General Pythagoras theorem part 1: The 3D case.

A long time ago I found a very simple proof for the general theorem Pythagoras. At the time the general public had almost zero access to internet resources and in those long lost years I could not find out if my proof was found yes or no.

As memory serves, Descartes was the one that gave a proof for the 3D version of the Pythagorean theorem… (But I never did read the proof of Descartes.)

Two weeks back I was cleaning out my book closet so I could store more bottles of beer for the ripening process and I came across that old but never perfectly finished proof.

And it entered my mind again because it is fascinating that just by constructing that perfect normal vector, you make it of unit length, calculate a few higher dimensional volumes and voila:
There is you proof of the general theorem of Pythagoras.

In this post we only look at the 3D example for the theorem of Pythagoras. But already here we use a normal vector together with the 2D theorem of Pythagoras in order to prove the result for 3D space.
Basically this is also precisely the way the proof works in all higher dimensions, ok ok the notations and ways of writing the stuff down is a bit more technical but if you understand the proof in this post you will immediately understand how the general proof works.

The general proof is based on the principle of natural induction, likely the reader is familiar with natural or mathematical induction because beside it’s elegance it is also easy to explain to first year students in exact sciences. Basically you prove some stuff for low values of n, say n = 2 or 3 for 2D and 3D space and after that you do the so called ‘induction step’ where you must show that if it holds for a particular value of n, the stuff you want to prove is also true for n + 1.

Here is a wiki on the subject: Mathematical induction
https://en.wikipedia.org/wiki/Mathematical_induction

__________

This post is five pictures long (size 550 x 775 as usual) so have fun reading it:

23Feb2017_generalized_Pythagoras_theorem01

23Feb2017_generalized_Pythagoras_theorem02

23Feb2017_generalized_Pythagoras_theorem03

23Feb2017_generalized_Pythagoras_theorem04

23Feb2017_generalized_Pythagoras_theorem05

In the last line of the proof it is important to remark that both the length of XY is done with the 2D version of Pythagoras, but the height h of triangle XYZ is also done with the 2D version of Pythagoras. And so you get the 3D version of the famous Pythagoras theorem.

See you in the next post where it is all a bit more abstract and not slammed down to just two or three dimensions. Have a nice life or try to get one.

CERN stuff on super conductivity and a primer on the general theorem of Pythagoras.

A few weeks back while cleaning out my book closet I came across that unfinished proof of the generalized theorem of Pythagoras that uses n-dimensional pyramids. (May be these are called simplexes and not pyramids, I still have to figure that out).

On the CERN stuff I can tell you I used a picture of CERN to explain a bit about super conductivity because at CERN they also run an experiment where they try to find magnetic monopoles…

It is now year number four where I constantly keep on telling that electrons are the long sought magnetic monopoles; electrons carry electrical charge, that is known in the scientific community, but they also carry two different magnetic charges.

As such electrons are much more like quarks that also carry electrical charge but also color charge, the fact that the electron carries only two magnetic  charges is the main explanation as why we only have electron pairs. If the official version of physics were a true description of reality, so electrons are truly magnetic dipoles, why only have electron pairs???

Super conductivity is caused by electron pairs, not by free electrons. A material can only become in a super conductivity state if first the so called Cooper electron pairs are formed.
If the official version is true and electrons are magnetic dipoles, in that case any applied magnetic field would have zero point zero influence on the formation of electron pairs.

That is crystal clear because all forces on the north pole of the electron would be canceled out by the forces on the south pole of the electron. Yet in practice, as not only CERN but the entire community of super conductivity research is telling us: In the presence of a too high magnetic field the material just not enters the state of super conductivity…

So you can cool your ass off, if magnetic fields are too high electron pair formation just does not set in. The next picture from CERN shows a bit of state space as where in super conductivity materials should get their super conductivity properties:

18Feb2017_critical_magnetic_field_and_super_conductivityLet me not put salt on every snail observed but the title should be ‘State space diagram of superconductors’ because ‘phase’ is related to 2D complex number stuff.

At last I would like to remark that although CERN is on a very expensive hunt for magnetic monopoles, they failed all of the time.
Now do CERN people talk about electrons being carriers of magnetic charge?
Come on; CERN people will fail all of the time.

