Benford’s law
What do absent aliens, dodgy dictators and financial fraudsters have in common? Benford’s law can help hunt them down.
Benford’s law states that lists of numbers related to some natural or human activities will contain a particular distribution of digits. If you take a list of the areas of river basins, say, or the figures in a firm’s accounts, there will always be more numbers that start with 1 than any other. Numbers starting with 2 are the next most common, then 3 and so on. A number will start with a 9 only 4.6 per cent of the time.
Read more: Fantastic figures – A tour of the most wonderful numbers
The world of numbers may be abstract, but it contains incredible sights. Come explore the many wonders in numberland
The pattern was originally suggested by astronomer Simon Newcomb in the 1800s in a riveting analysis of how people use books of logarithm tables. In the 1930s, the engineer Frank Benford rediscovered the result.
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Why on earth should Benford’s law exist? Drill down to the root cause of most natural processes and they depend on random things, like the jostling of atoms. That produces bell-shaped curves, where most of the values are in the middle. But if several natural phenomena are at play — which is the case in a huge number of fields — then it turns out that Benford’s law is what holds.
Spot the tricks people play with numbers:
No surprise then, that you can use it in lots of neat ways, especially to catch out miscreants. In 2009, for example, a suspiciously large number of vote tallies for one candidate in the Iranian elections began with a 7, suggesting vote-rigging.
The US Internal Revenue Service has scored several major successes by using Benford’s law to probe firms’ books for financial chicanery. And in 2013, a new application arose that brought it right back to its astronomical origins. Thomas Hair at Florida Gulf Coast University showed that the masses of thousands of confirmed and candidate exoplanets conform to the pattern. OK, it doesn’t tell us where to look for ET, but it gives us confidence that our ways of seeking exoplanets aren’t delivering spurious results.
Michael Brooks
Credit check
Ever wondered how a website knows you’ve typed your credit card number in wrongly before it’s sent it to your bank for verification? It’s probably thanks to a trick called the Luhn algorithm, the brainchild of the German-born American Hans Peter Luhn when he was working for IBM in 1954. A pioneer of mechanical data storage, Luhn was also a prolific inventor who held more than 80 patents, including one for .
But the algorithm is his enduring achievement. The digits of most major credit card numbers are chosen so that, if you apply the Luhn algorithm to them, the result will be divisible by 10. Get any single digit wrong, and the number that comes out the other end won’t end in a zero – and in the blink of an eye the computer says no.
Richard Webb
How to check your credit card number:
1. Write down the 16-digit number backwards.
2. Add together all the odd digits – the ones in first, third, fifth position and so on.
3. Next, take all the digits in even positions and double them. If any of these are two-digit numbers, add the actual digits of those numbers together to get a one-digit number. Now add those numbers up.
4. Add together your answers from steps 2 and 3. The last digit of this number must be 0.
This article appeared in print under the headline “Wonders ofnumberland”
