Tag Archives: Entropy

Borges and the infinite dance of entropy

24 Apr


As discussed in a previous post, time is not real. There is no flow: past, present and future cannot be sensibly defined and there is nothing yet to counter the position held by the second law of thermodynamics, namely that entropy – the general disorder of the universe – is always on the increase. Otherwise, I feel much as Augustine of Hippo did when he wrote of his understanding of time as a kind of hunch: ‘If no one ask of me, I know; if I wish to explain to him who asks, I know not.’

But ever-increasing disorder, that I can understand, both in the dictionary sense of: Entropy: lack of order or predictability; gradual decline into disorder – but also in a more general, or literary way.

Last night I read two late stories by Borges that seemed to be tugging at the same idea: that we live in a world governed by forces of increasing entropy. The stories were ‘The Book of Sand’ and ‘Blue Tigers’. While I do not wish to limit either of these to a single explanatory reading, it is interesting to consider the way they approach the same conceptual material through slightly different means. In ‘The Book of Sand’ (published in the collection of that name in 1975, when Borges was seventy-six) the narrator, a reclusive Borges figure who lives ‘alone, in a fifth-floor apartment on Calle Belgrano’ and who used to work – as Borges did – in the National Library on Calle México, is visited by a stranger who bears a strange book: an ‘infinite book’, in which, as the visitor explains: ‘No page is the first page; no page is the last. I don’t know why they’re numbered in this arbitrary way, but perhaps it’s to give one to understand that the terms of an infinite series can be numbered any way whatever.’ He goes on: ‘If space is infinite, we are anywhere at any point in space. If time is infinite, we are at any point in time.’

The narrator is sold. The book, as he can see, is unique. If you find a page – as he does, with  a small illustration of an anchor drawn in pen and ink – and then you attempt to find it again, you will not. That page will have gone, and will never return. Nor is it possible to find the book’s beginning, or its end. It is, the narrator decides, ‘a nightmare thing, an obscene thing  . . . that defiled and corrupted reality.’ But that realisation comes later. First, he must acquire it, and to do so he exchanges his pension (from the library) and his very valuable black-letter Wyclif Bible. The monstrous book obsesses him. He spends the day leafing through it, never finding the same page twice – infinite entropy – and the nights, during ‘the rare intervals spared [him] by insomnia’ dreaming of it.

In the end, he returns to the library in which he spent his working life, and which contains ‘nine hundred thousand books’ and he hides it there, ‘on one of the library’s damp shelves’.

This exploration of infinite chance, or – which may be the same thing –  infinite chaos, neatly reflects, or expands upon, the principle of the second law of thermodynamics; that entropy can only increase over time. And as if that were not enough, Borges re-visits the idea a few years later with his story ‘Blue Tigers’, published in his final collection, Shakespeare’s Memory (1983). Incidentally, both this volume and its predecessor, The Book of Sand, open with a variation on the same theme: a meeting between Borges and his doppelgänger. ‘The Other’, the opening story of the 1975 collection, tells of a meeting on the banks of the Charles River in Cambridge, Massachusetts, between a seventy-year-old Borges and his twenty-year-old, Geneva-dwelling self, while ‘August 25, 1983’ tells a parallel story between an eighty-four year old Borges and his sixty-one-year-old double. Curious – or, considering this is Borges, not so curious –  that the themes of time and chance should be so consistently, or insistently linked in each collection.

But to move on: ‘Blue Tigers’ tells the story of a somewhat tetchy individual, a Scottish professor of ‘Eastern and Western Logic’ [?!] at the University of Lahore. The year is 1904. He is obsessed (as was Borges) with tigers, especially, curiously, blue tigers, of which he dreams: ‘tigers of a blue I had never seen before, and for which I could find no word.’ One day he hears rumours of a blue tiger roaming near ‘a certain village miles from the Ganges.’ He has to go there: ‘Once again I dreamed of the blue tiger, throwing its long shadow as it made its way over the sandy ground. I took advantage of the end of term to make a journey to that village, whose name (for reasons that will soon be clear) I do not wish to recall.’

At the unnamed village, things do not go well for the Scotsman. Although the villagers speak vaguely of the tiger, and recite rumours of its deeds, he never catches sight of it. The villagers are wary of him, evasive. Moreover, he hates the jungle: ‘It crept virtually into the huts. The days were oppressive, and the nights brought no relief.’ Next to the village is a hill, which the villagers never ascend. They claim it has sacred properties and appear afraid of it. The Scotsman has the notion that the tiger lives up the hill so one night he climbs to the summit, which is not very high, and there he finds lots of tiny blue stones, in the shape of disks. They are the same blue as the tiger of his dream. He collects a few of the stones and puts them in his pocket. He returns to the village and sleeps. In the morning the stones have multiplied: ‘’When I opened my hand, I saw that it held thirty or forty disks: I’d have sworn I’d picked up no more than ten.” And so it continues. The stones, or disks are what the villagers call blue tigers, hence their evasiveness. The Scotsman’s relationship with his hosts becomes problematic. He is obsessed with the stones. They too are an embodiment of ever-increasing entropy: they increase in number without cease and the same stones never appear more than once. He returns to Lahore with a handful of stones in his pockets. They multiply. He experiments with them, cutting crosses in them, drilling notches through their centres. Mostly, the marked stones disappear ‘forever’. One stone, cut with a cross  reappears ‘from its journey into the void’, but it is an exception. ‘What mysterious sort of space was this, which in obedience to inscrutable laws or some inhuman will absorbed the stones and then in time threw an occasional one back again?’

Like the infinite book presented to the ex-librarian in ‘The Book of Sand’, these ‘insensate stones that propagate themselves’ are an abomination: they too defile and corrupt reality. The Scotsman seeks redemption at the mosque of Wazil Khan, plunging his hands into the water of the fountain of ablutions. There he is approached by a beggar, who asks for alms.

‘In the soft light I could make out his turban, his sightless eyes, his sallow skin, his grey beard. He was not very tall.

He put out a hand to me, and said, still softly:

“Alms, oh Protector of the Poor . . .”

I put my hands in my pocket.

“I have not a single coin,” I replied.

“You have many,” was the beggar’s answer.

The stones were in my right pocket. I took one out and dropped it into his cupped palm. There was not the slightest sound.

“You must give me all of them,” he said. “He who gives not all has given nothing.”

I understood, and I said:

“I want you to know that my alms may be a curse.”

“Perhaps that gift is the only gift I am permitted to receive. I have sinned.”

I dropped all the stones into the concave hand. They fell as though into the bottom of the sea, without the slightest whisper . . . ‘


Throughout Borges’ career, he was preoccupied, as he himself once said, with ‘games of time and infinity’, and he returned again and again to the theme of time, of the inexorable journey from a past we cannot revisit to a future we cannot know. But he was also, it would seem – especially in his later years – obsessed with the indecipherable nature of a reality in which matter – things – repeat themselves in the infinite dance of entropy.