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Last week I complained about a Math SE pathology in which OP asks a simple question, and instead of an answer gets an attempt at a socratic dialog. I ended by saying: I have been banging this drum for decades, but I will cut the scroll here. Expect a followup article. Seeing this, Scott Francis remarked: when you say “I have been banging this drum for decades" I hear echoes of EFnet #perl in the back of my head :) And yes, that is one of the things I was thinking of. Thirty years ago the regulars in the #perl IRC channel would play a cruel teasing game. A stranger would come into the channel and ask a simple technical question, like “how do I remove the first character from a string?” Instead of giving the answer, two or three people would reply perldoc perlre. In case it's not obvious — and there is no reason why it should be — this means you can run this command to get the manual for how to use Perl regular expressions. This manual was about 20,000 words long. People indulging...
4 months ago

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Claude and Merle Miller let me down

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.

3 months ago 1 votes
Reflector grids

Around here, these metal things are commonly found on streetside utility poles, attached maybe a meter off the ground. .image-group { display: flex; flex-direction: row; align-self: center; justify-content: center; gap: 4em; } .image-group .image { display: flex; flex-direction: column; align-self: center; align-items: center; } .image div { text-align: center; border: 0px; } Metal reflector Plastic reflector When I first noticed one of these I said “I wonder what the holes are for. Maybe to make it more visible? And what do they do with all the leftover rectangles after they've made one?” I eventually got a better idea: The little metal rectangles are the primary product, and after they have been stamped out of the metal sheet, there is this waste material left over with all the holes. Instead of throwing it away someone nails it to a utility pole to make the pole easier to see at night. I felt a bit silly that my first idea had been exactly backwards. I later learned that only the older ones are made of sheet metal. Newer ones are made of some sort of plastic, maybe polyethylene or vinyl or something, about the same thickness. They look pretty much the same. I can only tell them apart by feeling them. Still I wondered what the little rectangles had been used for. It turns out that the purpose is this: That's according to an old Philadelphia Inquirer article, Why yellow grids are on some Philly-area utility poles. (Patricia Madej, Aug. 31, 2019) The answer came as a bit of a surprise to Jay Lipschutz, 73, of Northeast Philly … His wife, Ruth, he said, had insisted they’re reflectors for drivers to see. She was right. Jay, my friend, your wide is smarter than you are. Listen to her. The article also tells us that the rectangular leftover is called a “grid reflector”. With a little more research I learned that one manufacturer of grid reflectors is Almetek. They cost $3.50 each. Pricey, for something they would have had to throw away. (Here's the old South Philly Review article that put me on to Almetek.) What kicked off this article was that I was walking around and I saw this similar reflector grid, which felt to me like it was a bit of a joke, like a teenager sneaking into a bar wearing a fake mustache: Hey, those aren't holes! When I saw this one I wondered for a moment if I was suffering some sort of mental collapse, and had misperceived the other grids as having actual holes. But no, this one really did have fake holes. (Also, it has been installed sideways. Normally they are oriented as the two above.) --> This isn't the first time I have written about ID numbers on utility poles hereabouts.

