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Author Topic: The Theory of Stretchy Thingys  (Read 14242 times)
Description: Ausdehnungslehre 1844
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jehovajah
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« Reply #225 on: December 09, 2014, 11:07:56 AM »

 cheesy

Thanks hgjf2. I do not want to become famous but I see no reason why that would not be a good and interesting project!

I would very much like you to get the ball rolling , that is to make initial contacts if you wish. I am maxed out right now with everything else, and do not want to distract from my programme unduly.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #226 on: February 25, 2015, 01:33:58 PM »

Some relevant background on M鐽ius
http://youtu.be/-ECOwPNkoys
<a href="http://www.youtube.com/v/-ECOwPNkoys&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/-ECOwPNkoys&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #227 on: May 11, 2015, 10:06:14 AM »

Loving this !

http://m.youtube.com/76tNP31_CQk
<a href="http://www.youtube.com/v/76tNP31_CQk&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/76tNP31_CQk&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
hermann
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« Reply #228 on: October 31, 2016, 03:41:13 PM »

Hallo Jehovajah,

when I first read your thread "The Theory of Stretchy Things" I was wondering what are you talking about.
I started right at the beginning. When I read your first post I had the impression that some important backgroud information was missing.
The mirracle was revealed when I read kram's thread on geometric algebra.

So in your first post of this thread some background inforamtion like the following would be helpfull for the uninitiated reader would be help full:

Hermann Günter Graßmann(1809-1877)

Hermann Graßmann developed a new branch of mathematics in his book "Die Ausdehnungslehre" from 1844. In this book he introduced the outer or exterior product. In modern notation written as Bivector or a wedge b. Graßmann published his book in the same year as Hamilton anounced the discovery of the quaternions. But did not receive the same fame as Hamilton during his lifetime. Perhaps he was not taken seriously by his contempories because he was only a high school teacher.
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jehovajah
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« Reply #229 on: January 05, 2017, 11:38:05 AM »

@hermann
Happy new Year in 2017.
Thank you for your continued support and posts in these threads .
I loved the walk by the river in the "Fractal" snow!!.

It has been a tough year for me to be able to continue working on these threads, but it is my aim to do so, until I die or finish the translations .

It is not that Hermanns work has not been translated either, because Kannenberg has done a wonderful job. Rather it is that Hermanns and Justus were High school teachers! This material was meant to be taught to elementary children up to Gymnasium level!

So why was it said to be so obscure?

My translations are an attempt to get behind that obscurantism.

When I tried to translate my poor German seemed a hindrance, but gradually I realised it was essential to revealing where other translators had gone too far in interpreting.

I found and tried to keep the analogicall statements or metaphorical descriptions of the ideas both Justus and Hermanns used to be both graspable and elegant!

So the exterior product is the" outward stepping" product, where the line segments jostle past each other in an outward stepping direction!  Like 2 feet that step or spread the legs further and further apart at each step!

The interior product was in contrast the colliding together product, where the 2 line segments got closer and closer until they met or collided, one of the line segments being perpendicularly dropped onto the other.

This kind of wordy description is anathema to most " serious" mathematicians! That is why it was rejected as unsuited to its audience!
In 1862 Robert Grassmann redacted Hermanns work into the more acceptable mathematical jargon of his day, and rescued Hermanns from Obscurity.

It's a great story, and does require some background, which is why I am focussing on Justus booklet now in the V9 thread .

When I finished the work in this thread I knew I had to go on to do the Einleitung or induction, and then on to the first chapter. But I also felt that Hermanns was relying on his Fathers unique contribution to the understanding of Geometry and Mathematics. So I started to focus on that work, once I got my hands on it.

I am surprised by how much of its content is actually standard mathematical education at primary level, but with the Grassmann twist!
For example: who knew that crystallography could be enhanced by these ideas? Or who thought that combinatorics would be structured by these notions?
Certainly not  Justus until he struggled through his intuitions!

And it is that dedication to intuitive exploration and adjustment using the methigpdologies of the Pythagorean school as adduced from intense study of Euclids extant works, including The Stoikeia, that sparkles through the Ausdehnungslehre of 1844

In addition to Hus Fathers influence, Hegel was a major influence on the Young Hermanns, even if he rejected the usual way Hegel was taught in his time .

So this little book, the Ausdehnungslehre, that took up so much of his spare time is a real gold nugget for many reasons .
That fact is attested to by so many famous physicists and Mathematicians who owe their intuitive insights to the work of the Grassmanns.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
hermann
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« Reply #230 on: August 27, 2017, 08:10:27 AM »

I propose to communicate in a brief form some applications of Grassmann's theory which it seems unlikely that I shall find time to set forth at proper length, though I have waited long for it. Until recently I was unacquainted with the Ausdehnungslehre, and knew only so much of it as is contained in the author's geometrical papers in Crelle's Journal and in Hankel's Lectures on Complex Numbers. I may, perhaps, therefore be permitted to express my profound admiration of that extraordinary work, and my conviction that its principles will exercise a vast influence upon the future of mathematical science.
« Last Edit: September 02, 2017, 08:35:33 PM by hermann » Logged

jehovajah
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« Reply #231 on: November 03, 2017, 10:31:14 AM »

It is amusing that the quote above represents the religious ideal of humility in an academic setting.

Thanks for the quote Hermann and it is a fitting  end quote for this thread .

It shows how the work of elementary educators is profoundly important to succeeding generations. Many adult academics strive to make important lasting contributions to their higher academic fields and are directed away from the foundations. Both Justus nd Hermann were serious about establishing the foundations of Prussian mathematics and physics in the reform of education ordered by the Prussian emperor.

They had nationalistic goals to make Prussia a leading scientific and industrial technological force to be reckoned ith. They drew heavily on the best in their day and spoofed this understanding the next generation, aiming to make them proud examples of Prussias self actualising dream.

They we're staunch supporters of the Emperor and against the attempted revolution brought on by the collapse of the economy after the defeats by France particularly in 1806. So their work was revolutionary in the zeitgeist of the time. But amazingly it was by returning to Pythagorean principles as expressed in Euclids work that the major revolution was effected! The Stoikeia revealed as a discourse in basic natural philosophy of dynamics and quantification of dynamic systems.
Klein attempted to academically harness the transformational dynamics and in so doing obscured the work of the Grassmanns to academics of his day, except those who could see its intuitive value.

Gauss and Ruler dominated the minds og academics who could not be seen to be placing the work of elementary teachers over the complex abstractions of their professors.

The move toward abstraction thus obscured the simplest observations of Justus. Hermann in attempting to be academically recognised tried to present these ideas abstractly, but failed to identify his audience correctly, like Justus, who aimed at elementary school teachers. It took Robert to redact the work in 1861 in a form suited to Acadmics.
Nevertheless it is the raw power of the 1844 version that resonates through its imperfections.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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