Monthly Archives: February 2008

Inflation Conversions – What's 1972£10,000 worth today?

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. Bertie was paid £10,000 for his part in a robbery in 1972. The article alleges that £10,000 in 1972 is equivalent to £200,000 today.

Lots of people think that that looks fishy, and have been sending me mail asking
if that makes any sense.

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Washington State and GOP Vote Counting Fraud?

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 of you who were hoping for a nice debunking
of the idea of fraud, but to me, something sure looks fishy.

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Abstract Algebra and Computation – Monoids

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 – where a group, the exemplar of symmetry, is seen as an
expression of the symmetries of a simpler structure.

We can see similar things as we climb up the stack of abstract algebraic
constructions. If we start looking for the next step up in algebraic
constructions, the rings, we can see a very different view of
what a ring is.

Before we can understand the categorical construction of rings, we need
to take a look at some simpler constructions. Rings are expressed in
categories via monoids. Monoids are wonderful things in their own right, not
just as a stepping stone to rings in abstract algebra.

What makes them so interesting? Well, first, they’re a solid bridge
between the categorical and algebraic views of things. We saw how the
category theoretic construction of groupoids put group theory on a nice
footing in category theory. Monoids can do the same in the other direction:
they’re in some sense the abstract algebraic equivalent of categories.
Beyond that, monoids actually have down-to-earth practical applications –
you can use monoids to describe computation, and in fact, many of the
fundamental automatons that we use in computer science are, semantically,

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Clarifying Groupoids and Groups

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 this stuff as I did the research to write the article, but which I never made clear in my explanations. I’ll try to remedy that with this post.

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More Groupoids and Groups

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. Today, I’m going to explore a bit more of the relationship
between groupoids and groups.

Before I get into it, I’d like to do two things. First, a mea culpa: this stuff is out on the edge of what I really understand. My category-theory-foo isn’t great, and I’m definitely
on thin ice here. I think that I’ve worked things out enough to get this right, but I’m
not sure. So category-savvy commenters, please let me know if you see any major problems, and I’ll do my best to fix them quickly; other folks, be warned that I might have blown some of the details.

Second, I’d like to point you at Wikipedia’s page on groupoids as a
reference. That article is quite good. I often look at the articles in Wikipedia and
MathWorld when I’m writing posts, and while wikipedia’s articles are rarely bad, they’re also
often not particularly good. That is, they cover the material, but often in a
somewhat disorganized, hard-to-follow fashion. In the case of groupoids, I think Wikipedia’s
article is the best general explanation of groupoids that I’ve seen – better than most
textbooks, and better than any other web-source that I’ve found. So if you’re interested in
finding out more than I’m going to write about here, that’s a good starting point.

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Friday Random Ten

  1. 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.
  2. The Beatles, “Mean Mr. Mustard”
  3. The Flower Kings, “The Devil’s Danceschool”: Brilliant instrumental piece by
    the Flower Kings, built around an improv by a Trumpet fed through a synth bender.
  4. Do Make Say Think, “You, You’re Awesome”: one of my favorite post-rock groups. Very typical of their sound.
  5. Tony Trischka Band, “Woodpecker”: Tony used to be my banjo teacher. I also think he’s the best banjo player in the world today – better even that Bela Fleck (another of his students). Tony’s playing is more sophisticated than Bela’s. He’s done more to revolutionize Banjo playing than anyone since Earl Scruggs. This track has some really interactions – unisons, and call/response type stuff between the sax and Tony’s banjo.
  6. The Silver Mt. Zion Memorial Orchestra and Tra-la-la Band, “Take These Hands and Throw Them Into the River”: Absolutely incredible music from A Silver Mt. Zion. This is, quite possibly, my favorite thing by them. Very intense, rather loud for ASMZ. Amazing piece of work.
  7. Glass Hammer, “Ember Without Name”: Very long, very good track by an American neo-progressive band. When I first listened to this album, I was rather depressed – the first track is dull and repetitive. I was expecting it to follow in that pattern. This track blew me away. It’s not quite up there with the great prog bands, but it’s really good.
  8. Mandelbrot Set, “And the Rockets Red Glare”: math-geek post-rock; what’s not to love?
  9. Boiled in Lead, “Rasputin”: Very, very silly. This is a comedic song by an electric folk-rock band. It tells the story of Rasputin, set to music built form Russian
    folk song melodies. With lyrics like “Rah Rah Rasputin, Russia’s greatest love machine”.
  10. Sonic Youth, “Incinerate”: a truly great track from Sonic Youth.

Idiot Math Professors, Fractions, and the Fun of Math

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 both sides of the argument.

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