Baseball statistician Bill James, the inventor of sabermetrics, devised what he called a “game score” to measure pitching performance in a baseball game. The larger the game score, the stronger the pitching performance. James’s game score is calculated as follows, with points added or subtracted for every out that the pitcher records: 1. Begin with […]

## Goedel’s Theorem for Dummies

When people refer to “Goedel’s Theorem” (singular, not plural), they mean the incompleteness theorem that he proved and published in 1931. Kurt Goedel, the Austrian mathematician, actually proved quite a few other theorems, including a completeness theorem for first-order logic. But the incompleteness theorem is the one for which he is most famous. To get […]

## The Different Number Scales

When you encounter a number, what sort of numerical information is it giving you? Is the number functioning merely as a label? Or is it counting how many? Does it denote a magnitude or merely indicate an ordering relation? All such questions address the issue of scale. When you see a number, it belongs to […]