Below are the 20 most recent journal entries recorded in ACW's LiveJournal:

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Saturday, January 19th, 2008
3:29 pm	Waiting for Venus again The planet Venus splits its time almost evenly between being our Morning Star and our Evening Star. I prefer evenings to mornings for my skywatching, so the Evening Star is definitely my preferred role for Venus. Since last August Venus has been hanging out in the pre-dawn sky, where I have seen it on one or two occasions, but I'm waiting impatiently for its next entrance into the evening sky, and this morning I actually went to the trouble of figuring out how long I have yet to wait. I used some numbers from Jean Meeus's incomparable Astronomical Algorithms. When Venus passes the sun on its way from the morning sky to the evening sky, the moment of passage is called the superior conjunction. Superior conjunctions are spaced at an average of a couple of hours short of 584 days; the exact number in Meeus is 583.921 days. The actual moment of any given conjunction might vary as much as two or three days from this ideal moment; it's affected by exactly where the Earth and Venus are in their elliptical orbits, and other minor influences. But the mean conjuction was close enough for me. Meeus gives the exact time of the first superior conjunction after 2000 January 1, and repeatedly adding 583.921 to that conjunction gives the answer, which is around 2008 June 6. It'll be very hard to spot Venus for a couple of weeks after that, it'll be so close to the sun, but then it will become visible very shortly after sunset, setting a few minutes after the sun, and a bit later every evening, until we have a nice couple of hours for admiring it. Then it will crawl back toward the sun, vanishing into the morning sky again around 2009 February 20. (Comment on this)
Monday, January 14th, 2008
9:15 pm	Lotsa J's In a fit of ennui this evening, I spent perhaps half an hour seeing how many Google hits there were for the strings "J", "JJ", "JJJ", "JJJJ", and so on, getting up to about 60 J's before running out of patience and off the bottom of my log-scale graph paper. From about 15 J's onward, the Google frequency of the strings declines by about 8% for each additional J. It's as if, when you are sitting there typing a long string of J's and you don't really care how long it is, each keystroke has an eight per cent chance of being the one on which you say, "Oh, the heck with it, that's enough J's.". Or maybe everybody is rolling D-12's, which provide an easy way to generate 8-and-a-third per cent chances. Of course I don't think anybody is doing this consciously. For certain magic numbers of J's, the frequency is far greater than this rough exponential decline would predict. Strings of 25 J's appear about three hundred times too often; strings of 50 J's are three thousand times more likely than the 8% model predicts. I was more surprised to see an thousandfold spike at 33 J's, until I realized that it was as close as one may come to a third of 100. So there seem to be spikes at numbers that are even fractions of 100, probably because Google is picking up fragments of ASCII graphics that are drawn in 100-column spaces. There are fewer occurrences than expected of runs of 6, 7, and 12 J's. I have no idea why this should be. Below about 10 J's, the frequency curve sweeps up sharply, because small numbers are special, so there. There are obvious extensions to this research: try other letters, or strings of the form "awwwwww", "kawaiiiiii", and so on. (4 Comments |Comment on this)
Wednesday, January 9th, 2008
2:59 pm	Sick, for a change In the last year or so I've been lucky enough to be very healthy, dodging virus after virus as they hit coworkers and family members. But my luck finally ran out. On Sunday afternoon I felt a little scratching in my throat. It wasn't bad enough to keep me from going treadmilling at the gym on Monday. On Tuesday I was a little worse but eventually made up my mind to go in to work. Today (Wednesday) it's pretty unpleasant. I can feel laryngitis closing in, and suspect that I'll be out of work for today and tomorrow. It's not really worth blogging about, except that I wanted to record when the cold started, in case I get postviral bronchitis, and so I can quantify whether I'm really resisting viruses better than I used. Also, I haven't written anything here for a month, so I figured I might as well. Current Mood: sick (1 Comment |Comment on this)
Tuesday, November 27th, 2007
