*If you can't solve a problem, then there is an easier problem you can solve: Find it.*— George Pólya

I'm playing two new (to me) problem-solving competitions that

*feel*extremely different: heads-up no-limit hold em*, and Chess Tactics Server*. Their distinct feels make me meditate on how we build decision rules to navigate life's complex environs.

Solving chess problems, the

**calculations**dominate. Tactical thinking feels systematic, step-by-step "100% valid." A board's

*terra firma*absolutism rapidly expands as I look at a problem. Conclusions snap into place in cascades. Nothing feels tentative. Except!: 1) How my attention seeks out the most

*fertile*regions of playspace to analyze. That part, my finding where to look first, second and third as my eyes take in a new board, feels like

**judgment**, not at all calculation. General rules can

*describe*how I prioritize the problem-scanning, but they

*don't fully specify*the process. [The best I've crystallized, in order: King safety for each side? What's

*en prise*? Sense who has space/play in which theaters — pawn structures & piece arrangements. Sense for trappable pieces, especially queens & rooks, or promotable pawns. Check for dangerous long diagonals and knight scope possibilities. By this time, I either see the answer or have the first candidate moves worth calculating. (If you enjoyed that parenthetical's chessiness, then do try CTS...it's the most critical few percent of each chess game that explains 80% of victories — without any of those boring-to-non-experts parts!) ] 2) How my attention realizes that it's "done," ready to commit to my answer. There's usually a satisfying "snap" of a best move, but it's not actually certain — it rests on my not having missed any important pregnant possibilities in the final boards I've envisioned. Chess computers like Deep Blue have to use glitteringly generalities to decide they've calculated "far enough" (that nothing really exciting is about to happen in the final positions of their trees), and I surely do too.

Heads-up NLHE, on the other hand, feels way more

**judgment**than calculation. I sense myself just scanning the situation (focusing on many factors with no clear rules for resolving the tensions among them) & letting my intuitions fight it out for a best decision. There is often no satisfying "snap" of correctness, just a least awkward move to play as a timer ticks down.

Poker is a way less

*solved*game than chess tactics, which may wholly explain why their best reasoning processes feel so different. The more exactly & formally we've discerned & distilled what's important for a class of decisionmaking, the more calculations will trump judgments. (Once the

*terra firma*gets built, it just wins. Unless its foundations turn out to be wrong.) I've witnessed several arcs of discerning & distilling in the poker world: most single-table tournaments & NL ring games are beatable through pure calculation now. (Cutting-edge judgments can still increase your edge in any game, but calculation is often

*sufficient*to create some positive edge.)

George Pólya:

Mathematics is regarded as a demonstrative science. Finished mathematics presented in a finished form appears as purely demonstrative [calculative], consisting of proofs only. Yet mathematics in the making resembles any other human knowledge in the making. You have to guess a mathematical theorem before you prove it; you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies; you have to try and try again. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference. Instrict reasoningthe principal thing is todistinguish a proof from a guess, a valid demonstration from an invalid attempt. Inplausible reasoningthe principal thing is todistinguish a guess from a guess, a more reasonable guess from a less reasonable guess. Certainly, let us learn proving, butlet us also learn guessing. To be a good mathematician, or a good gambler, or good at anything, you must be a good guesser.

This makes me ponder how the classical

**logic courses**can't apply to normal judgments, only to formalized calculations. Do you bet that teaching "logical fallacies" (as things to be avoided)

*actually*does more to

**help**shape our (children's) calculations

*or*does more to

**confound & confuse**our own fluid firsthand judgments about real-world situations?

Ilkka:

For all its glory, "logic" is virtually useless in any real-world reasoning and argumentation task. Nobody actually expresses their ideas logically, except in some rare circumstances where the discussion is about some microworld domain for which logical reasoning is possible in principle. And logic is used even less in coming up with the ideas and positions.Robin Hanson:

In this light, the weight that the first logic and argumentation textbooks give to propositional logic isabsolutely hilarious. I doubt that there has ever been a single situation anywhere where someone has successfully come to a solution and argued his case to others using propositional logic, for some nontrivial real-world issue.I was once amused to notice that the popular lists of logical fallacies are practically isomorphic with the lists of techniques of informal logic and argumentation.

Consider "Ad hominem",the most beloved of all logical fallacies. I am sorry, but I still don't consider the representatives of the multibillion dollar tobacco institute to be very credible when they claim that smoking is not harmful to health. Or "Appeal to authority". I again apologize, but for some reason I just tend to trust Richard Dawkins over a sideshow creationist preacher.

I bet it would be interesting to see someone present an argument for some nontrivial issue that is relevant to everyday life,in a way that the individual steps of the argument are made explicit and the argument does not contain any part that is structurally isomorphic with some well-known logical fallacy. I wonder if anyone could point me to an actual example. Until I see such an example, I think I stay in my opinion... or am I now committing the dreaded "Argument from ignorance"? *

Ben Kovitz:The Fallacy FallacyPeople love to collect lists of "fallacious" argument forms, with which to club opponents. Specialists have found little support for the idea that one can tell an argument is bad just by looking at its form. *

Systematic, rule-based [calculation] is a tiny sliver of your full powers of cognition, and it requires non-rule-based judgment to tell when and where it applies. For example, how can you tell that your cat is hungry? By the way he's purring and walking back and forth across the keyboard even as you keep trying to push him out of the way? That's probably part of how you can tell, but really there are a trillion factors going into that judgment, most of which you can't possibly be conscious of. And even if you identified the full rule that you're applying (assuming such a thing even exists), what rule could tell you that that rule is valid in this case?

If you held back on making judgments like "my cat is hungry" until you had a complete set of rules, which themselves had been validated by other rules, all the way to perfect bedrock rules that are rationally unchallengeable, your cat would starve before you did something. Yet, your brain has astounding powers to make

guessesof all sorts, based on negligible amounts of information. You're typing a wiki page, you sense this annoyance at the corner of your consciousness, and suddenly the amazing machinery of your brain puts a guess into your mind: "Hey, I'll bet Rufus is hungry." So then you place your bet and pour some food for him. The bet is not a sure thing, but nothing is.Fully systematic rules are ways to get things that you can define in advance, in environments where every possible observation is known, along with the appropriate response, so all that's left is to make the observation and then perform the response. Such perfectly understood regions of reality are only a tiny part of what's there, though. Most of the goodies live in the Yawning Void.