OMG! My german is bad. i have forgoteen so many prepositions , prefixes and conjunctions that it means my scanning gives me completely the wrong sensation! But i love it. I love it to death lol!:jester:
Reading Grassmann with the engagement i needed to find out if my sense that he was wrong or misinterpreted was itself wrong, is a meditative experience.
The first thing is the exact similarity between the ancient greek and german grammatic and syntactic forms. The PIE etymological denotation is certaimly evidenced by this example, but it also draws attention to the historical fact that the german states arose from the Holy roman Empire, the successor to the Greek Empire, whose Hellemization pokicy so altered the whole world.
It was pleasant to be reminded of this fact that i knew so well and ardently as a youth, since the magazine "The Plain Truth" ran so many powerful and enlightening articles on that fact, connecting the germanic states to the end time scenario in Revelations, the apocalyptic esxaton. The Koine greek in the New testament certainly has some echoes with Grassmann"s philosophy and outlook.
The next point i fell upon was Grassmann's eloquence, which he put to good use "whining" about his work and plan being essentially ignored due to prejudice or difficulties for his audience. I say whining with a bit of tongue in cheek,because Grassmann undoubtedly worked very hard to get where he ended up, and was a very successful teacher and professor. In fact Grassmann explains the causes of his long term lack of notoriety or controversy despite the controversial aims he set out in his Ausdehnungslehre part !.
Grassmann was a Wissenschaftler, that is an old style philosophical Scientist, not a mathematician. In that regard he was like Newton and of course like Hamilton. However Hamilton and Newton passed through Academia before they began to write philosophical science. The difference is profound,
I am at the same ime doing some research into the origin of the notion function.Like most of our mathematical terminology it has its origin in the grmanic academia who initiated the modern notations now well established, supersceeding in their progress earlier attempts at concise notations in mathematics and the sciences. The notion of function herefore represents the rigid militaristic social order that existed in the Roman empire and which passed on to the germanic states and peoples. The roman military machine was nothing if it was not an efficient and organised and structured society in which each person, rank, group and status new their duties and roles and how to carry them out efficiently towards a determined goal . These very notions underpin the notion of function, and made such perfect sense of the mathematical use at the time. It is not so revealing today.
It may be a comment on society but i really think that the notion of recipe has supersceded the notion of function, or even "flat-pack instructions".
But i digress. The point is that Grassmann did not have the social standing to write a philosophy of science, let alone one with such revolutionary aims, and such a far reaching plan!
Grassmann states that he had a plan to write the philosophy in 2 parts and he laid out the plan clearly in the Ausdehnungslehre part 1, which he called a Zweig of mathematics, and which interpreters have deliberately translated as a branch. He meant a root and a branch from mathematics!
A linear algebra to base and ground the various branches/roots of mathematics and then to gather them together in such a way as to superscede all these parts by a greater set of notions and notations that capped all of them! The Ausdehnungslehre was aiming to be the Keystone of Scientific philosophy, pushing back the notions to their most general and all encompassing view,even to their essential spiritual source.
His was to be a scientific philosophy, built on the most stringent format for scientific philosophy (Das Studium) and thereby to be judged as to its significance.:doh: :doh: :doh: :doh:
When published, the silence was deafening. Even his self promotion and the many mentions and uses of an 1847 Explanation he wrote by others especially a paper by Kysaeus did not bring forth the bubbling torrent of controversy and research he expected. The reason, he eventually got to find out, was due to his very plan to write an old style philosophical scientific treatise, (das Studium), like Newton.
To say it gave him pause for thought is an understatement. The Difficulty, because Grassmann says there was no real Critique of his work, And the opinions of all mathematicians of note, completely alterd his planned approach. Over the course of 17 yeas he had laboured to promote the book as a philosophical scientific treatise, while working to improve his social and academic status, winning prizes and high achievement awards everywhere. In !860 he wrote a book on Arithmetic theory, which drawing in part on his ideas in Ausdehnungslehre part1, but more importantly on Euclid's "Elemente" reprised him of the kind of mahematical notation and presentation that did sell well!
It is of interest to note that in so doing Grassmann covers the very ground that Hamilton covers so elequently in his work on Couples published in 1834, nearly 30 years earlier. However, Arithmetic was a common enough subject for Grassmann not to have needed to consult Hamilton's work, except in one area, the area of complex arithmatics.
Gauss not withstanding, Hamilton, it is acknowledged as the scientist who grounded the complex arithmetic in logical relations and mathematics, thus it would be strange if Grassmann was unaware of Hamilton's work. Hamilton was certainly aware of Grassmann's.
Arithmetic and Euclid, of course mean the Arithmoi. Grassmann, who did not consider himself to be a great mathematician says that in order to overcome the difficulty scientists et al were having with his work, and by then a few had begun to take note, particularly, Peano, Riemann , et al , he decided to follow their "advice" and fundamentally alter his plan, and present the ideas not philosophically, but mathematically, as Euclid had done. And as he had copied Euclid in his book on arithmatic. This was the strictest form of mathematical presentation he could manage, and he hoped that he had made his ideas more accessible by doing so.
