### Thursday July 30, 2015

###### •  college algebra • data science •  logarithms •  math education •  mathematics •  measurement •  scientific computing •  trigonometry •

Logarithmic scales are excellent for relating different measurements that exist on different scales. But not all measures are suitable for logarithmic measures. The amount of time your coworkers spend on their commutes is probably not appropriate. Your time may be 20 minutes and the next person is 30 minutes. Even if the third person’s unfortunate commute is 80 minutes, these all exist on the same scale. Nobody’s commute ranges into days or weeks.

It does not make sense to measure the height of people, which is more or less, normally distributed, because the difference between someone who is 1.6 meters (m) and someone who is 1.9m is better represented by the raw difference. If individuals’s heights varied from, for instance, 1.5m through 200m, then a logarithmic scale might make more sense.

A person’s height is a fairly constrained measurement. Length, more broadly, can be vary on many different scales. And space is big.1 My commute is 50km, but the distance from the Earth to the Sun is approximately 150 million kilometers and the distance from the Earth to the Andromeda is $2.4 \times 10^{19}$ kilometers. That’s a lot. And that is something we should measure on a logarithmic scale.

Image by Brett L. / Flickr.

1. Adams, Douglas. The Hitchhiker’s Guide to the Galaxy: The Original Radio Scripts. London: Pan, 1985, p. 39.