5:11 pm	The Magic the Gathering stress shift The good people at Language Log have been musing, in a series of interesting posts, over the pronunciation of the word "thanksgiving". In a lot of the United States the word is stressed on the second syllable, so we say "thanksGIVing", but common patterns of English stress would lead one to expect "THANKSgiving" (compare "GIFT-giving", "GRIEF-giving", "SHIT-kicking", and so on). This reminded me of something I've been meaning to post about, and since Google searches for +"magic the gathering" +"stress shift" come up empty, I think I may be the first to discuss this obscure topic, about a strange feature of the argot of certain gamers. My son is a moderately accomplished player of the card game, "Magic: the Gathering". In this game, players assemble decks of cards which they pit against each other in fantasy-themed duels. The individual cards each (potentially) provide the player with some specific ability. The game has some framework rules about the order of play and how to resolve certain kinds of ambiguity, but most of the rules of the game are written on the cards themselves. Let me present one example of a card, stolen from the Wikipedia article about Magic: Lord of the Pit (4BBB) Summon Demon Flying, trample During your upkeep, sacrifice a creature other than Lord of the Pit. If you cannot, Lord of the Pit deals 7 damage to you. 7/7 You don't need to know much about the game to understand what I'm going to talk about. At the top of the card is the card's name, and then follows a terse but complete description in Magic technical jargon of how the card must be played and what advantages and disadvantages it confers on the player. But I want to focus on the name. In ordinary English, the name Lord of the Pit would be pronounced with primary stress on the word pit. Ignoring the secondary stress on the word lord, we can write the stress pattern as "lord of the PIT". But the Magic players I have met would never pronounce the name that way. Instead, any phrase that is used as the name of a card undergoes a striking shift of stress, with primary stress falling invariably on the first word; it sounds like "LORD-of-the-pit". The same stress-shift rule applies to almost all cards with multiword names: "REACH-through-mists", "BLACK-lotus", and so on. In ordinary English, stress placement on a phrase often influences meaning. For example, a "goblin ASSASSIN" is an assassin who happens to be a goblin, while a "GOBLIN assassin" is an assassin whose victims are goblins. And even though the Magic card Goblin Assassin represents the former meaning, the name is always given the latter stress. This kind of stress shift often signals lexicalization, the process by which a phrase turns into the equivalent of a single word. An ordinary house painted white is always a "white HOUSE", but the (lexicalized) American Executive Mansion is the "WHITE house". The epithet "SON-of-a-bitch" is the lexicalized version of a phrase more naturally pronounced "son of a BITCH". I suspect that the Magic stress shift also represents lexicalization: the players are purposely ignoring the original meanings of the phrases that name their cards, and turning their names into "words" in their own right. (Comment on this)
4:56 pm	Unintuitive reversible double-knits A few knitters are among the brave souls on my friends list; you folks should take a look at the work of this guy. He's a friend of Dr. Wife's, so I've met him a few times, but I'll withhold his name since he seems to be trying to be anonymous on his (anti)blog. Look closely at the reversible double-knits, and take the time to click on the links to detailed photo links. The two sides differ in ways that are not possible in traditional double-knitting; sometimes he manages to put two completely different patterns on the two sides. (4 Comments |Comment on this)
Monday, November 26th, 2007
9:53 pm	The impossible chord My semianonymous reader "GK" sent me, by the agency of the United States Postal Service, no less, a photocopy of a page of piano music together with a fingering question. I responded within 24 hours, because GK had taken the precaution of including a stamped, self-addressed envelope. It would have been churlishness of historic proportions not to reply promptly. Nonetheless, GK will probably read this before my letter arrives at the chateau. That sort of ruins the fun of corresponding in ink, but on the other hand, I can hardly ignore such juicy blog material. GK is in the process of renewing an acquaintance with the piano that I believe had lapsed for something approaching two decades. I approve of the choices of Bach's first and second two-part inventions. About twenty years ago, when I was approaching the piano, warily, for the first time, I chose them too. For my third piece I wanted something a little harder, so I turned to Scott Joplin's Maple Leaf Rag. It took me several months, but I eventually limped through it. I can still play most of it. GK, like me, decided that ragtime would make an excellent counterpoise to Bach. But I would not have chosen William Bolcom's Graceful Ghost Rag. First of all, the damned thing has five flats. That's way out in the key-signature boonies, out where they are running out of notes to flatten, so they have to resort to putting flat-marks in front of D and G. That's right: the black key that