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Magician Turned Professor Talks About the Math Behind Shuffling Cards
An anonymous reader writes with this story about magician and professor of mathematics and statistics at Stanford University Persi Diaconis. "Now a professor of mathematics and statistics at Stanford University, Diaconis has employed his intuition about cards, which he calls 'the poetry of magic,' in a wide range of settings. Once, for example, he helped decode messages passed between inmates at a California state prison by using small random 'shuffles' to gradually improve a decryption key. He has also analyzed Bose-Einstein condensation — in which a collection of ultra-cold atoms coalesces into a single 'superatom' — by envisioning the atoms as rows of cards moving around. This makes them 'friendly,' said Diaconis, whose speech still carries the inflections of his native New York City. 'We all have our own basic images that we translate things into, and for me cards were where I started.' In 1992, Diaconis famously proved — along with the mathematician Dave Bayer of Columbia University — that it takes about seven ordinary riffle shuffles to randomize a deck. Over the years, Diaconis and his students and colleagues have successfully analyzed the effectiveness of almost every type of shuffle people use in ordinary life."
Cats aren't taking pleasure in tormenting prey, or playing with the mouse, they are tiring out an animal that has teeth and claws and could potentially hurt the cat. In the wild, even if a predator manages to kill the prey, if that prey manages to wound the predator so that the next time it goes on the hunt, it is not so strong or sharp, the predator is in trouble.
Have you ever gone fishing? The best way to catch many kinds of fish is to fight it for a while and tire it out. That's the hunting methodology that cats have evolved to use.
What would motivate a rabbit, horse or dog to eat its own shit?
At least in the case of rabbits, it is normal behavior. All rabbits do it. They eat high-cellulose diets, and require bacteria to break down the fiber. Cows manage that by having multiple stomachs and a long digestive tract. But rabbits are too small for that, so they use two passes. After the first pass, the poop comes out soft and green, and is re-eaten as it emerges from the anus. After the second pass, the poop is hard black pebbles, and is not eaten.
Many animals will eat the feces of their young to get rid of the odor that may attract predators.
Most dogs stop eating poop as they mature. Puppies often do it, but adult dogs usually don't, unless they are nursing a mother, which often eat the puppy poop. Folklore has it that you can stop a dog from eating poop by mixing mashed pumpkin into their food.
Also, it is entirely possible, (if unlikely) that you can shuffle a randomized deck of cards into sequential order.
Random does not mean completely out of order, it means unpredictable. I can roll five dice and come up with a large straight (12345). The random comes from not being able to predict from the previous state (22222 Yahtzee!) what the next state (12356 chance) will be.
A perfect riffle shuffle is not a random process since you can observe the initial state (123456 e.g) and predict the result (142536). That's true for whatever the starting state is.