Free Incandescence by Greg Egan

if they were, secretly, variations on a single theme. The elusive common thread had yet to be delineated, but it seemed plausible to Rakesh (albeit with all the fine details glossed over) that sufficient effort would eventually reveal one dazzlingly beautiful and powerful insight that accounted for the subtle fivefold symmetries they had charted.
    Parantham said, «So much for the cliché that embodiment is the antithesis of abstraction.» She sounded impressed, and Rakesh suspected that she'd looked more closely at the work-in-progress than he had.
    «I've always believed the opposite,» Fith replied firmly. «You don't need to turn every mathematical space into a kind of scape, and literally inhabit it, in order to understand it. Anchored in three dimensions, obeying mundane physics, we can still reason about any system you care to describe with sufficient clarity. That's what
general intelligence
means, after all.»
    «How long have you been searching for something like this?» Rakesh asked.
    «Thirteen hundred years,» Paba replied. Rakesh glanced at her précis; that was most of her life. «Not full-time,» she added. «Over the years, for one or two days in every ten or twenty as the mood has struck us.»
    Sida said, «I've known people who've given their whole lives over to the same kind of search, but if they find nothing in a century or two they usually become discouraged. The only way we could do this was by refusing to make it the be-all and end-all. The only way we could afford to try was by ensuring that we could also afford to fail.»
    «That sounds like a good strategy,» Rakesh said. He had never been drawn to the same ethereal heights himself, but he wondered if travelers could benefit from a similar approach. His youthful vow to leave his home world after exactly one thousand years, as if he'd expected fate to hand him the ideal destination at that very moment, seemed increasingly foolish. He might have passed another two or three centuries happily on Shab-e-Noor, if he'd found some way to make himself receptive to the kind of serendipity that had ultimately rescued him from the limbo of the node, without subjecting himself to the same miserable feeling that every day without success was wasted.
    The five of them sat talking until noon, then the quads took them to the guest shelter to eat. Rakesh's body was flexible enough to make use of almost anything — or at the very least to survive its ingestion without harm — but the quads had a garden that was equally flexible. Instructed in his tastes, within half an hour the plants were able to form fruits and leaves that even his wild ancestors would have found nourishing and delicious. Fith insisted on cooking them into a spicy stew, using tools rather than his mouth to manipulate the ingredients, no doubt having been briefed by Massa's library on certain peoples' preference for food wholly unmasticated by others.
    This, Rakesh thought, was the Amalgam at its best. Even these citizens who shared no molecular ancestry with him had made him welcome on their planet, in their town, at their meal. They had shared their ideas and discoveries, and listened attentively to his own stories and opinions.
    His next hosts would be very different. For one and a half million years, the Aloof had made it clear that they needed no one's company, no one's stories, and no one's opinions but their own.
    Nevertheless, it seemed that they wanted something now: some contact, some flow of information. It had started with Lahl, but Rakesh had no idea where it would end, or what the transaction would finally amount to. A disinterested exchange of scientific data? An act of trade, of mutual benefit? Munificence? Misunderstanding? Deception? Enslavement?
    He and Parantham stayed with their friends until the stars of the bulge filled the sky, then they prepared themselves to walk among them.

6
    «Three,» Zak said, «is a beautiful number. Three is what the map shows, which means somebody