goodmath

So, we've built up some pretty nifty binary trees - we can use the binary tree both as the basis of an implementation of a set, or as an implementation of a dictionary. But our implementation has had one major problem: it's got absolutely no way to maintain balance. What that means is that…

By way of the astronomy picture of the day, I encountered a really fantastic site about the analemma. The analemma is the apparent path that the sun takes in the sky during the year. If you record the precise position of the sun at the same time every day, instead of being in exactly the same…

I've mostly been taking it easy this week, since readership is way down during the holidays, and I'm stuck at home with my kids, who don't generally give me a lot of time for sitting and reading math books. But I think I've finally got time to get back to the stuff I originally messed up about…

Friday Not-So-Random Five I decided in honor of the new year, I'd do something a bit different this week. Instead of doing a random shuffle on my IPod, I separated out my favorites of the modern classical pieces that I discovered this year. Some of these are brand new recordings just released this…

Like my friend and blogfather [Orac][orac], I'm a huge fan of Doctor Who, and I've been greatly enjoying its renewed life in the new series on BBC. In fact, the current Doctor, played by David Tennant, has become my favorite of all of the Doctors - better than the usual fan favorite of Tom Baker,…

Being a Nice Jewish BoyTM, Christmas is one of the most boring days of the entire year. So yesterday, I was sitting with my laptop, looking for something interesting to read. I try to regularly read the [Panda's Thumb][pt], but sometimes when I don't have time, I just drop a bookmark in my "to read…

1. **Lunasa, "Feabhra"**: My favorite traditional Irish band. These guys are *really* traditional instrumental Irish - Uillean pipes, flute, guitar, bodhran, and bass. The pipe player is without doubt one of the best, if not *the* best in the world. I thought that I hated all kinds of…

Today, I'm going to show you a very simple, very goofy little language called "SCEQL", which standards for "slow and clean esoteric queue language". It's based on nothing but a circular queue of numbers with nothing but 8 commands. It's not one of the more exciting languages, but it can be a lot of…

The topology posts have been extremely abstract lately, and from some of the questions I've received, I think it's a good idea to take a moment and step back, to recall just what we're talking about. In particular, I keep saying "a topological space is just a set with some structure" in one form or…

In Haskell, there are no looping constructs. Instead, there are two alternatives: there are list iteration constructs (like foldl which we've seen before), and tail recursion. Let me say, up front, that in Haskell if you find yourself writing any iteration code on a list or tree-like structure,…

Over the weekend, in an attempt to cheer me up, a kind and generous reader sent me a link [to a *really* wonderful site of crackpot science][adams]. It's a crackpot theory about how physics has it all wrong. You see, there is no such thing as gravity - it's all just pressure. And the earth (and all…

This week's "Ask a ScienceBlogger" is an interesting one, but *very* tricky to answer. The question was proposed by fellow SBer [Dave Munger:][munger] **"What's a time in your career when you were criticized extremely harshly by someone you respect? Did it help you or set your career back?"** […

GM/BM has been pretty slow overall this week, both in new posts and in my responses to comments on previous posts. It was both bigtime deadline week on my project at work; and a very bad week for family health issues. My dad, who I've mentioned on this blog a lot of times because of the fact that…

Following in the footsteps of [orac](http://scienceblogs.com/insolence) and [PZ](http://www.scienceblogs.com/pharyngula) among others of my fellow SBers, I've taken the survey to find out which historical lunatic I am. And I must say, I'm pleased with the results! Which Historical Lunatic Are You?…

Don't forgot: GM/BM is a finalist in the weblog competition for best science blog. I've got no chance of winning, but there's a slim chance that I could make third or fourth. You can vote once per day.

Continuing from where we left off yesterday... Yesterday, I managed to describe what a *presheaf* was. Today, I'm going to continue on that line, and get to what a full sheaf is. A sheaf is a presheaf with two additional properties. The more interesting of those two properties is something called…

Suppose we've got a topological space. So far, in our discussion of topology, we've tended to focus either very narrowly on local properties of **T** (as in manifolds, where locally, the space appears euclidean), or on global properties of **T**. We haven't done much to *connect* those two views.…

While there's nothing mathematical about this bit of silly woo, I couldn't resist mocking it. There's a Japanese inventor who claims to have created a device that instantly ages wine through a magical homeopathic-sounding process of magically restructuring water molecules. For why I can't resist…

In my last topology post, I started talking about the fundamental group of a topological space. What makes the fundamental group interesting is that it tells you interesting things about the structure of the space in terms of paths that circle around and end where they started. For example, if you'…

This was posted on slashdot, and forwarded to me by several readers. It's worth listening to the first few minutes to get an idea of just how pathetically inummerate many people are. It might also help convince you to stay the hell away from *any* service provided by Verizon; my experience with…

So, Goodmath/Badmath was nominated for a weblog award for the best science blog. I was actually planning on ignoring it for two reasons. First, Pharyngula was nominated in the same category, and there is absolutely no way that I can *hope* to complete with PZ. And second, the Weblogs are kind of…

Our pathological language this week is [Underload][underload]. Underload is, in some ways, similar to Muriel, only it's a much more sensible language. In fact, there are actually serious practical languages called *concatenative languages* based on the same idea as Underload: [Joy][joy] and [Factor…

Tons of folks have been writing to me this morning about [the BBC story about an idiot math teacher who claims to have solved the problem of dividing by zero][bbc-story]. This is an absolutely *infuriating* story, which does an excellent job of demonstrating what total innumerate idiots reporters…

One thing I've been hearing a lot lately is discussions about Ethanol, and it's been really pissing me off. Can ethanol be a serious replacement for oil as a source of energy? I don't know. Because *both* sides are using really bad math to make their arguments. There are two fundamental questions…

Last time around, I walked through the implementation of a very simple binary search tree. The implementation that I showed was reasonable, if not great, but it had two major limitations. First, it uses equality testing for the search, so that the implementation is only really suitable for use as…

Yesterday at Pharyngula, PZ posted a description of his favorite signaling pathway in developmental biology, the [Notch system.][notch] Notch is a cellular system for selecting one cell from a collection of essentially indistinguishable cells, so that that one cell can take on some different role…

For this post, I'm doing a bit of an experiment. Haskell includes a "literate" syntax mode. In literate mode, and text that doesn't start with a ">" sign is considered a comment. So this entire post can be copied and used as a source file; just save it with a name ending in `".lhs"`. If this…

Haskell is a strongly typed language. In fact, the type system in Haskell is both stricter and more expressive than any type system I've seen for any non-functional language. The moment we get beyond writing trivial integer-based functions, the type system inevitably becomes visible, so we need to…

I'm sure that in the friday pathological programming languages, I have a fondness for languages that make your code beautiful: languages like [SNUSP][snusp], [Befunge][befunge], [Piet][piet], and such. Those languages all you two-dimensional layouts for their programs. [snusp]: http://scienceblogs…

Fellow [SBer Tara from Aetiology][tara] pointed me at [this bit of inanity][loonytune], which I can't resist mocking: [tara]: http://www.scienceblogs.com/aetiology [loonytune]: http://www.wdcmedia.com/newsArticle.php?ID=2306 >The mystery of the human genome has come into clearer focus as…