…,das Studium jenes Werkes wegen seiner,wie sie meinen, mehr philosophischen als mathematischen Form dem Leser bereitet…
This is a curious statement, and one which i have puzzled over greatly.
It says very plainly that the form of a subject or topic prepares the Reader or srudent.
This is not new but then it is new! It is saying or meaning form not content is what produces the student. Thus form of presentation of material is more influential on a reader than the actual content of that "presentation".
It is also revealing to find it in the vorrede of Grassmann's second revisionary work, after 15 years of failing to make substanial headway with his plans for the Ausdehnungslehre.
In a way it sums up the essential notion of The Ausdehnungslehre, Form is more powerful than detail, geometrical relationships override all the minute details of a form; structural arrangements and relationships govern the outcomes of activities more than the little details of the activities.
Think on it. It is a bold and beautiful idea, one which Grassmann probably discussed at length with his brother, Robert.
What was "das Studium jenes Werkes"?
My guess is that they were the essays Grassmann wrote based on the Philosophies of Descartes, Leibniz and Spinoza, with research into the pre-socratic philosophers to back his conclusions up.. I would venture that Kant and Newtonian philosophy figured in there somewhere.
You know i have never read Newton's philosophy in his principia, so i am going to have a look, but Grassmann clearly had read widely and gained some insight about form and its relation to aggregation structures, motion sequents amalgamations and the nature of space its intensity , density, vibration and harmony, the phusis of space.
My daughter has a book about greek philosophy on space. I think i am gonna read it.:psmurf:
Poncelet, Steiner et. al. projective Geometry.
I have remarked on certain misconceptions that people have of Newton's Principia particularly in regard to his conception of motiion in space. Newton did not use the notion of right to mean straight, as we do in the modern teaching of his work. He used it to mean, as Euclid did good and true to form. Thus,, whatever the form we conceive, a line is right if it conforms to it.
I have explained this in some detail with regard to Euclid's conception, Thus Newton explains the order of "rightness" in his opening "axioms" or statements to the principia, and when he gets to the "rank" or "order" of the celestiala right means a keplerian curved motion. Newton was illustrating an obvious geometric truth" the closer one gets to a spherical surface the flatter it seems, the closer to a circle the straighter it seems. Thus a tangent is a scaled approximation to a small region of a circle and infinitesimally actions may be resolved into straight lines. They must then be compounded to synthesise their true form.
Although i have to read his philosophy, i have read enough of Newton's conceptions to know he well understood relativity and its effect on calculation structures and frames of reference. He learned this, i might add from his mastery of Euclidean teachings, the Stoikeioon and others of the classical writers that he could lay his hand on through Barrow his tutor and Wallis his mentor.
In 1832 Jakob Steiner asked for a combinatorial characterization of convex polyhedra inscribed in a sphere.
This collection of synopses is very enlightening http://webcache.googleusercontent.com/search?q=cache:3J5f4fbLZxMJ:www.di.ens.fr/pub/Main/JS60/13-Naccache.pdf+jakob+Steiner+collected+works&cd=151&hl=en&ct=clnk&client=opera
Much of Steiner's Terminology finds its way into the Ausdehnungslehre.
As m German has improved i have gained better understanding of the text. This is not always a good thing! One tends to be literal or customary in translating in that circumstance, whereas scrabbling to make sense of a foreign speech leads t delightful serendipitous and analogous thought and thinking. It is perhaps in this state of mind that an author has the best chance of communicating the maelstrom of sentiment that clarifies into a single pure word or phrase or sentence.
Often a ohrse is writtten, and like Schroedingers cat it is full of potential, but every word thereafter squeezes that potential into narrower and narrwer possibility. \such a circumstance is pedantry at its best, but poetry at its worst. “`most of us without realising strike a xharacteristic balance between the two, and some of us are delightdul in our artistry of this characteristic of lingual communication,
Here Grassmann meant that The Subjects that a reader would have to study to apprehend the nature and intent of his work in the Ausdehnungslehre would depend on he knowledge and intellectual experience of the reader. Thus many normally intelligent readers would struggle with the particular form of the Ausdehnungslehre unless they had read widely in philosophy.
But the aphoristic terseness of this observation is suggestive of the work itself transforming the reader! only someone with bad german would insist on this meaning, but a poet would see it also: by changing a few word endings this meaning swims out
Das Studieren jenes Werkes wegen seiner, wie meinen sie, mehr philosophische als mathematische Form den Leser bereitet!