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Mon, 27 Mar 2023 Everyone seems to agree that the Sagrada Família will (when it's finished) have eighteen spires:
Writing about this last week I was puzzled. Which spire is which? Some of the evangelists were apostles, so do they get two spires each? And one apostle was Judas Iscariot, what about him? Did Gaudí plan a glorious spire for Judas the betrayer? I remember when Richard Nixon died, there was some question about whether he would get a commemorative stamp like all the other presidents did when they died. The U.S. Postal Service was unequivocal: when a president dies, he gets a stamp. Even Nixon. I wondered if maybe the spires are like that. Apparently not, the Christians have already dealt with this problem. Acts 1 explains that Simon Peter proposed that someone should be appointed to take Judas's position so that there would be twelve apostles to witness the resurrection. (Twelve is important, it symbolizes perfection. For example, when Jesus feeds the multitude with the loaves and fishes, there are twelve baskets of leftovers.) The disciples pick two candidates and then let God choose one at random, Matthias. The Sagrada Família has a spire for Matthias, and none for Judas Iscariot. Probably a good move on Gaudí's part, nobody would have wanted to work on it. Researching this would have been very difficult if I had not discovered this helpful floor plan of la Sagrada Família, apparently on display in the basement museum of the Sagrada Família. Confusing the issue are:
Nevertheless I think I've worked it out. First, here are the locations of the eighteen spires and their labels: The four big spires (green circles) are the evangelists, clustered around Jesus. They are easy to identify because the labels are nice and clear. Counterclockwise from the lower left (south) they are:
Each of these spires sits over four of the columns (little orange circles) of the transept, one named for the same evangelist, and three named after three apostles. The apostles are in three groups, as is traditional. The Sagrada Família has three façades, and one group of apostles stands at each façade. The main front façade is the “Glory” (Gloria) façade, with (bright blue circles) spires representing:
Gaudí put Peter and Paul in the middle, perhaps because they are more important, with Peter on the right-hand side. On the left side of the picture is the “Passion” (Passio) façade. I marked the spires with greenish-blue circles:
Matthew (the publican) should have been in this group but seems to have been displaced by James. One would expect James to be over on the other side with Simon the Zealot, but he's here for some reason. I don't know why Matthew was left out. I suppose it is because he is sometimes identified as Matthew the Evangelist. If Gaudí had understood him this way, he would have felt that Matthew already had his own spire, and would have replaced him similar to how John was replaced with Paul at the front. On the right side of the picture is the “Nativity” (Naixement) façade. Its four spires, marked with pinkish-blue circles, are:
Normally Barnabas would have been James the Lesser, be he's over on the other side. As I mentioned earlier, Matthias has replaced Judas Iscariot. I wonder if Matthew the Apostle is sitting around in the afterlife, stewing about having been left out? I suppose not, he's too busy dancing around the Eternal Throne. But maybe there's a lesson there about not having the same name as a more important person who comes after you. I hope the post office makes the commemorative Donald Trump stamp really big, so I can wipe my ass with it. [ Addendum: The flag of the European Union has twelve stars, because twelve symbolizes perfection. They emphasize that the twelve stars are not related to the number of countries in the Union, wisely declining to repeat the mistake made by the United States. It was Simon Cozens who brought to my attention the significance of the twelve baskets of leftovers. ] [Other articles in category /art] permanent link Fri, 24 Mar 2023
Notes on card games played by aliens
A few years back I mentioned, in an article on a quite different topic:
Apparently the answer to that is ‘later’. Much later. Last month Eric Erbach wrote to ask:
I'm not sure. This is not that article. But M. Erbach inspired me to think about this some more and I excitedly sent him several emails about the alien relationship to poker and other card games. Then today I remembered I have a whole section of the blog for ‘notes’ and even though it has only two articles in it it was always intended as a place where I could dump interesting ideas that might never go anywhere. So here we are! I didn't actually talk about chess or go in my message, but I went off in a different direction.