normally plays the familiar role of F sharp is suddenly pressed into service as G flat. Is that any way to treat a defenseless piece of ebony? And then there's the Chord From Hell. It's the very first stroke for the right hand in the first serious measure of the piece (preceded only by a pickup note and one measure of fairly innocent oom-pahs). And then, bam instant carpal tunnel syndrome. Mostly, the chord in question is just a high C and a high-high C played in unison, an octave. Anybody can play an octave with their outstretched thumb and pinky; it feels a little uncomfortable for a couple of weeks when you start piano, but almost all of the piano repertoire depends on the typical human hand being able to span an octave in reasonable comfort. If you want to know what it feels like, find a desktop computer keyboard. Put your right thumb on the Q key and your right pinky on the P. That's about how wide you have to spread to play an octave. (A laptop keyboard is a bit smaller, so maybe you have to stretch to the right square-bracket to get that octavy stretch.) So, two C's an octave apart? Piece of cake. Too easy. So Bolcom threw in a D-flat. Now, playing C-D-flat-C is about like hitting Q and P with your thumb and pinky while hitting the number 2 with your index finger. Now, if your hand is anything like mine, your index finger is somewhere above the 6 when you are straddling the Q and P keys, and you can maybe squinch it over to hit the 4 if you don't mind a little pain. The 3 is impossible, and the 2 is really impossible; you'd have to have your hand surgically altered to manage it. It's that stupid opposable thumb or something. Sometimes, such things are possible by a trick. If you look at the score, you might find that the left hand is conveniently close, and has a spare finger to lend to the treble, quick, while nobody's looking. In the case of the chord in the Graceful Ghost, alas, the left hand is off in Patagonia, an octave and a half to the left of the action. No finger can be spared. Short of the timely deployment of a nose, I can think of only one thing Bolcom might have had in mind: that the thumb should play both the C and the D-flat, by sort of mashing down on the crack between the two keys. This would be easier if the two keys in question were adjacent white keys, like B and C. C and D-flat is doable, barely, by sort of pressing the thumb against the side of the D-flat key and dragging it down by a judicious combination of friction and prayer. I actually managed it four or five times, each time with elaborate care and preparation. Of course, in the sheet music, said chord is a sprightly sixteenth-note in length, and Bolcom cheerily advises "Don't drag". Right. Having put in all the effort, it pains me to report that said chord actually sounds like a monkey-fart. The D-flat is a mere sound-effect, intended to make the chord sound out-of-tune and honky-tonky. To my knowledge the chord has no technical name, at least none suitable for polite society. I look forward to hearing GK's assault on this rag, and express my fond hope that no hospitalization will be required afterward. (6 Comments |Comment on this)
Sunday, November 25th, 2007
11:01 pm	Constitutional Law Sometime near the end of September or the beginning of October I took my daughter to an introductory fencing lesson at the Boston Fencing Club in Waltham. While I was cooling my heels during the class, I scrounged their bookshelf for reading material, and was surprised to find a constitutional law textbook, Constitutional Law: themes for the Constitution's third century, by Daniel Farber, William Eskridge, and Philip Frickey. It's one of those huge honking casebooks that you sometimes see law student poring through, highlighting every other line. I've never really looked inside a law textbook, and have always assumed that they would be unreadably arcane without the introduction to basic concepts and terminology that law students get in their first year. But as I leafed through the introduction, I found it to be quite clearly written, with the various issues laid out quite clearly and engagingly. There was, indeed, the occasional technical word or phrase, but the meaning was almost always clear from concept. (It help that I know a little bit of Latin.) I've gradually been getting interested in law in general, and constitutional law in particular, from listening to Nina Totenberg's reports on the Supreme Court on NPR. And I'm interested in civil liberties, and in particular in the whole issue of religious encroachment into the public school curriculum, especially in evolutionary biology but also in sex education. So reading these introductory pages got me thinking that maybe I could actually educate myself about some of these issues. Over the following few weeks I checked nearby libraries for a copy of the book, and was unable to find one. Used bookstores don't seem to carry them either. While I was looking for a