The Shocking “Truth” about Euclid’s Stoikeioon!

The breaking news is that the attack on Euclid between about 1780 and 1880 in the Prussian holy Roman empire was motivated by misconceived notions of the Stoikeioon. Few in the Prussian intellectual elite had access to the actual text, and therefore they were reduced to relying on redacted and theologically purged excerpts of what the text actually said and what it's intentions were.

The widely held and taught view that the Stoikeioon was a book on geometry derives from religious teachers recounting the impact of the material on roman emperors, who in being educated to befit their status often expressed the view that it's tedium should be communicated in a more interesting way! To which the reply was there is no royal road to learning Geometry!

The emperors and their children were not great scholars and therefore were not always able to grasp what they had access to. Thus no one informed the ignorant that geometry was but one small application of a system of knowledge and wisdom used to calculate the Astrologers art, and to divine the celestials Mechanics!

Thus the misguided attack on the Stoikioon stems from ignorance in the highest ranks of Prussian imperial society, and consequently reached down to its loyal subjects as gospel truth. It is therefore of no great wonder that those tasked with educating the nations young should find the emperor to have no clothes on!

The attack on Euclid starts in the entirely Euclidean debate about the parallel demand. Those that engaged in this debate in the Arabic Empire were in fact well versed in the actual texts and in Spherical trigonometry and Astrology besides. The debate was not about proving the demand, but about what relations could be explored where such a demand could not be used, such as on the surface of a spherical earth!. The importance of this question lay in a religious duty to always give the faithful Muslim, the correct direction or orientation to Mecca. The problem was solved in the 5 th century AD in the Persian part of the empire, so it is with some humour that the Prussian empire arising out of the dark ages of the medieval period, and struggling to catch up with thr Rennaisance should suddenly begin to tackle this question again, but with far fewer intellectual resources. The Russian empire also found itself in a similar catch up mode with Lobachewsky and Bolyai valiantly attempting to breal this " new" ground in ignorance of its prior thorough ploughing.

The Humboldt reforms in the Prussian empire opened up this debate on Geometry to the wider educational reform movement, which due to having to teach children provided the first real fundamental critical analysis of the didactic form of geometry in the higher learning institutes, and a much more direct system to engender the same insights and self actuating research into children. In doing so it provided a resounding critique of the Prussian concepts of Geometry which resounded all around Europe, only stopping at the door of the Arab empire who perhaps could not believe the ignorance portrayed by this critique?
http://www.1902encyclopedia.com/E/EUC/euclid-mathematician.html

The first six and, less frequently, the eleventh and twelfth books are the only parts of the Elements which are now read in the schools or universities of the United Kingdom ; and, within recent years, strenuous endeavours have been made by the Association for the Improvement of Geometrical Teaching to supersede even these. On the Continent, Euclid has for many years been abandoned, and his place supplied by numerous treatises, certainly not models of geometrical rigour and arrangement. The fact that for twenty centuries the Elements, or parts of them, have held their ground as an introduction to geometry is a

are, speaking generally, not too difficult for novices in the science ; the demonstrations are rigorous, ingenious, and often elegant; the mixture of problems and theorems gives perhaps some variety, and makes their study less monotonous; and, if regard be had merely to the metri-cal properties of space as distinguished from the graphical, hardly any cardinal geometrical truths are omitted. With these excellences are combined a good many defects, some of them inevitable to a system based on a very few axioms and postulates. Thus the arrangement of his propositions seems arbitrary; associated theorems and problems are not grouped together; the classification, in short, is imperfect. That is the main objection to the retention of Euclid as a school-book. Other objections, not to mention minor blemishes, are the prolixity of his style, arising partly from a defective nomenclature, his treatment of parallels depend-ing on an axiom which is not axiomatic, and his sparing use of superposition as a method of proof. A text-book of geometry which shall be free from Euclid's faults, and not contain others of a graver character, and which shall at the same time be better adapted to purposes of elementary in-struction, is much to be desired, and remains'yet to be written.

http://en.wikipedia.org/wiki/Euclid%27s_Elements
http://mathsisgoodforyou.com/topicsPages/geometry/euclideanandnoneuclidean.htm

Nevertheless, from this fundamental revision, several important elements of the Stoikeioon were brought to the fore in a new synthesis intended for children, but extended by Hermann Grassmann to the level of the highest institutes of learning. However, at the time, the reactionary groups including Gauss resisted these innovations until they could manage them in their own way to their own advantage.