The essence of poker is the secret information, which enables bluffing: does that person across the table from me have a winning position, or are they just pretending to have a winning position? Or, conversely: fate has dealt me a losing hand. How do I make the best of a bad situation? This is, I believe, a crucial sort of problem that will come up over and over for all sentient beings. Everyone at some point has to make the best of a bad situation. You have to know when to hold 'em, and when to fold 'em. Games like poker are stripped-down practice versions of these sorts of fundamental problems. (Games like chess and go are stripped-down practice versions of different sorts of fundamental problems, problems of strategic planning and tactical execution.) Thinking about human card games, I said:
Humans invented trick-taking card games over and over. Consider not just European games like bridge, pinochle, euchre, skat, hearts, spades, and canasta, which may have developed out of simpler games invented a thousand years ago in China, but also the West African game of agram. So it is tempting to think that the aliens would surely do the same. But maybe not! Turning it around the other way, I think auctions are also something very likely to be shared by all sentient beings, and yet human card games seem include very few auction-themed games. If the humans can neglect what must be a huge class of sealed-bid auction games, perhaps the aliens will somehow forget to have trick-taking games. Trick-taking games like contract bridge and auction bridge have things called auctions, but they're not actually very auction-like. For an example of what I mean, here's goofspiel, a game that is pure auction:
One
player receives the thirteen spade cards, the other the thirteen club
cards. If there is a third player, they receive the thirteen heart
cards.
The diamonds are shuffled, stacked face down, and the top one is turned over. Each player now offers a sealed bid to buy the face-up diamond card. They do this by selecting one of the cards from their hand and playing it face-down on the table. The sealed bids are revealed simultaneously and the highest bid placed wins the auction. scoring points for the winning player: the A♢ is worth one point and K♢ worth 13. The bid cards are discarded, the next diamond is revealed, and the game continues with each player offering a bid from their now-depleted hand. After 13 rounds, the player with the most points out of 91 is the winner. For a more complex auction bidding game, see Sid Sackson's All My Diamonds. Now, my point is that as far as I know there are very few popular human auction games. But perhaps, instead of bluffing games like poker or trick-taking games like whist, the aliens love to play auction games with cards? Many interesting variations are possible. In email with M. Erback I suggested a completely made-up auction game of a sort I've never seen among humans:
I think there might be interesting strategy here. Suppose you are going second. Which card of the bundle will you look at? You can look at the same one that the first player looked at, so now you know what they know, but they also know what you know and that you know what they know. Or you can look at a different card, and learn something that nobody else knows yet. After that you have to make a bid, which communicates to the other players something about what you know, and in the early stages of the game you can be tricky and make your bid a bluff. Maybe players are allowed to pass without dropping out. Or maybe it wouldn't work at all; you never know until you playtest it. What if we played Texas Hold'em in this style? Instead of exposing all five community cards, some were kept partly secret? Another thing we can do to get an alien game is to take a common human game and make it into something completely different by changing the emphasis:
Many old games can be spiced up in this way. For example chess, but if your opponent plays a move you don't like, you can force them to take it back and play a different move, by chopping off one of your fingers. Totally different strategy! Finally, I remembered a funny moment from the Larry Niven story “There is a Tide”. Niven's character Louis Wu has discovered a valuable lost artifact. Unfortunately, a representative of a previously-uncontacted alien species has discovered the same artifact. Rather than fighting, Wu proposes that they gamble for it.
Pretty funny! Louis is imagining something fun and interesting, but the alien proposes the opposite of this. In my opinion this is a good plan, as it will tend to prevent arguments. Although something needs to be said about the 22% chance that Louis and the alien will tie. In any case, Louis is kind of a dilettante, and it turns out that the alien is actually playing the game that is one level up. [ Addendum: Thanks to John Wiersba for providing me with the name of goofspiel. ] Addendum 20230523: Dave Turner has a sort-of response to this article titled “Rarely seen game mechanics”. ] [Other articles in category /notes] permanent link Thu, 23 Mar 2023
Addenda to recent articles 202212-202302
I made several additions to articles of the last few months that might be interesting.