On the other website we have reason number 45 as why electrons cannot be magnetic dipoles, as you have guessed it is about the above picture from CERN:

Reason 45: The critical magnetic threshold in super conductivity
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#15Feb2017

__________

After having said my views on fantastic organizations like CERN, why not do some elementary math like for example the 3D theorem of Pythagoras?

As memory serves the math ideas in the picture below were found centuries ago, but I have to say I do not know much historical development of the math ideas involved.

But I do know that I found a very simple proof to the most general theorem of Pythagoras and that is what will be in the next post and may one more extra post to finish it off.

Here is the teaser picture for the next post (or may be two posts on this subject of generalizing the theorem of Pythagoras):

18Feb2017_intro_generalized_Pythagoras_theorem

The good thing about the last line of calculations is:

We need the millennia old 2D theorem of Pythagoras in order to prove the century old 3D theorem of Pythagoras…

I don’t know how far I will push this detail but if I find it back in my book closet may be I will write a tiny bit more. End of this post, see you around and try to get a nice life in case you never understood those electrons in the first place.

Till updates.

Debunking the most successful relation between theory and experiment in physics using electron magnetic charge.

May be it is best that you first take a look at the video given below, think about it for some time and, hopefully, arrive at the conclusion that at Fermilabs they have a lot of shallow thinkers.

With QED the physics people use that as an abbreviation for quantum electro dynamics, inside theories like that they sometimes use a so called ‘coupling constant’. The physics professors think they have found a perfect relation between the theoretical value of this coupling constant and experimental evidence.

This coupling constant relates the magnetic properties of the electron to the so called Bohr magneton. The Bohr magneton is related to the mass of the electron pair and as such is related to a magnetic dipole.

Anyway the video showing a guy named Dr. Don Lincoln has all the hallmarks for ‘shallow and easy thinking’ that is so pregnant through all of physics; just do some bla bla bla before an audience and actually come away with it. Here it is:

QED: Experimental evidence.

Now from the get go of the discovery of electron spin it was known that the large magnetic properties of the electron could not be explained via a spinning electron; even if all electrical charge was concentrated on the equator of the electron it should spin with a large multiple of the speed of light.

An important conclusion we can draw from that is: the actual spinning of an electron is more or less insignificant.

Now the measurement of the magnetic dipole moment of the electron was not done via a measurement of the magnetic dipole moment of an electron but only via year on year making many measurements of the frequency that those electrons did send out as electro-magnetic radiation.

It is well known that electrons send em-radiation when they get accelerated, this is a very general principle on all levels of the em-spectrum. Electrons always behave the same whatever frequency they oscillate.

So if electron magnetic properties cannot be explained via the actual rotation of an electron, why do the shallow thinkers as Don Lincoln always portrait it this way? Here is what the idiots show the public:

13-02-2017_Dr_Don_Lincoln_idiot_explanation

Yes they compare it to a gyroscope…

Now congratulations with your stupidity my dear Fermilab Dr. Don Loncoln; usually electrons do not spin faster than the speed of light.

If you come up with explanations like this, it is very clear you do not understand how electro-magnetic radiation is crafted in the first place. It has to do with both an electrical charge and a magnetic charge getting accelerated. The important thing to notice is the localization of both charges on the electron itself…

All that talk of electrons being magnetic dipoles is nonsense.

__________

From the viewpoint of psychology, the idea that physics professors have about the accuracy of the magnetic dipole moment of the electron is of course a big big hinder for accepting that electrons carry two possible magnetic charges: a north charge and a south charge.

Here is the source of their smirks, laughs and arrogant behavior:

13-02-2017_just_a_coupling_constantBut this measurement is only based on measuring frequencies of em-radiation.

Yet electrical fields can also accelerate electrons and oscillating electrical fields can also produce em-radiation from the electrons…

For the time being lets leave it with that; imbeciles that bring up stuff spinning above the speed of light while waiving away reality are classified as shallow or pseudo scientists.

And at Fermilabs, USA based, they have plenty of those people.
Till updates.

Simple statistics on the video of the oversight of the Stern-Gerlach experiment + Dwave qubits (quantum bits) explained.