3 months ago 1 votes
Jonathan Chait

[ Content warning: angry, contemptuous ranting that accomplishes nothing. ] I didn't really know who Jonathan Chait was until last week when I unfortunately read this essay of his (from February 2016) on “Why Liberals Should Support a Trump Republican Nomination”. I've said a lot of dumb things in my life but I don't think I've ever been as wrong about anything as Chait was about this. I sure hope I haven't. But if I do ever find out I had been this wrong about something, I would want to retire to a cave or a mountaintop or something. “Hey, remember Dominus? Whatever happened to him, anyway?” “Oh, he said he was going away to cleanse himself of error, and might not be back for a long time.” And yet this guy is still shamelessly writing. And why not? Editors are still buying his essays and maybe people are even still reading them. Why? You'd think that people would look at this essay and say “yeah, that's enough Chait for me, thanks, next time I need an opinion I'll try someone else.” I get it, nobody's right all the time. Whenever you read anyone's essay you're taking a risk, like rolling a die. Sometimes the die rolls high, sometimes it rolls low, and some dice might have higher numbers to begin with. I've usually been well-served by Daniel Dennett's dice, and Robertson Davies'. But here people have an opportunity to toss a totally unknown die that they haven't tried before but that most likely rolls numbers from 1 to 6, and instead they toss the Jonathan Chait die when they know it has at least one side with a -1000. A long time ago, I wrote: I hate trying to predict the future; I don't think I'm good at it and I don't think anyone else is. I don't think anyone could have predicted the extent of the current fiasco, but I do think it should not have been hard to predict, in 2016, that liberals should not, in fact, have supported a Trump Republican nomination. Anyone can be wrong, even the wise cannot see all ends. But I think this one was maybe not so hard to see. Chait spends a lot of time comparing Trump with Arnold Schwartzenegger: both nominally conservative, both inexperienced in government, both assholes. I think the part that Chait ignored was that by 2016 — no, scratch that, by 1990 — it was perfectly clear that Trump was a liar, a thief, a racist, and a deadbeat, and that he had no respect for law or truth or ethics or anything other than his own convenience of the moment. (Here are just two examples. More recently, his ridiculous years-long insistence that Barack Obama was born in Kenya. And earlier, his equally ridiculous lies around his destruction of the Bonwit Teller building.) In that old essay I said: Most people who try don't seem to revisit their old predictions to see if they were correct, or to learn from their past errors, and the people who listen to them never do this. I looked around a little to see if Jonathan Chait had written an essay titled “I was wrong, I was so, so wrong, I just couldn't have been wronger” but I didn't find one and I also didn't find any recent essays that said anything like “here's why I think this new essay is more reliable than that embarrassing Trump one I wrote for The New Yorker in 2016.” I don't understand how Chait still has a job after writing this essay. Why isn't he selling shoes? How does a writer come back from this? Isn't there some charitable society for the protection for the public that could pay to have someone follow Chait around, quoting out loud from this essay, as a warning to everyone he meets for the rest of his life? It least now I've been warned. Now when I read “Jonathan Chait said recently…” I'll remember: “Oh, you mean Jonathan ‘Why Liberals Should Support a Trump Republican Nomination’ Chait! Thanks, I'll pass.” <

