Circle Games

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I may be rein­vent­ing a known thing in child de­vel­op­ment or psy­chol­ogy here, but bear with me.

The sim­plest games I see ba­bies play — games sim­ple enough that cats and dogs can play them too — are what I’d call “cir­cle games.”

Think of the game of “fetch”. I throw the ball, Rover runs and brings it back, and then we re­peat, ad in­fini­tum. (Or, the baby ver­sion: baby throws the item out of the strol­ler, I pick it up, and then we re­peat.)

Or, “peek-a-boo.” I hide, I re-emerge, baby laughs, re­peat.

My son is also fond of “open the door, close the door, re­peat”, or “open the drawer, close the drawer, re­peat”, which are solo cir­cle games, and “to­gether/​apart”, where he pushes my hands to­gether and apart and re­peats, and of course be­ing picked up and put down re­peat­edly.

A lot of toys are effec­tively solo cir­cle games in phys­i­cal form. The jack-in-the-box: “push a but­ton, out pops some­thing! close the box, start again.” Fid­get toys with but­tons and switches to flip: “push the but­ton, get a satis­fy­ing click, re­peat.”

It’s ob­vi­ous, ob­serv­ing a small child, that the pur­pose of these “games” is learn­ing. And, in par­tic­u­lar, learn­ing cause and effect. What do you learn by open­ing and clos­ing a door? Why, how to open and close doors; or, phrased a differ­ent way, “when I pull the door this way, it opens; when I push it that way, it closes.” Play­ing fetch or catch teaches you about how ob­jects move when dropped or thrown. Play­ing with but­ton-push­ing or latch-turn­ing toys teaches you how to han­dle the but­tons, keys, switches, and han­dles that are ubiquitous in our built en­vi­ron­ment.

But what about peek-a-boo? What are you “learn­ing” from that? (It’s a myth that ba­bies en­joy it be­cause they don’t have ob­ject per­ma­nence; ba­bies get ob­ject per­ma­nence by 3 months, but en­joy peek-a-boo long af­ter that.) My guess is that peek-a-boo trains some­thing like “when I make eye con­tact I get smiles and pos­i­tive at­ten­tion” or “grownups go away and then come back and are happy to see me.” It’s so­cial learn­ing.

It’s im­por­tant for chil­dren to learn, gen­er­ally, “when I act, the peo­ple around me re­act.” This gives them so­cial effi­cacy (“I can achieve goals through in­ter­ac­tion with other peo­ple”), ac­cess to so­cial in­cen­tives (“peo­ple re­spond pos­i­tively when I do this, and nega­tivey when I do that”), and a sense of so­cial sig­nifi­cance (“peo­ple care enough about me to re­spond to my ac­tions.”) At­tach­ment psy­chol­ogy ar­gues that when ba­bies and tod­dlers don’t have any adults around who re­spond to their be­hav­ior, their so­cial de­vel­op­ment goes awry — ne­glected chil­dren can be ex­tremely fear­ful, ag­gres­sive, or checked-out, miss­ing ba­sic abil­ities in in­ter­act­ing pos­i­tively with oth­ers.

It’s clear just from ob­ser­va­tion that the so­cial game of in­ter­ac­tion — “I make a sound, you make a sound back” — is learned be­fore ver­bal speech. Pre­ver­bal ba­bies can even ex­e­cute quite so­phis­ti­cated in­ter­ac­tion pat­terns, like mak­ing the tonal pat­tern of a ques­tion fol­lowed by an an­swer­ing state­ment. This too is a cir­cle game.

The baby’s fas­ci­na­tion with cir­cle games com­pletely be­lies the pop­u­lar no­tion that drill is an in­trin­si­cally un­pleas­ant way to learn. Rep­e­ti­tion isn’t bor­ing to ba­bies who are in the pro­cess of mas­ter­ing a skill. They beg for rep­e­ti­tion.

My per­sonal spec­u­la­tion is that the “crav­ing for drill”, es­pe­cially in mo­tor learn­ing, is a basal gan­glia thing; wit­ness how ab­nor­mal­ities in the gan­glia are as­so­ci­ated with di­s­or­ders like OCD and Tourette’s, which in­volve com­pul­sive rep­e­ti­tion of mo­tor ac­tivi­ties; or how some dopamin­er­gic drugs given to Park­in­so­nian pa­tients cause com­pul­sions to do mo­tor ac­tivi­ties like lin­ing up small ob­jects or hand-crafts. In­tro­spec­tively, a “gear can en­gage” if I get suffi­ciently fas­ci­nated with some­thing and I’ll crave rep­e­ti­tion — e.g. crav­ing to listen to a song on re­peat un­til I’ve mem­o­rized it, crav­ing to get the hang of a par­tic­u­lar tricky mea­sure on the pi­ano — but there’s no guaran­tee that the gear will en­gage just be­cause I ob­serve that it would be a good idea to mas­ter a par­tic­u­lar skill.

