Think Nuclear

Expressing the rate of increase or decrease of a quantity as a relative value has been recognized as a challenging proposition for a long time because a consistent relative increase results in compounding effects (think compound interest). The quantity that is commonly used to express such changes, the percent difference, has some serious shortcomings when combining relative changes or when comparing changes over different periods. Here I propose an alternative way of expressing such changes, which is similar to the percent difference but which overcomes these shortcomings.

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Earlier this year, a colleague of mine sent me an email on Bendford’s Law. He had run across it somewhere and was fascinated by it. It seems counterintuitive that small digits would occur more frequently in the leading digits of arbitrary numerical data. One is tempted to think that arbitrary data would be made up of arbitrary digits, but that turns out not to be the case. It’s a genuine numerical phenomenon, and below I have provided a couple of ways to explain it. I point out that, utlimately, this law results from the notation that we use to represent real values.

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