3 months ago 2 votes
Claude chokes on graph theory

.bad { border: thin solid red; } Having had some pleasant surprises from Claude, I thought I'd see if it could do math. It couldn't. Apparently some LLMs can sometimes solve Math Olympiad problems, but Claude didn't come close. First I asked something simple as a warmup: MJD: What is the largest number that is less than 1000? I had tried this on ChatGPT a couple of years back, with tragic results: ChatGPT: The largest number that is less than 1000 is 999. But it should have quit while it was ahead, because its response continued: ChatGPT: Any number that is less than 1000 will have three digits, with the first digit being 9, the second digit being 9, and the third digit being any number from 0 to 8. and then when I questioned it further it drove off the end of the pier: ChatGPT: Any number with four or more digits can be less than 1000, depending on the specific digits that are used. For example, the number 9991 is a four-digit number that is less than 1000. Claude, whatever its faults, at least knew when to shut up: MJD: What is the largest number that is less than 1000? Claude: 999 I then asked it “What if it doesn't have to be an integer?” and it didn't do so well, but that's actually a rather tricky question, not what I want to talk about today. This article is about a less tricky question. I have omitted some tedious parts, and formatted the mathematics to be more readable. The complete, unedited transcript can be viewed here. I started by setting up context: MJD: Let's say that the cube graph has as vertices the set and two vertices are connected with an edge if and only if their coordinates differ in exactly one position. This is a standard construction. Are you familiar with it? Claude asserted that it was familiar with this family of graphs. (Wikipedia on cube graphs) Then I got to the real question: Now let's say that the Keane number for a graph is the largest number such that: can be partitioned into connected subgraphs, and each pair of subgraphs is adjacent, in the sense that for each pair , there is an edge of with one vertex in and one in . If you understand so far, tell me the Keane numbers of the cube graphs , and . One way to think about this is: we have a graph, and we want to divide it up into connected subgraphs. We pick a single color for each subgraph and color the vertices of that subgraph with its color. And for each two colors, there should be vertices of those colors that share an edge. We're looking for the maximum possible number of colors. So if we produce a partition into subgraphs, that only proves that ; we still need a further argument to rule out the possibility of a partition into or more parts. Claude got this initial question right. The Keane numbers of and are obviously and . So far so good. Then I asked Claude for the Keane number of and this it was unable to produce. The correct number is . There are several essentially different partitions of into four parts, each of which touches the other three, so the number is at least . Here are two: In addition to these there is also a partition into parts of size , and one into parts of size . On the other hand, more than parts is impossible, and the proof is one sentence long: has only vertices, so any partition into or more parts must have a part of size , and this part can't be adjacent to the other four parts, because a single vertex has only three outgoing edges. I would expect a bright middle-schooler to figure this out in at most a few minutes. At first, Claude got the right number, but with completely bogus reasoning. To avoid belaboring the obvious, I'll highlight the errors but I won't discuss them at length. Claude: Let's find the maximum possible : One valid partition with exists: Take two opposite vertices (e.g., and ) Make these two single-vertex subgraphs Split the remaining vertices into two paths of vertices each Each subgraph is connected Each pair of subgraphs will have an edge between them The diagrams I showed earlier display some of the partitions that show , but the one Claude gave here does not, because two of its parts are not adjacent. Claude: Why can't be or more? If we had or more subgraphs, we would need edges between pairs only has edges total Some edges would need to be reused for multiple pairs But each edge can only connect one pair of subgraphs Therefore or more subgraphs is impossible Therefore, the Keane number of is . Would you like me to verify any part of this reasoning? So, right answer, but seemingly by luck, since there were serious errors in reasoning, in both the part and also in the part. I decided to ignore the second one. MJD: You said two of the subgraphs are and . You said each pair of subgraps will have an edge between them. What edge connects and ? Claude: Ah, I made a mistake. The vertices and differ in all three positions, so they are not adjacent in (they need to differ in exactly one position to have an edge between them). This means that