In 1938, the physicist Frank Benford made an extraordinary discovery about numbers. He found that in many lists of numbers drawn from real data, the leading digit is far more likely to be a 1 than a 9. In fact, the distribution of first digits follows a logarithmic law. So the first digit is likely to be 1 about 30 per cent of time while the number 9 appears only five per cent of the time.
That’s an unsettling and counterintuitive discovery. Why aren’t numbers evenly distributed in such lists? One answer is that if numbers have this type of distribution then it must be scale invariant. So switching a data set measured in inches to one measured in centimetres should not change the distribution. If that’s the case, then the only form such a distribution can take is logarithmic.
But while this is a powerful argument, it does nothing to explan the existence of the distribution in the first place.
A quick guide to the most important AI law you’ve never heard of
The European Union is planning new legislation aimed at curbing the worst harms associated with artificial intelligence.
This is the first image of the black hole at the center of our galaxy
The stunning image was made possible by linking eight existing radio observatories across the globe.
It will soon be easy for self-driving cars to hide in plain sight. We shouldn’t let them.
If they ever hit our roads for real, other drivers need to know exactly what they are.
The gene-edited pig heart given to a dying patient was infected with a pig virus
The first transplant of a genetically-modified pig heart into a human may have ended prematurely because of a well-known—and avoidable—risk.
Get the latest updates from
MIT Technology Review
Discover special offers, top stories, upcoming events, and more.