copy, I checked out Akhil Reed Amar's The American Constitution: a biography, which I finished on October 21. Some time in the next week I got up my courage and asked the people at the fencing club if I could borrow their copy. "Oh, that," said the guy. "You can just have it." I left a note for the person we thought was the original owner, somebody named Sandy, so he or she could get the book back if they wanted it. And since then, that's been my commuting reading. I'm about 250 pages in now. Sometimes it gets hard to follow, but the overall thread is very clear, and it's fascinating to read excerpts from famous historic decisions. The book starts out with a chapter on the history of American constitutional jurisprudence; the second chapter uses Brown v. Board of Education to sketch in the major styles of constitutional reasoning. The third, which I'm in the middle of, branches out into the general topic of race discrimination and how it's been adjudicated since Brown. So far I've really been enjoying this expedition into a realm of knowledge that has really only been a vague outline to me up until now. (9 Comments |Comment on this)
Saturday, September 1st, 2007
5:38 pm	Thirty-eighth run of 2007 On July 9 and again this morning I set new personal bests, of 25 laps in 62 minutes even and 61:27, respectively. This morning it was quite lovely out. I suspect my slow improvement is partly just ordinary athletic plateauing, and partly due to hot weather. I'll be curious to see whether I improve more as we get into cooler weather. I have not yet regaled you with a report on Liberty Field grafitti by the Watertown High class of 2007. The motto on the backboard behind the bleachers reads, "A PERFECT END TO A NEW BEGINNING". Apparently there is a song with a similar title by a group called Jonny Unite Us; I might have that garbled but I was reluctant to do serious research. One of the Watertown High sports teams spray-painted the motto "WHY CAN'T WE GET PAPAG" on the doors of their field locker. I would have guessed that it originally said "WHY CAN'T WE GET ALONG" and was then modified, but I don't have any actual evidence of this, not having examined the locker up close. Watertown has a big Armenian population (and is home to an Armenian cultural-heritage museum), so I'd assume they have a team member or something named Papagian. Watch out, Papagian. ETA: I misremembered both graffiti. On the backboard the seniors wrote "THE PERFECT END FOR A NEW BEGINNING"; and the athletes wrote "WHY CAN'T WE ALL GET PAPAG". (Comment on this)
Monday, July 23rd, 2007
9:04 am	Twenty-first run of 2007 In overcast, coolish weather, I beat my previous best run, which was only two days ago. 25 laps in 62:16. (1 Comment |Comment on this)
Saturday, July 21st, 2007
12:08 pm	Twentieth run of 2007 After my fourth run, on 2007 May 5, I found my left hip hurting in a way that concerned me, so I stopped running, waiting for it to stop hurting. I waited for three weeks before it got enough better to reassure me, and then I started doing little runs, both on the treadmill and at the track, to see whether it made it better or worse. It seemed to make no difference at all, so I ramped slowly up to my former running-times, and the hip seemed to keep getting better slowly. It didn't seem to care whether I ran or not, so I figured I might as well run. But the hiatus knocked my performance way back, and I just haven't felt up to blogging about it. I've still been running regularly, just not announcing every run. I told myself that when I recovered to my former level I would start blogging about it again. So this morning, by setting a new personal best, I officially reached my former level. I ran 24 laps in 60:11. There was one guy, around my age I think, who was running just ahead of me for about two or three miles; I would pass him, and he would spur himself and pass me, and that happened about three times until I was getting tired enough that to pace him would force me above my maximum heart-rate. (Comment on this)
Thursday, June 21st, 2007
9:40 pm	Three domestic dreams When I have dreams in a domestic setting, that is, dreams that happen in a place that is supposed to be my home, the actual setting is rarely (maybe never, I can't be sure) the house near Boston that I have lived in for about sixteen years. Instead, such dreams are always set in some version of the house near Detroit where I spent my first fifteen years, as well as my seventeenth ... for a total of sixteen years. The Massachusetts house is equal to the Michigan one in longevity. But the Michigan house is grandfathered into my neural network, apparently, the permanent associand of the concept "home". This morning I had three such dreams, all of which I remembered. 