goodmath

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April 3, 2008
Bad from the Bad Ideas Blog sent me a link to some clips from Ben Stein's new Magnum Opus, "Expelled". I went and took a look. Randomly, I picked one that looked like a clip from the movie rather than a trailer - it's the one titled "Genetic Mutation". Care to guess how long it took me to find an…
April 1, 2008
One of my fellow ScienceBloggers, Andrew Bleiman from Zooilogix, sent me an amusing link. If you've done things like study topology, then you'll know about non-euclidean spaces. Non-euclidean spaces are often very strange, and with the exception of a few simple cases (like the surface of a sphere…
April 1, 2008
I know better than to attempt to write an april fools day post that really tries to fool anyone. I'm not a good enough writer to carry that kind of thing off in a genuinely amusing way. On the other hand, I love april fools day pranks, and I generally like the silly mood of the day. So I thought…
March 31, 2008
In game theory, perhaps the most important category of simple games is something called zero sum games. It's also one of those mathematical things that are widely abused by the clueless - you constantly hear references to the term "zero-sum game" in all sorts of contexts, and they're almost always…
March 27, 2008
Suppose you've got a bunch of data. You believe that there's a linear relationship between two of the values in that data, and you want to find out whether that relationship really exists, and if so, what the properties of that relationship are. Once again, I'll use an example based on the first…
March 25, 2008
I'm going to jump into the framing wars again. As I mentioned last time, I think that most folks who are "opposed" to framing really don't understand what they're talking about - and I'll once again explain why. But on the other hand, I think that our most prominent framing advocates here at SB…
March 24, 2008
Several people have asked me to write a few basic posts on statistics. I've written a few basic posts on the subject - like, for example, this post on mean, median and mode. But I've never really started from the beginnings, for people who really don't understand statistics at all. To begin with…
March 23, 2008
As an introduction to a mathematical game, and how you can use a little bit of math to form a description of the game that allows you to determine the optimal strategy, I'm going to talk a bit about Nim. Nim is a simple two-player turn-taking game. The idea is you've got a collection of piles of…
March 19, 2008
Lots of people wanted game theory, so game theory it is. The logical first question: what is game theory? Game theory is typical of math. What mathematicians like to do is reduce things to fundamental abstract structures or systems, and understand them in terms of the abstraction. So game theory…
March 18, 2008
As you've probably noticed, things have been rather slow around here lately. I've got more posts in the works on group theory and abstract algebra - but they take a lot of time to research and write, so they'll be coming out slowly - one a week or so. In the meantime, I'm looking for other topics…
March 14, 2008
This is a complicated recipe. It takes a couple of days to do properly, and works best done with a slow-cooker. But it's worth it. It's a Taiwanese dish - a spicy beef noodle soup. It's pretty much the national dish of Taiwan - Taiwanese love this dish. There are annual competitions in Taipei for…
March 12, 2008
After yesterday's post about the great women of computer science, I noticed my SciBling MarkH over at the Denialism blog had discovered Vox Day and his latest burst of stupidity, in which he alleges that the greatest threat to science is.... women. Because, you see, women are all stupid. The…
March 11, 2008
At Science, Education, and Society, the Urban Scientist posts a meme to name five women scientists from each of a list of fields. Sadly, my fields are left off the list. So I'll respond in my own way by adding computer science. This is a very idiosyncratic list - it's women who are particularly…
March 11, 2008
Since I mentioned the idea of monoids as a formal models of computations, John Armstrong made the natural leap ahead, to the connection between monoids and monads - which are a common feature in programming language semantics, and a prominent language feature in href="http://scienceblogs.com/…
March 10, 2008
I'm jumping into this late, and it's at least somewhat off topic for this blog, although I'll try to pull a few mathematical metaphors into it. But Michael Egnor, that paragon of creationist stupidity, is back babbling about evolution and bacterial antibiotic resistance. This is a subject which is…
