Thursday, 11 December 2008

Sudoku puzzles show we're all capable of deductive reasoning

So much contemporary research in psychology focuses on the flaws in our thinking and the errors in our decision making. There is something refreshing therefore in a new study by Louis Lee and colleagues who have used the digit-placement puzzle Sudoku to argue, contrary to many others, that untrained people are capable of pure deductive reasoning - this is the ability to arrive at a logical conclusion by following the implications of one or more premises.

In an initial experiment, ten Chinese Hong Kong university students who'd never played Sudoku before were presented with an easy, difficult and fiendish version of the puzzle. They were told the rules, but weren't given any advice on strategies to follow. As the participants filled in the missing digits, they were asked to explain how they'd identified their solutions.

The participants solved only two digits per puzzle, thus showing how hard the puzzle is for naive players. However, for the answers they did find, the students were able to explain their deductive reasoning. "...[T]he solution to the puzzle Sudoku yields an insight into human competence that is in stark contrast to many psychological theories," the researchers argued. "Reasoners readily acquire the ability to make deductions about abstract contents, which are far removed from the exigencies of daily life and from the environment of our evolutionary ancestors."

Further experiments by the researchers showed that the initial deductive reasoning strategies that players deploy can only get them so far. To solve difficult and fiendish puzzles, players have to deduce several possible missing digits at once, and use those possible digits to deduce the answers to other parts of the puzzle. Some of us give up before making this transition. But for those of us who move onto this more advanced stage, Lee's team said "this shift in strategy is analogous to shifting from proofs in the first-order predicate calculus to proofs in the first-order modal predicate calculus" - in other words, it's a pretty impressive display of logical prowess and further evidence of our ability to "make deductions about abstract matters remote from our mundane life".
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ResearchBlogging.orgN.Y. Louis Lee, Geoffrey Goodwin, P. N. Johnson-Laird (2008). The psychological puzzle of Sudoku. Thinking & Reasoning, 14 (4), 342-364 DOI: 10.1080/13546780802236308

Post written by Christian Jarrett (@psych_writer) for the BPS Research Digest.

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