A Hindu view of Hermann Grassmann

 Hermann Grassmann made fundamental contributions to three different fields

1) Philology. Grassmann's dictionary of the Rg Veda remains unsurpassed. Grassman's law is a rule of Greek and Sanskrit phonology which predicted irregularities in certain nominal and verbal derivations from lexical roots containing aspirated stop consonants

2) Optics or Color Science. Grassman's Laws in this respect are actually empirical principles.

3) Mathematics. Alas, here he was ahead of his time. William Lawvere and other recent scholars consider that there is a philosophical angle to Grassman's mathematical work of a particularly fecund type. We may well wonder what would have happened if Grassmann had gained a University appointment. Would Hegelianism have evolved into a Scientific Method of great generality and practical import? Would Marxism have become an engine for peace, prosperity and ceaseless innovation? 

Lawvere writes- Grassmann in his philosophical introduction describes the two-fold division of formal sciences, that is, the science of thinking, into dialectics and mathematics. He briefly describes dialectics as seeking the unity in all things, and he describes mathematics as the art and practice of taking each thought in its particularity and pursuing it to the end. There is a need for an instrument which will guide students to follow in a unified way both of these activities, passing from the general to the particular and from the particular to the general.

Lawvere's claim is that category theory can serve as the required instrument. However, one could just as easily see Grassmann- a school teacher, like his father before him whose ideas he developed further- as being guided by the ideas of Pestalozzi & his followers- in particular Joseph Schmid . In other words, he had taught himself to make progress in mathematics and philology and so forth by following the same method as had been found optimal to teach little children of the poorer class to start thinking for and learning by themselves. It could also be argued that Grassmann was influenced by Schliermacher's Dialectics- indeed, this was the opinion of his brother who wrote his obituary.

A Hindu reading about Grassmann's achievements may well feel ashamed. Even if we have a hereditary duty to study the Rg Veda, we neglect it. We got very angry when foreigners sneer at our 'slumdogs' but did not show any dedication to teaching the poor and thus learning to overcome the poverty of our own stereotyped and imitative thinking. On the other hand, the true Hindu- if stupid and lazy and ignorant enough- can easily turn the tables on Left-Liberals like Lawvere simply by doing a bit of Googling.

This is what I propose to now do by appealing to the Yoneda lemma which, one could say, crystalizes Grassman's approach to both the Rg Veda and to Mathematics. Essentially the notion is that everything is known about x if all possible interactions of x are known. This is clearly not the case for the Rg Veda- which is why Grassman's translation fails- or indeed for the hapax legomenon that occurs in the Lord's Prayer. This is because the nature of some possible interactions is that they can't be known for any possible categorical theory of Knowledge. In other words, either there is no Scientific Method or Science too must have its mysteries of faith. 

It is fake cleverness of this type which keeps a country poor- or, if it gets rich by the efforts of its own poor- which nevertheless keeps its 'intellectuals' stupid and ignorant.