A summary of Edgar Allan Poe’s Maelzel’s Chess-Player.

§1–§4, §6–10, §11–14, and §15–18 describe the physical appearance, (public) operation, and cultural/historical context of the chess robot; §5 and §19 actually present the argument that the robot can't be a “genuine” (or “pure machine”) mechanical chess player — that it must have a human operator.

§5 sketches the outline of the argument:

Abridged Original Verbiage
It’s inconceivable that any physical computer could execute a free loop; all effectively computable algorithms are deterministic and primitive recursive.

Arithmetical or algebraical calculations are, from their very nature, fixed and determinate. Certain data being given, certain results necessarily and inevitably follow. These results have dependence upon nothing, and are influenced by nothing but the data originally given. And the question to be solved proceeds, or should proceed, to its final determination, by a succession of unerring steps liable to no change, and subject to no modification. This being the case, we can without difficulty conceive the possibility of so arranging a piece of mechanism, that upon starting it in accordance with the data of the question to be solved, it should continue its movements regularly, progressively, and undeviatingly towards the required solution, since these movements, however complex, are never imagined to be otherwise than finite and determinate.

A game of Chess (with at least one human player) is not deterministic.

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. Let us place the first move in a game of chess, in juxta-position with the data of an algebraical question, and their great difference will be immediately perceived. From the latter — from the data — the second step of the question, dependent thereupon, inevitably follows. It is modelled by the data. It must be thus and not otherwise. But from the first move in the game of chess no especial second move follows of necessity. In the algebraical question, as it proceeds towards solution, the certainty of its operations remains altogether unimpaired. The second step having been a consequence of the data, the third step is equally a consequence of the second, the fourth of the third, the fifth of the fourth, and so on, and not possibly otherwise, to the end. But in proportion to the progress made in a game of chess, is the uncertainty of each ensuing move. A few moves having been made, no step is certain. Different spectators of the game would advise different moves. All is then dependent upon the variable judgment of the players.

It would require groundbreaking research to design a computer which could cope with unpredictable inputs (such as an opponent player's choice of move).

Now even granting (what should not be granted) 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, and if we choose to call the former a pure machine we must be prepared to admit that it is, beyond all comparison, the most wonderful of the inventions of mankind.

There was (allegedly) no groundbreaking research involved in the robot's construction.

Its original projector, however, Baron Kempelen, had no scruple in declaring it to be a “very ordinary piece of mechanism — a bagatelle whose effects appeared so marvellous only from the boldness of the conception, and the fortunate choice of the methods adopted for promoting the illusion.”

§19 is a list of 17 items, which can be sieved into three broad categories: Noticing mistakes in the concealment of the human operator (#2, #4, #5, #9, #11, #12, and #14); speculating on circumstantial evidence of a human operator (#6, #7, #8, #10, #13, #15, #16, and #17); and continuing the argument which he started in §5 (#1, #3). I won't go into detail on those first two.

Abridged Original Verbiage
Polling and interrupts are both inconceivable — a computer could not possibly await inputs which arrive at an unknown delay.
1. The moves of the Turk are not made at regular intervals of time, but accommodate themselves to the moves of the antagonist — although this point (of regularity) so important in all kinds of mechanical contrivance, might have been readily brought about by limiting the time allowed for the moves of the antagonist. For example, if this limit were three minutes, the moves of the Automaton might be made at any given intervals longer than three minutes. The fact then of irregularity, when regularity might have been so easily attained, goes to prove that regularity is unimportant to the action of the Automaton — in other words, that the Automaton is not a pure machine.
Any game AI except totally complete minimax (which would guarantee the potential for a 0% loss rate) is inconceivable (except for intentionally handicapped versions of minimax). However, the robot sometimes loses. Therefore, it cannot have a game AI.
1. The Automaton does not invariably win the game. Were the machine a pure machine this would not be the case — it would always win. The principle being discovered by which a machine can be made to play a game of chess, an extension of the same principle would enable it to win a game — a farther extension would enable it to win all games — that is, to beat any possible game of an antagonist. A little consideration will convince any one that the difficulty of making a machine beat all games, is not in the least degree greater, as regards the principle of the operations necessary, than that of making it beat a single game. If then we regard the Chess-Player as a machine, we must suppose, (what is highly improbable,) that its inventor preferred leaving it incomplete to perfecting it — a supposition rendered still more absurd, when we reflect that the leaving it incomplete would afford an argument against the possibility of its being a pure machine — the very argument we now adduce.

Note that he argues for a true proposition (Maelzel's chess robot was human operated), by an invalid argument (that it’s not possible to build a chess robot — “this matter is susceptible of a mathematical demonstration, a priori”).

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