Sorting Pebbles into Correct Heaps

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Once upon a time there was a strange little species—that might have been biological, or might have been synthetic, and perhaps were only a dream—whose passion was sorting pebbles into correct heaps.

They couldn’t tell you why some heaps were correct, and some incorrect. But all of them agreed that the most important thing in the world was to create correct heaps, and scatter incorrect ones.

Why the Pebblesorting People cared so much, is lost to this history—maybe a Fisherian runaway sexual selection, started by sheer accident a million years ago? Or maybe a strange work of sentient art, created by more powerful minds and abandoned?

But it mattered so drastically to them, this sorting of pebbles, that all the Pebblesorting philosophers said in unison that pebble-heap-sorting was the very meaning of their lives: and held that the only justified reason to eat was to sort pebbles, the only justified reason to mate was to sort pebbles, the only justified reason to participate in their world economy was to efficiently sort pebbles.

The Pebblesorting People all agreed on that, but they didn’t always agree on which heaps were correct or incorrect.

In the early days of Pebblesorting civilization, the heaps they made were mostly small, with counts like 23 or 29; they couldn’t tell if larger heaps were correct or not. Three millennia ago, the Great Leader Biko made a heap of 91 pebbles and proclaimed it correct, and his legions of admiring followers made more heaps likewise. But over a handful of centuries, as the power of the Bikonians faded, an intuition began to accumulate among the smartest and most educated that a heap of 91 pebbles was incorrect. Until finally they came to know what they had done: and they scattered all the heaps of 91 pebbles. Not without flashes of regret, for some of those heaps were great works of art, but incorrect. They even scattered Biko’s original heap, made of 91 precious gemstones each of a different type and color.

And no civilization since has seriously doubted that a heap of 91 is incorrect.

Today, in these wiser times, the size of the heaps that Pebblesorters dare attempt has grown very much larger—which all agree would be a most great and excellent thing, if only they could ensure the heaps were really correct. Wars have been fought between countries that disagree on which heaps are correct: the Pebblesorters will never forget the Great War of 1957, fought between Y’ha-nthlei and Y’not’ha-nthlei, over heaps of size 1957. That war, which saw the first use of nuclear weapons on the Pebblesorting Planet, finally ended when the Y’not’ha-nthleian philosopher At’gra’len’ley exhibited a heap of 103 pebbles and a heap of 19 pebbles side-by-side. So persuasive was this argument that even Y’ha-nthlei reluctantly conceded that it was best to stop building heaps of 1957 pebbles, at least for the time being.

Since the Great War of 1957, countries have been reluctant to openly endorse or condemn heaps of large size, since this leads so easily to war. Indeed, some Pebblesorting philosophers—who seem to take a tangible delight in shocking others with their cynicism—have entirely denied the existence of pebble-sorting progress; they suggest that opinions about pebbles have simply been a random walk over time, with no coherence to them, the illusion of progress created by condemning all dissimilar pasts as incorrect. The philosophers point to the disagreement over pebbles of large size, as proof that there is nothing that makes a heap of size 91 really incorrect—that it was simply fashionable to build such heaps at one point in time, and then at another point, fashionable to condemn them. “But… 13!” carries no truck with them; for to regard “13!” as a persuasive counterargument is only another convention, they say. The Heap Relativists claim that their philosophy may help prevent future disasters like the Great War of 1957, but it is widely considered to be a philosophy of despair.

Now the question of what makes a heap correct or incorrect has taken on new urgency; for the Pebblesorters may shortly embark on the creation of self-improving Artificial Intelligences. The Heap Relativists have warned against this project: They say that AIs, not being of the species Pebblesorter sapiens, may form their own culture with entirely different ideas of which heaps are correct or incorrect. “They could decide that heaps of 8 pebbles are correct,” say the Heap Relativists, “and while ultimately they’d be no righter or wronger than us, still, our civilization says we shouldn’t build such heaps. It is not in our interest to create AI, unless all the computers have bombs strapped to them, so that even if the AI thinks a heap of 8 pebbles is correct, we can force it to build heaps of 7 pebbles instead. Otherwise, kaboom!”

But this, to most Pebblesorters, seems absurd. Surely a sufficiently powerful AI—especially the “superintelligence” some transpebblesorterists go on about—would be able to see at a glance which heaps were correct or incorrect! The thought of something with a brain the size of a planet thinking that a heap of 8 pebbles was correct is just too absurd to be worth talking about.

Indeed, it is an utterly futile project to constrain how a superintelligence sorts pebbles into heaps. Suppose that Great Leader Biko had been able, in his primitive era, to construct a self-improving AI; and he had built it as an expected utility maximizer whose utility function told it to create as many heaps as possible of size 91. Surely, when this AI improved itself far enough, and became smart enough, then it would see at a glance that this utility function was incorrect; and, having the ability to modify its own source code, it would rewrite its utility function to value more reasonable heap sizes, like 101 or 103.

And certainly not heaps of size 8. That would just be stupid. Any mind that stupid is too dumb to be a threat.

Reassured by such common sense, the Pebblesorters pour full speed ahead on their project to throw together lots of algorithms at random on big computers until some kind of intelligence emerges. The whole history of civilization has shown that richer, smarter, better educated civilizations are likely to agree about heaps that their ancestors once disputed. Sure, there are then larger heaps to argue about—but the further technology has advanced, the larger the heaps that have been agreed upon and constructed.

Indeed, intelligence itself has always correlated with making correct heaps— the nearest evolutionary cousins to the Pebblesorters, the Pebpanzees, make heaps of only size 2 or 3, and occasionally stupid heaps like 9. And other, even less intelligent creatures, like fish, make no heaps at all.

Smarter minds equal smarter heaps. Why would that trend break?