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Consider an idealized Newtonian universe with a uniform gravitational field. Roll a ball up one side of a radially symmetric hill, so that its velocity is zero at the top. Reverse time; the ball now appears to break symmetry spontaneously. Is this a paradox? Why or why not?

I guess everyone has their own completely unrealistic ideas of other people.

Find a property characterizing a subset W of a vector space V, such that W is obviously closed but nonobviously empty.

Suppose you want to give a choice to many people, in an attempt to simulate a random variable. For example, you may ask each person to say "Yes" or "No". However, they may then infer that you are using the result to decide whether to do something, and their response may be biased. You then desire choices with as little connotative difference as possible.

I currently have "Pick an element of {-1, 0, 1}". Any ideas for simple ways of improving this (using only text)?

(You can also vote here if you want, and haven't on chat.)

So it turns out most of Wikipedia (decently-sized, decently-written pages) has a diameter of three or four links, with occasional pairs requiring more. I've only tried five pairs; feel free to play around.

(Requires Algorithm::SixDegrees. May do unexpected things if page titles have weird characters or pages have lots of links.)

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Confused by the abundance of fictional militaries that adapt existing rank systems into mutual inconsistency? Here at last is a single definitive standard.

Admiral	Ackbar
Captain	Marko Ramius
Commander	James Bond
Ensign	Wesley Crusher
General	Jack O'Neill
Lieutenant	Louis Hoshi
Major	Major Major Major
Marshal	Éomer
Petty Officer	Master Chief
Sergeant	Schlock

For example, if you can't remember which of Commander and Ensign is higher, just decide whether Wesley Crusher could command James Bond. Simple!

Q: Why does it take longer to write code in Z[√-5]?
A: You have to refactor.

I've always felt that the simplest explanation goes as follows:

The initial chance of being correct is 1/3. There is always a goat behind one of the other doors, so opening that one gives you no extra information. Therefore, the probability remains the same.

Unfortunately, it hasn't proven very successful at convincing people.