December 29, 2013

# Brute force and ignorance

My grandfather, a high school maths teacher, characterised a mathematician as someone who would rather spend an hour working out the quick way to solve a problem than fifteen minutes doing it the slow way.

Computers are so fast nowadays that many traditional ‘recreational maths’ problems can be solved by some brute-force approach. Christian Robert translates an example from Le Monde,

A regular die takes the values 4, 8 and 2 on three adjacent faces. Summit values are defined by the product of the three connected faces, e.g., 64 for the above. What values do the three other faces take if the sum of the eight summit values is 1768?

and provides R code that just tries lots of possibilities. On my laptop, the code runs in about a quarter of a second.

More practically, the same applies to a lot of calculations in statistics –for example, if you need to work out what sample size is needed for an experiment, it’s often easier to simulate the experiment at different sizes and see what happens than to work out the solution mathematically.

There’s a similar problem for quizzes that are often made trivial by Google. Often, but not always. The famous Christmas quiz from King William’s College, on the Isle of Man is made easier by search engines, but still takes effort. For example, the first question:

In the year 1913: what famous club was founded at Vrijstraat 20?

You won’t get the answer just by Googling “Vrijstaat 20”, at least not yet (eventually Google will pick up on it), but with a bit of extra effort you can determine it must be PSV Eindhoven (select the white text, if you want the answer).

Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »