Doing the laundry used to be backbreaking toil. Haul the water, chop the wood, light the fire, heat the water, and now you are ready to begin the really tough part of the work. The old saying goes "Wash on Monday", because Monday is the day after your day of rest, and otherwise you won't have the strength to do the washing. And the saying continues: “Iron on Tuesday, mend on Wednesday”. Routine management of clothing takes half of the six-day work week. For this reason, washing is the work of last resort for the poorest and most marginal people. Widows are washerwomen. Prisons are laundries. Chinese immigrants run laundries. Anyone with enough money to outsource their laundry does so. The invention of mechanical washing machines eliminated a great amount of human suffering and toil. Machines do the washing now. Nobody has to break their back scrubbing soiled linens against a washboard. “Eskimo child with wooden tub and washboard”, c. 1905, by Frank Hamilton Nowell, public domain, via Wikimedia Commons. But the flip side of that is that there are still poor and marginalized people, who now have to find other work. Mechanical laundry has taken away their jobs. They no longer have to do the backbreaking labor of hand laundry. Now they have the option to starve to death instead. Is it a net win? I don't know. I'd like to think so. I'd like to free people from the toil of hand laundry without also starving some of them to death. Our present system doesn't seem to be very good at that sort of thing. I'm not sure what a better system would look like. Anyway, this is on my mind a lot lately because of the recent developments in computer-generated art. I think “well, it's not all bad, because at least now nobody will have to make a living drawing pornographic pictures of other people's furry OCs. Surely that is a slight elevation of the human condition.” On the other hand, some of those people would rather have the money and who am I to deny them that choice?

A modern presentation of the Peano axioms looks like this: is a natural number If is a natural number, then so is the result of appending an to the beginning of Nothing else is a natural number This baldly states that zero is a natural number. I think this is a 20th-century development. In 1889, the natural numbers started at , not at . Peano's Arithmetices principia, nova methodo exposita (1889) is the source of the Peano axioms and in it Peano starts the natural numbers at , not at : There's axiom 1: . No zero. I think starting at may be a Bourbakism. In a modern presentation we define addition like this: $$ \begin{array}{rrl} (i) & a + 0 = & a \\ (ii) & a + Sb = & S(a+b) \end{array} $$ Peano doesn't have zero, so he doesn't need item . His definition just has . But wait, doesn't his inductive definition need to have a base case? Maybe something like this? \begin{array}{rrl} (i') & a + 1 = & Sa \\ \end{array} Nope, Peano has nothing like that. But surely the definition must have a base case? How can Peano get around that? Well, by modern standards, he cheats! Peano doesn't have a special notation like for successor. Where a modern presentation might write for the successor of the number , Peano writes “”. So his version of looks like this: $$ a + (b + 1) = (a + b) + 1 $$ which is pretty much a symbol-for-symbol translation of . But if we try to translate similarly, it looks like this: $$ a + 1 = a + 1 $$ That's why Peano didn't include it: to him, it was tautological. But to modern eyes that last formula is deceptive because it equivocates between the "" notation that is being used to represent the successor operation (on the right) and the addition operation that Peano is trying to define (on the left). In a modern presentation, we are careful to distinguish between our formal symbol for a successor, and our definition of the addition operation. Peano, working pre-Frege and pre-Hilbert, doesn't have the same concept of what this means. To Peano, constructing the successor of a number, and adding a number to the constant , are the same operation: the successor operation is just adding . But to us, and are different operations that happen to yield the same value. To us, the successor operation is a purely abstract or formal symbol manipulation (“stick an on the front”). The fact that it also has an arithmetic interpretation, related to addition, appears only once we contemplate the theorem $$\forall a. a + S0 = Sa.$$ There is nothing like this in Peano. It's things like this that make it tricky to read older mathematics books. There are deep philosophical differences about what is being done and why, and they are not usually explicit. Another example: in the 19th century, the abstract presentation of group theory had not yet been invented. The phrase “group” was understood to be short for “group of permutations”, and the important property was closure, specifically closure under composition of permutations. In a 20th century abstract presentation, the closure property is usually passed over without comment. In a modern view, the notation is not even meaningful, because groups are not sets and you cannot just mix together two sets of group elements without also specifying how to extend the binary operation, perhaps via a free product or something. In the 19th century, is perfectly ordinary, because and are just sets of permutations. One can then ask whether that set is a group — that is, whether it is closed under composition of permutations — and if not, what is the smallest group that contains it. It's something like a foreign language of a foreign culture. You can try to translate the words, but the underlying ideas may not be the same.