making them single-vertex subgraphs would violate condition (2) since these subgraphs would not be adjacent. I need to rethink my claimed partition. Would you like me to try again to determine the Keane number of ? MJD: Yes. Claude: [finds a specific example showing , and remarks that “seems difficult”] is possible or is maximum. Would you like me to continue? MJD: Please go on. Claude: Let me try to prove is maximum in . Suppose we had subgraphs. Then: We need edges between different subgraphs Each subgraph needs to be connected: A subgraph with vertices needs at least edges A subgraph with vertices needs edge A subgraph with vertex needs edges There are edges total in If we have subgraphs: First, edges must go between different subgraphs That leaves only edges for internal connectivity But with vertices split into subgraphs: If any subgraph has vertices, it needs edges internally If any has vertices, it needs edges internally With vertices total divided into parts, at least one part must have vertices After using edges for that part and edges between parts, we don't have enough edges left to make all other parts connected Therefore is impossible, and the Keane number of is . Claude seems completely undirected here. Some of the things it says are correct facts, but it can't link the facts together into actual reasoning, except by accident. Sometimes it utters A followed by B where A implies B, and it seems exciting, but just as often B is a nonsequitur. This is not that different from how ChatGPT was two years ago. It can spout text, and often it can spout enough plausible, grammatically-correct text to suggest that it knows things and is thinking about them. Claude's text-spouting prowess is much more impressive than ChatGPT's was two years ago. But it is still just a text-spouter. I went on, trying to detect actual thinking. MJD: What if there were parts of vertices each? Claude's response here correctly applied its earlier analysis: four parts of size would use up four edges for internal connectivity, leaving for external connections, and we only need . Claude: I was too quick to conclude 4 was impossible. Let me try to find an explicit partition into 4 parts of 2 vertices each... MJD: You keep going until you think you ha e the right answer. Claude: Let me try to construct a partition of into parts of vertices each: … This time Claude tried this partition: It noticed that two of the four parts were not adjacent, and gave up without searching further. Claude: This makes me think really is the maximum. If Claude were a human mathematician, this would be a serious error. Finding one invalid partition proves nothing at all. Claude: My previous argument was wrong, but the conclusion might be right. Would you like me to try to prove more carefully that is impossible? There is no proof that is impossible, and I thought it would be unenlightening to watch Claude flounder around with it. But I wanted to see what would happen if I asked it to prove a false claim that should be easier because its premise is stronger: MJD: Try a weaker conjecture: prove more carefully the four parts of size 2 is impossible. Claude: Okay, let me prove that we cannot partition into four parts of size 2 each. Suppose we had such a partition , where each contains exactly two vertices. For any such , its two vertices must be adjacent (to be connected). This means they differ in exactly one coordinate. Therefore, each must be of one of these forms: Two vertices differing in 1st coordinate (like ) Two vertices differing in 2nd coordinate (like ) Two vertices differing in 3rd coordinate (like ) Consider any vertex in . It has exactly 3 neighbors: One differing in 1st coordinate One differing in 2nd coordinate One differing in 3rd coordinate Therefore, if is in : One of its neighbors must also be in That leaves only two edges from that could connect to other parts So can only help be adjacent to at most two other parts But each needs to be adjacent to all three other parts This contradiction proves no such partition exists. It's tempting to look at this and say that Claude was almost right. It produced 16 lines and at least 15 of them, on their own, were correct. But it's less impressive than it might first appear. Again Claude displays the pattern of spouting text, some of which is correct, and some of which is related. But that is all I can say in its favor. Most of its statements are boilerplate. Sections 2–4 can be deleted with nothing lost. Claude has buried the crux of the argument, and its error, in section 5. MJD: In step 5 I see that if is in , it can only help be adjacent to two other parts. But has size 2, so it contains a vertex other than . If connects to two other parts, couldn't the other vertex of connect to a third part? Claude: Ah, you're absolutely right! My proof attempt failed. Let me back up and try a different approach to the original question of whether can be partitioned into 4 parts that satisfy both conditions. … This time Claude