in the electron pair the electrons having opposite spin means a south pole to north pole connection.

I have four screen shots before I post the link to the video about computer models of chemical science stuff. So here we go:

This is the model with the earth as the center of the universe.

It took hundreds and hundreds of years to hammer this out of accepted knowledge: The earth is not the center of the universe. It is ironic that Sir Richard Catlow uses this in his video presentation while later he shows that molecular binding via electron pairs. Richard and his fellow chemistry and physics professors prove every day they are stupid by claiming electrons are tiny magnets…

This shows binding via north pole to north pole if we take the color red as a north pole…
Is this science or is it garbage?

I am 100% used to the fact my insights are always neglected. So I do not expect that a relative dumb person like Sir Richard Catlow will give some kind of serious answer. He just will keep on doing his weird stuff without a second thought that it is all not very logical. That is why I can say these people are a nutjob to start with.

The video also contains a jewel from long before the electron was discovered: A model for CH4, it is just so cute that some smart folks figured that out so long ago:

In reality methane is not a flat molecule, but this is ultra cute!

Chemistry and physics professors are all nutjobs because they keep on thinking that electrons are tiny magnets. They just are not scientists because they have zero experimental proof for the things they say about electron spin. They always use the Gauss law for magnetism as some kind of proof that magnetic monopoles do not exist, they have zero experimental proof for that all.

Ok, lets go to the video, it is about one hour long:

Why are they all that stupid year in year out?

End of this post, see you in the next one & thanks for your attention if you too think people so stupid should never get such much tax payer money…

What is the repeated conjugate ‘determinant style’? (Also: Repeated adjoint matrix.)

3D complex numbers, Matrix representation

This post is easy going for most people who have mastered the art of finding the inverse of a square matrix using the so called adjoint matrix. I was curious what happens to a 3D circular number if you take the conjugate ‘determinant style’ twice. In terms of standard linear algebra this is the same as taking the adjoint of the adjoint of a square matrix.

It is well known by now (I hope anyway) that 3D complex and circular numbers contain a set of numbers with a determinant of zero, you can’t find an inverse for them. To be precise, if you take some circular 3D number, say X, and you make some limit where you send X into a not invertible number, you know the inverse will blow up to infinity.
But the conjugate ‘determinant style’ does not blow up, on the contrary in the previous post we observed that taking this kind of conjugate gave an extra zero eigenvalue in this conjugate.

In terms of linear algebra: If a square matrix is not invertible, it’s adjoint is ‘even more’ non invertible because a lot of the eigenvalues of that matrix turn to zero.

And although the inverse blows up to infinity, the cute result found is that it blows up in a very specific direction. After all it is the fact that the determinant goes to zero that blows the whole thing up, the conjugate ‘determinant style’ is as continuous as can be around zero…

It’s a miracle but the math is not that hard this time.

Four pictures for now and I plan on a small one picture addendum later.
So lets go:

Isn’t it cute? This infinity has a direction namely the number alpha…;)
Small correction: It should be taking the conjugate TWICE…

All in all this is not a deep math post but it was fun to look at anyway. May be a small appendix will be added later, so may be till updates inside this post or otherwise in some new post.
Added Sunday 16 April: A small appendix where you can see what the adjoint taking process is doing with the eigenvalues of a 5×5 diagonal matrix. The appendix was just over one picture long so I had to spread it out over two pictures. You understand fast what the point is if you calculate a few of the determinants of those minor matrices. Remark here with a 5×5 matrix all such minors are 4×4 matrices so it is the standard setting and not like that advanced theorem of Pythagoras stuff.
Well it all speaks for itself:

Ok, that was it for this update. Thanks for the attention and see you in another post.

Factorization of the determinant inside the space of 3D circular numbers. Aka: The conjugate ‘determinant style’.

3D complex numbers, Matrix representation

A few weeks back I was thinking in writing finally some post about general theory for spaces with arbitrary dimension. It soon dawned on me that the first post should be about the impossibility of solving X^2 = -1 on spaces of odd dimension for both the complex and the circular method of mulitplication on those spaces. So post number one should be about the fact the famous number i does not exist in spaces with dimensions 1, 3, 5 etc.
And what about the second post? Well you can always factorize the determinant inside such spaces, that is a very interesting observation because the determinant is also the product of all eigenvalues. These eigenvalues live traditionally in the complex plane and as such a naive math professor could easily think that the determinant can only be factorized inside the complex plane. So that would be a reasonable post number two.
Since all these years I only did such a factorization once I decided to do it again and that is this post. The basic idea is very simple: If you want to find an expression for the inverse of a general 3D circular number, you need the determinant of that number. From that you can easily find a factorization of the determinant. It’s as simple as efficient.