Justus Grassmann began a family effort to implement the Humboldt reforms in Stetin which resulted in a revised text book for geometry being developed and promoted in their region. This then led on to reforms in the arithmetic and algebraic curricula. Due to Robert Grassmann publishing business he managed to promote the families work to a wider Audience, but his success has to be contextualised. There were many educational regions and many educational reformers tasked with delivering the reforms effectively. The Grassmanns work at the primary level of Prussian education was just one of many. If it were not for Hermann's unique contribution the Grassmann reforms would have been a lost treasure in Stetin, doing its job and being superseded by each new reform and eventually lost to history. It is the Ausdehnungslehre of Hermann and Robert Grassmann that rescues them from a Gauss imposed obscurity. It was Gauss intention to secure his contribution to Prussian advancement in the geopolitical arena, and this he hoped to do through his Student Riemann. The Grassmanns were a buzzing fly to be swatted down, dangerous innovators at worst, primary educators at best. They certainly were not in Gauss league and he felt Hermann could be ignored and his ideas given to Riemann under Gauss tutelage. I doubt if Gauss ever took time to seriously critique Die Ausdehnungslehre, rather he recognised in it his own ideas and got Riemann to do further research in that vein, giving him Hermann's book as a jumping off point. It is only because Robert was a mathematics lecturer that he recognised what Riemann had done in 1854 and he collaborated ith Hermann to rewrite his book to get as much advantage out of the situation as possible. Although Robert completely dominates the 1862 version, it doers allow Hermann to re introduce his 1844 version to a more appreciative audience who could not fail to recognise his priority over Riemann.
Unfortunately the Academic board again refused to give Grassmann the recognition he deserved due to his unorthodox education, but they had to recognise the international impact of his ideas. Klein explains that the religious fervour of the Grassmanians and the Hamiltonians was to be discouraged as not the right image for international mathematics!

As pointed out earlier, the Prussian idealistic movement filtered out into the rest of Europe, where it met with mixed response. Many malcontents attempted to use its fresh approach to eduction to destabilise the status quo, others simply appropriated what they thought they could get away with if dressed up in national esteem terms. Particularly the turmoil in France allowed many French intellectuals to plagiarise Prussian ideas and dress them up as their own. However Laplace and Lgrange and Fourrier were among the few that responded to the times with genuinely innovative thinking giving credit where it was due, or engaging in genuine new untouched areas of research.

In Britain A N Whitehead and his student Bertrand Russell attempted to engender a reform in the british educational system inspired by the Prussian reforms and the work of the Prussian intellectuals and the Grassmanns.

In America the scientific community there was also influenced by emiigrés who brought across Prussian reform ideas and developed them as there own. A case in point is Gibbs who undermined Hamilton's contribution by utilising his version of the Grassmann analysis.

Meanwhile, in all this turmoil and advantage taking, the reputation of Euclid was besmirched, and this was used as an excuse to sidestep the then notions of Geometry, allowing new and fresh approaches to be developed for the technical demands of the industrial and scientific and technological revolution. Although now one can look back over a period of reinventing the wheel, which always takes the naive response: look how clever the ancient Greeks were, they had a form of technology similar to ours!– in fact the agenda in Prussia was to develop self actuating research and understanding. The philosophers wanted to harness the resource of Prussian innovation, homegrown with that unique Prussian cultural background. For too long knowledge and wisdom had been imported or bought- in by wealthy patrons leaving the native talent impoverished and under resourced to do their own research and development. Thus this spirit of selbsttätigkeit also travelled with the Prussian reforms and juiced the reworking of received didactic information in ones own terms.

Even though the early reform educators in Prussia got the author of Geometry wrong, because Euclid was a professor of Philosophy not geometry, they would still have had to critique the genuine authorities works in the same way to demonstrate self actuation. The point is they were willing to do the work, tackle any so called authority and recommend reforms that would better prepare their pupils. This gave Euclid the unexpected chance to be looked at again with fresh questioning eyes, and much of hat he actually taught to be brought to the table. What Euclid actually taught was entry level undergraduate philosophy in the Platonic Academy. He developed a course in the Platonic theory of Ideas/Form which transcended its Astrological purpose and became a favourite of the Tekne, the skilled artisans for who philosophy would become a fast way to senior positions in the artisans guilds!

Today expected skill goes along with the title Doctor of Philosphy, and the same applied in Euclid's day. An artisan became a master of his trade if he also had a recognised training in philosophy. Of course the Stoikeioon was at just the right level for most Tekne who wanted this type of recognition. The Stoikeioon however would only have been the first stage in the training of an Astrologer.

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