did find a correct partition into four parts, showing that . MJD: How did you come up with that example partition? Claude: I should be honest - I didn't find it systematically. I was trying different arrangements somewhat randomly until I found one that worked. … I don't think these is any sense in which this is true, but at this point I hadn't yet internalized that Claude's descriptions of its own internal processes are text-spouting just like the rest of its output. In any case, I ignored this and asked it to analyze its own earlier mistake: MJD: Earlier you purported to prove that was impossible, saying that edges would be needed to connect the parts, and that this did not leave enough edges to connect the parts internally. You didn't analyze this carefully, so you missed the solution where all four parts have vertices each. Do that analysis more carefully than you did last time and explain why that counting method does not rule out a partition of into . Claude: (details elided) So this counting argument shows: We need 10 edges We have 12 edges Therefore the counting argument does not rule out a partition My earlier analysis erred by not being explicit about the numbers. I just had a vague sense that we needed "too many" edges, without actually counting them. This shows the importance of precise counting rather than relying on intuition about what seems like "too many". Claude got the counting part right, although I think the final paragraph is just spouting, especially the claim “I just had a vague sense that…”, which should not be taken seriously. [ Digression: This reminds me of a section in Daniel Dennett's Consciousness Explained in which he discusses the perils of asking humans about their internal processes. The resulting answers, he says, may provide interesting informaiton about what people think is going on in their heads, but we should be very wary about ascribing any accuracy or insight to these descriptions. Dennett makes an analogy with an anthropologist who asks a forest tribe about their forest god. The tribespeople agree that the forest god is eight feet tall, he wears a panther skin, and so on. And while this might be folklorically interesting, we should be very reluctant to conclude from this testimony that there is actually an eight-foot-tall fur-clad god in the forest somewhere. We should be similarly reluctant to ascribe real existence to Claude's descriptions of its “vague senses” or other internal processes suggested by its remarks like “Ah, let me think...” or “Ah, you're absolutely right!”. Claude has even less access to its own mental states (such as they are) than a human would. ] As I pointed out earlier in this article, there are several essentially different solutions to the problem of partitioning into four parts. Claude has found one of them, the one I showed above on the left. I wanted to see if it could find another: MJD: Are there any other partitions that are not ruled out by that argument? Or is 2+2+2+2 the only possibility? Claude: Let me think about what other partitions could satisfy the edge-counting constraint. If we have parts, need edges between parts, and have total edges, then we can use up to edges for internal connectivity of parts. Possible partitions of vertices into parts could be: (needs internal edges) (needs internal edges) (needs internal edges) (needs internal edges) (needs internal edges) So from just edge counting: (Claude concludes that none of these is ruled out by edge-counting.) So the edge-counting argument alone doesn't rule out any of these distributions of part sizes. We'd need additional arguments to determine which are actually possible in . MJD: Why didn't you consider ? Claude: Ah, you're right - I should have considered ! For : The part of size needs at least internal edges to be connected The parts of size each need internal edge So that's internal edges needed Plus edges needed between parts Total needed = edges We have edges available So this case is also not ruled out by edge counting. I apologize for missing it in my list. Would you like me to check if there are any other distributions I missed? Oh, such failure! Failures that I have highlighted are clearly false statements, But the failure here is much worse. Again, everything Claude said was correct! And yet deeply wrong! A bright middle-schooler could have missed this also. It was a bit of a trick question. Not because it's ambiguous, but because problem with is not in line with the direction that the discussion was taking at that point. There is nothing wrong with from an edge-counting point of view! But I think a human mathematician, even a very young one, would have been more likely to answer the question I actually asked, which was “Why didn't you consider ?”, and from there might have quickly come to the useful conclusion that it doesn't need to be considered. Claude didn't do anything like that. MJD: doesn't work. Think about it more. Claude: Let me think more carefully about a potential