Photopic Sky Survey. 12 Events That Will Change Everything, Made Interactive. Imagining the Tenth Dimension.
Charts/Tools. How Quantum Suicide Works". 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.
If the quark is spinning counterclockwise, the gun won't go off. Nervously, the man takes a breath and pulls the trigger. Go back in time to the beginning of the experiment. But, wait. This thought experiment is called quantum suicide. Perpetual Energy? StarTalk Radio Show. Unit Conversions. Touch Trigonometry. The Tesseract. Weierstrass functions. 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. In fact, it is absolutely convergent. It is also an example of a fourier series, a very important and fun type of series. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x. Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr. 6174 (number) 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. (Leading zeros are allowed.)Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2. 9990 – 0999 = 8991 (rather than 999 – 999 = 0) Collatz conjecture. 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 3n + 1 conjecture, the Ulam conjecture (after Stanisław 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][2] the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud),[3][4] or as wondrous numbers.[5] Take any natural number n.
If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO[6]) indefinitely. Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such problems In 1972, J. Statement of the problem[edit] In notation: (that is: applied to. Making sense of a visible quantum object.