I also think that some kinds of so­cial in­ter­ac­tion among adults are effec­tively cir­cle games.

Ar­gu­ment or fight­ing, in its sim­plest form, is a cir­cle game: “I say Yes, you say No, re­peat!” Of course, so­phis­ti­cated ar­gu­ments go be­yond this; each player’s “turn” should con­tribute new in­for­ma­tion to a log­i­cal struc­ture. But many ar­gu­ments in prac­tice are not much more so­phis­ti­cated than “Yes, No, re­peat (with vari­a­tions).” And even in­tel­lec­tu­ally rigor­ous and civil ar­gu­ments usu­ally share the ba­sic turn-tak­ing ad­ver­sar­ial struc­ture.

Now, if the pur­pose of cir­cle games is to learn a cause-and-effect re­la­tion­ship, what are we learn­ing from ad­ver­sar­ial games?

Keep in mind that ad­ver­sar­ial play — “you try to do a thing, I try to stop you” — kicks in very early and (I think) cross-cul­turally. It cer­tainly ex­ists across species; pup­pies do it.

Al­most tau­tolog­i­cally, ad­ver­sar­ial play teaches re­sis­tance. When you push on oth­ers, oth­ers push back; when oth­ers push on you, you push back.

War, in the sense we know it to­day, may not be a hu­man uni­ver­sal, and cer­tainly isn’t a mam­malian uni­ver­sal; but re­sis­tance seems to be an in­her­ent fea­ture of so­cial in­ter­ac­tion be­tween any be­ings whose in­ter­ests are im­perfectly al­igned.

A lot of so­cial be­hav­iors gen­er­ally con­sid­ered mal­adap­tive look like ad­ver­sar­ial cir­cle games. Get­ting sucked into repet­i­tive ar­gu­ments? That’s a cir­cle game. Fal­ling into ro­man­tic pat­terns like “you want to get closer to me, I pull away, re­peat”? Cir­cle game. Be­ing shock­ing or reck­less to get at­ten­tion? Cir­cle game.

The frame where cir­cle games are for learn­ing sug­gests that peo­ple do these things be­cause they feel like they need more prac­tice learn­ing the les­son. Maybe peo­ple who are very com­bat­ive feel, on some level, that they need to “get the hang of” push­ing back against so­cial re­sis­tance, or con­versely, learn­ing how not to do things that peo­ple will re­act badly to. It’s un­satis­fy­ing to feel like a ghost, mov­ing through the world but not get­ting any feed­back one way or an­other. Maybe when peo­ple crave in­ter­ac­tion, they’re liter­ally crav­ing train­ing data.

If you always do A, and always get re­sponse B, and you keep want­ing to re­peat that game, for much longer than is “nor­mal”, then a cou­ple things might be hap­pen­ing:

  • Your “learn­ing al­gorithm” has an un­usu­ally slow “learn­ing rate” such that you just don’t up­date very effi­ciently on what ought to be am­ple data (in gen­eral or in this spe­cific con­text).

  • You place a very high im­por­tance on the A-B re­la­tion­ship such that you have an un­usu­ally high need to be sure of it. (e.g. your al­gorithm has a very high thresh­old for con­ver­gence.) So even though you learn as well as any­body else, you want to keep learn­ing for longer.

  • You have a very strong “prior” that A does not cause B, which it takes a lot of data to “dis­prove.”

  • You have some­thing like “too low a rate of stochas­tic­ity.” What you ac­tu­ally need is vari­a­tion — you need to see that A’ causes B’ — but you’re stuck in a lo­cal rut where you can’t ex­plore the space prop­erly so you just keep swing­ing back and forth in that rut. But your al­gorithm keeps re­turn­ing “not mas­tered yet”. (You can get these effects in al­gorithms as sim­ple as New­ton’s Method.)

  • You’re not ac­tu­ally try­ing to learn “A causes B.” You’re try­ing to learn “C causes D.” But A cor­re­lates weakly with C, and B cor­re­lates weakly with D, and you don’t know how to speci­fi­cally do C, so you just do A a lot and get in­ter­mit­tent re­in­force­ment.

Th­ese seem like more gen­eral ex­pla­na­tions of how to break down when rep­e­ti­tion will seem “bor­ing” vs. “fas­ci­nat­ing” to differ­ent peo­ple or in differ­ent con­texts.