partition. Consider the part of size : To be connected, it needs at least edges internally One vertex in must connect to all other vertices in But in , each vertex has only edges total If one vertex in uses all its edges internally to connect to the other vertices in , it has no edges left to connect to other parts But every part needs to be adjacent to every other part Therefore is impossible, not because of edge counting, but because: Either isn't connected (if we don't use enough internal edges) Or can't connect to all other parts (if we use too many internal edges) This shows why just counting edges isn't enough - we also need to think about the structure of and how the edges can be arranged. Terrible. This is so muddled I wasn't even sure what to highlight as the errors. Yes, if one vertex in uses all its edges internally to connect to the other vertices in , it has no edges left to connect to other parts. But the other three vertices in have two edges each, so could easily connect to the other three parts. And, of course, Claude has still missed the main point, which is that one needn't consider , because and has only vertices. MJD: There is a much simpler argument why 4+2+2+1 won't work. Claude: Ah, let me think... In a partition: The single vertex in the part of size has degree in But it needs to connect to all three other parts! It needs all three of its edges just to be adjacent to the other parts So it can't connect to all three other parts AND connect to three different vertices This is a much simpler contradiction. I was making it too complicated by thinking about the part of size when the part of size immediately shows it's impossible. MJD: How many vertices are.in ? Claude: has vertices (all binary strings of length ): And now I see an even simpler argument why is impossible: vertices, but only has vertices! Finally! I would love to know what really happened here. What caused Claude to emit a sentence connecting with having only vertices? MJD: So remind me, did you decide that is , or ? I wasn't sure it would remember this, by which I really mean that I wasn't sure it would be able to pick out from its previous mass of statements which one was correct. But whether by luck or not, it did answer the question correctly: Claude: Earlier I found a valid partition of Q_3 into 4 parts: I verified that: Each part is connected Each part is adjacent to every other part Therefore . I haven't yet proven that . Would you like me to try to prove that parts is impossible? MJD: Please go ahead. I found Claude's attempt at this interesting, but not in a good way. After reading it I shrugged and quit the conversation. Claude: parts is impossible in . Five parts would require different edges just to connect all pairs of parts to each other. Each such edge must be distinct because a single edge can only connect one pair of parts. Each vertex in has degree . With vertices, the total number of edges is . Out of these edges: must be used to connect different parts to each other That leaves only edges for internal connectivity of parts But with vertices split into parts, some part must have size Any part of size must use at least one edge internally to be connected If one part uses one edge internally, that leaves only one edge for all other parts But if any other part has size , it also needs an internal edge With vertices in parts, at least two parts must have size Therefore edges is not enough for internal connectivity Thus . Claude says that with vertices in parts, at least two parts must have size or more. This is wrong, because you could have . But highlighting that wrong statement doesn't get at why this answer is so bad. It's bad because the conclusion that appears next is a complete nonsequitur. The argument can be fixed up. I would put it like this: As Claude observed, we have only edges available for internal connections A part with vertices requires at least edges for internal connections Let the sizes of the parts be . Since , we need at least edges for internal connections But we have only . It's true that edges is not enough for internal connectivity. But in my opinion Claude didn't come close to saying why. Back in the early part of the 20th century, we thought that chess was a suitable measure of intelligence. Surely a machine that could play chess would have to be intelligent, we thought. Then we built chess-playing computers and discovered that no, chess was easier than we thought. We are in a similar place again. Surely a machine that could hold a coherent, grammatical conversation on any topic would have to be intelligent. Then we built Claude and discovered that no, holding a conversation was easier than we thought. Still by the standards of ten years ago this is stunning. Claude may not be able to think but it can definitely talk and this puts it on the level of most politicians, Directors of Human Resources, and telephone santizers. It will be fun to try this again next year and see whether it has improved.

