# All of CTVKenney's Comments + Replies

The VARIANCE of a random variable seems like one of those ad hoc metrics. I would be very happy for someone to come along and explain why I'm wrong on this. If you want to measure, as Wikipedia says, "how far a set of numbers is spread out from their average value," why use E[ (X - mean)^2 ] instead of E[ |X - mean| ], or more generally E[ |X - mean|^p ]? The best answer I know of is that E[ (X - mean)^2 ] is easier to calculate than those other ones.

Maybe entropic uncertainty [https://en.wikipedia.org/wiki/Entropic_uncertainty] (conjectured by Everett as part of his "Many Worlds" thesis, and proved by Hirschmann and Beckner) is along the lines of what you're looking for. It's a generalization of the Heisenberg uncertainty principle that applies even when the variance isn't well defined.

Variance has more motivation than just that it's a measure of how spread out the distribution is. Variance has the property that if two random variables are independent, then the variance of their sum is the sum of their variances. By the central limit theorem, if you add up a sufficiently large number of independent and identically distributed random variables, the distribution you get is well-approximated by a distribution that depends only on mean and variance (or any other measure of spreadout-ness). Since it is the variance of the distributions you we... (read more)

Apollo Creed problems and Clubber Lang problems -- framing, and how to address the latter?

Dear CraigMichael,

I am by no means a guru. It seems like you prefer Apollo Creed problems to Clubber Lang problems because you're more able to motivate yourself to do Apollo Creed problems. I feel the same way. I find it exciting to start new projects, and grueling to continue my existing projects. My advice:

If you need to solve a Clubber Lang problem, then in moments of clarity, you should establish habits/systems to solve the Clubber Lang problem that don't require you to be motivated on any given day.

E.g. go for a jog even when you're not feeling ... (read more)