Sunday, 27 July 2014

The Reflection principle & Borges's Aleph

Leibniz wrote, in section 56 of the Monadology: “Each simple substance has relations that express all the others, and is in consequence a perpetual living mirror of the universe”.

Borges's Aleph is a small spot only viewable from a certain angle when lying on the floor of a rodent infested Buenos Aires cellar. In it, everything in the Universe is simultaneously viewable. Yet, Borges comes to the conclusion that it is a false Aleph. Why?

Well, for the purposes of the higher criticism- i.e. writing tendentious shite about modish Modernist texts we haven't re-read since we were ourselves equally psilosophical College Sophomores- one approach is to argue that, by any Reflection Principle which itself has enough structural features- or a, Tarski type, suitably dense Relation Algebra- to fully specify the pre-image/pratibimba or Universal Set (V) for any given empirically observed Aleph, it must be the case that there is no way of distinguishing if that Aleph is merely partial or actually complete. Indeed, by a Rabzorov Rudich type argument, the probability is overwhelming that it must simply be false.

A merely literary mimesis of the above requires, as so often happens on this blog, making a distinction between cataphatic and apophatic theology.

Whitman's method was cataphatic- i.e. listing sonorous shite. Borges, notoriously, was a heteroclite Whitman- his lists undermine themselves. He gives us a credible Aleph by means of a vetriginously veridical cataphasis- 'On the back part of the step, toward the right, I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realised that this movement was an illusion created by the dizzying world it bounded. The Aleph’s diameter was probably little more than an inch, but all space was there, actual and undiminished. Each thing (a mirror’s face, let us say) was infinite things, since I distinctly saw it from every angle of the universe. I saw the teeming sea; I saw daybreak and nightfall; I saw the multitudes of America; I saw a silvery cobweb in the center of a black pyramid; I saw a splintered labyrinth (it was London); I saw, close up, unending eyes watching themselves in me as in a mirror; I saw all the mirrors on earth and none of them reflected me; I saw in a backyard of Soler Street the same tiles that thirty years before I’d seen in the entrance of a house in Fray Bentos; I saw bunches of grapes, snow, tobacco, lodes of metal, steam; I saw convex equatorial deserts and each one of their grains of sand; I saw a woman in Inverness whom I shall never forget; I saw her tangled hair, her tall figure, I saw the cancer in her breast; I saw a ring of baked mud in a sidewalk, where before there had been a tree; I saw a summer house in Adrogué and a copy of the first English translation of Pliny — Philemon Holland’s — and all at the same time saw each letter on each page (as a boy, I used to marvel that the letters in a closed book did not get scrambled and lost overnight); I saw a sunset in Querétaro that seemed to reflect the colour of a rose in Bengal; I saw my empty bedroom; I saw in a closet in Alkmaar a terrestrial globe between two mirrors that multiplied it endlessly; I saw horses with flowing manes on a shore of the Caspian Sea at dawn; I saw the delicate bone structure of a hand; I saw the survivors of a battle sending out picture postcards; I saw in a showcase in Mirzapur a pack of Spanish playing cards; I saw the slanting shadows of ferns on a greenhouse floor; I saw tigers, pistons, bison, tides, and armies; I saw all the ants on the planet; I saw a Persian astrolabe; I saw in the drawer of a writing table (and the handwriting made me tremble) unbelievable, obscene, detailed letters, which Beatriz had written to Carlos Argentino; I saw a monument I worshipped in the Chacarita cemetery; I saw the rotted dust and bones that had once deliciously been Beatriz Viterbo; I saw the circulation of my own dark blood; I saw the coupling of love and the modification of death; I saw the Aleph from every point and angle, and in the Aleph I saw the earth and in the earth the Aleph and in the Aleph the earth; I saw my own face and my own bowels; I saw your face; and I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon — the unimaginable universe.'

Rabindranath Tagore said- 'Kadombini moriya proman korilo she more nai' (Kadambari dies only to prove she was still alive) and though he was referencing the baroque Sanskrit novel, not his beloved  sister-in-law's suicide, there is a univocity to this epigram which redeems that too hirsute and prolix Sage.

By contrast, Borges's various Kadambaris- whose V precludes Victoria Ocampo, for whom Rabi had a lech- whether called Beatrice Viterbo or Teodolino Villar, did not die merely to prove they were alive but, like the risen Christ at the end of the Gospel of John, in order to become the protagonist of such Epic Agons as, were each written down in a book, not the World- nay, not the Library of Babel!- could contain them all. 
Which is why their Alephs are false and Zahirs forgettable. 
If only because 'Borges & I' represents a Red Queen's race.

In this respect, Borges ever trembles on that threshold boldly crossed by both true Mannerists (e.g Riti kavya a la Jagganath Pundit) & proto-Marxists (as in the subaltern Shlok of Nund Reshi) videlicet; Love is a Second Creation. Its God Grief.

What of Cantor's Aleph & the too Christian Godel?

'Hao Wang records Godel’s argument in item 8.7.14 of his Logical Journey- 'Consider a property P(V, x), which involves V. If, as we believe, V is extremely large, then x must appear in an early segment of V and cannot have any relation to much later segments of V. Hence, within P(V, x), V can be replaced by some set in every context. In short, if P does not involve V, there is no problem; if it does, then closeness to each x helps to eliminate V, provided chaos does not prevail.”

This sounds a bit like the Secretary problem also known as the 1/e stopping rule. If so, we have a proof of the (almost) Trinity

“There is also a theological approach, according to which V corresponds to the whole physical world, and the closeness aspect to what lies within the monad and in between the monads. According
to the principles of rationality, sufficient reason, and preestablished harmony, the property P(V, x) of a monad x is equivalent to some intrinsic property of x, in which the world does not occur. In other
words, when we move from monads to sets, there is some set y to which x bears intrinsically the same relation as it does to V. Hence, there is a property Q(x), not involving V, which is equivalent to P(V, x). According to medieval ideas, properties containing V or the world would not be in the essence of any set or monad”.

  But those properties  would be in the Holy Ghost against whom alone sins are unpardonable.
But, what is Sin (Evil being Empty) other than its own corpus delecti?
Thus all Sin is formally identifiable as a failure to properly dispose off Sacrifice's surplus.
What is unpardonable is to ascribe e's excess over 'two-ity' to anything but V
Wherever two are gathered, there is the lover & the rival.
When they disperse there remains only the Zahir of their Aleph.
And that is always the smallest coin in circulation amongst us.
So, drink up, & spend that penny already.

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