goodmath

With the insanity that's been going on in the financial world lately, a bunch of people have asked me to post a followup to my earlier posts on the whole mortgage disaster, to try to explain what's going on lately. As I keep saying when people ask me things like this, I'm not an economist. I don'…

So, as it turned out, I made a major screwup in my post earlier today on modes of operation. Rather than just edit the post, I'm adding a new post with the corrected description of the counter mode, and a bit of explanation. I figure that if I screw up badly, it's more honest to make a second post…

Sorry for the slow pace of the blog lately. I've been sick with a horrible sinus infection for the last month, and I've also been particularly busy with work, which have left me with neither the time nor the energy to do the research necessary to put together a decent blog post. After seeing an…

My apologies for how slow the blog has been lately. I've been sick with a horrible sinus infection for the last month. I saw an ENT on wednesday, and with massive doses of antibiotics and steroids, I'm finally on the mend, so hopefully things will get back to normal soon. Marillion, "Thunder Fly…

This is about as off-topic as it gets, but I can't resist posting. Y'see, I'm a spectacularly uncoordinated person. I can trip over nothing. If you throw me a ball, the chances of my being able to catch it are frighteningly low. When I was in high school, my physics teacher invented the Carroll…

As promised, now we're going to look at the first major block cipher: the DES. DES stands for "data encryption standard"; DES was the first encryption system standardized by the US government for official use. It's an excellent example of a strong encryption system; to this day, while there are…

Where encryption starts getting really interesting, in my opinion, is block ciphers. Block ciphers are a general category of ciphers that are sort of a combination of substitution and transposition ciphers, and sort of something entirely different. They're really fascinating things, but they're…

I was away on vacation this week, which explains the near-total silence on the blog. But at least you'll get a FRT from me. And some nice posts on cryptography and game theory coming next week. Gogol Bordello, "Dub the Frequencies of Love": Eastern european gypsies meet punk meets reggae.…

The second major family of encryption techniques is called transposition ciphers. I find transposition ciphers to be rather dull; in their pure form, they're very simple, and not very difficult to crack, even without computers. But some of the most sophisticated modern ciphers can be looked at as…

Solas, "Darkness, Darkness": One of my favorite Irish bands doing a great cover of an old song. A Silver Mt. Zion, "Goodbye Desolate Railyard": a decent ASMZ track, but not an outstanding one. Mogwai, "Acid Food": Anything by Mogwai is terrific. This is no exception. Kansas, "Myriad": One…

An alert reader sent me link to a href="http://africa.reuters.com/odd/news/usnPEK21146.html">stupid article published by Reuters about the Olympics and Astrology. It's a classic kind of crackpot silliness, which I've described in numerous articles before. It's yet another example of…

I found a fun meme via Rev. BigDumbChimp, involving food. I'm a sucker for anything involving eating. Venison: Nope. Nettle tea: yes. Didn't like it. Huevos rancheros: Yes, yummy. Steak tartare: nope. Crocodile: Yup. Mediocre. Not a bad flavor, but it had a nasty texture. Black…

Someone sent me some questions about information theory; or actually, about some questions raised by a bozo creationist arguing about information theory. But the issues raised are interesting. So while I'm nominally snarking at a clueless creationist, I'm really using it as an excuse to talk…

One of the things that I always like to talk about is how a natural expression of randomness will periodically produce something that appears non-random - and in fact, if it doesn't, then it's not really random! This weeks friday random 10 is a great example of this. In the past, when I've been…

To understand why serious encryption algorithms are so complex, and why it's so important to be careful with the critical secrets that make an encryption system work, it's useful to understand something about how people break encryption systems. The study of this is called cryptanalysis, and it's…

So, last time, we looked at simple substitution ciphers. In a substitution cipher, you take each letter, and pick a replacement for it. To encrypt a message, you just substitute the replacement for each instance of each letter. As I explained, it's typically pretty each to break that encryption -…

The starting point talking about encryption is to understand what the point of it is; what it's supposed to do, what problems it's supposed to avoid. Encryption is fundamentally about communication: you've got two parties who want to communicate, but don't want anyone else to be able to listen in…

As you've probably heard, the US customs service has, recently, asserted the right to confiscate any and all computers and/or digital storage carried by anyone crossing the US border. They further assert the right to demand all passwords, encryption keys, etc., from the owners. They even further…

Someone sent me another stupid Jewish article. It's still not the wonderful relativity denial that I lost, but it's pretty delicious as stupidity goes. This time it comes from Chabad. For those who aren't familiar with it, Chabad is a Chasidic organization, which originally formed around people…

Kansas, "Byzantium": an example of why Kansas fans waited so long for Kerry Lofgren to return to the band. The guy's a brilliant songwriter. Even with Walsh's voice clearly aging and suffering from abuse, this is fantanstic stuff. Isis, "Wrists of Kings": Fairly hard post-rock. I like Isis a…

Once again, you, my readers, have come through with some really high-grade crackpottery. This one was actually sent to me by its author, but I didn't really look at it until several readers sent me the same link because they thought it was my kind of material. With your recommendations, I took a…

Moving on from simple zero-sum games, there are a bunch of directions in which we can go. So far, the games we've looked at are very restrictive. Beyond the zero-sum property, they're built on a set of fundamental properties which ultimately reduce to the idea that no player ever has an…

I've been getting peppered with requests to comment on a recent argument that's been going on about math education, particularly with respect to multiplication. We've got a fairly prominent guy named Keith Devlin ranting that "multiplication is not repeated addition". I've been getting mail from…

There's one kind of semi-mathematical crackpottery that people frequently send to me, but which i generally don't write about. Given my background, I call it gematria - but it covers a much wider range than what's really technically meant by that term. Another good name for it would be numeric…

Before we move beyond zero-sum games, it's worth taking a deeper look at the idea of utilities. As I mentioned before, in a game, the scores in the matrix are given by something called a utility function. Utility is an idea for how to mathematically describe preferences in terms of a game or…

The Flower Kings, "Underdog": a neo-progressive track with the lead played by a bagpipe and a steel guitar. How can you not love that? Broken Social Scene, "Ibi Dreams of a Pavement": A post-rock track with vocals. Very good stuff - very dense. Like I said it's got vocals, but they're not the…

When I last wrote about game theory, we were working up to how to find the general solution to an iterated two-player zero-sum game. Since it's been a while, I'll take a moment and refresh your memory a bit. A zero-sum game is described as a matrix. One player picks a row, and one player picks a…

Back in May, we here at ScienceBlogs got an offer to get an advance screener copy of Randy Olson's new movie, "Sizzle", if we promised to review it. I hadn't seen any of Olson's movies before, but I've been involved in a few discussions with him as part of the Great Framing Wars, and while I…

So my fellow SBer PZ is in all sorts of hot water with Catholics over a blog post. I didn't really want to poke my nose into this, but there's been so much noise about it, that it's really unavoidable. But I think I've got a rather different opinion on this than most bloggers I've seen so far.…

Another cool, but frequently overlooked, data structure in the tree family is called the B-tree. A B-tree is a search tree, very similar to a BST in concept, but optimized differently. BSTs provide logarithmic time operations, where the performance is fundamentally bounded by the number of…