3 months ago 2 votes
Furniture Mecca

[ Content warning: shitpost ] It's that time of year again! Furniture Mecca is having their annual sale. This year the sale will run until Friday the 28th. At closing time on that day any remaining furniture will be hurriedly moved to the owner's other furniture store, Furniture Medina.

3 months ago 2 votes

More in history

Then They Came for the Palestinians : How to Respond to the Kidnapping of Mahmoud Khalil

On March 8, Department of Homeland Security agents kidnapped Mahmoud Khalil, a Palestinian organizer and graduate student at Columbia University who had permanent residency in the United States. Donald Trump’s State Department arbitrarily revoked his residency. They are holding Khalil in Louisiana, over a thousand miles from his home. This is part of Donald Trump’s promised crackdown on Palestine solidarity activism at Columbia University and other schools around the country. Above all, however, it is a test, and how we respond will determine what happens to the rest of us later—as Martin Niemöller described in his well-known poem. Here, we will explore the stakes of this moment and share experience from anarchists whose comrade was similarly kidnapped for participating in the Occupy ICE movement in San Antonio, Texas in 2018. The Antisemitic Plan to Smear Palestine Solidarity as Antisemitic The Trump regime has promised to deport millions of undocumented people, and their efforts are already underway. The kidnapping of Mahmoud Khalil is something different. Khalil is a permanent resident of the United States who is being targeted for political reasons. Trump is seeking to set an additional precedent in order to open a new front in his campaign to purge the United States of dissidents. This is the culmination of two years of planning. In April 2023, the billionaire-backed Heritage Foundation published Project 2025, a playbook to overhaul the federal government of the United States in order to consolidate autocratic power in the hands of Donald Trump. Although Trump temporarily distanced himself from Project 2025 during his campaign, it proved to be a solid predictor of his game plan once in office. In October 2024, the Heritage Foundation followed up Project 2025 with Project Esther, a playbook for repressing those who oppose the genocide of Palestinians. In the text of their report, the Heritage Foundation depicts all concern for Palestinians as participation in “a global Hamas Support Network” and explicitly accuses Jewish Voice for Peace and many other Jewish people of being “antisemitic” for refusing to support Zionism. At the same time, the report relies heavily on anti-Semitic tropes such as fearmongering about George Soros. This exemplifies the way that the far right has sought to appropriate concerns about antisemitism to promote racism, Islamophobia, and antisemitic conspiracy theories. A slide from a Heritage Foundation presentation about Project Esther. Note that “Soros” and Jewish Voice for Peace are at the tops of the columns titled “Masterminds” and “Organizers.” The chief source of Trump’s appeal is that he has been able to channel the considerable anger of the downwardly mobile away from those who hold power and towards scapegoats, creating a pressure valve for a wide range of resentments. But in order to scapegoat people without consequences, it is necessary to undermine their social ties, to prevent others from identifying with them, to carve up society into isolated and mutually hostile factions. Reducing all empathy for Palestinians to support for Hamas is a discursive maneuver intended to frame all who speak out against genocide as legitimate targets for Trump’s government. In addition to demonizing Palestinians, Project Esther lays the groundwork to attack Jewish people as “antisemites” if they don’t get on board with Christian Nationalist priorities. This strategy weaponizes an existing rift that cuts through the Democratic Party—the question of whether Palestinians deserve to be treated as human beings—in order to create the conditions for a fascist takeover of the United States as well as further colonial violence abroad. The ones who stand to gain the most from this strategy are not Zionist Jews, but authoritarian gentiles. In view of the significance of Project 2025, we should not underestimate how central Project Esther is to the Trump administration’s strategy. This will help us to understand the kidnapping of Mahmoud Khalil. The core of Trump policy is performative violence. That is why they have kidnapped an activist who has never been charged with a crime, whose wife—an American citizen—is eight months pregnant, who has a legal right to reside in the United States according to all established precedents. That is why they intentionally targeted a negotiator, the same way that the Israeli government routinely murders negotiators in Palestine. The point is to be shocking, to terrorize, to show that they can do things in public that the Biden administration had to do secretively. Everyone who has excused or minimized the genocide of Palestinians—for example, by spending at least as much time talking about the 1139 Israelis killed on October 7, 2023 as they do addressing the tens of thousands of Palestinian, Lebanese, and Syrian people slaughtered since then—must understand that today, supporting Israel means supporting Trump’s brand of fascism. The escalating violence of the Israeli colonial project helped create the conditions for Trump’s return; now that he is back in office, excusing Israeli colonialism can only facilitate Trump’s own consolidation of power. As we argued on the night of the 2024 election, The Biden administration has already done much of the work to desensitize the general public to the program that an emboldened second Trump administration will attempt to carry out—above all, by supporting the Israeli military in carrying out a brutal genocide in Gaza. In so doing, Biden and Harris have accustomed millions of people to the idea that human life has no inherent value—that it is acceptable to slaughter, imprison, and torment people based on their status in a targeted demographic. You either embrace the struggle for the liberation of Palestine or you become an accomplice in the rise of fascism. This was always true, but today there is no possible excuse not to recognize it. Even if your sole concern is fighting antisemitism and you do not care what happens to people of any other ethnicity, you pave the way for antisemites to gain power by standing aside as Palestinians are kidnapped. Like Palestinians, Jewish people are on the hit list of potential scapegoats, and what befalls one scapegoat will eventually befall another. If there are no serious consequences for the kidnapping of Mahmoud Khalil, then soon enough, the Trump administration will push the envelope, moving on to kidnap other activists who obstruct the far-right agenda. Likewise, the Israeli genocide of Palestinians is a template for bloodshed that will be used