Mechanical Turk (example)

In 1836, there was a sen­sa­tion called the Me­chan­i­cal Turk, allegedly a chess-play­ing au­toma­ton. Edgar Allen Poe, who was also an am­a­teur ma­gi­cian, wrote an es­say ar­gu­ing that the Turk must con­tain a hu­man op­er­a­tor hid­den in the ap­para­tus (which it did). Be­sides an­a­lyz­ing the Turk’s out­ward ap­pear­ance to lo­cate the hid­den com­part­ment, Poe care­fully ar­gued as to why no ar­range­ment of wheels and gears could ever play chess in the first place, ex­plic­itly com­par­ing the Turk to “the calcu­lat­ing ma­chine of Mr. Bab­bage”:

Arith­meti­cal or alge­braical calcu­la­tions are, from their very na­ture, fixed and de­ter­mi­nate. Cer­tain data be­ing given, cer­tain re­sults nec­es­sar­ily and in­evitably fol­low But the case is widely differ­ent with the Chess-Player. With him there is no de­ter­mi­nate pro­gres­sion. No one move in chess nec­es­sar­ily fol­lows upon any one other. From no par­tic­u­lar dis­po­si­tion of the men at one pe­riod of a game can we pred­i­cate their dis­po­si­tion at a differ­ent pe­riod Now even grant­ing that the move­ments of the Au­toma­ton Chess-Player were in them­selves de­ter­mi­nate, they would be nec­es­sar­ily in­ter­rupted and disar­ranged by the in­de­ter­mi­nate will of his an­tag­o­nist. There is then no anal­ogy what­ever be­tween the op­er­a­tions of the Chess-Player, and those of the calcu­lat­ing ma­chine of Mr. Bab­bage It is quite cer­tain that the op­er­a­tions of the Au­toma­ton are reg­u­lated by mind, and by noth­ing else. In­deed this mat­ter is sus­cep­ti­ble of a math­e­mat­i­cal demon­stra­tion, a pri­ori.

(In other words: In an alge­braical prob­lem, each step fol­lows with the pre­vi­ous step of ne­ces­sity, and there­fore can be rep­re­sented by the de­ter­mi­nate mo­tions of wheels and gears as in Charles Bab­bage’s pro­posed com­put­ing en­g­ine. In chess, the player’s move and op­po­nent’s move don’t fol­low with ne­ces­sity from the board po­si­tion, and there­fore can’t be rep­re­sented by de­ter­minis­tic gears.)

This is an amaz­ingly so­phis­ti­cated re­mark, con­sid­er­ing the era. It even puts a finger on the part of chess that is com­pu­ta­tion­ally difficult, the com­bi­na­to­rial ex­plo­sion of pos­si­ble moves. And it is still en­tirely wrong.

Even if you know an un­bounded solu­tion to chess, you might still be 47 years away from a bounded solu­tion. But if you can’t state a pro­gram that solves the prob­lem in prin­ci­ple, you are in some sense con­fused about the na­ture of the cog­ni­tive work needed to solve the prob­lem. If you can’t even solve a prob­lem given in­finite com­put­ing power, you definitely can’t solve it us­ing bounded com­put­ing power. (Imag­ine Poe try­ing to write a chess-play­ing pro­gram be­fore he’d had the in­sight about search trees.)

For more on this point, see “Method­ol­ogy of un­bounded anal­y­sis”.

Parents:

  • Methodology of unbounded analysis

    What we do and don’t un­der­stand how to do, us­ing un­limited com­put­ing power, is a crit­i­cal dis­tinc­tion and im­por­tant fron­tier.