But now I have repeated it in the space of 3D circular numbers I discovered that part of this factorization behaves very interesting when you restrict yourself to the subset of all 3D circular number that are not invertible. That is that taking the conjugate ‘determinant style’. The weird result is that taking this kind of a conjugate increases the number of eigenvalues that are zero. So this form of conjugation transports circular numbers with only one eigenvalue zero to the sub-space of numbers with two eigenvalues zero.

For years I have been avoiding writing general theory because I considered it better to take one space at a time and look at the details on just that one space. May be that still is the best way to go because now I have this new transporting detail for only what would be the second post of a general theory, it looks like it is very hard to prove such a thing in a general setting.

Luckily the math content of this post is not deep in the sense if you know how to find the inverse of a square matrix, you understand fast what is going on at the surface. But what happens at the level of non-invertibles is mind blowing: What the hell is going on there and is it possible to catch that into some form of general theory?

I tried to keep it short but all in all it grew to a nice patch of math that is 8 pictures long. Here is the stuff:

At the end of this post I want to remark that the quadratic behaviour of our conjugate ‘determinant style’ is caused by the fact it was done on a 3D space. If for example you are looking at 17 dimensional number, complex or circular, this method of taking a conjugate is a 16 degree beast in 17 variables. how to prove all non-invertible numbers get transported to more and more eigenvalues zero?

May be it is better to skip the whole idea of crafting a general theory once more and only look at the beautiful specifics of the individual spaces under consideration.

End of this post and thanks for your attention.

Comparison of the ‘Speed = the Square’ equation on 7 different spaces.

3D complex numbers, 4D complex numbers, Uncategorized

This post is very simlilar to a few back when we calculated the results on 4 different spaces. This time I hardly pen down any calculation but only give the results so we can compare them a little bit.
The way most professional math professors tell the story of complex numbers it goes a bit like this: We have the real number line, the complex plane and on top of that a genius named Hamilton found the quaternions. On top of that there are a bunch of so called Clifford algebra’s and oh we math professors are just so good. There is no comparison to us, we are the smartest professionals in the world!

Well that is very interesting because it is well known these so called ‘professionals’ could not find the 3D complex numbers for about 150 years. So how come they all say we have this and that (complex plane and quaternions) and that’s enough, we are just perfect! Why they keep on saying rubbish like that is the so called Dunning-Kruger effect. That’s something from psychology and it says that people who lack understanding of some complicated stuff also lack the insight that they are stupid to the bone when it comes to that particular complicated stuff. So the views of professional math professors is very interesting but can be neglected one 100 percent, it’s just Dunning-Kruger effect…

If you look at the seven results of the ‘Speed = the Square’ equations, the solutions form a strickt pattern that only depends of the number of dimensions and if it is the complex or the circular multiplication. So every time a math professor goes from the complex plane to the wonderful world of quaternions you now know you are listening to a weirdo.

I said I only give results but since I have never ever introduced the 4D circular numbers I just extrapolated the other six spaces to the solution that lives in that beautiful space. So the last example is a bit longer.

Anyway although the math depth of this post is not that very deep (solving a differential equation that wants the derivative to be the square of what you differentiate), it clearly demonstrates solutions of all 7 different spaces look strikingly similar.
But because of the Dunning-Kruger effect likely the math professors will keep on telling total crap when it comes to complex numbers. Why am I wasting my time on explaining math professor behaviour? Better go to the five pictures of our post. Here we go & bye bye math professors.

May be I should write some posts about general complex number theory on spaces of arbitrary dimension. On the other hand I found the 3D complex numbers back in the year 1990. So if after all those years I will once more try to write some general theory one thing will be clear: Math professors will keep on trying to convince you of the beauty of quaternions or that garbage from the Clifford algebra’s.

Why, as a society, do we keep on wating tax payer money on math professors? Ok, they do not everything wrong but all in all it is not a great science or so where the participants are capable of weeding the faults out and grow more of the good stuff.
Let me end this post and thank you for your attention.

Correction: My spinning plasma model for sun spots is likely not correct.