…,das Studium jenes Werkes wegen seiner,wie sie meinen, mehr philosophischen als mathematischen Form dem Leser bereitiet
He adopted some of the notation and terms used in his book on arithmetik, and defined and explained as best he could any unfamiliar and new terms. He specifically wrote this vorrede to give the reader a heads up as to what the major changes were and what to particularly pay attention to..
This is as far as i got, this morning. He was saying that the depth of the work was beyond him, but that he hoped he had given sufficient insight for the more mathematical readers to judge whether he was on to something extraordinarily marvelous(!) or not. He had done concise applications of the theory to certain physical as well as mathematical examples to indicate the method, the depth and the power of his "overarching" algebra . He was not short on self promotion of his works importance, but even this "deliberately inflammatory" language did not result in the kind of Buzz Grassmann dearly hoped for.
He left it up to God , the angels and history to decide whether these "truths" were worthy of such emphatic description!
Grassmann then like Hamilton felt that Euclid was a good starting place, but not a misunderstood treasure. The recent opinions and advances in science in his day were seen as supeior to ancient knowledge, and grassmann, not ntypically was excited and motivated by the new frontiers of science and technology and wanted to stake a claim in the goldrush of new ideas that explained everything. His mistake he believed was in his title, linking his scientific ideas to mathematics. He got a response from mathematicians who said as a text book it was more a philosophical reader than a mathematical one. Nobody picked up on his clear statement that it was a science reader.
When preparing students for examinations, they need a textbook, and Grassmann wanted to prepare a textbook for the physical sciences, drawing together the fundamaental mathematical notions and pilosophy and praxis and mathesis necessary to ground them in physics and mechanics in particular. However, he wanted to also provide them with modern powerful and sophisticated techniques that would advance the study of mechanics and physics, and make him a famous and respected professor of science. It did not work out like that:doh:
Nobody it seems read the vorrede to part one, in which he states that he would point out the substantial differences in his approach over the traditional in outline (Die Gegenstaende) which would form the content of the second part of the textbook that he had yet to write and publish. Or if they did, they did not get it, the difficulty being his old style "latin" format, the Scholarly studies of a philosophical nature, expected in a doctorate or a Phd thesis not in a textbook. It took Grassmann 15 years to put his finger on the problem.
Consequently he so massively altered his far reaching and glorious plan that he completely rewrote Ausdehnungslehre part one and incorporated it in his new Ausdehnungslehre Mathematisches WISSENSCHAFT. Thus there is no need to read part 1 inorder to follow part 2 , they are now simply combined into the whole scientific theory, But presented mathematically.:doh: :doh: :doh: :doh:
I do not know which is worse: philosophical ruminations, or mathematical denotations. In any case he jumped out of the pan into the fire!Who wants to read a mathematical text book?
Of course, some did, in particular, some guy called Saint Versanne who immediately launched a damaging plagiarism case against Grassmann. Grassmann was vindicated, but the promotion of his work was significantly delayed, and consequently overtaken by events and other more "accessible" authors , especially academicians.
Grassmann had achieved some measure of recognition and respect for is ideas, but few took them where he wanted to go. Despite making some outrageous claims in his work, Grassmann was a modest enough man, and this i think lead to others interpreting his claims and vision more moderately than he wished. He believed his insights and notions were revolutionary, others did not quite see it like that: after all how revolutionary can "simple" geometry be?
For your consideration i answer: absolutely fundamentally revolutionary! Grassmann was not dealin with geometry but the abstract and deeper, more general notions behind geometry, even the "spiritual "source of geometry. I believe that Grassmann was blinded by the modern pontifications of his peers to recognise the source of his insight. I believe his linguisitic ability took him deeper into the classical greek notions than anyone else, in the sense that he intuitively "got" them.
The Stoikeioon do not declare themselves as geometry. That is a denotation given by others to the purpose oftheir use of the Stoikeioon. The Stoikeioon present themselves as teaching material for those who want to reach a high level of skill in their chosen field of construction requiring artisanry.They pragmatically arrange fundamental notions in an order that facilitates this. The fundamental notions are thus available for study for an even deeper understanding, and this i believe Grassmann and Hamilton were lead into by he clever arrangement of the Stoikeion.
The Stoikeioon is a masterpiece of Educational material designed to generate beautiful manipulations of space that last forever through the skill and artistry of artisans of all trades. Especially with Phusis a poerful and enduring system is achievable. The Stoikeioon and Phusis, ultimatel Harmonia and Phusis are the 2 Sophias thaf creat beauty and order and long lasting structure in our Kosmos. This is wht Grassmann essentially grasped,but could not write.
My comment is : Way to go Grassmann:knight: :sherlock: :psmurf:
However, i perceive that both Grassmann and Hamilton highlight a deeper system of "propsitions" The Euclidean Stoikeioon. This philosophical science course of pragmatic technical drawing and calculation underpins every aspect of the sciences and arts of the modern world, from fractal quantumness, to universal fractal goodness!:chef: :banana: :beer: :wine: :heart: :flirt: :love: MMMM! i am going to get me some!