logarithmic scale

On an ordinary ruler, each equal step adds the same amount: 1, 2, 3, 4. On a logarithmic scale, each equal step multiplies by the same factor instead: 1, 10, 100, 1000. Moving the same distance always means the same fold-increase, not the same plus-increase. This is the natural way to display quantities that span enormous ranges.

The trick is to mark each position by the logarithm of the value rather than the value itself. Because logs turn multiplication into addition, multiplying a quantity by 10 shifts it a fixed step along the axis. That compresses a span from 1 to a billion into just nine evenly spaced marks, making both tiny and huge numbers visible on one chart.

Log scales underlie many famous measurement systems: the Richter scale for earthquakes, decibels for sound, pH for acidity, and stellar magnitudes for brightness. A crucial caution when reading them: a difference of 1 on the scale means a tenfold (or other fixed-factor) change in the actual quantity, so a 6 is not merely a bit more than a 5 — it is ten times more.