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Like any scientist, I love a good mystery. Sometimes it’s fun when they are long, complicated, involve subtle and difficult layers, and require a vast effort to unravel. And sometimes it’s cool when they are simply stated and simply solved. Like asking "Where does the water in Saturn’s upper atmosphere come from?"
A man sits down before a gun , which is pointed at his head. This is no ordinary gun; it's rigged to a machine that measures the spin of a quantum particle . Each time the trigger is pulled, the spin of the quantum particle -- or quark -- is measured. Depending on the measurement, the gun will either fire, or it won't. If the quantum particle is measured as spinning in a clockwise motion, the gun will fire.
Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x .
6174 is known as Kaprekar's constant [ 1 ] [ 2 ] [ 3 ] after the Indian mathematician D. R. Kaprekar . This number is notable for the following property: Take any four-digit number, using at least two different digits.
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz , who first proposed it in 1937. The conjecture is also known as the 3 n + 1 conjecture , the Ulam conjecture (after Stanislaw Ulam ), Kakutani's problem (after Shizuo Kakutani ), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse ), or the Syracuse problem ; [ 1 ] the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers , [ 2 ] or as wondrous numbers . [ 3 ] Take any natural number n .
Can an object that is visible to the naked eye be in two places at the same time? Common sense and experience told us that the answer is "no" -- until recently. In this presentation, physicist Aaron O'Connell tells us a little about the bizarre rules of quantum mechanics, which were thought to be completely different for human-scale objects -- but are they really ?