A philosopher, a mathematician and a student walk into a bar

A philosopher, a mathematician and a student walk into a bar…

December 28, 2014

A philosopher, a mathematician and a student walk into a bar. A drinking game played out between friends in a bar and a complicated mathematics study into cause and effect, may seem worlds apart.

But University of Canterbury mathematics professor Mike Steel has just published two papers showing how a game with three or more players can shed light on how causes can interact in unexpected ways to produce different effects. Cause and effects is fascinating, Distinguished Professor Steel says.

``You often read that some new diet or lifestyle will put you at higher risk of disease based on some correlation. In some cases that might be true, but in others it’s just because there’s some other background factor.”

``A classic example is the strong association between the amount of ice cream eaten on any given day and the number of people who drown that day. Eating ice cream does not really make you more likely to drown, the correlation is just due to weather – on hot days more people are swimming, and also, coincidentally, also eating ice cream.

``We say that weather screens-off ice cream from drowning. Once you specify the weather then ice-cream consumption has nothing to do with drowning.”

In a paper with a leading United States-based philosopher of science, Professor Elliott Sober, Professor Steel showed how causes can conspire to screen-off effects from each other in unusual ways.

The discovery involved coming up with an example, which can be described as a hypothetical bar game involving three players. The three players shake their fists and simultaneously reveal either an open hand or a clenched fist, and then drink (or not) a glass of tequila.

But Professor Steel says there’s a twist – if two players reveal the same hand type then each of them tosses a coin to decide if they drink or not, while in a three-way tie, all three players roll dice.

``The rules of the game are finely tuned so that various surprising things hold, for instance the hand actions of the players all act as causes of the effects (whether particular players drink or not) and each cause screens-off one effect from the other, as does all three causes, yet no pair of causes does this.

``The analysis of the game is quite easy; the hard part was coming up with it in the first place. I call it the Sober way to drink tequila (in honour of my co-author Professor Sober). I’ve demonstrated it a couple of times in talks – but not usually with tequila,” he says.

The game itself is not the goal, it just provides a concrete example of a phenomenon that tells us more about how causes and effects can interact.

More recently, Professor Steel investigated what happens when more than three people play this game. This is described in a paper to be published next month. With Colorado-based mathematician Amelia Taylor and her student Denali Molitor he used a whole range of mathematical tricks – including a classical result from 1852 and a famous result from algebraic topology.

A simple explanation of the 3-player problem can be found at www.math.canterbury.ac.nz/~m.steel/files/misc/tequila.pdf

ENDS

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