goodmath

I wasn't really sure of quite how to start this off. I finally decided to just dive right in with a simple function definition, and then give you a bit of a tour of how Haskell works by showing the different ways of implementing it. So let's dive right in a take a look at a very simple Haskell…

Before getting to the meat of the tutorial, I thought it would be good to provide some setup information in a distinct, easy to find place. This short post will tell you where to find a Haskell implementation and related tools. Haskell Implementations I'm testing my examples for these articles…

In algebraic topology, one of the most basic ideas is *the fundamental group* of a point in the space. The fundamental group tells you a lot about the basic structure or shape of the group in a reasonably simple way. The easiest way to understand the fundamental group is to think of it as the…

Before diving in and starting to explain Haskell, I thought it would be good to take a moment and answer the most important question before we start: **Why should you want to learn Haskell?** It's always surprised me how many people *don't* ask questions like that. Haskell is a valuable…

As you may have noticed, lately, I've been fascinated by Haskell. I haven't done anything much in it until quite recently; it's been sitting in my to-do queue for a long time. This weekend, I was hacking away on a Haskell implementation of an interesting (but currently unimplemented) language from…

PEAR is gone. Yes, I know I'm late with this news; folks like [PZ](http://scienceblogs.com/pharyngula/2006/11/shhhdont_tell_deepak.php), [Orac](http://scienceblogs.com/insolence/2006/11/news_too_good_to_confine_to_j…) and [Jeff Shallit](http://recursed.blogspot.com/2006/11/pear-has-finally-rotted.…

1. **Kate Bush, "Pi"**. I've been waiting for this to show up in my shuffle for the FRT! Kate Bush, singing the digits of π! 2. **Suzanne Vega, "Knight Moves"**. This is an old favorite of mine. The lyrics have some personal significance, but it's a lovely song. 3. **Explosions in the Sky, "Have…

Todays tidbit of torture is a simple little language called [Leszek][leszek], with an implementation available [here][leszek-impl]. Leszek is based on the idea of *iterative string rewriting*, which is actually a useful and valuable concept. Of course, Leszek takes it to an extreme of insanity…

One year ago on Thanksgiving day, my friend John Vlissides died. I'm sure that many of you have heard of John. He was one of the so-called "Gang of Four" who wrote the "Design Patterns" book that set off a huge fad in software engineering (and quite typically for John, he always insisted on…

One of my fellow ScienceBloggers, [Karmen at Chaotic Utopia](http://scienceblogs.com/chaoticutopia/2006/11/puzzling_at_a_simpleminde…) pointed out a spectacularly stupid statement in [Casey Luskin's critique of Carl Zimmer][lutkin] (*another* fellow SBer) at the Discovery Institutes "Center for…

So, as promised, it's time for part two of "The Creationists and the Shrinking Sun". The second main tack of the creationists and the shrinking sun is to *not* use the bare measurements of an allegedly shrinking sun as their evidence. Instead, they use it as evidence for a very peculiar theory. It'…

One of the more pathetic examples of bad math from the creationist camp is an argument based on the claim that the sun is shrinking. This argument has been [thoroughly debunked](http://www.talkorigins.org/indexcc/CE/CE310.html) by other folks, so I haven't bothered to add my two cents here at GM/BM…

Due to work stuff, I'm very busy this week, and I don't have time to write a detailed pathological language post, so I chose something that doesn't take a lot of explanation, but which is delightfully twisted. It's a language called [Muriel](http://web.archive.org/web/20021205092706/http://demo.…

1. **Trout Fishing in America, "I Get Ideas"**. Trout is a great band; they do both children's music and adult music. This is one of their children's songs, but I love it anyway. What's not to like about a song that features shampooing with peanut butter? 2. **Gordian Knot, "The Brook The…

In my ongoing search for bad math, I periodically check out Uncommon Descent, which is Bill Dembski's blog dedicated to babbling about intelligent design. I went to check them today, and *wow* did I hit the jackpot. Dembski doesn't want to bother with the day-to-day work of running a blog. So he…

