Endower Institute researchers today announced the discovery of a completely new kind of number, the "like number." Like numbers are the first new kind of number to be introduced into mathematics since Donald Knuth's "surreal numbers." Surreals were previously considered the most exotic form of numbers, but like numbers, according to lead researcher Dr. Pangloe, are "an even wilder expansion of the conventional idea of what a 'number' is allowed to be."

Unlike most mathematical concepts, "like numbers" were not discovered by a process of abstract reasoning, but through analysis of natural language. In fact, according to Dr. Pangloe, "Most people have an intuitive understanding of like numbers." He blames the failure of mathematicians to study like numbers on "an archaic attachment to the Victorian notion of 'formal' proof. This fetish for 'formality' has blinded so-called mathematicians from embracing what was right in front of them all along."

Like numbers, although they lack familiar numerical properties such as transitivity, associativity, and operability, have a range of new properties such as plausibility, gynormity, and pertinence (or, in some formulations, prurience.) Like numbers form an algebriac structure and support all the operations of a conventional field—addition, multiplication, subtraction, and division—but also allow for allusion, revision, recreation, and interpretation, among many other previously unknown operations.

A like number is notated using a new technique called indifferent expressions—similar in form to lambda expressions. As a conventional number is defined in lambdas as a higher-order anonymous function, a like number is defined in indifference as a higher-order inscrutable gesture. Indifferent expressions, however, are much more general in their potential applications than lambda expressions, and methods are now being developed to apply them not only to mathematical entities but to social phenomena and physical objects. "Just a few days ago," said Dr. Pangloe, "one of my students, in my presence, altered the deadline on his paper from three weeks to like a month. I myself have on several occasions reduced—my wife can testify—three, six, even ten drinks to like one. These are just the kind of real-world applications that mathematicians have been allowed to ignore for much too long."

The research will be published in the forthcoming inaugural edition of the Journal of Experimental Mathematics (Endower Institute J-16). This new publication will be edited by the leading members of the controversial X-Math movement. "It's time," said Dr. Pangloe in his office, pointing to a poster behind him with the movement's symbol, a flaming brain, "for mathematicians to leave behind their obsolete elitist claims of a special status among the sciences and embrace more modern, creditable methods."

Zemurray Gardens

Samuel Zemurray was the original banana republican. His Zemurray Fruit Company would later be folded into United Fruit, and Zemurray would race to United Fruit's rescue when it was in danger; but even in the 20s Huey Long could center his foreign policy on the principle that US soldiers should not be fighting in Central America at the behest of a banana peddler.

But then what are the Zemurray Gardens? Did this hard-edged businessman possess an inner domesticity, did he retreat to a flowery sanctuary to soften his heart? Alas, no; the gardens that bear Zemurray's name were planted against his wishes. When he bought 150 acres of pine woods he reserved a certain portion for his home and assigned the rest to timberland. He thought gardening wasteful.

His wife, Sarah, did not agree. While he was away she hired a gardener and began to plant in secret. The soil (I know it well) was not friendly: thin soil, roots thick as carpets or hard and heavy as rocks, dirt so clayey—what was once the silt in the soil of the land above the Pontchartrain is now the land below the Pontchartrain—so clayey, so dense and heavy, that it holds shapes. (I once repaired a wall by packing wet dirt over a framework of sticks; it was meant to be temporary, but it has lasted five years.) They lay paths through the pine woods and lined them with azaleas, thousands of azaleas of every color. She waited, perhaps, until the azaleas were blooming; then she told her husband. I would like to think that beauty moved him; whatever his reason, he spared the garden. Now above board, she enlarged and dramatized her garden: clearings with statuary, a hill, a mirror lake, an island, cypresses, camellias, a bamboo grove.

But even when I saw it the garden still had a sense of secrecy, layer after layer hidden from each other. From the highway without could be seen only pines behind pines; from the house (the gardens remained private, open only when the azaleas were blooming) and the bright garden and sward attached to it, dark paths led away into the woods. The paths were tunnels really, with dirty floors, excavated just wide enough for a jeep, stretching on and on in brilliant hypnotic monotony, color and shade, high interwoven pines swaying and admitting sunlight in waves as they swayed, sunlight on the azaleas.

Azaleas are too little celebrated in literature because they are difficult to evoke. Their flowers are of no particular size—on the order of pennies and buttons; their leaves and stem are plain and spare; and their colors are frustratingly pure—no glossiness, iridescence, variegation or sheen, just pure bright colors straight off the palette. If pigment was a stuff that fell like snow, if it had fallen on the paths here red, here yellow, here orange, and the paths had been cleared by a careless shoveler, who threw drifts of pigment over the bushes beside the path: that was how it looked. And in the shade of the azaleas sparks smoldered, the coralred berries of ardisia, and bits of broken mirror still full of sky, the skyblue of Canterbury bells.

You could—I did—go around and around this way; but you could also turn off towards the lake; or (since someone left the gate open) you could turn off on footpaths through the timberland, and, if you knew how to venture into unfamiliar woods without getting lost, rest your eyes on green and green for a time. But getting back, you could leave the paths for the lake; and stand on the bridges or sit on the island, or turn off into one of the sheltered clearings, and visit with the improbable figures of Actaeon and Diana, having long ago gotten over their bewilderment at finding themselves in so strange a land. Somewhere there was a grove of moso bamboo, thirty feet high. Somewhere there was the cemetery of the first settlers here, men of England.

This garden held gardens, gardens inside gardens, all mutually secret and enclosed. Gardeners speak lightly of rooms; Zemurray Gardens was a labyrinth—not a maze, not urgent or perplexing, but a labyrinth, long, slow, meditative and sacred.

