goodmath

For your amusement and edification, the following is a very simple interpreter for fractran programs which, in addition to running the program to generate its result also generates a trace to show you how the program executed. ;; A Trivial Fractran Interpreter ;; ;; Copyright 2006 Mark…

It's friday, so it's time for more of my highly warped taste in music. 1. **Tempest, "Turn of the Wheel"**. Tempest is a really cool band. They're a cross between an electrified folk band and a neo-progressive rock band. Strong Irish and Swedish influences on the folky side, and a vaguely ELP-ish…

Today's pathological language is based on a piece of work called Fractran by John Conway of game theory fame. It's a really fascinating bugger; absolutely insanely difficult to program in, but based on one of the most bizarrely elegant concepts of computation that I've ever seen. It's amazing that…

Yesterday, Karl Rove was interviewed by Robert Siegel on NPR. I just about passed out from shock when I heard the following exchange: (transcript via [raw story](http://www.rawstory.com/news/2006/Rove_dukes_it_out_with_NPR_1025.html)) >MR. SIEGEL: We're in the home stretch, though. And many…

Time to get back to some topology, with the new computer. Short post this morning, but at least it's something. (I had a few posts queued up, just needing diagrams, but they got burned with the old computer. I had my work stuff backed up, but I don't let my personal stuff get into the company…

While I was waiting for stuff to install on my new machine, I was doing some browsing around the web, and came across an interesting article at a blog called "The Only Winning Move", titled [Scheme Death Knell?](http://theonlywinningmove.blogspot.com/2006/10/scheme-death-knell.html). It's not a bad…

Sorry for the sudden silence on the blog. My computer died on me yesterday, and so I've been rather cut off. I'm in the process of setting up my gorgeous brand new MacBookPro, and things should be getting back to normal pretty quickly, except that I lost a couple of prepared posts in the crash, so…

Todays entry isn't so much a pathological language itself as it is a delightful toy which can be used to *produce* pathological languages. I'm looking at Chris Pressey's wonderful language [ALPACA](http://catseye.mine.nu:8080/projects/alpaca/), which is a meta-language for describing different…

Remember Granville Sewell? He's the alleged mathematician who wrote the very non-mathematical "A Mathematician's View of Evolution", which I fisked [a few weeks ago](http://scienceblogs.com/goodmath/2006/10/second_law_slop_from_granville…). Well, he's back with a response to the people who…

Chad, over at [Uncertain Principles](http://scienceblogs.com/principles/2006/10/cranky_book_meme_voted_off_t…) found an interesting meme, which I thought would be fun to take a stab at: >What authors have you given up on for good? And why? Darn good question, that is. I'm often fascinated by…

So, after the last topology post, we know what a manifold is - it's a structure where the neighborhoods of points are *locally* homeomorphic to open spheres in some ℜn. We also talked a bit about the idea of *gluing*, which I'll talk about more today. Any manifold can be formed by *gluing together…

After my binary fingermath stuff, a few people wrote to me to ask about just how binary really works. For someone who does the kinds of crazy stuff that I do, the idea of different number bases is so fundamental that it's easy to forget that most people really don't understand the idea of using…

To do multiplication with your fingers in binary is very easy: it's just a mixture of addition and bit-shifting. The only real trick is memory: to multiply a×b, you need to remember the binary digits of both x and y, which can be a bit of a trick for 10 digit binary numbers. The trick that I like…

As expected, the Lancet study on civilian deaths in Iraq has created a firestorm on the net. What frankly astounds me is how utterly *dreadful* most of the critiques of the study have been. My own favorite for sheer chutzpah is [Omar Fadil](http://politicscentral.com/2006/10/11/…

I've gotten a lot of mail from people asking my opinion about [the study published today in the Lancet][lancet] about estimating the Iraqi death toll since the US invasion. So far, I've only had a chance to skim the paper. But from what I can see about it, the methodology is sound. They did as…

