goodmath

Yesterday, I posted [this article][bozo] about the bozo who didn't like his college calculus course because it wasn't Christian enough. One of the commenters pointed out that there's actually a site online where a college professor from a Christian college actually has [a collection of "devotionals…

Sorry for the delay in the category theory articles. I've been busy with work, and haven't had time to do the research to be able to properly write up the last major topic that I plan to cover in cat theory. While doing my research on closed cartesian categories and lambda calculus, I came across…

By way of Pharyngula, I saw something that I simply had to repeat here. Every august, James Kennedy - a thoroughly repulsive ultra-fundy preacher from Coral Ridge Ministries - runs a conference called "Reclaiming America for Christ". At this years conference, he featured a speech by Paul Jehle…

Lots of folks have been asking me to write about φ, the golden ratio. I'm finally giving up and doing it. I'm not a big fan of φ. It's a number which has been adopted by all sorts of flakes and crazies, and there are alleged sightings of it in all sorts of strange places that are simply *not* real…

Quaternions Last week, after I wrote about complex numbers, a bunch of folks wrote and said "Do quaternions next!" My basic reaction was "Huh?" I somehow managed to get by without ever being exposed to quaternions before. They're quite interesting things. The basic idea behind quaterions is: we…

Ω is my own personal favorite transcendental number. Ω isn't really a specific number, but rather a family of related numbers with bizzare properties. It's the one real transcendental number that I know of that comes from the theory of computation, that is important, and that expresses meaningful…

I received an email from someone with some questions about information theory; they relate to some sufficiently common questions/misunderstandings of information theory that I thought it was worth turning the answer into a post. There are two parts here: my correspondent started with a question;…

If you look at the history of math, there've been a lot of disappointments for mathematicians. They always start off with an idea of math as a clean, beautiful, elegant thing. And they seem to often wind up disappointed. Which leads us into todays strange numbers: irrational and transcendental…

Today's treat: [Thue][thue], pronounced two-ay, after a mathematician named Axel Thue. Thue is a language based on [semi-Thue][semi-thue] grammars. semi-Thue grammars are equivalent to Chosmky-0 grammars, except that they're even more confusing: a semi-Thue grammar doesn't distinguish between…

Over at his blog, William Dembski, my least-favorite pathetic excuse for a mathematician, [has cited an article][dembski] written by one John Davison about the theory of evolution. According to Dembski, this article explains "why the naked emperor still lingers"; that is, why the theory of…

One of the annoying things about how we write numbers is the fact that we generally write things one of two ways: as fractions, or as decimals. You might want to ask, "Why is that annoying?" (And in fact, that's what I want you to ask, or else there's no point in my writing the rest of this!) It's…

Looks like I've accidentally created a series of articles here about fundamental numbers. I didn't intend to; originally, I was just trying to write the zero article I'd promised back during the donorschoose drive. Anyway. Todays number is *e*, aka Euler's constant, aka the natural log base. *e*…

The category theory series is finally winding down; I've got one topic I'd like to write about, and then I'll have had my fill of category theory for a while. I don't want to dive right in to another really deep topic like topology, so I'm looking for some subjects that people are interested in…

After the amazing response to my post about zero, I thought I'd do one about something that's fascinated me for a long time: the number *i*, the square root of -1. Where'd this strange thing come from? Is it real (not in the sense of real numbers, but in the sense of representing something *real*…

While taking a break from some puzzling debugging, I decided to hit one of my favorite comedy sites, Answers in Genesis. I can pretty much always find something sufficiently stupid to amuse me on their site. Today, I came across a gem called ["Information, science and biology"][gitt], by the all…

Today we'll finally get to building the categories that provide the model for the multiplicative linear logic. Before we jump into that, I want to explain why it is that we separate out the multiplicative part. Remember from the simply typed lambda calculus, that [we showed that the type system was…

I was reading an article on Slashdot the other day about a recent discovery of what might be a MECO. A [MECO][wiki-meco] is a "magnetospheric eternally collapsing object"; if this were true, it would be a big deal because according to relativity, either black holes exist and MECOs don't, or MECOs…

I was hoping for a bit of a vanity post for todays pathological programming language in honor of my 40th birthday (tomorrow), but I didn't have time to finish implementing my own little piece of insanity. So it'll have to wait for some other occasion. Todays pathological programming language is a…

I've been taking a look at William Dembski's paper, "[Information as a Measure of Variation][imv]". It was recommended to me as a paper demonstrating Demsbki's skill as a mathematician that isn't aimed at evolution-bashing. I'm not going to go into too much detail about it; it's just not that good…

In the comments on [my post mocking Granville Sewell's dreadful article][sewell], one of the commenters asked me to write something about why evolution is frequently modeled as a search process: since there is no goal or objective in evolution, search seems like a strange approach. It's a very good…

Things are a bit busy at work on my real job lately, and I don't have time to put together as detailed a post for today as I'd like. Frankly, looking at it, my cat theory post yesterday was half-baked at best; I should have held off until I could polish it a bit and make it more comprehensible. So…

So, we're still working towards showing the relationship between linear logic and category theory. As I've already hinted, linear logic has something to do with certain monoidal categories. So today, we'll get one step closer, by talking about just what kind of monoidal category. As I keep…

A reader sent me a link to *yet another* purported [Bayesian argument for the existence of god][unwin], this time by a physicist named Stephen Unwin. It's actually very similar to Swinburne's argument, which I discussed back at the old home of this blog. The difference is the degree of *dishonesty…

This weekend, I came across Granville Sewell's article "[A Mathematicians View of Evolution][sewell]". My goodness, but what a wretched piece of dreck! I thought I'd take a moment to point out just how bad it is. This article, as described by the [Discovery Institute][diref], purportedly shows:…

Back during the DonorsChoose fundraiser, I promised a donor that I'd write an article about the math of zero. I haven't done it yet, because zero is actually a suprisingly deep subject, and I haven't really had time to do the research to do it justice. But in light of the comment thread that got…

Today, we're going to take a look at a brilliant language called Befunge. Befunge is the work of an evil genius named Chris Pressey. Normal programming languages are based on a basically one-dimensional syntax; the program is a string, a sequence of characters, and it's processed by reading that…

A reader sent me a link to [this amusing blog][blog]. It's by a guy named George Shollenberger, who claims to have devised The First scientific Proof of God (and yes, he always capitalizes it like that). George suffers from some rather serious delusions of grandeur. Here's a quote from his "About…

Time to come back to category theory from out side-trip. Category theory provides a good framework for defining linear logic - and for building a Curry-Howard style type system for describing computations with *state* that evolves over time. Linear logic provides a way of defining a valid *model*…

Issue number 58 of [the Tangled Bank][tb] is now live at Salto Sobrius. Head on over, take a look, and plan to spend some time reading some of the net's best science blogging from the last two weeks. [tb]: http://saltosobrius.blogspot.com/2006/07/tangled-bank-58.html

[Monday][yesterday], I said that I needed to introduce the sequent calculus, because it would be useful for describing things like linear logic. Today we're going to take a quick look at linear logic - in particular, at *propositional* linear logic; you can expand to predicate linear logic in a way…