Category Archives: 3D complex numbers

And now we are with three…

In Oct 1990 (estimated) I found the 3D complex numbers, a few years back I discovered that a guy named Dennis Morris has found them too. Dennis even wrote a book about it, this book was published twice and I was able to get a hand on the second publication.

For normal humans the book from Dennis is a good starter, for me it has the depth of a bird bath.

We do not complain, today on the preprint archive I found the next pdf file:

On a novel 3D hypercomplex number system
http://arxiv.org/pdf/1509.01459v1.pdf

And this work has not the depth of a bird bath, it is much more the depth of a human bathtub.
There ar some dumb typo’s, for example table 1 contains a very stupid error so that has to be corrected.

The writer of the preprint article goes under the name of Shlomo Jacobi and since his residence was Israel we might jump to the conclusion he was a Jew. Let religion be no problem because after all the Muslims were once far ahead of the Western powers but because one of their religious leaders declared math as being from the devil, Muslims find themselves at the receiving end of military powers for about one thousand years…

Now back to our Jewish pdf file: Table 1 should be corrected and I, Reinko Venema, I give them a big applause because if you scroll down to page 39 you observe they have found the 3D exponential circle too!

Well I have found all exponential curves in all possible dimensions, so I am very pleased to invite the Jewish mathematical community upon further investigations into this math detail.

End of this update, till updates.

Correction on the 08 Dec 2015 post; there are two typo’s…

It is not a big deal because every person who understands a bit about how matrix representations work sees instantly these must be two typo’s.

But recently about once a week I am scanning how this new website is doing in search engines like Google. And I am very satisfied, every post can now pop up as a separate search result and for example on pictures to my surprise the next picture popped up as pic number six if you search for ‘3d complex numbers’.
This is the version with the two typo’s in it:

0002=02Dec2015=teaser_6D_complex_numbersAnd here is the corrected version:

0009=02Dec2015=teaser_6D_complex_numbers_corrected

So it is not a big deal but if a search result ends that high it is not unwise to correct it.
And to be honest, I know for years that you can craft let’s say 15 dimensional complex numbers from 3D and 5D complex numbers.
But to be honest, I had never done it until the December update from last year.

And I have learned some stuff too, only if you dive into those technical details like how those basis vectors are actually related you appreciate it so much more.
You know the nicest thing about higher dimensional complex numbers is very simple: I know for sure I am about one of the first humans to hang around in those spaces.
Beside the mathematical beauty the stuff has, it has also that old stuff like discovering new lands that is basically baked into the human genome.

Ok, enough of the phylosofical bla bla. Till updates.

Short stuff on the 3D Mandelbrot fractal.

About a year ago I decided to take about two years to make it to the 3D Mandelbrot set. So I tried to learn one of those modern programming languages like C++, I did build a new computer because on my old system C++ would not run. And so on and so on.

Decades ago I tried to learn a computer programing language known as Basic. When I found out how those kind of programming languages evaluted an integral, I almost had to vomit.
In those long lost years I already developed a fundamental dislike against programming.

Now I am 52 years of age and it is still the same; me writing computer code is not a happy thing to do. So I killed the project of being the first person on this planet to view the 3D Mandelbrot set using the 3D complex or circular multiplication…

I never made it beyond what is in C++ a ConsoleApllication; you get your output in an old fashioned DOS screen and no graphics at all. And how to embed this into a thing you can actually fly through, I have given up on that.

So I did not write much code, but the results had all you expected it should have: Strong sensitivity to initial conditions and so on and so on.

Well here is the kernel of the 3D Mandelbrot set for the circular multiplication.
Circular simply means we are using 3D circular numbers X = x + yj + zj^2 where j^3 = 1.

In this kernel we have to use so called ‘dummy variables’ because computers are so stupid you cannot tell them how to calculate the next round of variables This despite in the year 2016 most desktops have multiple cores, your programming language still uses the old von Neuman principles.

