Free Will and the Perfect Pool Table

Being of a philosophical bent, I enjoy discussions of philosophical concepts such as free will. Recently I had a reverie that shows to me that we do have free will, even though there are a great many people who claim that free will does not exist and that it is only an illusion. My reverie began with a pool table.

In physics we can make great progress in a situation by removing extraneous factors, solving the situation without them and reintroducing them while making corrections. So, to begin with, our pool table has all of the accoutrements: felt, bumpers, pockets, pool cues, ordinary pool balls and a cue ball, etc. Allow me to remove the felt and replace it with a frictionless surface, something infinitely slippery. The bumpers have to be replaced also and are replaced with perfectly elastic bumpers. These bumpers return every erg of energy transferred to them by a colliding ball, back to the ball. The pockets have to go (for now) and the balls have to reconstituted with some also perfectly elastic material of exactly equal mass and size and shape. (Ordinary cue balls are ever so slightly larger than the others and they will have to be made equal to the others (in all ways) for a time.)

Now, once these ball are set in motion, they never stop. When they collide, momentum is conserved, momentum being the product of the mass and velocity of a moving object. So, if one ball hits another and some speed is transferred, since the balls are of the same mass, the amount one ball slows is equal to the amount the other speeds up. This is true even if one ball hits two others simultaneously, the total speeds lost equal the total speeds gained.

This situation is analogous to a sample of gas trapped in a bottle. The gas molecules are analogues of the balls and the bottle is effectively the bumper. As long as the bottle and gas are the same temperature and that doesn’t change, the analogy is perfect (albeit the molecules are much smaller, move much faster, etc.). We can describe this state mathematically perfectly and we can predict any particular situation in either the past or the future of such a system (where the molecules are, how fast they are going, etc.). This is a fated or deterministic mini-universe.

But now let us add the real-world pool table items back in. If we were to just add the pockets back, some of the balls would leave the table by falling into the pockets and the balls that remained would have to have paths that repeated themselves and which didn’t involve colliding into a pocket. If the felt is added back, so is friction and the balls in motion will then stop at some point due to that friction. Also, the not perfectly elastic bumpers will absorb some of the energy of the balls colliding with them. We end up with an imperfect, non-deterministic game, one in which the result of any balls being set in motion becomes quite uncertain. The only thing we can say for certain is the balls will come to a stop after each “play.” The motions are somewhat but not perfectly predictable, which allows for the skills of elite pool players.

Every time the cue ball is struck (the cue ball being made slightly larger than the other balls so it strikes them ever so slightly above the equator, minimizing the chances of a ball being hit slightly below the equator which can result in the struck ball flying off of the table (now you know)), the table ends up in a new state, that is the positions of the balls involved in collisions is almost guaranteed to be different as well as somewhat unpredictable.

So, as a player of any pool game, you must make decisions based upon the state of play. Some of those games require the balls to be sunk in numerical order (they are numbered to facilitate this) while others just require the balls be nudged into any pocket through a collision with the cue or other balls in any way one can. If a ball is sunk during a play, another turn is earned. So, decisions have to be made. Should I try to sink this ball or that ball? If I sink that ball, will the cue ball be in a position to sink another ball (or the next numbered ball in the sequence) and, if it won’t be properly positioned, can I make it properly positioned by some skill of my possession.

All of these “decisions” involve free will. I make this claim because two different pool players will sometimes play a particular situation differently. It is not the case that the “state” of the table determines the next play. The skill set of the player is involved. One is better with short shots, another excels at longer shots. One player can make very fine massé shots, another not so well. One player excels at bank shots, etc. So, the universe cannot dictate how a table will be played, and a player cannot either. Even giving a player’s particular skill set, occasionally they will play a shot that invokes a weakness rather than playing to their strengths time after time. When queried about that “decision” later, they invariably acknowledge the multiple approaches they were considering. And occasionally state that “they don’t know why they chose the route they did” or they felt more confident “in the moment” in that path, or…. And sometimes they get frozen in a state of indecision, that is they have two paths forward that they cannot distinguish between and they get “stuck” not being able to decide. And other times we make decisions to be perverse out of a desire not to be predictable (e.g. a chance averse golfer taking a big chance to win a tournament).

I think much of the debate about the existence of free will is based upon a faulty definition. Most people describe free will as a conscious decision making ability. But many, many of the decisions we make are subconscious, that is we are not aware which of our thoughts or feelings added up to the decision involved. Such decisions come up most obviously when we struggle with making a decision consciously and go with a “gut feeling.” Your gut may have a great many neurons, but I doubt it thinks per se.

If one uses a definition of free will that includes both conscious and unconscious decision making, I think it is quite clear that we have free will, that we can choose to do things one way and when faced with the exact same situation again, choose to do it differently.

The reason free will is important is that if we do not have the ability to make our own choices, that our response to situations was either hardwired into our brains or programming in by social conditioning, then we are not responsible for our actions, our engineers and programmers are. How could we punish criminals or send sinners to Hell without them having the ability to do other than what the situation triggers? How indeed?