It has always been an obvious truth to me that Hermann Grasmann was inspired by the insights of Newton.
It was Kant who was the primary link. though him,a a whole generation of Prussian Intelligentsia were inculcated into Newtonian philosophy. While the debates petered out about rationalism ( that is religious and divine inspiration) and empiricism( that is pragmatic and evidence based reasoning), the Prussian society underwent the most radical educational reforms under the Humboldt reforms. The debate shifted from who was right to what was right to teach the new generation, so they could take their rightful place in the world, and dominate the geopolitical landscape.
The best of what was in the world was imbibed, digested and redacted to the cause, and Newtonian philosophy was at the heart of the debate. The Prussian Renaissance took it on board along with the best of the material from Europe as devised by the French Ecole. Thus the works of Legendre, Lagrange, and other European intelligentsia were deeply scrutinised. Leibniz and the Bernooullis and Euler were among the most renowned scientists of their day, along with Boyle, Gilbert's work and the works of the American inventors and the British Royal Philosophical society, in whom Faraday and Lodge and Chandrasekhar represented an international dimension of collaboration.
The Prussian Renaissance sucked it all in, because it had to quickly become a world power to survivE the international upheaval, all around it, threatening its borders, its constitution and its hegemony.
Among the keenest debates wasthe atureandveracity of Mathematics. Few knew or understood that this subject was an invention of the early renaissance in Italy and those influenced by Rome. Prior to the early 1500's the subject was unknown, so it was a valid question..
The renaissance was a worldwide reaction to millennia of dogmatism, and credos. The recent and dominat effect of the Arabic empire on the institutions in the west resulted not only in commercial and political success and conquest, but also a revolution in thinking rivalling the intellectual pedigree of Hellenism. The world was ready for a new god and all his servants and trappings, especially one that was swell endowed with riches and wisdoms.
The Arabic empire not only conquered land in the name of Allah, but under Islam conquered minds. Every knowledge and wisdom in the world was gathered, sifted and returned, purged to the Islamist and Islamic scholars. The effect was evident in Architecture, riches, and the benefits to the Islamic peoples and regimes. That this was pro
Amanda did not seem to matter. The evidence was overwhelming in favour of it. Particularly in Spain, where Mohommed took refuge before returning to military and religious triumph in the middle east and beyond, the Arabic empire was sable to establish a secure toehold through trade, which eventually led to an expansionist drive to conquer the country to secure profitable trade routes.
Thus a vast wealth of treasures and wisdoms lay on the doorstep of a dark northern european continent ravaged by disease and plague and poor political management and endless wars. Therenaissancewasan intellectual reaction to thispoorstate of affairs, in the light of the enlightenment in the south states of Europe. The intellectual heritage of the Greeks,Romans,Chinese, werefedbacktothepeolle in a purified state, as Arabic or Moorish wisdom. Amongst these was the wisdom of Aristotle and his Lyceum. The trivium of his Lyceum and the later quadrivium that developed, wasthe basis ofaliberal arts education for all Islamist scholars, and formed the curriculum of higher Learning in all Arabici nstitutions.
This was soon emulated in the Italian universities or rather seats of learning at the time , from which by degrees the network of colleges and universities slowly spread, either by willing acceptance or in rank rivalry to "Moorish" ways. In this rivalry the west rediscovered it's original Hellenistic documents, stored in monasteries and Vatican libraries, and antiquarian stockpiles. These valueless documents suddenly became extremely valuable as the western traditions struggled to reassert themselves.
That which was purified by Islamic scholarship was repurified by western Christian thinkers who sought to demonstrate the primacy of their traditions . In so doing they returned not to the Christian theology, but to the Greek , and so pagan mythologies. From these, they hoped to recreate a purer, authentic western tradition, one which brought the eyes ofthepeoples back onto theeuropean hegemony and away from the alluring east or Arabic states.
This was not just done by debates. The reconversion was bloody and determined . The clerics and Kings inspain connived in the centuries long Spanish Inquisition, which became a model for many western kings to reassert political, social and religious control over their peoples. One way or another, they freed themselves from thearabic hegemony to regain political a di a iCal control, at any cost. One cost was remaining true to the knowledge of the ancients.
Very often some " new" truth was discovered that downgraded the old wisdom and updated the new powers and authorities. Quite often it was just a repackaging of the old. Sometimes it was genui Ely. Ew, because the old had been lost or destroyed , but some genius had reinvented the " wheel", so to speak. Later researchers found that unknown to the inventor the idea had been developed prior to them.
At this time the notion, a Pythagorean distinction, was developed of a subject called mathematics. It was obscure enough to fall into the hands of the propagandists who desired to break the hold of the quadrivium on higher learning. Thus by distinguishing some of the rhetorical studies as mathematics, they were able to gradually shape subject boundaries towards other topics that they wanted to introduce, particularly art and architecture for the grand rebuilding projects they had in mind.
So wha is Mathematics arose as a natural question when redefining curriculum and subject boundaries. This question arose Keen,y in the time of Isaac barrow. And both Wallis and Newton were propagandists for the subject boundary, even if they never actually defined it.
By the time of the Prussian Enlightenment, the Prussian renaissance, elements of the quadrivium had ome to define the consensus on mathematics, mixed in with some poor scholarship on Euclids work. The Neo platonic academy was asserted over the Aristotelian, and therefore Islamic Lyceum model, but it wassomeweird ix true of the two which was actually learned, and the taught.
It was because this. Ixturewasso inconsistent that the Prussian scholars took it to task and attempted to straighten it out. This imprecisely where Justus Grassmann enters the fray, in order to provide a world class primary education system in Sczeczin his home district . As a cleric with a philanthropic heart nada great nationalistic or imperial pride he laboured all his life to raise the standard of public education in his district. It is quite feasible that Jakob Steiner was one of his pupils!
Justus decided to tackle the inconsistencies in geometry, gleaned from the works of Legendre and some Prussian philosophers who commented on how geometry and mathematics were disconnected. The Arithmetic model was always correct, but the geometric one introduced inexact measurements and quantities. Strange magnitudes and approximate methods. To the theologians this was evidence that Mathematics was synthetic. But equally theologians recognised that by Neo , god displayed an arithmetical and geometrical mind. So was mathematics revealed to us by discourse?
The 2 sides of the argument engaged in intense philosophical debate, but it was the empiicists who deigned to settle the argument by demonstration. The school system in Szceczin was a huge experiment to show that the synthetics notion was " right", logically.
In the course of demonstrating this conviction to be true,Justus inspired his family and friends, and2 sons to continue in his work to establish his vision. Thus, in a very personal way, nis 2 sons Robert and Hermann scoured the intellectual world to prove their father right. The intellectual world atthetimewas heavily influenced first by Newton,them the French Ecole movement , and then by the Leibniz,Bernoulli Euler Axis. In the light of this Gauss struggled to make a name for himself and the Prussian Academy. In the end he was quite ruthless in engineering a place in the international community for himself and Prussia. Consequently he missed the chance to back the Grassmanns grass roots efforts and so achieve his aim.
The promotion of Riemann, while carefully engineered has not had the fundamental impact that the primary school teachers in Sczeczin have had on the way we view reality. But in that view we clearly see the return through Newton, to the classical world view of the Pythagorean school of thought and Analysis and then synthesis .