Exactly one month ago I posted the update about the historical oversight on the Stern-Gerlach experiment from 1921. This experiment is just so confusing; how can a magnetic field split a beam of electrons in two parts?
If electrons are really magnetic dipoles, this should hot happen.
But it happens, hence I jumped to the conclusion electrons are beside electric monopoles also magnetic monopoles. As such they carry two magnetic charges known as north and south.

The video with the historical oversight had 1222 views on 03 Jan 2017, that would amount for about 9 views a day. This is very little if you compare that, for example, if Miley Cyrus brings out another ass shaking video but hey this was about an experiment in physics done about one century ago.

Right now the video has 1702 views and that means it has about 19 to 20 views a day since 03 Jan.
So the daily number of views has doubled but it is only 10 views extra a day.

But ok ok, I still accept it would be a long long battle; if there are truly about 100 thousand physics professors really thinking that electrons are magnetic dipoles because some fancy math says it is so, stuff has turned into dogma.
When I found the magnetic charge solution for myself I strongly remember asking myself:
BUT ELECTRONS ARE MAGNETIC DIPOLES, IS THAT RIGHT???

And there are some problems with the official version: The only thing that says electrons are magnetic dipoles is the Gauss law for magnetism. Tiny problem: electrons were discovered much time later…

Anyway I still advertise viewing the Stern-Gerlach experiment oversight because it is a treasure trove of not only historical facts but it also rings home that people like Albert Einstein, Niels Bohr, Erwin Schrödinger, Wolfgang Pauli etc etc just had NO CLUE WHATSOEVER on the fundamental importance of the outcome of the Stern-Gerlach experiment.

So once more the video:

The Stern-Gerlach Experiment And The Discovery Of Electron Spin – Sandip Pakvasa [2016]

The great thing about electrons having two magnetic charges it that you understand so much stuff from nature on a far deeper level. That is very rewarding and you can compare that for example to the discovery of the nucleus of the atom.

Now the title of this post says ‘Dwave qubits explained’ but if I would do that I would have to keep up a long story as why the formation electron pairs are needed for super conductivity (electron pairs are a north and a south charge together more or less magnetically neutral ensuring the super conductivity) while unpaired electrons are not neutral in the magnetic sense.

And so on and so on.

No, let me only post a picture from Nature, the famous Nature scientific outlet is somewhere I can never publish because they have so called ‘peer review’. Of course ‘peer review’ will never allow for crazy ideas that say electrons carry two different magnetic charges…

That is why university people and me will never be friends; we just do not speak the same language.

Here is the picture from the Nature outlet:

02-02-2017_Dwave_qubit

Picture source:
Figure 1: Superconducting flux qubit.
http://www.nature.com/nature/journal/v473/n7346/fig_tab/nature10012_F1.html

Dwave qubits are macroscopic objects, they are not small quantum systems but as you see in the picture above the folks from Dwave computer have succeeded into generating two electrical currents that go in opposite directions.

Ok ok, let me share just one simple to understand detail:

The two currents are unpaired electrons, although Dwave computers use super conductivity unpaired electrons do not follow the stream of super conductivity…

So after initialization, the two currents will die out.
I wonder if the people at Dwave are aware of this line of reasoning.

Let’s leave it with that, have a nice life or try to get one & till updates.

How permanent magnets work, the official version against what I think of it.

When you for the first time encounter magnets (when you were a child or so) it is clear they are magical things. When you as a reader are still young and later in life you get kids too, always make sure there are a few magnets in their collection of toys. (And also ensure there is enough simple plain version of Lego, later in file this is good for their geometrical insights.)

Let me first summarize how permanent magnets are made:

  1. Pieces of metal are heated until they get above the so called Curie temperature.
  2. The pieces of metal are fixated in place and a strong magnetic field is applied, very slowly the pieces of metal are cooled down.
  3. Hammering the metal while it cools down seems to help a lot.
  4. When cooled down the magnets are ready to use but they often get a sanding and a paint job to make them look nice and add a layer that prevents rust.

What is the Curie temperature?
Answer: That is the temperature when you heat a permanent magnet above that temperature it will loosed all of it’s (permanent) magnetism.

