Alexander Piatigorsky & Yoneda's lemma

Can concepts like 'sacred/profane', 'pure/impure' be used by phenomenology in the same way as they are used by religion and anthropology? 

Alexander Piatigorsky, a Russian orientalist and dissident who came to London in the Seventies and taught at SOAS, thought not. Swami R. Vaidyanathan- a physicist trained under Lord Rutherford who became a music composer and author of a philosophy of 'Masquism'- would have agreed. 

Piatigorsky gives this example

It is certainly true that an Iyer who became a monk- e.g. the Kanchi Shankaracharya- would have been disabled from crossing the black water in line with the Boston philosopher's argument. However such a monk has no caste. An Iyer priest or pious householder would not be able to maintain 'madi' rules of purity and thus during his foreign sojourn would not be able to discharge his dharmic functions. He could not be said to be a Smarta Brahmin at this time- save in so far as such may exist in other places under such modified rules of conduct as are applicable outside the 'paratakantam' sub-continent. 

However, on returning to his natal place, if his character showed no blemish, he could be readmitted to caste status by a prayaschitham ceremony. However, some Iyers did not bother with any such mummery though, obviously, at the time of marriage or other samskars, something of the sort may have been done by the priests. Absent such ritual, his status would be as a lapsed 'Brahminbandhu' but his progeny from a wife of the same ritual status could always be admitted to full Brahminical rites. The complicating factor had to do with property inheritance contingent upon the performance of a prescribed ritual activity. If this had been properly delegated, they could be resumed but the matter was justiciable. To keep clear of the Courts, some Smarthas would have to reject a chance to travel abroad lest some jealous relative try to seize what was effectively ancestral property on the grounds that a required ritual duty was not being properly discharged. 

Such is the religious, or legal, view. It appears compatible with the 'phenomenological' doctrine put forward by the prospective 'theoretical physicist'.

Strictly speaking there are only 'interactions'.  Any 'category theory' which seeks to interpret such interactions must, if broad (and thus useful) enough, ultimately put all groups (which we may think of as mini-categories) on an equal footing. This yields something like a Yoneda lemma. To know everything about an entity it is necessary and sufficient to know everything about its interactions. It is foolish to think of it as either establishing or following rules. Invoking the Kantian Transcendental subject or the Upanishadic Atman doesn't change the fact that interactions exceed their scope. 

Piatigorsky gives the example of the Iyer physicist to illustrate his point that

Christianity is a universal flight from that Devil which the Koine speaking Rabbis of the Second Book of Maccabees called 'kategoros'. Universal Religion is in the sphere of Yaami, Life, Evolution, the River breaking its banks as it swells towards its annihilation in but itself as Ocean. On the other side is the Law, Justice, and Yama- Death- who presides over both. But the same thing could be said of Mathematics and thus the 'meta-concepts' of Science which regulate its canonical representation. 

I don't suppose I'd have gained much had I had the chance to drink with Piatigorsky. Indeed, I may have done, all unawares, back in the Eighties. I hope he now drinks with Voevodsky and that at the Tavern at the end of the river of stars, Tamil's fugitive Melodies and Time's fruitless Mathematics now have univalent foundations.