V9

[jehovajah]

http://m.youtube.com

[jehovajah]

http://www.gaalop.de/wp-content/uploads/134-1061-Zamora.pdf
Having identified this as a candidate geometric algebra for " bubbles" , it occurs to me that particular solutions or views may topologically fit a toroidal with one, two or three holes.

In any case this is a 9 dimensional algebra which I am still constructing......slowly!

[jehovajah]

The history of ring and group theory

<a href="http://www.youtube.com/v/VSB8jisn9xI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/VSB8jisn9xI&rel=1&fs=1&hd=1</a>

[jehovajah]

Vortex Based Maths and it's influence on wave Mechanics etc.

<a href="http://www.youtube.com/v/sK&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/sK&rel=1&fs=1&hd=1</a>

<a href="http://www.youtube.com/v/lDomfhKBqIc&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/lDomfhKBqIc&rel=1&fs=1&hd=1</a>

I have left it in link form to relieve pressure on older machines .

[jehovajah]

One of the beautiful things about Normans range of interests is his frankness and no BS approach. Consequently things which I only suspected as sn undergraduate Maths student , oh 42 years ago he is explicitly stating as the case. That is there is a big cover up of certain fundamental difficulties with mathematics. At the same time the Hegelian resolutions are also available!

One thing I would point to as a reason why Norman has difficulties which he has to resolve is precisely because mathematicians hate too much Philoophy! Thus they do not know that Hegel even exists, generally speaking! Most still use Aristotelian logic without realising there is another way!

<a href="http://www.youtube.com/v/Y3&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Y3&rel=1&fs=1&hd=1</a>
<a href="http://www.youtube.com/v/Y3-wqjV6z5E&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Y3-wqjV6z5E&rel=1&fs=1&hd=1</a>

The relevant section in this masterly discussion is how modulo arithmetics underpin our number field concepts. Thus Vortex Base Mathematics is not as it appears to some as insignificant mumblimgs( sorry Marko but you do ramble) it is about the fundamental dynamics if our decimal system, and the topological spaciometric representation of the Arithmoi that underpin it.

Why use a sugar cube when you can use a doughnut, right?,  

[hermann]

May be my little program is helpful for creating the tables in HTML or LaTex.
http://www.wackerart.de/mathematik/geometric_algebra.html#rainy_days

Hermann

[jehovajah]

Thanks for the contribution, Hermann .

I will look through the programming code to see how to adapt it.

It will be good to be able to do this stage automatically.

The next stage of combining products would then be more accessible.

Hermanns products and combinations are only one possibility. However, because the combinations are derived from the products of geometers, astronomers and Astrologers of his time his choices have immediate geometrical/ spaciometric applications.

However his thought process is a unique pattern worth learning. At the level of creating new combinations and new interpretations of products one is on ones own. Musean " numbers" are a case in point. Charles Muse has done the tables, but few of us even see any relevance to say physical phenomena at this stage.

Hermann on the other hand provides a course or doctrine into this kind of thought pattern and how to apply it. This is the main reason why I am not rushing to complete the tables,which are repetitively boring  and have a prospect of not being applicable to any current fractal generator.

The Newtonian Triples I was able to apply to a quaternion reference framed generator, but the twist in the presented image is due to the orientation  of the axes relative to each other. In the quaternion block i,j,k are assigned the orthogonal triple, but in the Newtonian triples the axes are not orthogonal. Hermanns line segment method gives us the freedom to create 6 axial directions where the 3 axes are equally spaced on the spherical surface.

However I knew the 6 roots of unity are defined in a circle, not on a sphere, so I was not able to understand let alone verify that the map from the  roots of unity labels to the  3 dimensional space axes labels was going to give a "true" representation, and whether I could defeat the embedded quaternion Algebra by imposing on the embedded programming.

When I get to Hermanns Rechtsystem I hope this aspect will be clearer to me. But I already intuit that the 3 dimensional set up in the programming space is not what I thought it was, an expression of reality, but rather it is a system of evaluation and a commonality enabling us to agree on any axial direction in space.

Hence by freeing the orthogonal system from any product association, we can establish any axis direction through it, and then define the axis products at that level.

All very good untill you try to look "backwards " at how these calculations evaluate in the orthogonal system. Doing that begs the question: what are the products of the orthogonal axis  elements!

That is the bit that requires some understanding. Do we as I suspect ignore that question, or is there some root of unity model that not only produces a rotation result at that level, but also maintains the relationship at the desired level?

My suspicion is no.

To design the Newtonin triples I used a general group product table with the required modulus. There were several abelian choices, but only one seemed to match the quaternion product rules. I then abandoned the quaternion product rules and used the group product structure, assigning a fixed label to each product to ensure I had a closed set that matched the orthogonal labels.

I can write about it now, but then I could not grasp what I was doing, I just followed my intuition.