As [PZ](http://scienceblogs.com/pharyngula/2006/11/chopra_go_play_with_steve_ir…) pointed out, Deepak Chopra is back with *yet another* of his clueless, uninformed, idiotic rants. This time, he's written [an article trying to "prove" that there is an afterlife](http://www.intentblog.com/archives/…

While I was researching yesterdays post on Archimedes integration, one of the things I read reminded me of one of the stranger things about Greek and earlier math. They had a notion that the only valid fractions were *unit* fractions; that is, fractions whose numerator is 1. A fraction that was…

A lot of people have asked me to write something about "Archimedes Integration", and I'm finally getting around to fulfilling that request. As most of you already know, Archimedes was a philosopher in ancient Greece who, among other things, studied mathematics. He invented a technique for computing…

By way of PZ, I just found [the website of Jonathan Coulton](http://www.jonathancoulton.com/songs/), a musician who seems to specialize in humorous and geeky songs. The music is good; the lyrics are absolutely fantastic. Here's an example that he gives away, called "Mandelbrot Set". (For embedding…

I'm going to start moving the topology posts in the direction of algebraic topology, which is the part of topology that I'm most interested in. There's lots more that can be said about homology, homotopy, manifolds, etc., and I may come back to it as some point, but for now, I feel like moving on.…

Today's pathological language is a bit of a treat for me. I'm going to show you a twisted, annoying, and thoroughly pointless language that *I* created. The language is based on a model of computation called [Actors](http://en.wikipedia.org/wiki/Actor_model), which was originally proposed by…

1. **Porcupine Tree, "Prepare Yourself"**. Porcupine Tree is a strange bad, which started out as an elaborate joke. This is off of their most progressive album, "The Sky Moves Sideways". It's a brilliant piece of work. 2. **Dream Thater, "Blind Faith"** 3. **Dirty Three, "Dream Evie"**. Ah, Dirty…

While waiting for I was innocently browsing around the net looking at elementary math curriculums. I want to be able to teach my kids some fun math, just like my dad did with me when I was a kid. So I was browsing around, looking at different ways of teaching math, trying to find fun stuff. In the…

I thought it would be fun to do a couple of strange shapes to show you the interesting things that you can do with a a bit of glue in topology. There are a couple of standard *strange* manifolds, and I'm going to walk through some simple gluing constructions of them. Let's start by building a Torus…

After my [initial post about manifolds](http://scienceblogs.com/goodmath/2006/10/manifolds_and_glue.php), I wanted to say a bit more about gluing. You can form manifolds by gluing manifolds with an arbitrarily small overlap - as little as a single point along the point of contact between the…

Todays programming pathology is programs as art. Start with a really simple stack based language, add in a crazy way of encoding instructions using color, and you end up with a masterpiece of beautiful insanity. It's not too exciting from a purely computational point of view, but the programs are…

As you may have heard from some of the other ScienceBlogs, our SciBling Shelley Batts, of [Retrospectacle](http://www.scienceblogs.com/retrospectacle/) is competing for a scholarship being given to bloggers. Shelley's a great writer, and on her way to becoming a great scientist. Please head over to…

I came across an article yesterday about programming languages, which hit on one of my major peeves, so I can't resist responding. The article is at greythumb.org, and it's called [Programmer's rant: what should and should not be added to C/C++](http://www.greythumb.org/blog/index.php?/archives/…

A while ago, I wrote about Dembski's definition of specified complexity, arguing that it was a non-sensical pile of rubbish, because of the fact that "specified complexity" likes to present itself as being a combination of two distinct concepts: specification and complexity. In various places,…

Back in the early days of Good Math/Bad Math, when it was still at blogger, one of the most widely linked posts was one about the idea of *dimension*. At the time, I said that the easiest way to describe a dimension was as *a direction*. If you've got a point in a plane, and you want to say where…