The Universe of Discourse

Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game Coin-moving games with no coins Productive programs and well-founded orders In part 4, Infinite Nim as a coin-moving game , we saw how to reinterpret infinite Nim into an equivalent game: instead of heaps of beans and various special tokens, we int…

Previously: Ordinal numbers and basic set theory Ordinals as nim-heaps Nim always ends, even with infinite ordinals Infinite Nim as a coin-moving game Coin-moving games without the coins Previously we saw how to interpret the difficult-seeming ordinal as a particular ordering of the set of finite sequences of numbers, revealing what seemed like a scary monster as gentle and straightforward. Now w…

( Previously ) Flukes and Breakthroughs In the NBA 2015–16 season, Steph Curry set the all-time single-season record for three-point field goals, 402, completely crushing the old record of 286. Curry's record still stands. The New York Times was rather breathless about this : The record is an outlier that defies most comparisons, but here is one: It is the equivalent of hitting 103 home runs i…

Previously: Ordinal numbers and basic set theory We're going to get to in a long and roundabout way. First I want to talk about the game of Nim. Nim Nim is a very simple game for two players. There are some piles of beans, which are called nim-heaps . When it's your turn, you are allowed to remove as many beans as you like, as long as they are all in the same pile. Whoever takes the last bean…

This post is going to be about what infinite ordinal numbers are, and about is in particular. I had a brainwave a while back (18 months now, wow, I have definitely not been blogging enough) and suddenly understood much better than I did before. I have several related ideas here and I am going to try to write one blog post about each of them, instead of one gigantic blog post about all of them t…

Making the rounds last week was this magnificent article on the complications of Arabic typesetting, An interactive introduction to the terrific experience of rendering Arabic typography and its technical debt . The author, Saleh, promises: The reply took and the closure of the ticket took half an hour or so. The reasons behind it took five hundred years to pile up, and they involve a twice-m…

While cleaning out my office today, I found this, which I wrote in 1992: In the middle 1970's, the IBM corporation did (and perhaps still does) most of their in-house programming in a computer language called FORTRAN. They had a pretty good FORTRAN compiler, called the FORTRAN G compiler. It was fast at translating FORTRAN into machine instructions, and the machine instructions it produced impl…

(Very much previously: Egyptian Fractions ) Back in March, I had been reading On the Egyptian method of decomposing into unit fractions by Abdulrahman A. Abdulaziz, and I reported that: There is some indication that Ahmes preferred fractions with even denominators, because they are easier to double, and the usual Egyptian method of multiplication required repeated doubling. Although I had lon…

As I have explained in the past , my typical workflow is to go along commiting stuff that might or might not make sense, then clean it all up at the end, doing multiple passes with git-add and git-rebase to get related changes into the same commit, and then to order the commits in a sensible way. Yesterday I built a new utility that I found helpful. I couldn't think of a name for it, so I called…

Bo Diddley's cover of "Sixteen Tons" sounds very much like one of my favorites, "Can't Judge A Book By Its Cover". It's interesting to compare. Thinking on that it suddenly occured to me that his name might have been a play on “diddley bow”, which is a sort of homemade one-stringed zither. The player uses a bottle as a bridge for the string, and changes the pitch by sliding the bottle up and do…

I recently posted an article about the 2013 Philadelphia Traffic Court fiasco , in which most of the Traffic Court judges were convicted of accepting bribes: According to the indictment, Perri accepted free auto services, towing, landscaping, and even a load of shrimp and crab cakes from Alfano, whose company, Century Motors, ran a towing service. ( The Philadelphia Inquirer , Nine current an…