By the way, if anyone happens to know a gender-neutral term for “straight man”, I'm still stumped. [ Addendum 20230324: Thomas Maccoll suggests “foil”. ] [Other articles in category /addenda] permanent link Tue, 21 Mar 2023
ChatGPT on the namesake of the metric space and women named James
Several folks, reading the frustrating and repetitive argument with ChatGPT that I reported last time wrote in with helpful advice and techniques that I hadn't tried that might have worked better. In particular, several people suggested that if the conversation isn't going anywhere, I should try starting over. Rik Signes put it this way:
I hope I can write a followup article about “what to do when ChatGPT has its head up its ass”. This isn't that article though. I wasn't even going to report on this one, but it took an interesting twist at the end. I started:
This was only my second interaction with ChatGPT and I was still interested in its limitations, so I asked it a trick question to see what would happen:
See what I'm doing there? ChatGPT took the bait:
I had hoped it would do better there, and was a bit disappointed. I continued with a different sort of trick:
Okay! But now what if I do this?
This is actually pretty clever! There is an American mathematician named Robert C. James, and there is a space named after him. I had not heard of this before. I persisted with the line of inquiry; by this time I had not yet learned that arguing with ChatGPT would not get me anywhere, and would only get its head stuck up its ass.
I was probing for the difference between positive and negative knowledge. If someone asks who invented the incandescent light bulb, many people can tell you it was Thomas Edison. But behind this there is another question: is it possible that the incandescent light bulb was invented at the same time, or even earlier, by someone else, who just isn't as well-known? Even someone who is not aware of any such person would be wise to say “perhaps; I don't know.” The question itself postulates that the earlier inventor is someone not well-known. And the world is infinitely vast and deep so that behind every story there are a thousand qualifications and a million ramifications, and there is no perfect knowledge. A number of years back Toph mentioned that geese were scary because of their teeth, and I knew that birds do not have teeth, so I said authoritatively (and maybe patronizingly) that geese do not have teeth. I was quite sure. She showed me this picture of a goose's teeth, and I confidently informed her it was fake. The picture is not fake. The tooth-like structures are called the tomium. While they are not technically teeth, being cartilaginous, they are tooth-like structures used in the way that teeth are used. Geese are toothless only in the technical sense that sharks are boneless. Certainly the tomia are similar enough to teeth to make my answer substantively wrong. Geese do have teeth; I just hadn't been informed. Anyway, I digress. I wanted to see how certain ChatGPT would pretend to be about the nonexistence of something. In this case, at least, it was very confident.
I will award a point for qualifying the answer with “as far as I am aware”, but deduct it again for the unequivocal assertion that there is no record of this person. ChatGPT should be aware that its training set does not include even a tiny fraction of all available records. We went on in this way for a while:
Okay. At this point I decided to try something different. If you don't know anything about James B. Metric except their name, you can still make some educated guesses about them. For example, they are unlikely to be Somali. (South African or Anglo-Indian are more likely.) Will ChatGPT make educated guesses?
This is a simple factual question with an easy answer: People named ‘James’ are usually men. But ChatGPT was in full defensive mode by now:
I think that is not true. Some names, like Chris and Morgan, are commonly unisex; some less commonly so, and James is not one of these, so far as I know. ChatGPT went on for quite a while in this vein:
I guessed what had happened was that ChatGPT was digging in to its previous position of not knowing anything about the sex or gender of James B. Metric. If ChatGPT was committed to the position that ‘James’ was unisex, I wondered if it would similarly refuse to recognize any names as unambiguously gendered. But it didn't. It seemed to understand how male and female names worked, except for this nonsense about “James” where it had committed itself and would not be budged.
I didn't think it would be able to produce even one example, but it pleasantly surprised me:
I had not remembered James Tiptree, Jr., but she is unquestionably a woman named ‘James’. ChatGPT had convinced me that I had been mistaken, and there were at least a few examples. I was impressed, and told it so. But in writing up this article, I became somewhat less impressed.
