Proof that Playing Too Much Minesweeper Is Not Good for You

Minesweeper Faith

When playing Minesweeper, I can click on a square and know that it is clear. How? By logical deduction.

But that logical deduction depends on assumptions. First of all, I assume that the programming of the game is sound and that the numbers on the screen are an accurate and honest count of the number ofmines in adjoining squares. Secondly, my knowledge depends that the logical reasoning that goes into my conclusion is in fact sound. To play effectively, I must believe that what I conclude from my logical reasoning is coincides with the actual placement of the mines in the grid.

I can play Minesweeper. I can make deductions about the placement of the mines, make decisions accordingly, and avoid clicking on mines. It works over and over again.

To play Minesweeper requires faith. My faith is borne out again and again. The confirmation of the faith is simple and quick.

Poker Faith

The mathematics of permutations and combinations and the principles of probability that underly the game of poker are extensions of logic and deduction from the same foundations of mathematics that underly the game of Minesweeper. I must believe in the soundness of the reasoning that goes into them, and I must believe in the honesty of the game, if I am to play poker with any sense of it as a genuinely winnable game — "winning" here meaning more or less that in the long run I'll win more money at it.

A big difference between poker and Minesweeper is that with the latter game, my faith in mathematical reasoning is immediately confirmed. The stochastic nature of poker, on the other hand, means that I can play a hand "correctly" (i.e. in such a way as to maximize my expected win) and lose — or for that matter play very far from correctly and win. The mathematical reasoning that tells me that this cell is definitely free and that one definitely contains a hidden mine is far less definite for poker, saying only that if I play a particular hand in particular circumstances many times over, on average I should expect my average win or loss to be close to a particular value.

To play poker requires faith; but that faith must bear up to the challenges of short-term results. Faith takes a substantial beating at the poker table. ... but the mathematical reasoning in which I place my faith tells me that to lose faith is to lose.

Once last year, while playing in side games at the World Series of Poker, in Las Vegas, I took a substantial loss at a $20-$40 high-low split seven-card stud game. I kept having to throw away hand after hand that started well but caught bad cards on fourth street, or got punished when I caught that fourth good card but caught worthless bricks on the last three cards. Again and again I committed my money to a pot only to see it vanish into hopelessness. I busted out of the game and returned to my hotel room in a terrible state. I raged at my losses, pummelling my bed with a pillow, screaming with frustration with each blow. How could this have happened to me? I was playing as well as I knew how, and I had lost, badly. The law of averages was on my side; what had gone wrong?

And then I wondered, just how unlucky had I been? I took out pencil and paper and began to calculate roughly how often I should get a decent starting hand, and how often that hand will catch good or bad on fourth street. The numbers I worked out showed that I ought to be catching bad a majority of the time, and that in fact my luck had been bad, but not outrageously so.

I had undergone a crisis of faith, and through something analogous to meditation and prayer found the balance I needed to stay the course.

Faith and Science

Even the most zealous adherent to logical positivism must eventually rely on her faith in positivism to accept and believe in a number of invisible and undetectable things. That is what is so troubling about quantum mechanics, for example: reason and careful scientific observation lead to conclusions about the nature of the world and the fundamental entities that make it up that run deeply contrary to common sense and daily experience. The practice of empirical science demands a great deal of belief in invisible things, phenomena not apparent to the senses except through elaborate constructions of instruments, and so on. Such belief is rewarded by confirmation, by consistency of results, and so on. Quantum-dependent devices such as semiconductors work. So do vaccines and epoxy glue.

An ordinary human being cannot work things out from first principles all the time. She has to trust her memories, trust consensus faith in consensus constructions, and so on. "I have studied this carefully and determined it for myself" devolves into "The person who asserts this has good credentials, and there are people out there who might have checked this out, and until someone says otherwise it's a good bet that this is true." One cannot accept the validity of science without making many leaps of faith. Above all, one must have faith in the consensus of the community of science.

And then there is Gödel's theorem. In its strictest form it states that in a self-consistent theory of numbers there must exist propositions that, while true, are not provable within that system; any number theory in which all true statements are provable will be inconsistent, and so all false statements are provable in it as well.

The larger implication of Gödel's theorem is that this situation of unprovable truths is the case in ANY logical system. (Handwaving proof: an isomorphism exists between said logical system and a number theory. Gödel's theorem can be proven in that number theory, and so the isomorphic proof stands in the logical system under consideration.) So there exist truths that cannot be proven under a given logical system. In particular, there exist truths that cannot be proven within the logical system that comprises science, rational empiricism, and logical positivism.

In other words, it is scientifically inevitable that there are truths that exist outside of science. If they can be reached at all, they can only be reached by faith.

Does my brain and my sensory apparatus constitute a logical system? If so, then there are truths than I cannot perceive or deduce from my perceptions. What if I include the things that I can make and use in this logical system? Then there are truths that cannot register on my instruments any more than I can perceive them directly. This strongly suggests (although it does not in fact prove) that there exists truths that I cannot perceive or comprehend. The faith I place in logic, therefore, tells me of the likelihood of the transcendental, the ineffable, beyond the reach of reason, philosophy, or even emotion.