Here is the kernel with the dummy variables written as capital X, Y and Z while we only want to know how the x, y and z evolve over the iterations… :

int i = 1;
float x = 0f;
float y = 0f;
float z = 0f;
float X = 0f;
float Y = 0f;
float Z = 0f;

while ((i < 80)&(x*x + y*y + z*z < 1600))
{
i = i + 1;
X = x;
Y = y;
Z = z;
x = X * X + 2 * Y * Z + C0;
y = 2 * X * Y + Z * Z + C1;
z = Y * Y + 2 * X * Z + C2;
}

__________

0007=14Jan2016=Mandelbrot_in_3DOh oh my dear Mandelbrot baby, now I have thrown you into the river I will never be the first human to observe your intrinsic details. Let it be, let it be because for the rest of my life I can still hate that stupid computer code writing.

Till updates.

Some people will do everything wrong…

This is a very short update from a guy that likely goes under the name of Alen.
Now for years Alan has a very weird page hanging out there and he tries to describe the 3D complex numbers as they should be in his view…

Very very likely this is the approach Hmilton took for 12 to 15 years; it leads to all kinds of horrible difficulties, technical disasters and an end result useless to all people on the globe.

Now you must not jump to the conclusion that I hold this Alen person for some idiot. It is rumored that at any given time there are about 100 thousand professinal math workers out there and I do not mean high school teacher but people from the universities and stuff like that.

All these people cannot find higher dimensional complex number systems themselves either…
Ok, enough of the bla bla bla en prepare yourself to dive in the blurry and fuzzy mindset of how people thought 3D complex numbers must be (it is always with something squared that is minus one…):

N-DIMENSIONAL COMPLEX NUMBERS.
http://www.alenspage.net/ComplexNumbers.htm

Matrix representations and how to craft them.

Here it is still 01 jan 2016 so a happy new year.
In this update with five pictures with the standard size of 550 by 550 pixels we are going to look at how to craft matrix representations for higher dimensional complex numbers.

It is all rather basic stuff.

Here we go with post number 1 in the year 2016:

0006=01Jan2016=matrix_representation01

 

0006=01Jan2016=matrix_representation02

 

0006=01Jan2016=matrix_representation03

0006=01Jan2016=matrix_representation04

0006=01Jan2016=matrix_representation05

Yeah yeah, every point of this graph represents a 3D complex number that if you craft the matrix representation of it, it is a unitary matrix.

So the next time you see a physics professional professor writing stuff like SU(3) you instantly know you are dealing with some form of idiot life…

From Hamilton to my first try.

It seems that the irish math guy sir Hamilton has sought three dimensional complex numbers for a staggering long period of 15 years. After 15 years he found the four dimensional quaternions, that is nice stuff but for differentiation and integration the quaternions are about the biggest disaster there is around.

Therefore, beside linear transformations, there is no functional analysis on the quaternions.

In this post I originally wanted to give you some link to some stuff that was labeled under the name ‘Alan’s pages’ but I cannot find them back. Alan did everything wrong just like Hamilton did:
Basically they start with the comlex and try this to extend to 3D space; that stuff is guaranteed to fail hard.
Anyway, my first try was a surface named the Riemann surface of the logarithm although at the time I found it I did not know what Riemann surfaces were. This update is five pictures long each 550 by 550 pixels. Have fun reading it.

0005=20Dec2015=Hamilton_and_first_try01

0005=20Dec2015=Hamilton_and_first_try02

0005=20Dec2015=Hamilton_and_first_try03

0005=20Dec2015=Hamilton_and_first_try04 0005=20Dec2015=Hamilton_and_first_try05In another development I wrote reason number 12 as why electrons have to be magnetic monopoles, later this week I will hang this into the other website on the page on magnetic stuff. It is about the plasma they use in nuclear fusion reactors, the plasma is not stable and the physics professors do not understand why this is.
Well these torus shaped fusion reactors constantly accelerate the plasma particles until they get relativety effects, the basic concept of torus shaped reactors is basically what is wrong with it…

Anyway, till updates.

Cauchy-Riemann equations for the complex plane and for 3D complex numbers.

 

In itself the name of ‘Cauchy-Riemann equations’ is a terrible way of naming these equations because it says nothing about why they are important.

