Beorn

CB Bucknor strikes again, this time saying the runner did not touch first base. He very clearly did

Japanese seems fairly easy to learn.

Trump tells Americans to get over paying $4 a gallon.

In 1905, Einstein published special relativity. In 1915, he published general relativity. Einstein was just trying to understand the universe. But without Einstein's math, Google Maps would be wrong by 11 kms every single day. Let me tell you why - this is very interesting :)) Your phone doesn't "talk" to GPS satellites. It only listens. Each satellite is broadcasting one thing, constantly: "I am satellite 'A', and it is currently 14:23:00.000000." Your phone receives signals from 4 satellites simultaneously. Because light travels at a known speed, tiny differences in arrival time tell it exactly how far it is from each satellite. 'A' satellite tells you: you're somewhere on a sphere of radius 20,000 km. 'B' satellite: that sphere intersects another sphere - now you're on a circle. 'C' satellite: that circle intersects a third sphere - now you're at 2 points. 'D' satellite: eliminates the last ambiguity and only one point remains. That's you! Except there's a problem nobody thought about until Einstein. The satellites are orbiting at 20,200 km altitude, moving at 14,000 km/h. Two things happen to their clocks simultaneously: - Special relativity: Moving clocks tick slower. At orbital velocity, the satellite clock loses 7.2 microseconds per day - General relativity: Clocks in weaker gravity tick faster. At that altitude, gravity is weaker. The clock gains 45.9 microseconds per day. Net effect: 45.9 - 7.2 = +38.7 microseconds per day. In 38.7 microseconds, light travels 11.6 kilometers. So without correction, the system would accumulate 11.6 km of error. Every single day. In a week, your navigation is useless. The fix is one of the most elegant things in all of engineering. Before each satellite launches, its atomic clock is physically tuned to tick slightly slower than it would on Earth - by exactly 38.7 microseconds per day. Once in orbit, relativistic effects speed it back up. And it arrives at exactly the right rate. Einstein's 1915 paper is baked into the hardware of your phone's navigation system. The next time Google Maps routes you correctly, you're experiencing general relativity. You just didn't know it.