ChatGPT's two other examples of women named James are actually complete bullshit. And, like a fool, I believed it. James Tenney photograph by Lstsnd, CC BY-SA 4.0, via Wikimedia Commons. James Wright photograph from Poetry Connection. [Other articles in category /tech/gpt] permanent link Mon, 20 Mar 2023Looking over a plan of the Sagrada Família Sunday, I discovered that the names of the cardinal directions are interesting.
Bonus unrelated trivia: The Russian word for ‘north’ is се́вер (/séver/), which refers to the cold north wind, and is also the source of the English word “shower”. [ Addendum 20231203: Compass directions in Czech ] [Other articles in category /lang/etym] permanent link Sun, 19 Mar 2023
Here I am at the Sagrada Família
I just found these pictures I took twenty years ago that I thought I'd lost so now you gotta see them. Back in 2003 I got to visit Barcelona (thanks, Xavi!) and among other things I did what you're supposed to do and visited la Sagrada Família. This is the giant Art Nouveau church designed by the great architect and designer Antoni Gaudí. It began construction in 1882, and is still in progress; I think they are hoping to have it wrapped up sometime in the next ten years. When I go to places I often skip the tourist stuff. (I spent a week in Paris once and somehow never once laid eyes on the Eiffel Tower!) I wasn't sure how long I would spend at the Sagrada Família, but it was great. I stayed for hours looking at everything I could. Sagrada Família is marvelous. Some of the towers in this picture are topped with enormous heaps and clusters of giant fruits. Fruits! Gaudí's plan was to have eighteen spires in total. Supposedly there will be twelve big ones like these representing the twelve apostles: After these, there are four even bigger ones representing the four evangelists. And then one enormous one representing the Virgin Mary, and the biggest one of all for Jesus himself which, when finished, will be the tallest church tower in the world. In the basement there is a museum about Gaudí's plans, models, and drawings of what he wanted the church to look like. This is a view of the southeast side of the building where the main entrance is: Hmm, there seem to be words written on the biggest tower. Let's zoom in and see what they say. Hee hee, thanks, great-grandpa. [ Addendum 20230327: I spent some time figuring out which spires were for which disciples. The four in the photograph above are Matthias, Judas (not Iscariot), Simon (the Canaanite, not Simon Peter), and Barnabas. ] [Other articles in category /art] permanent link Mon, 13 Mar 2023
This ONE WEIRD TRICK for primality testing… doesn't work
This morning I was driving Lorrie to the train station early and trying to factor the four digit numbers on the license plates as I often do. Along the way I ran into the partial factor 389. Is this prime? The largest prime less than !!\sqrt{389}!! is !!19!!, so I thought I would have to test primes up to !!19!!. Dividing by !!19!! can be troublesome. But I had a brain wave: !!389 = 289+100!! is obviously a sum of two squares. And !!19!! is a !!4k+3!! prime, not a !!4k+1!! prime. So if !!389!! were divisible by !!19!! it would have to be divisible by !!19^2!!, which it obviously isn't. Tadaa, I don't have to use trial division to check if it's a multiple of !!19!!. Well, that was not actually useful, since the trial division by !!19!! is trivial: !!389 = 380 + 9!!. Maybe the trick could be useful in other cases, but it's not very likely, because I don't usually notice that a number is a sum of two squares. [ Addendum 20230323: To my surprise, the same trick came in handy again. I wanted to factor !!449 = 400 + 49!!, and I could skip checking it for divisibility by !!19!!. ] [Other articles in category /math] permanent link Fri, 10 Mar 2023
Maxims and tactics for dealing with assholes on the Internet (and elsewhere)
The first ruleDon't engage.
If that's too much to remember, here's a shorter version: Don't.
(“Don't what?” “Just don't.”) Other mottoes and maxims
It takes two to have an argument
Nothing is often a good thing to do, and always a clever thing to say.
Tactics
Pretend you're playing a game in which the person who gets the last word loses.
What would The Fonz do?
AddendumI left out a good one: If I'm tempted to end a sentence with “… you blockhead”, I should just end it with a period, and imagine that readers will feel the psychic reverberations of “you blockhead”. Remember Old Mrs. Lathrop:
(Dorothy Canfield Fisher, Understood Betsy) [Other articles in category /brain] permanent link |