And over everything, the trees swaying. Even when the air was still, the trees were swaying. On my first visit I looked up at the pines swaying and listened to their creaking and thought: If a real storm ever hits this place it will be a disaster. I was right. The storm came. (Yes, that one, I have heard and written the name often enough). The trees fell and broke, the paths collapsed—it happened to me, how strange that a path could just disappear—the storm came and Zemurray Gardens was destroyed. You can look at pictures of it on Flickr—it is worth doing—but these photographers pictured the wrong things; they gave the wrong idea. But I remember it, in my mind and in my garden. The ardisia is just starting to spread.


The Kptsha-Knr (preferred spelling) were a reclusive tribe of hunter-browsers discovered deep in the rainforest by university researchers who got lost on their way to Seattle in 1922. They had been isolated from outside contact, with Europeans or with other natives for their entire history. In fact, they believed themselves to be the only people in the world.

The language of the Kptsha-Knr, Qx, was a true isolate, having no relationship to any other known language (although recent efforts have been made to link it to Basque). Qx exhibits many unique features, not least a grammar described by the first researchers as "polyanalytic" and a quality of "neutrality" between speech and nonspeech sounds which allows the language not only to be spoken but also clicked, coughed, sighed, sputtered, swallowed and sneezed.

Once Kptsha-Knr researchers had subjected the university researchers to the surgical liberation necessary for them to pronounce the language, they began corroboration on a dictionary. This thousand page scholarly folio dictionary (Qx declensions and conjugations are mathematically incompressible) would become a bestseller on the strength of a popularized ethnography of the Kptsha written by a visiting journalist, I Saw The Captchas: Among the Backwards Primitive Subhuman Others: As Told by the Dauntless Manly Discoverers Who Penetrated Their Stagnant Isolation and Exposed Their Feeble Barbarism to the Hard Gaze of Civilized Man. (The book is curiously difficult to find in modern libraries and appears to have been removed from a number of bibliographies with white-out.)

A brief "Captcha craze" caught the imagination of the world. For a time it seemed that everyone was doing the Cap Cha Cha, singing Captain Captcha's Cap Chap, or sporting slang straight from the Captcha lexicon—who can forget F. Scott Fitzgerald's immortal short story Time for Knprd or Dorothy Parker's lyric,

Say you'll come up
And we'll brgrp.

But the fad could not last, and the Captchas were forgotten and neglected until finally, in the 1950s, their culture was destroyed by the arrival of rock and roll.

The Captchas might have faded from memory entirely were it not for a film made in the last years of the Captcha craze, Captcha the Flag. An early talkie, the film's wooden acting, hokey script, and "Dialogue-coach voices discussing with gravity the fine points of roasting a chipmunk" (during the scene in which the Nameless Heiress has discovered a half-starved Henry Stark in the woods after her plane crash) endeared it to the hipster subculture of the 1990's. (The film is not available in restoration, due to the difficulty of separating the dialogue in the Captcha scenes from background static.)

Thus when programmers in the early 2000s began discussing the idea of a countermeasure for spam that would be "like the Navajo code, only more so," the Captcha lexicon was the natural choice. And so the Captcha, extinct, unremembered, unmourned, speak once more.


Ideas are the smallest units of thought that can be communicated. Ideas may run to many words in expression because they require a structure of words to reproduce their context. Word are required to transmit to one context a thought that is wordlessly implicit in another, an idea, which may be a limitlessly subtle inflection of its original context. At the right time, a few gestures, indeterminate in themselves, totally dependent for their meaning, may express all that a sentence can tell at the wrong time. (I indulge in the parable of an ancestor who on the hunt, by no more than the slightest stirring of the arm and extension of the finger, indicated, "No, the other way," and turned failure into success.)

The constituents of the minimum unit of communicable thought must be units of incommunicable thought. I name these evocations, since they are recognized as evocative. The mind cannot make its own evocations; it must collect them as surely as a bird must collect grit for its gizzard. And like a gizzard stone a single evocation may remain in use for a long time, with a valency that internally and unconsciously parallels the external and conscious use of a tool.

Being incommunicable, evocations cannot be defined. Yet they can be traced. What is it that the mind seeks out, hoards, counts over? What mental experiences, without uses of their own, are approached with the same gravity as the most useful tasks? Review the mind's senses: how an image burns onto the mind's eye; how a word echoes and echoes in the mind's ear.

Victims of trauma are at the mercy of recurrence and flashback—at the mercy of the little things, the little fragments of experience, the mere reminders that reel them backwards into memory. This is a warped mirror and retrogradation of a healthy movement of the mind. Reminders drag backwards into memory; evocations lead forward to ideas.

Though evocations are usually single words or images, they need not be. Some evocations are ideas in themselves, constituent to more complex ideas. Whole works of art, whole journeys, whole friendships may be valent as evocations. In certain moods the whole world seems to me the evocation of some superb and singular idea I would lose my soul to enphrase—like an utterer of God's true name, a seraph would circle me to either side, declaring that I had gained the world, and lost the world to come.

A simple example of the use of evocations is at hand. A word catches the attention of a reader. The word is obscure, a little grandiloquent, but it charms him. It has a good rattling rhythm to it, almost a swing. A single stop between two liquids to one side, and a liquid and a sibilant to the other anticipate a euphonious final consonant cluster. Moreover it has a valency that he cannot quite define. Some time later this reader becomes conscious of blogs and the interesting things being done with them. Surely this is an opportunity; but what can he do? He lacks the quickness and lightness for blogging as such. Too often has nothing to say. So he puts the thought aside until he reads Boswell tell how Johnson wrote out a number of the Rambler with the printer's devil looking on. Then he has an idea: "Of course—not ruricolistThe Ruricolist!"