From the Archives: Parable of the Chessman

This article appeared in February of this year, and originally appeared the year previous. An inattentive reader made the unlikely claim that I was reluctant or unable to answer the question addressed here. I reprint the article as a reminder that I suffer from the opposite problem; namely, a chivalrous (or, perhaps, a neurotic) inability to stop discussing the issue even after it is clear that discussion is futile.

Parable of the Chessmen

I have been asked whether the electrons in a brain move “according to” the laws of physics as opposed to moving “according to” the willpower of the thinker.

The question is ambiguous because there are two meanings of “according to.” The dichotomy proposed by the question is a false one — the choice is not between a brain-electron moving “according to” (meaning 2) someone’s will OR moving “according to” (meaning 1) the laws of Newton.

Note the differences here between a proscriptive and a descriptive use of the phrase “according to”. If I shake my head to signify a negative, that is according to my will and according to the convention that a head-shake means ‘no’. That is proscriptive, in accord with a final cause. If Jack Ketch chops my head with an ax, the fall of my head into the basket is “according to” Newton’s laws of gravity. That is descriptive, in accord with a mechanical cause.

The head might indeed make the same motion, but asking for an account of the mechanics is not the same as asking for an justification for my refusal.

It is not an ‘either-or’ question.

The motion of the brain electron, if we are asking how it moves, is answered in terms of mechanics (meaning 1); if we are asking why or for what purpose it moves, is answered in terms of final cause (meaning 2).

Obviously the motion is the same in both cases.

The question is not a choice of either-or. It is both-and. Every motion in the universe BOTH has a mechanical cause AND has a final cause.

Let me use a parable.

If I push a chessman with my finger two inches, from one square to the next, using two ounces of pressure over two seconds, the motion of the chessman can be described in terms of the mass of the chessman, the pressure of the finger, the duration and the direction and the amount of thrust.

This is a description of the physics of the object moving on the chessboard. It is only concerned with the physical aspects of reality.

The same move can be described by the notation “Queen to King’s Bishop Seven (Checkmate)” or written in algebraic notion as “Qxf7#”.

Please note that this description does not mention the mass of the chessman, the direction and direction of the finger motion, or any else about the physical circumstances. The color of the chessman is not mentioned; the substance, whether wood or plastic or marble, of which the chessman is made is not mentioned. The only thing that is mentioned is the form of the move in its most pure and abstract form. The final cause of the move (the goal is to achieve checkmate and win the game) is noted by the octothorpe sign (#).

Please note that the octothorpe sign does not denote any information about the physical chessman or the physical impulse of motion. It denotes neither mass, nor length, nor duration, nor candlepower, nor temperature, nor moles of substance, nor amperage. It does not denote any physical quantity.

There is one event (Queen to King’s Bishop Seven) that can be described in two ways, (1) telling the mass and distance moved over the time elapsed (2) telling the formal meaning of the move Qxf7#.

The first way of telling may not violate the rule that F=ma. The chessman did not violate the laws of conservation of mass or momentum by moving to the square KB7.

The second way of telling may not violate the rules of chess. The King who cannot move out of check, capture the threatening chessman, or block the threat, is checkmated.

A bit of wood carved to look like a crowned woman has two aspects: first, it is made of matter and obeys all the laws of matter, including conservation of momentum. Second, it is a symbol for the chessman in a chessgame called a ‘Queen’ which can move any number of squares horizontally or diagonally. The Queen obeys all the laws of chess, and cannot, for example, jump over enemy chessman as a Knight can do.

The two sets of rules have nothing to do with each other.

Qxf7# is a legal move even if the chessman is large and brass or small and plastic, heavy or light, painted white or silver, or even exists no other place than in the mind of the chessplayer.

The rule of physics, F=ma is not and cannot be violated by any chessman made of matter anywhere in the universe, since the intertialess chessmen used by the Galactic Patrol of the Lensman universe do not exist.

There is no rule in chess that even refers to any physical property. For example, there is no rule in chess that a king may escape check by suddenly changing into reverse-entropy states prone to antigravity and floating off the board. The laws of thermodynamics, gravity and momentum are never, ever violated in chess. Likewise, there is no rule in physics that says no eighth row pawn may become a queen. Elevating a pawn does not violate any law of thermodynamics.

Obviously, when two people sit down to a chessboard in the park and take out little figures made of wood or brass and play a game, the chessman obey both sets of rules, the rules of physics and the rules of chess.

The rules (meaning 1) of physics are a description of the way matter moves. The rules (meaning 2) of chess are a proscription defining the game and its play. “Rules (meaning 1)” is not equal to “rules (meaning 2)”. The same word ambiguously is used to refer to two different and contrary concepts.

Were we ever to ask whether a chessman EITHER obeys the rules of chess OR obeys the rules of physics, the question is incoherently formed. It is not an either-or question.

A chessman both obeys the rules of physics and the rules of chess. The two sets of rules describe two different dimensions or aspects of reality that have no necessary relation to each other.

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