It is important to me that Hermann constructs the. Product rules from his line segment tables. This means that the roots of unity represent a construction process not some mythical " numbers" out there, but rather a thought pattern process in me, subjectively.

Applying this to the definition of spaciometric orientations is the unusual part. Until Hermanns work I was left with the definite impression that that was " cheating!"

There are a lot of fundamental misconceptions I had to let go to understand where Hermann was coming from and how muddled our thought patterns actually were/ are!

[jehovajah]

Some seemingly outrageous claims made by Marko Rodin for the Rodin coil during his Vortex based Mathematics presentation now make sense,

<a href="http://www.youtube.com/v/4gHhAA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/4gHhAA&rel=1&fs=1&hd=1</a>

<a href="http://www.youtube.com/v/4gHhAA-9o_8&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/4gHhAA-9o_8&rel=1&fs=1&hd=1</a>

[jehovajah]

The spatial distribution of modulo 9 is demonstrated in this video

<a href="http://www.youtube.com/v/64gIN&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/64gIN&rel=1&fs=1&hd=1</a>

<a href="http://www.youtube.com/v/64gIN_mPOrw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/64gIN_mPOrw&rel=1&fs=1&hd=1</a>

The diagonal Spaciometry actually means the whole space can be rolled up onto a torus with the addition parallelograms spiralling round the form.

Using just the 9 digits we can form this pattern within the decimal system. This is therefore a modulo 9 pattern Within a modulo 10 system. The result is the modulo9 pattern spiral within the modulo 10 system.

[jehovajah]

I am glad I waited for the results of researching Hermann Grassmanns thoughts because my surmising was off target. It was close but now with a richer everyway standing of Grassmanns Method i understand these Caylry-Grassmann rank arrays as elements for product designs.

These product designs based on Normans Grouo theoretic explanation, mix the additive and multiplicative knittings in a way that isolates both systems from each other. To use them I now have to decide on subjugation order, and then use that to decide on an axial representation.

All of this I was doing intuitively bumbling along, but now I can use Grassmann speak to describe it more clearly!

[jehovajah]

The cyclus group 1,2,3,4,5,6,7,8,9 is the group that controls rotation for a 9 line segment system. The way the permutations work I will now be able to work though Grassmann Style, but it is already clear that Randy Powlells Abha vortex based Mathematics is a credible version of this system, and the uses to which it has been put are a creditable model well capable of modelling Magneto Thermo sono electro complex behaviours!

[flexiverse]

Of course, being a parallel world time traveller,  it's basic knowledge to us that the universe is indeed represented by 196883-dimensional field, the monster group.

It's no coincidence that modular functions like j-invariant are related to the monster.

It will be a long time yet, but soon people will think beyond the number line and think in terms of fields and multi-dimensions.
Without this it's impossible to understand how anti gravity and multi dimensional time travel is achieved.
The universe is a multi dimensional fractal you see.

[jehovajah]

I found this channel on Comninatirial theory, so it has encouraged me to take this course and to translate Justus Grassmanns Combinatorual Doctrine in this thread.

The V9 group or ring I will analyse following Hermanns example in "The Quaternions place in the Doctrine of Extending Magnitude "thread. This means that I start with product design , and then establish the general pattern of an extending magnitude that fulfills that product. This method , using the associative design step ensures closure , and it is closure that establishes the " group" or " ring" members or elements.

http://youtu.be/pCJNjW8kMIg

<a href="http://www.youtube.com/v/pCJNjW8kMIg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/pCJNjW8kMIg&rel=1&fs=1&hd=1</a>

[jehovajah]

Thanks for contributing to the thread flexiverse.

I hope you will elaborate on your point re the humongous group and other points . With regard to dimensions I have written a lot on the uses and misuses of that concept, especially the science fiction interpretation.

I have a view on the dimensionality of space, but it was only when I stumbled onto Hermann Grassmann that I found out that I had been living in Wonderland like Alice. The rabbit hole goes deeper!

[jehovajah]

As I begin the process of implementing the V9 group Grassmann style, I have to admit a certain sense of satisfaction and sense of growing understanding of what I am asking Quasz to do, and how to ask it.

The Cyclus group, I realise is a for next loop equivalent!

In modern computing we have come a long way with regard to the for next loop, and it is now a much more general and flexible notion than the cyclus group can ever be!  Using the for next loop in its various implementations( while, until , if ..) we can perform many more product design actions than Hermnn dreamt of!

The quaternion output results can be directly implemented by the cyclus group constraints or likenings or by the algebraic constraints Hamilton set out for label switching. The results will be the same because the behaviours are homologous.

Everything that Hermann has highlighted has had a direct bearing on or implementation in computer, syntax, coding and function or product construction.

The realisation dawns that the real field of Hermanns method is in computer programming , and not just for Maths programming either, but across the whole range of modern computer programming including Wolfram Alpha and Mathematica.