We want to adapt baseball to be played on the moon. Is there any way to make it work? My first impression is: no, for several reasons. The pitched ball will go a little faster (no air resistance) but breaking balls are impossible (ditto). So the batter will find it easier to get a solid hit. We can't fix this by moving the plate closer to the pitcher's rubber; that would expose both batter and pitcher to uncceptable danger. I think we also can't fix it by making the plate much wider. Once the batter hits the ball, it will go a long long way, six times as far as a batted ball on Earth. In order for every hit to not be a home run, the outfield fence will have to be about six times as far way, so the outfield will be times as large. I don't think the outfielders can move six times as fast to catch up to it. Perhaps if there were 100 outfielders instead of only three? Fielding the ball will be more difficult. Note that even though the vacuum prevents the pitch from breaking, the batted ball can still take unexpected hops off the ground. Having gotten hold of the ball, the outfielder will then need to throw it back to the infield. They will be able to throw it that far, but they probably won't be able do it accurately enough for the receiving fielder to make the play at the base. More likely the outfielder will throw it wild. I don't think this can be easily salvaged. People do love home runs, but I don't think they would love this. Games are too long already. Well, here's a thought. What if instead of four bases, arranged in a -foot square, we had, I don't know, eight or ten, maybe or feet apart? More opportunities for outs on the basepaths, and also the middle bases would not be so far from the outfield. Instead of throwing directly to the infield, the outfielders would have a relay system where one outfielder would throw to another that was farther in, and perhaps one more, before reaching the infield. That might be pretty cool. I think it's not easy to run fast on the Moon. On the Earth, a runner's feet are pushing aganst the ground many times each second. On the Moon, the runner is taking big leaps. They may only get in one-sixth as many steps over the same distance, which would give them much less opportunity to convert muscle energy into velocity. (Somewhat countervailing, though: no air resistance.) Runners would have to train specially to be able to leap accurately to the bases. Under standard rules, a runner who overshoots the base will land off the basepaths and be automatically out. So we might expect to see the runner bounding toward first base. Then one of the thirty or so far-left fielders would get the ball, relay it to the middle-left fielder and then the near-left fielder who would make the throw back to first. The throw would be inaccurate because it has to traverse a very large infield, and the first baseman would have to go chasing after it and pick it up from foul territory. He can't get back to first base quickly enough, but that's okay, the pitcher has bounded over from the mound and is waiting near first base to make the force play. Maybe the runner isn't there yet because one of his leaps was too long and to take another he has to jump high into the air and come down again. It would work better than Quiddich, anyway.

Last summer I was privileged to visit the glorious Letterpress Museum in Paju Book City, where I spent several hours and took a collection of photos that are probably not of interest to anyone but letterpress geeks, and perhaps not even to them. Looking back at the photos it's not always clear to me why I took each one. But some of them I can remember. For example, this one: This is not exactly letterpress. It is a device for engraving lettered signs on thin strips of metal or perhaps plastic. Happily I don't have to spend too much time explaining this because Marcin Wichary has just published an extensively-illustrated article about the Latin-script version. The only thing different about this one is the fonts, which are for writing Korean in Hangeul script rather than English in Latin script. Hangeul has an alphabet of 24 letters, but there's a difficulty in adapting this engraving technique for written Hangeul: The letters aren't written in a simple horizontal row as European languages are. Instead, they are grouped into syllables of two or three letters. For example, consider the consider the Korean word “문어”, pronounced (roughly) "moon-aw". which means “octopus”. This is made up of five letters ㅁㅜㄴㅇㅓ, but as you see they are arranged in two syllables 문 ("moon") and 어 ("aw"). So instead of twenty-four kinds of templates, one for each letter, the Korean set needs one for every possible syllable, and there are thousands of possible syllables. Unicode gets around this by… sorry, Unicode doesn't get around it, they just allocate eleven thousand codepoints, one for each possible syllable. But for this engraving device, it would be prohibitively expensive to make eleven thousand little templates, then another eleven thousand spares, and impractical to sort and manage them in the shop. Instead there is a clever solution. Take a look at just one of these templates: This is not a Hangeul syllable. big { font-size: x-large; } Rather, it is five. The upper-right letter in the syllable is the vowel, and the template allows the operator to engrave any of the five vowels ㅣㅓㅏㅕㅑ to produce the syllables 잉 엉 앙 영 양 pronounced respectively "ing", "ông", "ang", "yông", and "yang". Similarly this one can produce six different syllables: The upper-left part can be used to engrave either of the consonants ㅅ or ㅈ and the upper-right part can be used to engrave any of the vowels ㅣㅓㅏ, to produce the combined set 싱 성 상 징 정 장. I'm not sure why this template doesn't also enable vowels ㅕㅑ as the other one did. In the picture at top you can see that while the third template can be used to engrave any of the three syllables 송 승 숭 the operator has acutally used it to engrave the first of these. This ingenious mechanism cuts down the required number of templates by perhaps a factor of five, from ten boxes to two.