The existence of such a Curie temperature is also in favor of my version of how permanent magnets work but let me build it up slow and steadily and not bring you into confusion.

Now the professional professors know that it are the unpaired electrons that are the root cause of permanent magnetism. Here is a picture of how those professionals think it is, all magnetic metals have so called domains inside their crystalline structure and this is more or less schematic how it is supposed to work:

04jan2017_official_explanationIn the upper part of the picture you see that even after a full century a lot of people still think the electrons are actually spinning, but why should electrons spin frantically with a precise speed anyway? Also in the above picture you see the habit of using vectors to represent magnetic dipole moment, that is ok only not on the level of individual electrons.

It is good that professional physics people pointed out the unpaired electrons, but they still think that those electrons themselves are magnetic dipoles. Here they have a giant problem they never talk about: if an unpaired electron is a magnetic dipole, it is obvious that an electron pair is also a magnetic dipole. But why do electron pairs never contribute to macroscopic magnetism?

__________

Ok, now we use my version of reality and in my version of reality electrons always carry a negative electric charge and each electron carries also one of the two magnetic charges there are: north charge or south charge.

This explains electron pair formation in the first place but this post is not about electron pair formation instead we try to understand all those metals that can have permanent magnetism.

What all those metals that can be permanently magnetized have in common is very easy to understand: They have lots of unpaired electrons below the outer electron shells.

The best picture I could find was this (the electron pair in the most outward shell is not realistic of course, thar violates the so called ‘Aufbou prinzip’ but it was the best picture I could find):

03jan2017_iron_electron_shell_configurationYou see the unpaired electrons inside the iron atom.

Now you understand why there is such a thing as Curie temperature; if heated enough the unpaired electrons will be removed from the iron atom.

And if electrons carry magnetic charge, you understand as when making permanent magnets while cooling them slowly down inside a strong applied outside magnetic field ensures the electrons will land there where it like to be.

And this, my dear reader, is an explanation of how permanent magnets work without the need for electrons that are glued into place. Electrons like to move around in their orbitals so once more if they were magnetic dipoles they could not hold on to a permanent state of magnetism…

__________

And so on and so on, my easy to understand insight the magnetism of the electron is much better compared to one century of physics professors.

Let’s leave it with that, thanks for your attention.

More on electrons, the discovery of electron spin and how permanent magnets work.

Back in the year 1921, almost one hundred years ago, Herr Stern and Herr Gerlach conducted a very intriguing experiment. They heated up silver until it was a gas and they did send the beam of silver ions through an inhomogeneous magnetic field.
They observed the beam splitting into two streams of silver ions, they thought they had found ‘spatial quantization’…

Here is a picture of a schematic set up of the Stern Gerlach expeirment:

03jan2017_exp-stern-gerlach-1The upper side of the magnetic field is stronger compared to the strength of the bottom field, Stern and Gerlach expected the beam to split in the direction of the gradient of the magnetic field.

At present day we know that a beam of electrons also gets split, when three years ago I did read the results from this experiment I was buffled, baffled and bewildered: it was ok by me that a part of the beam went up towards the strongest parts of the magnetic field.

But why was a part of the beam attracted to the weaker parts of the magnetic field?????
This makes no sense, after all in those years I nicely believed electrons were magnetic dipoles because everybody said so. Let me demonstrate in a gedanken experiment why this behavior of the electrons is very strange if electrons are magnetic dipoles:

Begin Gedanken Experiment:

Let an electron cannon send a beam of electrons into an inhomogeneous magnetic field, if electrons are indeed magnetic dipoles in that case you can view them as little vectors. These vectors can point anywhere, together all vectors from a sphere.

Only one of the vectors of that sphere is in perfect anti-alignment with the magnetic field. If we think of the vectors as pointing from the south to the north pole, only the vector that points perfectly south will have perfect anti-alignment.

All vectors that are not perfectly aligned will be pulled into alignment, so if electrons are magnetic dipoles it is expected that almost all electrons will go to the strongest part of the magnetic field.

End Gedanken Experiment.