While looking at the sitemeter referrals to GM/BM, I noticed a link from "New Aids Review", a denialist website that that I mentioned in [my critique of Duesberg.](http://scienceblogs.com/goodmath/2006/09/pathetic_statistics_from_hivai…) The folks at NAR are continuing to pull bad math stunts, and…

There is another way of doing math on your fingers, which gives you a much greater range of numbers, and which makes multiplication particularly easy. It's a bit more work to get used to than the finger abacus, but it has a lot less limitations. Someone in the comments of the finger-abacus post…

There's bad news on the math front. Penny Smith has *withdrawn* her Navier Stokes paper, because of the discovery of a serious error. But to be optimistic for a moment, this doesn't mean that there's nothing there. Remember that when Andrew Wiles first showed his proof of Fermat's last theorem,…

Suppose you want to do some math, but you don't have an abacus handy. Oh, the horror! What do you do? No problem! Your hands make a *great* two-digit soroban-type abacus. The four beads on the lower deck are your four fingers; the bead on the upper deck is your thumb, as illustrated in this…

A reader sent me a link to an article by that inimatable genius of the intelligent design community, Granville Sewell. (As much as I hate to admit it, Sewell is a professor of mathematics at Texas A&M. I don't know what his professional specialty is, but if his work in that area is anything…

It's friday again, which means I get to bore you with my bizarre taste in music. 1. **Spock's Beard, "A Guy Named Sid".** SB is a fantastic neo-prog band, one of my favorites. This is a track off the first album after their long-time lead singer/songwriter left the band. It's definitely a big…

Todays dose of pathology is another masterpiece from the mangled mind of Chris Pressey. It's called "[Version](http://catseye.mine.nu:8080/projects/version/)", for no particularly good reason. It's a wonderfully simple language: there's only *one* actual kind of statement: the labelled assignment.…

A few months ago, I wrote about the Poincare conjecture, and the fact that it appeared to finally have been solved by a reclusive russian mathematician named Grisha Perelman. Now there's news that *another* classic problem may have been solved. This time, it's the Navier-Stokes equation,…

Manifolds So far, we've been talking about topologies in the most general sense: point-set topology. As we've seen, there are a lot of really fascinating things that you can do using just the bare structure of topologies as families of open sets. But most of the things that are commonly associated…

As [Tara](http://scienceblogs.com/aetiology/2006/10/aids_and_viral_load.php), [Nick](http://aidsmyth.blogspot.com/2006/09/viral-load-paradigm-shift-not-real…), and [Orac](http://scienceblogs.com/insolence/2006/10/more_distortion_of_peerreview…) have already discussed, there's been a burst of…

Doing square root on the abacus is a lot like doing it on paper. The big difference? It's actually *easier* on the abacus. What I find pretty cool is that I'm a rank beginner at the abacus. I never actually tried to use one before I started writing these posts. But I can do that root *faster* on…

If you've got a connected topology, there are some neat things you can show about it. One of the interesting ones involves *fixed points*. Today I'm going to show you a few of the relatively simple fixed point properties of basic connected topologies. To give you a taste of what's coming: imagine…

1. **Steven Reich, "Explanations Come To An End Somewhere"**: one movement from one of Steven Reich's recent works, the "You Are" variations. I think it's some of the best stuff he's ever written. 2. **Fiddlers Four, "Pickin' the Devil's Eye"**. Another Darol Anger project, and as usual, it's very…

Joy of joys, [Cat's Eye Technologies](http://catseye.mine.nu:8080/projects/), the home of Chris Pressey, one of the most prolific designers of thoroughly bizarre languages is back up! And so, today, we're going to take a look at one of his masterpieces, the language *Smith*. This is one of my…

To do a square root on an abacus, you use partitions to do a paper algorithm for square root using the abacus. The catch is that most people don't even *remember* how to do square roots on paper, if they ever learned it at all. (In fact, in school, *I* didn't learn the classical paper algorithm; we…