goodmath

One of the things I discovered since writing part one of my Erlang introduction is that Erlang has grown a lot over the last few years. For example, the idiom of tagged tuple as a way of creating a record-like structure has been coded into the language. There is, unfortunately, a bit of a catch.…

In my last post on group theory, I screwed up a bit in presenting an example. The example was using a pentagram as an illustration of something called a permutation group. Of course, in my attempt to simplify it so that I wouldn't need to spend a lot of time explaining it, I messed up. Today I'll…

ScienceBlogs recently branched out and opened up a German-language edition of ScienceBlogs in cooperation with a German media firm. Over at the in-house blog Page 3.14, our blogging goddess, Ginny, is asking for help with what languages readers think SB should assimilate next. Do us a favor, and…

Astute readers will remember a couple of encounters I had with Sal Cordova from Uncommon Descent a few months ago (here, in the comments, and here). Not too long after that, Sal made a fairly big deal about the fact that he was returning to grad school, and had to stop blogging at UD because the…

In the last post, I talked about what symmetry means. A symmetry is an immunity to some kind of transformation. But I left the idea of transformation informal and intuitive. In this post, I'm going to move towards formalizing it. The group theoretic notion of immunity to transformation is defined…

I recently started eating beef again, after 18 years of abstaining. Last weekend, I made a big batch of Chili using beef, and it was fantastic. So I thought that was a good excuse to give you my chili recipe. This is real chili. Up here in NY, usually when you see chili, it's ghastly stuff.…

Isaac Newton was a total nutjob. Did you know that he tried to pop his own eyeball out with a knitting needle as a part of an experiment? That he nearly blinded himself staring into the sun? That he was an avid alchemist? Why do we pay so much respect to a person who was clearly mentally…

As I said in the last post, in group theory, you strip things down to a simple collection of values and one operation, with four required properties. The result is a simple structure, which completely captures the concept of symmetry. But mathematically, what is symmetry? And how can something as…

The point of set theory isn't just to sit around and twiddle our thumbs about the various definitions we can heap together. It's to create a basis on which we can build and study interesting things. A great example of that is something called a group. Once we've built up sets enough to be able to…

There's been some talk among the sciencebloggers about the idea of intellectual property, and href="http://www.scienceblogs.com/clock/">Bora over at "A Blog Around the Clock" asked me to convert my thoughts into a post. It's a serious topic, which is worth giving some deep consideration, and…

When last we left off, I'd used set theory to show how to construct the natural numbers; and then from the natural numbers, I showed how to construct the integers. Now, we can take the next step in building up the full tower of numbers, showing how if we've got the natural numbers defined in sets…

An alert reader pointed out that William Brookfield posted a response to my two part debunking of his argument for design based on a mangling of the second law of thermodynamics. I debated whether it was worth responding to; Mr. Brookfield's got so little readership that I never noticed his…

Several commenters pointed out that I made several mistakes in my description of Erlang. It turns out that the main reference source I used for this post, an excerpt from a textbook on Erlang available on the Erlang website, is quite out of date. I didn't realize this; I assumed that if they…

Because of the holiday, I'm posting my recipe early this week. It's actually too late, but I don't let little things like reality worry me. This is my thanksgiving turkey stuffing. The origins of this stuffing date back to my discovery of the "black turkey" recipe. I tried it one year, and the…

Even though this post seems to be shifting back to axiomatic set theory, don't go thinking that we're done with type theory yet. Type theory will make its triumphant return before too long. But before that, I want to take a bit of time to go through some basic constructions using set theory. We'…

This is a very simple, authentic chinese dish. It's a great example of what real chinese food is like - it's a lot lighter and more delicate than what's typically passed off as Chinese food in the US. You should really go to a chinese grocery store for the bean sprouts: you'll get them fresher,…

When Cantor's set theory - what we now call naive set theory - was shown to have problems in the form of Russell's paradox, there were many different attempts to salvage the theory. In addition to the axiomatic approaches that we've looked at (ZFC and NBG), there were attempts by changing the…

I haven't written a basics post in a while, because for the most part, that well has run dry, but once in a while, one still pops up. I got an email recently asking about proofs by contradiction and counterexamples, and I thought that would be a great subject for a post. The email was really…

I was visiting my mom, and discovered that I didn't leave my set theory book on the train; I left it at her house. So I've been happily reunited with my old text, and I'm going to get back to a few more posts about the beautiful world of set theory. When you talk about set theory, you're talking…

This dish is one of my own creations. It's inspired by reading Ming Tsai's cookbooks, and seeing how he combines things. But as far as I know, he doesn't do anything like this. You really need catfish for this. I've tried it with other fish, but it just doesn't work as well. Catfish has a unique…

My fellow SBer Craig McClain sent me a link to yet another an example of how mind-bogglingly innumerate people are. At least, for once it's not Americans. The British lottery put out a "scratch-off" game called "Cool Cash". The idea of it is that it's got a target temperature on the card, and to…

Ladies and gentlemen.. For your pleasure and edification, allow me to present... The singing Tesla coils! Yes, if you're clever, and you're willing to do a whole lot of work, you can operate a Tesla coil so that the sparking from the coil produces a particular pitch. Even you're even more clever…

Now, it's time for the final chapter in my "visits with old friends" series, which brings us back to the Good Math/Bad Math all-time reader favorite crackpot: Mr. George Shollenberger. Last time I mentioned George, a number of readers commented on the fact that it's cruel to pick on poor George,…

There was an interesting discussion about mathematical constructions in the comment thread on my post about the professor who doesn't like infinity, and I thought it was worth turning it into a post of its own. In the history of this blog, I've often talked about the idea of "building mathematics…

One of my favorite comfort foods is a mac&cheese tuna casserole. That's real mac&cheese, not any of that glow in the dark orange garbage. It amazes me just how many people have never actually had a proper, home-made macaroni and cheese! It's really good eating (unlike the glow in the dark…

As promised, today I'm going to talk about how to compute the strongly connected components of a directed graph. I'm going to go through one method, called Kosaraju's algorithm, which is the easiest to understand. It's possible to do better that Kosaraju's by a factor of 2, using an algorithm…

This past week, I discovered a new digital music download site, called Bitmunk. It's less expensive than iTunes or Amazon, and has a fantastic selection of obscure bands. Through Bitmunk, I found a couple of terrific new neo-progressive bands, which has me on a serious prog kick. So for today, I'…

My friend, fellow ScienceBlogger, and BlogFather Orac asked me to take a look at href="http://www.jpands.org/vol12no3/carroll.pdf">a paper that purportedly shows that abortion is a causative risk factor for breast cancer, which he href="http://scienceblogs.com/insolence/2007/10/…

One of the problems with many of the interesting graph algorithms is that they're complex. As graphs get large, computations over them can become extremely slow. For example, graph coloring is NP-complete - so the time to run a true optimal graph coloring algorithm on an arbitrary graph grows…

The bulk of this part of the review is looking at the total train-wreck that is chapter 4, which contains Bittinger's version of dreadful probabilistic arguments for why Christianity must be true. But before I do that, I need to take care of one loose end from part 1. I should have included…