Errrrr

I haven't really updated my blog lately (again). I had a Crown camp over the weekend, and I was crazy busy last week. I'll probably pick up my planned series on Time Control tomorrow or so, but for now, I'll share a neat little thing I was doing today. I googled "er", "err", "errr", and so on, took down the number of results, and plotted them in Mathematica. Here's the result, with number of "r"s on the x axis and number of results on the y axis (it's actually the logarithm of the result, to keep them at a manageable size).

I've only gotten up to 60, but it's actually non-zero all the way up to 128 "r"s, at which point Google tells you the search string is too long. It starts off with a gorgeous example of exponential decay (though since it's log data, it's not really exponential decay. Double exponential decay, maybe?), but then goes into a more random jittering pattern. The log data goes down in a pretty straight line, which means the original data goes down roughly exponentially. Of course, that doesn't take into account that weird spike at around 50. Who knows what's up with that?

Complex Numbers

A wonderfully readable brief explanation of imaginary and complex numbers from - The New York Times?

Lockhart's Lament

I've probably already showed this link to a lot of people I know, but if not, you ought to read this. It's an essay entitled "A Mathematician's Lament", written by Paul Lockhart, a teacher of mathematics. It's more commonly referred to as just "Lockhart's Lament". It's a really fantastic read, especially if you've never pursued math beyond high school or early college - you have no idea what you missed. Of course, I'm not saying that everyone should be a math major, but I'm saying that the tedious drills that schoolchildren do are about as far away from real math as they could possibly be. You can read the whole thing here (it's a pdf), but keep reading for some of my favorite quotes.

Every Base is Base 10

Solitaire Meets Number Theory

First off, when I say solitaire, I don't mean the game that everyone calls "Solitaire". That's Klondike. Solitaire refers to any card game that can be played by just one person. The solitaire game I'll be talking about here is called Pyramid. The rules are pretty simple: first, you lay out cards in a pyramid of 7 rows (first 1 card, then 2, then 3, etc). The goal is to remove all the cards from the pyramid, and you can only remove cards in pairs that add up to 13 (where A = 1, J = 11, Q = 12, and K = 13). So, for example, you can remove an A and a Q, 6 and 7, 5 and 8, or a K by itself. You can also only remove cards that aren't covered by other cards. You can see in the image how each card is covered directly by two others, plus a bunch more farther below

If you get stuck, you can draw cards one at a time from the rest of the deck, called the Stack. So, that's all well and good, but what on earth does math have to do with this? Read on, dear reader.