Yet in practice about 50% of the electrons go up and the other 50% go down…

And I was just puzzled so much; how can the weaker parts of the magnetic field attract magnetic dipoles??? After one or two days I ran the experiment again in my head but at some point I don’t know why I thought ‘Let’s try a magnetic monopole’.

To my amazement a magnetic monopole did give the results as we know them from the Stern Gerlach experiment. And I just thought by myself ‘Hey hey Reinko, not so fast because electrons are not magnetic monopoles but magnetic dipoles. It is even in the Maxwell equations Reinko so think before you speak’.

But a day later I was walking around in the local park thinking about chemical bonds; if electrons were magnetic monopoles that would also explain why we only have electron pairs in chemistry.

Anyway now after three years I have about 40 reasons as why electrons cannot be magnetic dipoles but on the universities where about 100 thousand ‘professional’ physics professors are deployed there is zero reaction to my insights.
On the contrary; they avoid talking about me like I am having the pest…

__________

Back to the year 1927 at the Solvay Conference people like Niels Bohr and Wolfgang Pauli argued that for free electrons it would make no sense to do some kind of Stern Gerlach experiment.
Here is a screen shot of a video I will link below to:

03jan2017_stern_gerlach_for_free_electronsSo five years after the experiment and four years after publication all those guys like the Einstein / Bohr / Pauli / Schrödinger / Dirac / Heisenberg / Bose complex, none of those men understood the basic nature of the electron:

An electron is a localization of electrical charge and one of the two magnetic charges.

As such there are two types of electrons: a magnetic monopole north and a south variant.
Also known as ‘spin up’ or ‘spin down’.

The next documentary is about one hour long, if you know nothing about electron spin it is a bit much to swallow in one time. But for me it was a true treasure trove, the guy that gives the talk is eighty years old and has given lectures in quantum physics for decades and decades:

The Stern-Gerlach Experiment And The Discovery Of Electron Spin – Sandip Pakvasa [2016]

Ok I see this post is getting a bit too long so a detailed explanation upon how permanent magnets work is skipped to some future date. In the meantime we have only scratched the surface when it comes to the ‘official version of electron spin’ versus my little set of 40 reasons as why electrons cannot be magnetic dipoles. You can find it in my page on magnetics:

A primer on the electrons that are the long sought magnetic monopoles.
Author: Reinko Venema.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff.htm#27Oct2015

It is now 23.27 hours and I have more stuff to do in my life so till updates & how permanent magnets work will be dealt with in a new post. (By the way for me it is completely weird and strange that the professional physics people still do not understand permanent magnets. They think the electrons are glued in place…)

Don’t forget to roast the ‘professional’ physics professors with their crazy ideas about electrons.

See yah around.

Happy new year! + I hope you drank enough beer during the feast while I only post a picture showing math superiority before cracking down on physics professors in the next post…

Once more a happy new year! Luckily the number 2017 is a prime number but let us not talk on 2017-dimensional complex number systems but keep it simple:

In the next post I will explain to you how permanent magnets work in detail, you might think ‘wow man permanent magnets are studied for centuries and longer’ but my point is they had it wrong on important details.

But if you go to a high paid physics professor and you say ‘wow man your ideas upon permanents magnets are based upon electrons being the source of magnetic dipole behavior’, most of the time you get a cold shoulder.

These imbeciles, those professional physics professors they cannot even explain permanent magnets and they only do ‘bla bla bla the Gauss law of magnetism says that more bla bla is the only way forward’.

That kind of behavior is very interesting, why make nonsense to be your basic line of reasoning?

________

I have nothing more to say; in the next post I will explain how permanent magnets work, how they get permanent magnetism and how they can loose it.

For the time being because I am well aware of how arrogant all these physics professors are, I simple post and infinite product that shows how my own brain handles the stuff that flows in:

03jan2017_math_superiority_exposed

By the way, I crafted the outcome of this limit to 1/2 because when we talk electrons in the next post they are known as spin half particles. Beside this it is estimated that all professional physics people will react strongly dismissive of the simple fact that electrons cannot be magnetic dipoles…

Come on, this is the year 2017 and there will be no mercy for the physics professors.
Let’s leave it with that.

 

A more or less perfect visualization of the Riemann zeta function observed.

