It has to be the most significant aspect of reading Grassmann's own words: it is a transformative experience of immense beauty ans subtlty. The old divisions melt away and a new vision is born. Sundering differences are softened and new meaning given to the distinctions in life. Combinations that heretofore were not considered now are elements of a new synthesis. And all this is merely the change of terminology, how we get to grips with the ephemera of space.
In the light of further documents giving background family history, I have now been able to evaluate the massive impact of Robert Grassmann on his older brother, Hermann. Despite his relative youth, Robert had an easier academic passage into the remainder of his life. It is evident that he was a polymath and a talented communicator, with a great facility and application to study and writing. This stood him in good stead for his later exploits, but us heart was set on reforming philosophy on scientific grounds. He believed that the natural sciences had achieved this, but philosophy had not, and it eas his ambition to so establish philosophy.
In the meantime we may deduce that Herrmann had to struggle to express himself, and to be found worthy. His beliefs and humility seem to have consigned him to a second or third rate status in the family. Judging by other sources, it would seem appropriate to say he suffered from autism, which came across as extreme shyness, and poor language skills, both of which he strove to overcome. In the meantime his study was the work of his Father with regard to space.
He was, however given to visions and ecstatic experience, and this shows in the development of his ideas . Whatever his personal shortcomings or health issues he always believed hard work would eventually put it right. His genius was discovered only when he submitted some groundbreaking presentations to various examining boards Nd colleges, in his attempts to gain qualification for teaching status. However it also began the unfortunate reputation of his obscurity in writing. By all accounts his German is bad, and yet he became a note able linguist with groundbreaking contributions to the study of languages and their origins and developments.
In stark contrast, Roberts rise appeared meteoric and and fortunate. The difference seems to be the diffidence with which Hermann presented himself. Robert was a driving energetic personality who took full advantage of the family position in Stetin to found several publishing enterprises . All were relatively profitable and successful, but subjected to various un controllable circumstances.
While Hermann painstakingly attempted to rise up the ranks in the teaching profession Robert easily sailed through the qualifying boards and was given several advantageous positions, and took several enterprising opportunities. Both , however we're hard workers, but Roberts particular gift was in publishing and printing. Both were assiduous researchers as was necessary to hold a teaching post, and both wrote text books for the classes they were employed to teach. It is just that Robert did more of this more quickly and with greater flare for communicating ideas.
Roberts works therefore form an important backdrop to understanding Hermann's because Robert became Hermann's publisher and collaborator, especially on the extensively revised Ausdehnungslehre. After Hermann's death Robert wrote extensively on the Ausdehnungslehre, producing his own version of the subject matter, putting Hermann's in context.
Although they collaborated, and Robert makes it sound like a particularly creative activity and certainly an intense one, for Hermann!, Hermann's allusions in his vorredeto 1862 are less glowing, more sarcastic! It is not that Hermann objected to the collaboration, but more that Robert took full editorial control of the project! It became visibly less Hermann's and more Roberts Ausdehnungslehre! This is the source of those vague allusions to the Mathematician, and the obscure derision of pandering to the parlour room classes of polite society!
What I am alluding to here is the clash between a conformist and a nonconformist! Certainly the aims of the 1862 version were so radically alien to Hermann that he pointedly comments on it. It is therefore significant to note that Ausdehnungslehre1862 is a collaboration, aimed at a different readership than perhaps herrmann's original audience, and promoting Roberts philosophical theory over and above Hermann' metaphysical exploration.
Hermann was nonconformist in a way Robert could never be, but Robert had aims to overturn the very foundations of philosophy. Thus he subconsciously used his brothers nonconformist to push his own revolutionary ideas. Hermann on the other hand was only interested in the truth as he saw it. Yes his book never got a wide reception as he had hoped, but classically he appears to have resigned himself to obscurity on that metaphysical front. He moved on to a more successful career in philology. However Robert who had a great work in him to complete saw the results that Hermann had arrived at as fundamentally crucial to his argument about the scientific basis of philosophy. Thus he needed Ausdehnungslehre to write a section in his grand philosophical theory. However, as a publisher he needed the book to sell! So the revisions he enforced made the book more saleable, and that was because it made the theory more accessible he argued. However Hermann realised thst this was not his theory but Roberts interpretation. As such it was no longer a metaphysical text, but had become a conformist Mthematical text.
Hermann never had a chance to put his right, which is the reason for his hopeless Vorredeto to the 1862 version, until a resurgence in interest meant he could republish his original with a full explanation!
There is a serendipitous point here. Maybe it required Roberts revision to get it well known in the Prussian mathematical circles, and maybe without this period of conforming we may never have received the wisdom that is in the original, but also Hermann's work had seeded in the surrounding countries, particularly in Italy and France, where rival works began to be developed, based on Hermann's insights. So out of self interest Robert neede to defend the primacy of Hermann's work. In so doing his contacts in Prussian society made Hermann's meagre tract an instant national treasure, a secret pleasure! Thus it required rewriting to comment on its unique importance to philosophy of Mathematics.
Gauss may not have directly held Hermann back, but his brother Robert did on gauss behalf! At the time Robert became heavily involved in revising Hermann's book, gauss and Riemann were preparing and presenting Riemann's Habilitäts lectures on the manifold. It is clear tht Robert attended to these lectures as a state qualified mathematical teacher and recognised Hermann's ideas in it, but also how far in advance of Riemann Hermann was! To also find that a copy of Hermann's first book had been critically read by gauss was too much of an opportunity to miss.
Clearly he could not claim preeminence over Gauss, but to publish in detail the solution to Riemann lectures was a publishing coup he thrilled at. Hermann was not so keen, because it meant abandoning his plans for the first book, and handing over his vision to a mathematician, not a metaphysicist! However Robert prevailed and the 1862 version was produced and had very moderat success. The extent of that success was that on the death of Riemann all mathematical eyes turned to Hermann,not Robert, for leadership.
It was only after Hermann rid that Robert attempted through his own version to establish his leadership of this important area of "manifold geometry", as well as to promote his radical revision of the basis of philosophy.
He had some measure of success, but has forever been overshadowed by his brother Hermann's slim volume of Ausdehnungslehre 1844, no matter how voluminous his own life's work may be.
Das Studium jedes Werkes wegen seiner Form dem Leser bereitet is a publishers dictum. It is a phrase that Robert clearly used effectively on Hermann, who felt that his work possibly was difficult to follow, and this possibly explained why it never sold in large numbers. Little did he realise Roberts subconscious motivation for revising his earlier work. Not until it was in printers block did he realise how extensively it had been reworked as a mathematical treatise.