By Benjamin Rosenbaum
18 June 2012
There's an angle, aq, which is like breakfast in a muddy room, like the weight of the morning: pale-gold as butter and heavy as doubt.
It lies between the angle ap (sharp and rueful as sand under your bottom lip) and the angle ar (stern and scouring as winds of incandescent plasma slashing through your fringe, as you make your way through the cloud-vaults of some middle heliosphere).
Let's call our protagonist Not Very—though a more accurate translation of en's actual name would be any linear function mapping the set of all sets containing algorithmically computable functions onto the set of all sets containing no such functions.
The angle aq was timelike for Not Very, and it had passed, and Not Very had consumed or expelled or involuted those elements of en's surround which served en for purposes analogous to sustenance, extension, and glorification of present being, and Not Very was feeling sorry for enself; and so en went to see how it was going with the new places Unlike Themselves was making.
Much of what was timelike for Unlike Themselves was spacelike for Not Very; in addition, their ontologies were skew, so it was difficult to converse. We all know how difficult it is, to live together across incommensurability. But Not Very was lonely, or as close to lonely as you can be in an ontologic space in which the category "number" does not obtain (and in which, therefore, you cannot have more, or fewer, friends). So even difficult conversation was better than none.
Not Very wandered among static images of Unlike Themselves' history, until en found the images in which Unlike Themselves was wandering among images of Not Very's now. That's how they beat the time-skew problem: Not Very would express sentiments and opinions aloud, then shuffle through the images to find those which contained (and had always already contained) Unlike Themselves' responses.
Ontology still divided them. This "counting"—apparently a kind of measuring related to sets and entities—seemed terribly important to Unlike Themselves. Not Very's world, in turn, was richer in modality: Not Very had Coulds, and Woulds, and even Shoulds; en could be mournful or giddy over hypotheticals. For Unlike Themselves, there was only Is.
aq passed, stern and scouring.
"What are you making?" Not Very asked of the emptiness. Then shuffled, shuffled through the images, for the answer.
"Oh, places," Unlike Themselves was saying.
"Do the places have many?" Not Very asked eagerly. "Many" had something to do with counting.
"The places are many," Unlike Themselves said patiently. "Manyness is a property of places. You could ask 'how many.'"
"Ah yes," said Not Very. "And then you will specify a spot on the 'number line,' and that will have something to do with the places. I remember."
The memory was disappointing. We'll call what Not Very did then a "frown."
"Yes," said Unlike Themselves. "But here is something for you. You have infinity, yes?"
Not Very nodded, suppressing a twinge of jealousy. Not Very's universe was physically finite, so en had only mathematical infinity—it was one of the Coulds. It was as close as Not Very came to counting: none, Self, Other, some, infinity. But Unlike Themselves' universe had real infinity: its freedom, its terrifying oceanic release.
There was no definite measure of size where Not Very was; no finite "biggers" and "smallers." Certainly Not Very's world had no endpoint; certainly it was contiguous; certainly Not Very had never fallen into some pothole of unbeing where world was lacking. Finity made little everyday difference for Not Very. But still: Not Very's time and space were bounded, their countlessness a symptom of poverty, not abundance.
Unlike Themselves said: "Look—see, how I shape this little aspect of the place . . . ?"
Unlike Themselves had twisted something, and let the place unfold, angling its axes so they could glimpse its whole history at once. Age enough for myriad complexities to bloom, architectures of energy and matter and sentience; but not a limitless age. The place curved in on itself, pulled together by its isness, munching meditatively on its own time-tail. A finite universe, like Not Very's.
"But now if I do this—"
A twist the other way, and a new place: this one bloomed, exploded like a firework, rushed endlessly on, blown outwards by invisible breath.
Compared to the infinite, the finite is precisely nothing: were the first universe subtracted from the second, it would leave it utterly intact. Not Very felt an echo of that incessant outward pressure within enself, a longing acute and ghostly as neutrinos slicing through a moon.
"Only that little twist!" Unlike Themselves said. "Only that tiny tweak—"
On a finite hinge, Not Very thought, swings the door from finity to infinity.
"Have I upset you?" Unlike Themselves asked.
"No," Not Very said. "I can mourn better now. Now I know what it looks like—that little twist . . . it is good to mourn precisely!" (Let us call what Not Very showed then, "tears"; let us call it "laughter.") "It is well. It is well."
as was approaching, an angle drowsy and thick as a pattering rain of hydrogen nuclei falling onto the outer surface of a red and dying galaxy. Time for Not Very to see about other things.
"Thank you," Not Very said, and Unlike Themselves smiled, grateful that their overlap encompassed gratitude.