goodmath

Don't you dare use the number 271277229129081016424883074559900780951 under any circumstances. It's mine, mine I tell you, and if you use it, or copy it, I can have you arrested and sent to do hard time in prison. And it doesn't matter whether you use it in decimal, like I used above, or it's…

This is something that came up in some of the comments on the recent "nimbers" post, and I thought it was worth promoting to the front, and getting up under an easy-to-find title in the "basics" series. In a lot of discussions in all different areas of math, you encounter talk about sets and…

I came across a link to an excellent article that provides an example of one of my professional bugaboos: the truly awful way that we often design software in terms of how the implementer thinks of it, instead of how the user will think of it. Take a look at that link to see what I mean. The…

Rachel's, "Even/Odd": Rachel's is a very classically-oriented post-rock ensemble - violin, bass, woodwinds. They're absolutely brilliant. "Even/Odd" is a short, extremely rhythmic track with an interesting pulse with an almost siren-like string lead played over it. Very, very cool. Rush, "…

I thought that it would be fun to stick with the "stack-based" theme of last week's pathological post, but this time, to pick an utterly pointlessly twisted stack based language, but one that would be appreciated by the mascot of one of my fellow ScienceBlogs. Orac, this one's for you! :-) Our…

So, today we're going to play a bit more with nimbers - in particular, we're going to take the basic nimbers and operations over nimbers that we defined last time, and take a look at their formal properties. This can lead to some simpler definitions, and it can make clear some of the stranger…

An astute reader pointed me towards a monstrosity of pompous bogus math. It's an oldie, but I hadn't seen it before, and it was just referenced by my old buddy Sal Cordova in a thread on one of the DI blogs. It's a "debate" posted online by Lee Spetner, in which he rehashes the typical bogus…

Before diving off into real content, the name of my little π-calculus monstrosity has been chosen. As several people recommended in the comments, I'm going to go with Pica. So, today, we're going to take the dive, and start looking at some interesting semantics of the language. The goal of this…

(A substantial part of this post was rewritten since it was first posted. I managed to mangle things while editing, and the result was not particularly comprehensible: for example, in the original version of the post, I managed to delete the definition of "mex", which continuing to use mex in…

Our corporate masters at Seed have added a new blog to ScienceBlogs, and it looks like a real winner. It's called the Denialism Blog, and it's off to a roaring great start with "The Unified Theory of the Crank. Go check it out!

Since my post on datatypes for my π-calculus language, I've gotten a bunch of questions from people who (I guess) picked up on the series after the original post where I said that the idea of the series was to see if I could create a programming language based on it. The questions are all…

While browser over at programming.reddit.com, I came across something simultaneously hideous and amazing. I've showed quines before as part of the pathological programming posts: a quine is a program which, when run, generates itself as an output. I've even written about a programming language…

Today's friday programming language insanity is a tad different. I'm going to look at another twisted stack-based language. I've got a peculiar fondness for these buggers, because back in the day, I was a serious Forth addict. One of the ideas that's actually come up in serious programming…

(This issue came to a happy conclusion. After the uproar generated by this being publicized by so many blogs and websites, the publisher got in touch with Shelley, gave her permission to use the figures, apologized, and promised to do some internal legal education so that this won't happen again…

When I'm bored, I'll periodically take a look at the blogs published by the bozos at the Discovery Institute. I can generally find something good for a laugh. So I was doing that tonight, and came across yet another example of how they try to distort reality and use slimily dishonest math to try…

Finally, as I promised a while ago, it's time to look at the sign-expanded forms of infinites in the surreal numbers. Once you've gotten past the normal forms of surreal numbers, it's pretty easy to translate them to sign-expanded form. Suppose you've got a surreal number in normal form: Σωyry.…

Before moving on, there's one question that I thought was important enough to promote up to the front page, instead of just answering it in the comments. A commenter asked about process replication, !P, wanting to know if it terminates. The answer comes in two parts. !P does process creation on…

As I mentioned a while back, I was loaned the Library of Congress discard of George Shollenberger's book. Since he's made such a big deal about how unfair I've been by not reading and considering his argument, I've actually forced myself to read it. (See what I'm willing to do for you, my faithful…

The shuffle generated interesting results this week. Apothecary Hymns, "The Marigold". Apothecary Hymns sounding extremely Tull-like. Good stuff. Mogwai, "Katrien". Mogwai is simply brilliant: one of the greatest post-rock groups out there. I keep getting more of their stuff, and I haven't…

As promised, this week, I've got a new friday pathological programming language. This one is another 2-dimensional language, but it's pretty different from any of the 2d languages I'm written about before. It's called "Flip", and the warped minds behind describe it as being sort of like "…

Ok, I give up. I've stayed out of the framing debate until now, but I just can't take it anymore. As much as I respect people like PZ and Larry Moran, the simple fact is: they've got it wrong. And not just them: there is a consistent problem with the political left in America when it comes to…

Given a calculus, one of the things that I always want to see is how it can do some kind of meaningful computation. The easiest way to do that is to start building numbers and basic arithmetic. To be able to do this, we're going to need one more bit of syntax. What we want to do is specify a…

I came across this while looking through the referrals to GM/BM. This is an incredibly cool video of a strange phenomenon called the Kaye effect. It includes high speed video of the effect, and a demonstration of their mathematical analysis of the effect, and their prediction and verification of…

As I did with my first attempt at explaining π-calculus, I think that before getting into any of the deep semantics, it's good to look at a few examples of things you can build with π-calculus. But before getting to the meat of the post, I'll give you the answer the puzzle I left in the last post…

I've used the term innumeracy fairly often on this blog, and I've had a few people write to ask me what it means. It's also, I think, a very important idea. Innumeracy is math what illiteracy is to reading. It's the fundamental lack of ability to understand or use numbers or math. And like…

Now that things are settling down a little bit, I wanted to get back to the stuff I was writing about π-calculus. But looking back at what I've already written, I think I did a terrible job of introducing it. So I'm going to start over, and try to be more clear. I'll start with a basic refresher…

I'm currently reading "I am a Strange Loop" by Douglas Hofstadter. I'll be posting a review of it after I finish it. A "strange loop" is Hofstadter's term for a Gödel-esque self-referential cycle. A strange loop doesn't have to involve Gödel style problems - any self-referential cycle is a strange…

Michael Egnor is at it again. The guy is pretty much the energizer bunny of anti-evolution bullshit. This time, he's purportedly refuting an article by Dr. Steven Novella, a Yale professor of neurology. So, why am I butting my nose in to a discussion between two doctors? For two reasons: First…

I've been swamped lately, learning to manage my new commute, and being overwhelmed by my new job. So I've been a bit lax about the blog; I've missed three weeks in a row for the friday pathological programming; and I haven't been posting my friday random tens. I don't have time to do a FPP post…

When I left off yesterday, we'd reached the point of being able to write normal forms of surreal numbers there the normal form consisted of a finite number of terms. But typically of surreal numbers. that's not good enough: the surreals constantly produce infinites of all sorts, and normal forms…