Corrections

Oops I likely made a many year mistake when it comes to the magnetic stuff. Many years ago I had the idea that the magnetism as found in sun spots could possibly explained by spinning plasma underneath the solar surface.
After all if electrons are magnetic monopoles, a spinning cylinder shaped plasma should eject lots of electrons along it’s magnetic field lines. That makes the spinning plasma a terrible good magnet because is a lot of positive charged plasma is spinning that creates strong magnetic fields.

After the original idea it took me about one year there could be a possible mechanism on the sun that creates such spinning plasma structures: The sun rotates faster at the equator as it does at the poles.

Now sun spots often come in pairs with opposite magnetic polarity and in my view I thought the leading sun spot was the one created by a bunch of rotating plasma under it.

It is easy to understand that if the root couse of sun spots was a rotating column of plasma underneath them, on the opposite hemispheres of the sun the leading sun spot should have opposite magnetic polarity. That one always checked true, but for the rotational hypothesis to be true over the solar cycles the polar magneticity of the leading sun spot should always be the same.

And that is where likely my old idea is crashing right now. In the next picture you see what is more or less observed in the last change of the solar cycle, for me this is not funny.

SC24 and SC25 stand for Solar Cycle 24 & 25 and again: for me this is not funny:

Yes it is what it is. But at least as soon as I discover I have made a serious mistake I tell that as soon as possible.
All in all this mistake does not have any impact on the tiny fact that it is impossible for electrons to be tiny magnets, electrons are magnetic monopoles and as such we have two variants of them. So the Gauss law for magnetism is just not true for an individual electron, it is nonsense to say magnetic field lines always loop in on themselves.

But after seven years of explaining this kind of mistakes, that stuff known as the science of physics is not capable of cleaning herself of stupid ideas.

Let’s leave it with that, this correction is a set back but the weirdo’s classified as the physics professors still have to give some experimental proof that electrons are indeed ‘tiny magnets’.

Solving the ‘Speed = the Square’ equation on the space of 4D complex numbers.

3D complex numbers, 4D complex numbers

Unavoidable I had to write some post after the video on the quaternion from Hamilton. Now my 4D complex numbers commute so they are very different from the standard version of quaternions. Just like in the complex plane the multiplication is ruled by the imaginary unit i that has the defining property of i^2 = -1. On the space of four dimensional complex number I mostly write l for the first imaginary component, the defining property is of course that now the fourth power equals minus one: l^4 = -1.
In 2018 I wrote about 20 introdutionary posts about the 4D complex numbers. That is much more as you would need for the quaternions of Hamilton but on the quaternions you can’t do complex analysis and that explains almost all of the difference.
You can view the quaternions as three complex planes fused together by the common use of the real line. My 4D complex numbers can be viewed as a merge of two complex planes in the sense that there are two planes clearly ‘the same’ as a complex plane.
This post is once more one of the ‘Speed = the Square’ equations and just as on the other spaces we looked at we choose the initial condition such that it is the first imaginary unit l. As such our solution is easily found to be f(t) = l / (1 – lt) because if you differentiate that you get the square. So from the mathematical point of view this is all rather shallow math because all we have to do is find the four coordinate functions of our solution f(t). For that you need to calculate the inverse of 1 – lt and to be honest after so much years I think almost all math professors are just to fucking stupid to find the inverse of any non real 4D compex number Z let alone if you have something with a variable t in it like in 1/(1 – lt).

I did my best to write this as transparant as possible while also keeping it as short as possible. For an indepth look at how to find the inverse of a 4D complex number, look for Part 17 in the intro series to the 4D complex numbers. (Just use the search function for this website for that.)

This post is just three pictures long so lets hope that is inside your avarage attention span. And it’s math so without doubt a lot of people will digest this with a speed of one picture a week! No I am not being sarcastic or so, I just like as how I evolved to the math place I am now. Often that also goes very slow but it has to be remarked the math professors are much more slow slow slow because they could not find the 3D complex numbers in all of human history.
Let’s dive into the picture stuff:

One of the funny things of the math of this post is that on the one hand it is very simple: You only need high school math like the quotient rule for checking my claims are true and differentiation mimics the multiplication on the 4D complex numbers. On the other hand you have those math professors likely not capable of finding these easy coordinate functions for themselves.
But this post is not meant as an anti math professor rant but more upon the beauty of simple math you can do on say the space of 4D complex numbers.
See you in the next post.