It has been a long time since my last update and that is caused by some stupid medical condition I still have and in my native language it is known as a ‘peesschede ontsteking’.
In practice this means I must do all typing on my computer keyboard with my left hand because in the evening I still cannot use my right hand.

Let me spare you the details but the long durance of the pain could even date back to the time when I was a dumb 15 year old with a broken wrist not seeking medical help.

So for the time being no long updates on perfect new hybrid number systems, it takes too much pain to write those long math stories down. So I retreat and just post a link to what is a very good Youtube video on the Riemann zeta function and it’s continuation into it’s analytic continuation.

Here is the video from the 3Blue1Browne guy:

Visualizing the Riemann zeta function and it’s analytic continuation

Nice vid isn’t it?

Last year on 26 March 2015 I wrote an update on where to find the zero’s of the Riemann zeta function in the 3D complex number system. I still consider this being an important publication although that human garbage known as the ‘professional math professors‘ said nothing all these months, I still think it is worth the trouble and try to post a new link to it:

From 26 March 2015: Zeta on the critical strip (3D version only).
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#26March2015

May be it is best to leave this update with that;

Zero point zero point zero point zero reaction of so called ‘professional math professors’ upon finding the zero’s of the Riemann zeta function in dimensions above 2.

Once an overpaid imbecile, always an overpaid imbecile.
Let’s leave it with that.

__________

Update from 19 Dec: I did not include yesterday a more easy to understand analytic continuation that I wrote myself this year; it is the analytic continuation of the geometric series and as such I am debunking the stuff some of the children of a lesser God seem to think:

1 + 2 + 4 + 8 + 16 + ….. = -1.

Nottingham professors from math and physics seem to think that

1 + 2 + 3 + 4 + 5 + ….. = -1/12.

This is also nonsense and there are many ways to prove this is not the case but inside theoretical physics this is actually used: that is the process of renormalization. Every time professional physics professors encounter an infinity in their calculations it is not that they say ‘Something must be wrong with our theory’. No if they encounter stuff like 1 + 2 + 3 + 4 + etc, they replace it by -1/12.

It works pretty well in order to get rid of those singularities they say.

Anyway here is the link to what I had to say on that subject:

From 15 April 2016: Debunking the Euler evaluation of zeta at minus one.
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff04.htm#15April2016

You can find the analytic continuation of the geometric series in the fifth picture.

Let me close this extra update with the Youtube video from those weird weird Nottingham professors that started it all:

ASTOUNDING: 1 + 2 + 3 + 4 + … = -1/12

And indeed if it were true it would be very very astounding.
What for me is TRULY ASTOUNDING is that the very professors you see doing their show is that they think the harmonic series is divergent. The harmonic series is also the zeta function evaluated at 1:

1 + 1/2 + 1/3 + 1/4 + … = infinity.

So the Nottingham professors think that the harmonic series is divergent (that is correct of course) while the sum of all integers is convergent to be -1/12.

Welcome to the world of 21-th century science. Till updates.

The second hybrid: a 4D mix of the complex and the circular plane.

Update from 30 Nov: My health problems persist, my right wrist is still swollen and hot all the time. So after one week it is clear I need to see a doctor…
Anyway I can type text with one hand so here we go:

In this update I talk about the circular plane because I want to use the same language in 2D as in 3D or higher, yet for those living in the mud this stuff is mostly named split complex numbers. There are more names going round: for those people that do not understand what the conjugate of a number is and how to find those, they name it hyperbolic numbers.

This update is about finding the log of the first and only imaginary unit of the circular (also named split or hyperbolic) numbers. This mathematical goal can only be achieved by replacing the real scalars in the circular plane by numbers from the complex plane.
That replacement stuff is known in my household as the Sledgehammer Theorem, this theorem says you can more or less always replace scalars by higher dimensional numbers. But this has to make some sense; for example you have a number from the complex plane like z = a + bi, now if you replace the two real numbers a and b with general numbers from the complex plane you did not gain much.  As a matter of fact you gained nothing at all because you are still inside the complex plane and other people will only laugh at you:

That is just like the way Donald Trump will expand the US economy

For myself speaking I do not understand that a math result as in this post is more or less unknown to the professional math community. How can it be that Euler has all that stuff of finding the God formula while century in century out the math professors make no progress at all?

