One of the most notorious episodes in the Aleph Club’s history of course was the time it agreed to purchase an infinite library from a mysterious South American salesman passing through on business.
“It will be just like that time we commissioned a life-size map of London,” muttered Ambrose darkly. But the Club Secretary was not a man easily deterred.
“It stands to reason that an infinite library will contain absolutely everything that a gentleman of good-standing ought to know.”
“And plenty that is absolutely none of a chap’s business.”
The impasse was however eventually resolved when the South American proposed taking his offer to the Oroborus Society across the road, which everyone agreed was absolutely out of the question.
The first problem was finding space for the new acquisition. Naturally, the Aleph Club boasted an extensive reading room of snug leather armchairs and crackling fireplaces, and quite exceptional views out across the Park; yet even then, several hours with a tape-measure and a piece of chalk was singularly unable to produce an infinite volume of storage. The purchase of infinite additional property along the Mall was deemed prohibitively expensive, and unlikely to be approved by the local council. Nevertheless, the Club Secretary was eventually able to satisfy himself that since an infinite library would take an infinite amount of time to unpack, the issue of actually providing infinite space could be infinitely postponed — or at least left for his successor to deal with at an infinitely later date.
As it transpired however, the entire library was delivered all at once in several musty wooden crates, which sat in the lobby and willingly submitted to a decidedly finite enumeration by several members of the Committee. The Club Treasurer immediately suspected fraud, until he noticed that each volume withdrawn from the crates was in fact infinitesimally smaller than the last, and that the entire series would therefore neatly converge into a finite number of inbuilt wooden shelves previously reserved for old copies of Wisden’s Almanac. The Chairman of the Hanging Committee complained that at a certain point, the books would become too small to be seen, which rather undermined the point of having a library; the Chair of the Works and Garden Committee objected that at a certain point, the books would become too small for anyone to be seen reading them, which was far more to the point; but then Ambrose remarked that at a certain point, the books would be too small for anyone to tell if the Chair of the Works and Garden Committee was reading one or not, and this was generally agreed to be a satisfactory compromise.
The second problem arose a few weeks later when the Wine Steward — uncharacteristically befuddled by a disagreeable vintage — took the unusual step of actually borrowing one of the new books. This particular volume explained that through a simple process of repetition and permutation, its own text could be made to replicate that of any other book within the infinite library. Various mathematical squiggles and syllogistic maxims were duly offered as proof. The Wine Steward wasn’t sure if he understood all of this, and when he didn’t understand something he always made sure to deflect suspicion with a hearty chuckle; but when he was unable adequately to explain the source of his humour, the natural fear of missing out took over, and everybody else immediately demanded to borrow the book and tempers began to fray.
Fortunately, the Head Porter was quick-witted enough to reason that an infinite library must presumably include an infinite number of copies of each of its infinite number of books — the Wine Steward’s book notwithstanding — and every effort was hence made to locate the literary doppelgängers. These proved to be both plentiful and readily discovered, which again caused the Club Treasurer no small degree of agitation at the prospect that they might indeed have been swindled after all. An infinite amount of additional storage space was subsequently created for these more desirable books by simply doubling the catalogue number of every volume already in the collection, and thereby leaving all of the odd catalogue numbers free to fill. The Club Secretary was delighted at having apparently acquired two infinite libraries for the price of one, and inquired as to whether he could get even better value for money by cataloguing everything to an even higher power; but by that point, someone had found a book that promised to list all the volumes in the library that didn’t list themselves, and he had to spend a few days in the country to recover.
The third and final problem was only surfaced a few months after the initial purchase. One of the more serious-minded, younger members of the Club had sequestered himself in the infinite library with a lot of notepads and pencils, and had finally declared that there was a volume missing. This book — he complained — differed from the first book in the collection by the first word on the first page, and it differed from the second book in the collection by the second word on the second page, and it differed from the third book in the collection by the third …
The Club Treasurer was understandably delighted that his persistent anxieties had finally been vindicated, but equally concerned at the subsequent failure to locate the mysterious South American. Ambrose remarked that an infinite library would presumably contain a book — indeed, an infinite number of books — detailing where the rogue could be found, but this comment was considered to be in very poor taste. It was decided therefore that the Aleph Club would sell the infinite library to the Oroborus Society across the road; the President of the Society seemed delighted at the prospect, although he could not shake a nagging doubt that something like this had happened before.
Paul Dicken has worked in academia and politics, and now lives in rural England where he continues to write fiction.