goodmath

This post started out as a response to a question in the comments of my last post on groupoids. Answering those questions, and thinking more about the answers while sitting on the train during my commute, I realized that I left out some important things that were clear to me from thinking about…

In my introduction to groupoids, I mentioned that if you have a groupoid, you can find groups within it. Given a groupoid in categorical form, if you take any object in the groupoid, and collect up the paths through morphisms from that object back to itself, then that collection will form a group…

Metaphor, "Call Me Old and Uninspired or Maybe Even Lazy and Tired but Thirteen Bodies in my Backyard Say You're Wrong": Very cool (if silly) track from one of the best neo-progressive bands I found via Bitmunk. I love Bitmunk. The Beatles, "Mean Mr. Mustard" The Flower Kings, "The Devil's…

A bunch of people have been sending me links to a USA Today article about a math professor who wants to change math education. Specifically, he wants to stop teaching fractions, and de-emphasize manual computation like multiplication and long division. Frankly, reading about it, I'm pissed off by…

Sorry for the lack of posts this week. I'm traveling for work, and I'm seriously jet-lagged, so I haven't been able to find enough time or energy to do the studying that I need to do to put together a solid post. Fortunately, someone sent me a question that I can answer relatively easily, even in…

Godspeed You! Black Emperor, "Antennas to Heaven": What can you really say about the greatest post-rock ensemble ever? The Windmill, "Please Keep War Stories to a Minimum": a recent post-rock discovery of mine, via bitmunk. Excellent group. Rachel's, "An Evening of Long Goodbyes": Rachel's is one…

One of the staples of chinese cooking is fried rice. Unfortunately, what we get in American restaurants when we order fried rice is dreadful stuff. The real thing is absolutely wonderful - and very different from the American version. The trick to getting the texture of the dish right is to use…

Today's entry is short, but sweet. I wanted to write something longer, but I'm very busy at work, so this is what you get. I think it's worth posting despite its brevity. When we look at groups, one of the problems that we can notice is that there are things that seem to be symmetric, but which…

A bunch of people have sent me links to an article about MapReduce. I've hesitated to write about it, because the currently hyped MapReduce stuff was developed, and extensively used by Google, my employer. But the article is really annoying, and deserves a response. So I'm going to be absolutely…

So far, I've spent some time talking about groups and what they mean. I've also given a brief look at the structures that can be built by adding properties and operations to groups - specifically rings and fields. Now, I'm going to start over, looking at things using category theory. Today, I'll…

I'm a big fish eater. In general, given a choice about what to eat, I'm usually happiest when I get to eat a nice fish. Even now that I've started eating beef again, most of the time, I'd rather eat a nice piece of wild salmon than pretty much anything made of beef. When it comes to cooking fish…

Haven't done this in a while: 10 random tracks from my iPhone: Porcupine Tree, "The Sky Moves Sideways" Mogwai, "I Chose Horses". Mellowness from one of the greatest Post-Rock groups around. Thinking Plague, "Lux Lucet". Thinking Plague is one of the strangest things I listen to. I don't know…

I managed to trash yet another laptop - the city commute through the subways seems to be pretty hard on computers! - so while I'm sitting and slowly restoring my backups, I was looking through the folder where I keep links to crankpots that I'd like to mock someday. I noticed one that I found…

When we start looking at fields, there are a collection of properties that are interesting. The simplest one - and the one which explains the property of the nimbers that makes them so strange - is called the characteristic of the field. (In fact, the characteristic isn't just defined for fields…

After last week's New Hampshire primaries, I've gotten a lot of email requesting my take on the uproar surrounding recounts and voting machines. For those who haven't heard, there's been some chatter about cheating in the election. In polls leading up to the election, Barack Obama was leading by…

When I learned abstract algebra, we very nearly skipped over rings. Basically, we spent a ton of time talking about groups; then we talked about rings pretty much as a stepping stone to fields. Since then, I've learned more about rings, in the context of category theory. I'm going to follow the…

Today is the 70th birthday of Donald Knuth. If you don't know who Knuth is, then you're not a programmer. If you're a programmer and you don't know who Knuth is, well... I have no idea what rock you've been hiding under, but you should probably be fired. Knuth is one of the most famous and…

I was just perusing my stats on sitemeter - and to my amazement, I discovered that Good Math/Bad Math had its 2 millionth view this weekend. 2 million pageviews! I never dreamt that this little blog would ever see a number like that. Astonishing! Over 1.3 million visits to the blog so far! Thank…

Sorry, but as a software guy, I just couldn't resist mocking the sheer insane hypocrisy of this. There's a right-wing political site out there, called RedState.com. RedState is serious far-right - constantly bemoaning the nanny-state, the culture of entitlement, the virtues of personal…

I decided to do a little bit of something useful with Erlang, both to have some code to show, and to get some sense of what it's like writing something beyond a completely trivial example. Because the capabilities of Erlang shine when you get into low-level bit oriented things, I thought that…

I've been sent Yet Another Proof of God. This one goes to rather a lot of trouble to appear to be mathematical. I thought that it would be fun to rip it apart. For a change, this one is from an Islamic moron, rather than the usual Christian moron. Alas, it's pretty much as stupid and shallowly…

Sorry that the blog has been so quiet lately; I managed to catch a vicious flu for the first time since I started getting flu shots, so I've been feeling too ill to write. I'm still far from recovered, but I'm feeling well enough to share a bit of delightful foolishness with you. After seeing my…

Yet another alert reader just sent me a link to this extremely humorous blog. It's not recent, but it's silly enough that it's worth pointing out even now. I'm not one hundred percent sure that this isn't a parody. Looking at the blog as a whole, I think it's serious. Pathetic, but serious.…

If you're looking at groups, you're looking at an abstraction of the idea of numbers, to try to reduce it to minimal properties. As I've already explained, a group is a set of values with one operation, and which satisfies several simple properties. From that simple structure comes the basic…

After that nasty diversion into economics and politics, we now return to your regularly scheduled math blogging. And what a relief! In celebration, today I'll give you something short, sweet, and beautiful: quotient groups. To me, this is a shining example of the beauty of abstract algebra. We've…

Look folks, I don't want to become an economics blogger! Stop sending me economics questions. I hate to disappoint my readers and not answer their questions, but this economics stuff is almost terminally dull to me. The mortgage posts have gotten an insane amount of traffic, which has in turn…

I've received an amazing number of requests in the short period of time since my last post to explain "Tranching". I mentioned it off-handedly, but a lot of people have heard about its role in the whole sub-prime mess, and wanted to know just what it means. I don't particularly like writing about…

Reading the news lately, I've come across an amazing example of how ubiquitous bad math can be used. Most of you have probably heard about what's been called "the sub-prime crisis". Despite a lot of media hand-wringing about how complicated it all is, the sub-prime crisis is really a very simple…

Here at ScienceBlogs, we have a back-channel where the bloggers can get together and chat. In one of our threads, I was telling a story about work, and an interesting question came up. What's the collective noun for a bunch of geeks? Collective nouns are cool and funny. Some of them are…

I've gotten both some comments and some e-mail from people in response to my mini-rant about Erlang's macros. I started replying in comments, but it got long enough that I thought it made sense to promote it up to a top-level post. It's not really an Erlang issue, but a general language issue, and…