# goodmath

### Posts by this author

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 -…