again and again as long as there are no significant consequences. If politicians like Trump retain their sway by inflicting violence, they will have to continuously expand the range of people they target and the intensity of that violence, just as the Nazis did between 1933 and 1945. What Will It Take? For now, a judge has ordered a temporary delay in the expulsion of Mahmoud Khalil from the United States. But this should reassure no one. If we count on judges to restrain Trump, we will have no recourse when Trump’s administration simply ignores the laws, and no plan when he manages to replace them with loyal flunkies—or has his flunkies replace the laws themselves. On March 10, demonstrators gathered in New York City for a protest that took the streets, resulting at one point in tussles with police. On March 11 and 12, further protests will ensue in New York, Chicago, Minneapolis, and elsewhere. But the point of these protests must not be to petition the authorities. Donald Trump is not a well-meaning public servant looking to represent his constituents. He is a power-hungry sadist who benefits from our displays of grief and impotent rage. Politics in the United States today is a question of relations of raw force. When we take the streets, we are not addressing Trump or his ghoulish underlings; we are addressing each other. We are setting out to demonstrate that resistance is possible, that there are tactics that can exert concrete leverage against our oppressors, that there are enough people invested in solidarity that it can become a social force capable of compelling Trump and his lackeys to stand down. At the March 10 demonstration in New York, participants handed out fliers to this effect: Fascist politicians need the police. But we know masses of people can get the better of the police, their cars, equipment, cameras. All we have to do is to start acting like our friends, neighbors, and our own lives are at stake. All other options have been exhausted. We have to pull down the new fascism before it consolidates control. If we settle for waving signs and chanting, our fate is sealed. If we remember the summer of 2020, we stand a fighting chance. Mahmoud Khalil. Learning from Experience Mahmoud Khalil is not the first person in recent history to be targeted by ICE for political activism. To get more perspective, we reached out to anarchists in San Antonio whose comrade was kidnapped during the Occupy ICE movement in 2018. This isn’t the first time that something like this has happened. In 2018, ICE targeted a filmmaker and student for their participation in the Occupy ICE camp in San Antonio. They were targeted as a consequence of their activism; the authorities used their political beliefs and tweets as evidence against them. Both our movement and the campaign to free our friend were held back by our decision to defer to the lawyers. The lawyers wanted to run a PR campaign based on respectability politics and innocence narratives, erasing our radical politics from the conversation. As time went on, the lawyers related with hostility and suspicion towards some participants in the movement. Deferring to the lawyers and separating the legal support from the movement itself was detrimental to both. We gave up many tools that we could have used to fight; this contributed to fragmenting our movement. There was no rally, no day of action, no unrest, no political scandal. Not even a phone zap! In 2018, we were aware of the example of the Northwest Detention Center resistance, at which ICE detained the activist Maru Villaplanado. Maru Villaplanado was ultimately released and granted legal status due to a campaign of pressure and mobilization. Unfortunately, this knowledge did not lead us to take the kind of action that could have made a difference for our friend. Many of us were young and inexperienced. We did not know better than to trust the lawyers. We didn’t know how to draw on the experience of other movements before us or around the country. Since then, we have learned that lawyers should have a very limited influence on our movements. They should focus on their work in the courts. We must prioritize organizing a strong political response, as that is the only real source of power and pressure that we can draw upon outside the legal system. There is no silver bullet or magic combination of tactics that would be guaranteed to stop Mahmoud’s deportation. However, if we limit ourselves to depending upon a legal system that has no regard for the humanity of its captives while the state targets an activist on explicitly political grounds, we will fail while simultaneously sabotaging ourselves. We wonder how differently things might have gone if we had called for national days of action. We wonder if there was some chance that we could have stopped them from deporting our friend. We don’t know the answer because we didn’t try. To have any chance of saving Mahmoud Khalil or any of the millions of immigrants in the crosshairs of the white supremacist state, we will need movements that are resilient, that grow in numbers and combativeness. Palestinian, immigrant, Black, Indigenous, and working-class organization and action must create a political crisis that interrupts the deportation machine. If we lead with an organized political response, we will have a better chance of stopping the deportation of Mahmoud and our other comrades and of interrupting the entire system it relies on. I hope that everyone who is confronting this tragedy today can learn something from our experience and put those lessons into practice. This is not the first time this has happened. If our enemies have their way, it won’t be the last. It is up to us to organize in defense of our friends, families, and neighbors. -Some Cicadas from Abolish ICE, San Antonio, Texas We Are Made for Each Other Let us conclude by expressing gratitude for the courage of Mahmoud Khalil and others who have risked their own freedom in order to express solidarity with other people. In doing so, they show us what is best in humanity—and that gives us a reason to fight for ourselves and each other. Khalil has already distinguished himself in the fight to create a world without ethnic cleansing or genocide. It remains for us to do the same in return. For everyone who has met Mahmoud, they can attest to his incredible character, humbleness, selflessness, and his love for helping others. He is always willing to stand up for the oppressed. He is funny, kind, and sometimes a little messy. He constantly puts his needs last when it comes to helping others. I always tell him that sometimes he needs to put himself first. He always responds with, “People are made for each other, and you should always be willing to lend a helping hand.” -Mahmoud Khalil’s wife (identified thus, rather than by name, in the original source) There is a fundraiser for Mahmoud Khalil here. The Palestine solidarity movement on Columbia campus in spring 2024.

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