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Best of 2010: Benford’s Law And A Theory of Everything

In May, we saw how a new relationship between Benford’s Law and the statistics of fundamental physics may hint at a deeper theory of everything

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.

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Our best illustrations of 2022

Our artists’ thought-provoking, playful creations bring our stories to life, often saying more with an image than words ever could.

How CRISPR is making farmed animals bigger, stronger, and healthier

These gene-edited fish, pigs, and other animals could soon be on the menu.

The Download: the Saudi sci-fi megacity, and sleeping babies’ brains

This is today’s edition of The Download, our weekday newsletter that provides a daily dose of what’s going on in the world of technology. These exclusive satellite images show Saudi Arabia’s sci-fi megacity is well underway In early 2021, Crown Prince Mohammed bin Salman of Saudi Arabia announced The Line: a “civilizational revolution” that would house up…

10 Breakthrough Technologies 2023

Every year, we pick the 10 technologies that matter the most right now. We look for advances that will have a big impact on our lives and break down why they matter.

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