Similarity Clusters

Once upon a time, the philoso­phers of Plato’s Academy claimed that the best defi­ni­tion of hu­man was a “feather­less biped”. Dio­genes of Sinope, also called Dio­genes the Cynic, is said to have promptly ex­hibited a plucked chicken and de­clared “Here is Plato’s man.” The Pla­ton­ists promptly changed their defi­ni­tion to “a feather­less biped with broad nails”.

No dic­tio­nary, no en­cy­clo­pe­dia, has ever listed all the things that hu­mans have in com­mon. We have red blood, five fingers on each of two hands, bony skulls, 23 pairs of chro­mo­somes—but the same might be said of other an­i­mal species. We make com­plex tools to make com­plex tools, we use syn­tac­ti­cal com­bi­na­to­rial lan­guage, we har­ness crit­i­cal fis­sion re­ac­tions as a source of en­ergy: these things may serve out to sin­gle out only hu­mans, but not all hu­mans—many of us have never built a fis­sion re­ac­tor. With the right set of nec­es­sary-and-suffi­cient gene se­quences you could sin­gle out all hu­mans, and only hu­mans—at least for now—but it would still be far from all that hu­mans have in com­mon.

But so long as you don’t hap­pen to be near a plucked chicken, say­ing “Look for feather­less bipeds” may serve to pick out a few dozen of the par­tic­u­lar things that are hu­mans, as op­posed to houses, vases, sand­wiches, cats, col­ors, or math­e­mat­i­cal the­o­rems.

Once the defi­ni­tion “feather­less biped” has been bound to some par­tic­u­lar feather­less bipeds, you can look over the group, and be­gin har­vest­ing some of the other char­ac­ter­is­tics—be­yond mere featherfree twoleg­gi­ness—that the “feather­less bipeds” seem to share in com­mon. The par­tic­u­lar feather­less bipeds that you see seem to also use lan­guage, build com­plex tools, speak com­bi­na­to­rial lan­guage with syn­tax, bleed red blood if poked, die when they drink hem­lock.

Thus the cat­e­gory “hu­man” grows richer, and adds more and more char­ac­ter­is­tics; and when Dio­genes fi­nally pre­sents his plucked chicken, we are not fooled: This plucked chicken is ob­vi­ously not similar to the other “feather­less bipeds”.

(If Aris­totelian logic were a good model of hu­man psy­chol­ogy, the Pla­ton­ists would have looked at the plucked chicken and said, “Yes, that’s a hu­man; what’s your point?”)

If the first feather­less biped you see is a plucked chicken, then you may end up think­ing that the ver­bal la­bel “hu­man” de­notes a plucked chicken; so I can mod­ify my trea­sure map to point to “feather­less bipeds with broad nails”, and if I am wise, go on to say, “See Dio­genes over there? That’s a hu­man, and I’m a hu­man, and you’re a hu­man; and that chim­panzee is not a hu­man, though fairly close.”

The ini­tial clue only has to lead the user to the similar­ity cluster—the group of things that have many char­ac­ter­is­tics in com­mon. After that, the ini­tial clue has served its pur­pose, and I can go on to con­vey the new in­for­ma­tion “hu­mans are cur­rently mor­tal”, or what­ever else I want to say about us feather­less bipeds.

A dic­tio­nary is best thought of, not as a book of Aris­totelian class defi­ni­tions, but a book of hints for match­ing ver­bal la­bels to similar­ity clusters, or match­ing la­bels to prop­er­ties that are use­ful in dis­t­in­guish­ing similar­ity clusters.