It would be better to name the stuff involved like ‘Chain rule equations for partial derivatives’ because if that would be the case you would understand why these equations are worth your precious time anyway…

This update is 8 pictures of size 550 by 550 pixels or about 5 pages of A4 size if crafted in the A4 size format.
Now why are CR equations important?
Very simple: You can find the derivative of a function just like on the real number system or in the complex plane. That is why CR equations are the basic food for understanding higher dimensional complex number systems…

Enough of the bla bla, here are the 8 pictures:

 

0004=12Dec2015=CR_equations01

 

0004=12Dec2015=CR_equations02

0004=12Dec2015=CR_equations03

0004=12Dec2015=CR_equations04

0004=12Dec2015=CR_equations05

0004=12Dec2015=CR_equations06

0004=12Dec2015=CR_equations07

0004=12Dec2015=CR_equations08

This stuff is basic stuff so it should be hanging out on this new website.

Till update my dear reader.

Eight pages on 6D numbers (containing 3D and 2D complex numbers).

The day before yesterday I finished an 8 page long update on six dimensional complex numbers from the viewpoint of inclusion and extension.

So basically I show that the complex plane and the 3D complex numbers are included in the 6D space while the other way around you can make a 6D space starting with the 2D and 3D complex spaces.
Link:
Inclusion and extension of complex spaces
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#06Dec2015

0002=02Dec2015=teaser_6D_complex_numbers

Well well, I still have a long learning curve to do on this new website because you can also make pictures shown at their real size…

Ok, now the previous website has gotten so much attention it would be time to post a bit more stuff in here. After all after just a few weeks and almost no content at all weirdly enough it already ranks relavtively high in the search engine stuff.

Another problem to be solved is that the comment section does not work and even the categories are disfunctional… Very likely this wordpress theme is developed by somebody that has no math insight at all. Why can I make categories while they do not work???
Beat’s me. Anyway, till updates.

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

When learning about higher dimensional complex numbers, one of the things you must first understand that the complex plane as known for centuries simply does not live in three dimensional space. If you look at it from a historical perspective people always tried to start with the two dimensional complex plane and tried to expand that into three dimensions.

It does not work that way; for example you can make 21-dimensional numbers by using 3-dimensional and 7-dimensional numbers. The dimension nicely breaks down via the prime number theorem (every natural number can be uniquely written as the factors of prime numbers).

Since 2 is not a divisor of 3, it is impossible to find the complex plane in a three dimensional world…

Now years ago I proved that for the complex multiplication the number i does not exist, yet now I started this new website why not give the same proof for the circular multiplication?

Click on the picture below to read that exiting proof… 😉
(On my browser I first have to click on the picture and after that enlarge it to get the readable stuff.)

0001=24Nov2015=i_lives_not_in_3D_proof

Picture size is 550 pixels wide by 1650 pixels high, I tried to write it in such a way that advanced high school folks could understand it.

Till updates.

Integral calculus done with matrix diagonalization.

Two days ago I posted a nice six page long update about two nasty integrals that are very hard to crack using standard math.
May be it is also possible via other methods I do not know…

04-10-2015=teaser_picture_new_integration_method

In the previous month I made it a math challenge to crack this nasty looking integral with the cosine stuff in it, the picture above is a so called teaser picture and it dates back to 4 Oct 2015 introducing the math challenge.

Next is a new teaser picture from two days back:

 

21-11-2015=teaser_for_integral_calculus_with_diagonalization

Now for my old eyes it is a bit hard to read but you see some thing with e to the power tau times t in it, this is a new exponential circle just like the unit circle in the complex plane.

Well for me all this php stuff that builds this website is still very new to me, but the good thing is it can make internet pages on the fly using a database. (For example if you select a category you get all posts and pages related to that category and I do not have to make a separate page for that myself. So this should act as a strong improvement…)

Anyway here is a link to the latest update:

Integral calculus done with matrix diagonalization
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#21Nov2015

Ok, later this week I will take on the boring task of writing a few pages on stuff like ‘introduction to higher complex numbers’ and stuff. Now for most people higher dimensional complex numbers are a show very far away from their daily lives or from their bed so to say.
But for centuries people tried to find them, yet these people they all failed.

Back in 1990 I found them and some American guy named Dennis Morris has found them too, yet the mathematical community completely does not react at all showing the incompetence of the average professional math employee…

If you give these people a pot of gold, they think it is a pot of stolen copper.

Let’s leave it with that my dear reader, till updates.