Cruise ship versus battleship

Posted on 4 March 2013 by John

I heard someone ask an audience once

Would you rather spend a couple days on a cruise ship or on a battleship?
Would you rather spend a year on a cruise ship or on a battleship?

Presumably most people would rather spend a couple days as a passenger on a cruise ship rather than working on a battleship. But after a while, having no purpose and no responsibility becomes miserable. You can only play so much shuffleboard before you go out of your mind. (Relaxation can be its own purpose for a couple days, but not for a year.)

Functional means

Posted on 2 March 2013 by John

Functional means are a way of inducing a mean M_f from a differentiable function f.

$M_f(x, y) = (f')^{-1} \left( \frac{f(y) - f(x)}{y-x} \right)$

If f(x) = x², M_f(x, y) = (x + y)/2 is the arithmetic mean.

If f(x) = 1/x, M_f(x, y) = √(xy) is the geometric mean.

Seems like this should be useful for something.

Source

Related post: Means and inequalities