Sort­ing Pebbles Into Cor­rect Heaps

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’not’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?