14Benford's Law

Introduction

Benford's law refers to some fascinating statistics that occur in the natural world, i.e. they were discovered, not created. These statistics are fundamentally different than anything discussed thus far in that they refer to individual digits of numbers (principally the first digit), not to the numbers themselves. For example, 123.2, 1.45, and 1 500 000 all have the same first digit, whereas 223.2 has a different first digit than the first three numbers. The occurrences and properties we will learn about from looking at these numbers are unlike anything examined (in this book) before.

History

Before the advent of electronic computers and pocket calculators, most mathematics/physics/engineering calculations were performed using logarithms. The simplest way to explain logarithms without actually deriving the mathematics is to say that logarithms are a system which reduces multiplication and division to addition and subtraction and raising a number to a power or to a root reduces to multiplication or division. This latter attribute implies that it is only necessary to know the logarithms of numbers between one and ten. The logarithm of thirty, for example, is just the logarithm of ten times three, which in turn is the logarithm of ten plus the logarithm of three.

Logarithms of the numbers from one to ten, to many decimal places, were published in weighty books. A book of these tables of logarithms was found on the desk of just about every working ...

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