Dork Scratchings

This reminder has been on a wall in my house for ~15 years As a programmer for 22 years I've fixed thousands of bugs, and created many times more.  Very often it appeared that the problem I was trying to fix had multiple independent causes.  However I have found - almost invariably - that if you dig long enough you'll find a single cause for all the problems you are seeing.  In fact the moment you hit on the right theory is often really obvious because it suddenly explains a whole bunch of other things that have been going wrong!  But, I wondered, can this observation be proven mathematically?  It turns out it can! The Debugger's Theorem If a system that usually works currently isn't working, then it is more likely than not that there's just one thing causing all the observed problems. Proof Let $P_0$ be the probability that the system has no problems, $P_1$ be the probability that one independent problem has occurred, $P_{2+}$ the probability that...

Queqiao and Chang'e-4 Exciting news from the BBC Website: China Moon mission lands Chang'e-4 spacecraft on far side .  The page includes a video with sinister background music as if to suggest they're the baddies (a la Drax in Moonraker).  However, the part that really intrigued me was the mention of the L2 Lagrange point - the first I've ever seen in a news story! As I described in my post Lagrange Points   there are 5 locations in the Earth-moon-Sun plane in which - in the rotating frame of reference and taking centrifugal forces into account - there is no overall force and an object can be parked indefinitely.  One of them is just beyond the moon and is called L2 . Now the problem with landing a probe on the far side of the moon is that you can't talk directly to it: there's a big rock in the way!  So, according to the BBC article the Chinese Space Agency has parked a satellite Queqiao at L2 to relay messages.  This left me a bit confused...

Imagine you were a hamster in a hamster ball living on a hilly surface.  Base camp is surrounded on all sides by high summits, but you have a powerful catapult there that can fire you to the top of any of them.  Once fired you can influence your trajectory, but it's hard work and you don't have much energy in your little legs.  Suppose you know where you want to end up beyond the hills.  What's the best strategy for getting there?