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Showing posts from September, 2014

Closed timelike Curves: Solving the "Grandfather Paradox" and foiling Quantum Cryptography.

•Entering a closed timelike curve tomorrow means you could end up at today. On June 28, 2009, the world-famous physicist Stephen Hawking threw a party at the University of Cambridge, complete with balloons, hors d'oeuvres and iced champagne. Everyone was invited but no one showed up. Hawking had expected as much, because he only sent out invitations after his party had concluded. It was, he said, "a welcome reception for future time travelers," a tongue-in-cheek experiment to reinforce his 1992 conjecture that travel into the past is effectively impossible. But Hawking may be on the wrong side of history. Recent experiments offer tentative support for time travel's feasibility—at least from a mathematical perspective. The study cuts to the core of our understanding of the universe, and the resolution of the possibility of time travel, far from being a topic worthy only of science fiction, would have profound implications for fundamental physics as well as for practi…

Benford's Law: How Tax Frauds are caught...

If you list all the countries in the world and their populations, 27% of the numbers will start with the digit 1. Only 3% of them will start with the digit 9. Something very similar holds if you look at the heights of the 60 tallest structures in the world — whether you measure in meters or in feet. 

This phenomenon — called Benford's Law —helps auditors detect fraud in things like taxes and elections, but it also connects up in striking ways to modern physics and mathematics (e.g., power laws in statistical distributions, as well as ergodic theory).

Benford's Law often strikes people as unintuitive because it seems that every digit should have an equal opportunity to start country populations or heights of skyscrapers, like this:

(The delightful figures are from

This egalitarian intuition about leading digits turns out to be misleading. The situation where every digit is equally likely to start numbers is actually the anomalous one. 


The fact…