Claude My relationship with Claude has its ups and downs, and I'm still trying to figure out what to use it for and what not. It's great at rewriting my job application cover letters to sound less like an awkward nerd. Last week I was in the supermarket and decided to try asking it something I've been wondering for a long time: MJD: What is the song "Mercy Street” about? What is the connection with Anne Sexton? Who is "Mary"? I thought Claude might do well with this. I had had a conversation with it a while back about Pixies songs, which I was satisfied with. But this time Claude let me down: Claude: … The "Mary" referenced in the song is likely Mary Gray Staples, who was the name of Sexton's childhood doll. … (I thought: What? Am I supposed to believe that Dreaming of the tenderness is about a doll?) MJD: Mary Gray Staples is an unusual name for a doll. Are you sure about that? Claude: You're right to question this - I made an error. Mary Gray was actually Anne Sexton's great-aunt, not the name of her doll. … The doll references in Gabriel's song likely connect to Sexton's imagery in other poems, but Mary specifically refers to her great-aunt. MJD: I don't remember a doll in Gabriel's song. Claude: You're absolutely right - I apologize for the error. There isn't actually a reference to a doll in Peter Gabriel's "Mercy Street" lyrics. … The "Mary" referenced in the song is indeed Anne Sexton's great-aunt Mary Gray… MJD: Are you sure? Wikipedia says that Mary Gray Staples was the birth name of Sexton's mother. Claude: You're absolutely right, and I apologize for the confusion. … Claude just flubbed over and over. I wonder if the grammatical error in “Mary Gray Staples, who was the name of …” is a kind of a tell? Perhaps Claude is fabricating, by stitching together parts of two unrelated sentences that it read somewhere, one with “Mary Gray Staples, who was…” and the other “… was the name of…”? Probably it's not that simple, but the grammatical error is striking. Anyway, this was very annoying because I tend to remember things like this long past the time when I remember where I heard them. Ten years from now I might remember that Anne Sexton once had a doll with a very weird name. Merle Miller A while back I read Merle Miller's book Plain Speaking. It's an edited digest of a series of interviews Miller did with former President Truman in 1962, at his home in Independence, Missouri. The interviews were originally intended to be for a TV series, but when that fell through Miller turned them into a book. In many ways it's a really good book. I enjoyed it a lot, read it at least twice, and a good deal of it stuck in my head. But I can't recommend it, because it has a terrible flaw. There have been credible accusations that Miller changed some of the things that Truman said, embellished or rephrased many others, that he tarted up Truman's language, and that he made up some conversations entirely. So now whenever I remember something that I think Truman said, I have to stop and try to remember if it was from Miller. Did Truman really say that it was the worst thing in the world when records were destroyed? I'm sure I read it in Miller, so, uhh… maybe? Miller recounts a discussion in which Truman says he is pretty sure that President Grant had never read the Constitution. Later, Miller says, he asked Truman if he thought that Nixon had read the Constitution, and reports that Truman's reply was: I don't know. I don't know. But I'll tell you this. If he has, he doesn't understand it. Great story! I have often wanted to repeat it. But I don't, because for all I know it never happened. (I've often thought of this, in years past, and whatever Nixon's faults you could at least wonder what the answer was. Nobody would need to ask this about the current guy, because the answer is so clear.) Miller, quotes Truman's remarks about Supreme Court Justice Tom Clark, “It isn't so much that he's a bad man. It's just that he's such a dumb son of a bitch.” Did Truman actually say that? Did he just imply it? Did he say anything like it? Uhhh… maybe? There's a fun anecdote about the White House butler learning to make an Old-fashioned cocktail in the way the Trumans preferred. (The usual recipe involves whiskey, sugar, fresh fruit, and bitters.) After several attempts the butler converged on the Trumans' preferred recipe, of mostly straight bourbon. Hmm, is that something I heard from Merle Miller? I don't remember. There's a famous story about how Paul Hume, music critic for the Washington Post, savaged an performance of Truman's daughter Margaret, and how Truman sent him an infamous letter, very un-presidential, that supposedly contained the paragraph: Some day I hope to meet you. When that happens you'll need a new nose, a lot of beef steak for black eyes, and perhaps a supporter below! Miller reports that he asked Truman about this, and Truman's blunt response: “I said I'd kick his nuts out.” Or so claims Miller, anyway. I've read Truman's memoirs. Volume I, about the immediate postwar years, is fascinating; Volume II is much less so. They contain many detailed accounts of the intransigence of the Soviets and their foreign minister Vyacheslav Molotov, namesake of the Molotov Cocktail. Probably 95% of what I remember Truman saying is from those memoirs, direct from Truman himself. But some of it must be from Plain Speaking. And I don't know any longer which 5% it is. As they say, an ice cream sundae with a turd in it isn't 95% ice cream, it's 100% shit. Merle Miller shit in the ice cream sundae of my years of reading of Truman and the Truman administrations. Now Claude has done the same. And if I let it, Claude will keep doing it to me. Claude caga en la leche. Addendum The Truman Library now has the recordings of those interviews available online. I could conceivably listen to them all and find out for myself which things went as Miller said. So there may yet be a happy ending, thanks to the Wonders of the Internet! I dream of someday going through those interviews and producing an annotated edition of Plain Speaking.