Every day I am puzzled by this because I am not ultra smart or so, it is only my emotional system is a bit different: I never get scared when hunting down some good math

__________

Anyway from the mathematical point of view I am proud of this ten picture long update: it is as close as possible to the calculation that unearthed the very first exponential circle. That was the discovery that in the complex plane the log of i is given by i pi over 2.

24nov2016_4d_hybrid_numbers01

24nov2016_4d_hybrid_numbers02

24nov2016_4d_hybrid_numbers03

24nov2016_4d_hybrid_numbers04

24nov2016_4d_hybrid_numbers05

24nov2016_4d_hybrid_numbers06

24nov2016_4d_hybrid_numbers07

24nov2016_4d_hybrid_numbers08

24nov2016_4d_hybrid_numbers09

24nov2016_4d_hybrid_numbers10

Need a cold shower by now?

Want to restore your faith in the old masters with their superior use of math?

Try the next video from the Youtube channel, it only uses insights from the circular plane and he runs fast and far: The Lorentz boost inside special relativity:

Split complex numbers and the Lorentz boost.

Let’s leave this update with that, have a good life or try to get one.

Update from 04 Dec 2016: I would like to post the number one wiki when you do an internet search of split complex numbers. (There are all kinds of names going round, but the circular plane is also the split complex number plane for sure.)
As usual all that stuff has the conjugate wrong, but in the next wiki you see more or less the combined wisdom of the math community when it comes to expanding the complex plane to higher dimensions. (It is a dry desert, human brains are not that fit for doing math):

Split-complex number.
https://en.wikipedia.org/wiki/Split-complex_number

Once more: those people have got it wrong about how to find the conjugate and as such you can also find lots of pdf files about circular (or split-complex) numbers that say they are hyperbolic numbers.
The common fault is that they use the conjugate just as if you conjugate an ordinary complex number from the complex plane.

I remember I did that too for a couple of years until it dawned on me that we are only looking at the projections of the determinant; it has nothing to do with lengths, even in the complex plane it is not the norm of the complex number but it’s matrix representation and the determinant.

All stuff you find on this on the internet is nothing but shallow thinking.

End of this update, see yah in the next post.

The pull back map applied to the coordinate functions of the 3D exponential circle.

In this post, number 50 by the way, I am trying to use as elementary math as possible in order to use the pull back map from the 3D circular number system to the complex plane.

With this the pull back map and the 3D circular number system are treated so basic that with only high school math and a crash course in the complex plane students can understand what I am doing.

So for reading this post number 50, what do you need in mathematical knowledge?
1) Understand how to write cos(a + b) and sin(a + b) in terms of cos a and sin b.
2) Understanding of e to the power it in terms of cos t and isin t.
3) Understanding of the roots of unity as found inside the complex plane, in particular being able to calculate all three roots of unity when we take the third root of the number 1.

That’s all, so basically all first year students in math, physics and chemistry could understand this post at the end of their first year on a local university.

__________

The words above are only one reason to write this post; to be honest for me it took a long time to write down for the first time the coordinate functions for the 3D exponential circle.

And I never did give much solid proof for that these coordinate functions have indeed the properties as described. It all more or less came out of the sleeve as some kind of monkey trick.

Therefore for myself speaking, this post giving the results in it also serves as a proof that indeed there is only one class of coordinate functions that do the job. They can only differ in the period in time they need to go around, if you leave that out the triple of coordinate functions becomes unique.

All in all the goals of this post number 50 are:

1) To do the pull back of an exponential circle as simple as possible while
2) In doing so give some more proof that was skipped years ago.

__________

This update is seven pictures long, each 550 x 775 pixels in size.
Hit the road Jack:

03nov2016_pull_back_map01

03nov2016_pull_back_map02

03nov2016_pull_back_map03

03nov2016_pull_back_map04

03nov2016_pull_back_map05

03nov2016_pull_back_map06

03nov2016_pull_back_map07

 

I think I have nothing more to say, so see you around my dear reader in post number 51.

Till updates.