Borges's 'search for al-Mutasim'

  Borges summarises his own 'search for al-Mutasim' as follows

a man... falls among people of the vilest class

the ultimate 'fex urbi' such as might gather in the catacombs 

and adjusts himself to them, in a kind of contest of infamy.

Theirs is a reverse cursus honorus- like that of Flavius Clemens, the Roman Consul, who aspired, not to the pomp and glory of a Senate funded Triumph rendering him Divine for a day, but, rather, an ignoble abasement to a Jewish carpenter which could only end in an equally ghastly death upon the gibbet. 

All at once - with the miraculous consternation of Robinson Crusoe faced with the human footprint in the sand - he perceives some mitigation in this infamy: a tenderness, an exaltation, a silence in one of the abhorrent men. "It was as if a more complex interlocutor had joined the dialogue."

Christ is that interlocutor where any two are gathered in his name.  

He knows that the vile man conversing with him is incapable of this momentaneous decorum;

The decorum of the Mass arises from a personality far greater than any set of persons.  

from this fact he concludes that the other, for the moment, is the reflection of a friend, or of the friend of a friend.

That sounds like Second Corinthians, 3.18- 'But we all, with uncovered face beholding as in a glass the glory of the Lord, are changed into the same image, from glory to glory, even as by the Spirit of the Lord.'

Rethinking the problem he arrives at a mysterious conviction: some place in the world there is a man from whom this clarity emanates; some place in the world there is a man who is this clarity. The student resolves to dedicate his life to finding him.

Why does that man have to be on earth now? It is sufficient for him to have existed some where at some time. But, on the reflection theory, there may well be a supremum of the set of extant 'reflections'. That's close enough. 

Borges, of course, was aware that- for his Christian readers- there was nothing particularly Indian or Islamic about the story he imputes to an Indian Muslim. Thus he adds 

the conjecture that the Almighty is also in search of Someone,

if so, it is likely that he is moving much faster than even the swiftest of his seekers. But what is sought is itself moving very much faster.  Thus the space of the search is expanding too rapidly for seeking to be worthwhile. We might square the circle by putting the all highest in pursuit of the lowest. But, with rational expectations, this means everybody is in pursuit of the lowest because that is where they can be overtaken by what they seek- unless the lowest's rate of sinking too is eponential. 

and that Someone in search of some superior Someone (or merely indispensable or equal Someone), and thus on to the end - or better, the endlessness - of Time,

Space-Time would be expanding exponentially- this ultimately leads to heat death 

or on and on in some cyclical form.

There's a crunch and then a contraction.

Borges wasn't a mathematician but, as a librarian, he might have been attracted, by the title, to Hardy's little book 'orders of infinity' which developed the calculus of Paul du Bois-Reymond  who first used a diagonal-like method in 1875  to construct real functions that grow faster than any given sequence of functions, whereas Georg Cantor, who bitterly attacked his use of infinitesmals, formalized the diagonal argument in 1891 to prove the uncountability of the real numbers and classify infinite cardinalities.

Consider the introduction to Hardy's book

 If, like Whitehead, you dispense with space as a container and focus of processes (or functions) then what really matters is how fast different functions grow or how quickly they converge to a steady state. 

In the fictional novel Borges is pretending to review, the search terminates just as in Attar's 'parliament of the birds', the thirty birds do find the Simurgh- which turns out to be themselves! But, it may be, they must search again to become more truly the Simurgh constituted by themselves. Can this process continue infinitely? The answer depends on whether error correction is faster than error accumulation. The imaginary novelist, Mir Bahadur Ali, issues a revised edition. Borges says it is inferior the original. Even if the search is perfect, the account of it may degrade. We lose what we gain the more we seek to explain what it is.

I believe Borges was aware of the influence of Karl Krause on Spanish literature & considered Yrigoyen (whom he passionately supported) as being part of that tradition. Krause used the German term das Urbild (meaning "the archetype," "prototype," or "original image" which both thought & reality seek to mirror) to describe the ideal or perfected model of humanity. This concept was fully laid out in his foundational 1811 book, Das Urbild der Menschheit (translated as 'The Ideal of Humanity' in English). Perhaps Yrigoyen's political failure disillusioned Borges. The project of creating a rationally harmonious Human League (Menschheitsbund) appeared to have run aground wherever you looked. 

Borges, a Republican and spirited anti-Fascist, was appalled by the terrible suffering caused by the Spanish Civil war and its aftermath. The temptation for a society to retreat into some non-human fabricated reality- as happens in Tlon, Uqbar- might be too great to be resisted