March 6, 2008
While doing some reading on rings, I came across some interesting stuff about Monoids and syntax. That's right up my alley, so I decided to write a post about that. We start by defining a new property for monoids - a kind of equivalence relation called a monoid congruence. A Monoid congruence…
March 4, 2008
When I first talked about rings, I said that a ring is an algebraic abstraction that, in a very loose way, describes the basic nature of integers. A ring is a full abelian group with respect to addition - because the integers are an abelian group with respect to addition. Rings add multiplication…
February 29, 2008
This recipe is based on a recipe for Moroccan spiced duck breasts, fromThe Soul of a New Cuisine, Marcus Samuelsson's new African cookbook. Chef Samuelsson is the guy who's responsible for getting me to eat beef after not touching the stuff for nearly two years. He's a very interesting guy - born…
February 28, 2008
Yet another reader sent me a link to a really annoying article at a site called "Daily Tech". The article has been more than adequately debunked by Darksyde at Daily Kos, but it's a very typical example of a general kind of argument made both for and against global warming, which I find extremely…
February 28, 2008
By now, we've seen the simple algebraic monoid, which is essentially an abstract construction of a category. We've also seen the more complicated, but interesting monoidal category - which is, sort of, a meta-category - a category built using categories. The monoidal category is a fairly…
February 24, 2008
Granville Sewell, over at UD, has decided to pretend that he just discovered my earlier critique of his "though experiment" where he claims to simulate the universe. The reason that I say "pretend" is that Sewell originally edited the article that I was mocking in response to my post; now, months…
February 22, 2008
Boiled in Lead, "Blackened Page": An interestingly mysterious song, written by one of my favorite fiction writers, the brilliant Steven Brust. J.S. Bach, "Cantata #77": Bach's Cantata's are some of the finest pieces of music ever written. Amazing. Mandelbrot Set, "And the Rockets Red Glare": very…
February 21, 2008
I was asked by a reader to take a look at yet another crackpot theory of everything. This time, it's the Cognitive Theoretic Model of the Universe. This one is as cranky as any, but it's actually got some interestingly silly math to it. Stripped down to its basics, the CTMU is just yet another…
February 21, 2008
Over at Adventures in Ethics and Science, Janet Stemwedel, our resident ethicist, has been writing about academic dishonesty and how professional researchers should respond to it. I've been on the receiving end of dishonesty on three occasions - ranging from a trivial case (arguably not dishonest…
February 18, 2008
In the last post on groups and related stuff, I talked about the algebraic construction of monoids. A monoid is, basically, the algebraic construction of a category - it's based on the same ideas, and has the same properties; just the presentation of it is different. But you can also see a monoid…
February 18, 2008
A bunch of us today are trying to point out some incredible hypocrisy and downright despicable slime being spewed by the idiots who want to blame autism on vaccines. The blame-vaccines crowd likes to use publicity stunts to try to build up their case. It's the only tactic left to them, because…
February 13, 2008
After yesterday's article about conversion between the value of british pounds in the '70s versus british pounds today, someone sent me a link toan article at the National Review Online, which just about had me rolling on the floor laughing. The problem is, it's dead serious. It's written by an…
February 12, 2008
I've been getting a ton of questions about an article from the Independent about a guy named Bertie Smalls. Bertie was a british thief who died quite recently, who was famous for testifying against his organized crime employers back in the 1970s. The question concerns one claim in the article.…
February 11, 2008
I've been getting a lot of mail from people asking for my take on the news about the Washington GOP primary. Most have wanted me to debunk rumours about vote fixing there, the way that I tried to debunk the rumours about the Democratic votes back in New Hampshire. Well, sorry to disappoint those…
February 10, 2008
In the last couple of posts, I showed how we can start looking at group theory from a categorical perspective. The categorical approach gives us a different view of symmetry that we get from the traditional algebraic approach: in category theory, we see symmetry from the viewpoint of groupoids -…