1. Son in trouble. My 19-year-old son was entrusted with a key of some sort, which he was supposed to return to me. He may or may not still have it. We argue about it in the (Michigan, of course) kitchen: "Do you have it?" He's evasive. It turns out he was hanging out with some other kids, and they got into some sort of trouble involving an abandoned house. He saw something there, a stain of some sort on the floor, perhaps, and it freaked him out, and now he doesn't even want to think about the key until this business with the creepy stain is sorted out. In the middle of the heated discussion, the front doorbell rings. A neighbor from across the street has come over to chew us out. My son involved their daughter in that (presumably something about the abandoned house), and he is not to see her any more. I wake up before I can deliver the obvious retort: why aren't you talking to my son about this? Or better yet, your daughter? Because who he sees is his business, and hers. The neighbor and the abandoned house are all dream-stuff, as is our living in the Michigan house as if it were our family home. I had a bit of trouble getting back to sleep. It was about 5:45 am. The beginnings of my riposte to the stupid neighbor I must have uttered out loud, because my wife asked if I'd had a bad dream. "No, just a dramatic one," I said. 2. Crocheted pet horse. The action moves across the front of the Michigan house, from the kitchen and front door into the living room. I'm lounging on the living-room couch, which in the dream is an odd piece of furniture whose seat is about four or five feet above the floor. There is an odd creature standing on the carpet next to the couch, close enough for me to stroke. It is a pet miniature horse which belongs to my daughter, which we acquired recently. It's a dear thing, about three or four feet tall, so I have to lie on my side on the couch and reach down to stroke it. Instead of hair, it seems to have a crocheted coat, all very beautifully worked, as if it were a giant crocheted stuffed horse come to life. I notice that it is wearing many necklaces of cheap beads, as if it had been at Mardi Gras or something. "Where did you get these?" I ask it. "S. came to visit," replies the horse. It's a magic horse; of course it can speak. S. is a real-life friend of ours. "She gave them to me." "Ohh," I say, because this would be completely characteristic of S. "S. really loves you, doesn't she?" "Oh, yes," says the horse. This too would be completely characteristic: S. would kvell over a magic pet horse. I remember, oddly, that I knew that the horse was housebroken, but I don't remember what "arrangements" we had for it. It develops that S. has her own opinions about the horse's name, which differ from our opinions, though I don't remember any of the candidate names. I'm slowly untangling and removing the necklaces from the precious thing, and explaining to it that its name is really X, not Y, when I wake up. This time I have no trouble getting back to sleep. 3. Mom's piano lessons. Now the action retreats toward the den. I'm walking out of the living room into the den when I see my mother standing in the door to her bedroom. I can't see very well, because my glasses have broken: the nose bridge is cracked and I can't center the lenses over my eyes. But I think that my mom is naked, or almost so. I don't think anything of this; I know that she is ailing and spends most of her time in bed, so if she doesn't want to bother hauling her clothes on, that's OK. I make some comment to this effect, and she answers in a slightly confused fashion, as if she doesn't realize that she isn't wearing anything. That's all right too: she's not as lucid as she once was. I sit down at the piano, and I realize that my parents have gotten a new one to replace the ancient Steinway mini-grand. This one is a lovely modern thing, with an avant-garde design; the keyboard is not straight, but curves out and back in a sort of bell shape, the middle octave protruding about a foot. I remember that the idea was that it was supposed to be ergonomic, but in real life it would probably be unplayable. I remember looking at the weird shapes they'd had to make the keys in order for them to fit around the curve of the keyboard. I start to think about picking out a tune, and I remember the particular tune: it's MacArthur Road, a pretty reel in the unusual key of E major. I get confused about the key. E major, or E-flat major? I could swear it has an F natural in it. (In real life it has an F-sharp.) A particular piano arrangement comes to mind (much more clearly than I could imagine such a thing in real life), but the actual execution is beyond my poor piano skills. I start trying to pick it out anyway. The notes I play in the dream are wrong in real life: the actual tune starts with B, G-sharp, while in the dream it starts E, B. My mom sits down next to me and starts to tell me a story about a piano class she went to when she was a kid in Jerusalem. "There were twelve students and six pianos, so we had to sit two at a piano. I sat with another girl, and I liked her a lot, but I was very clumsy at the piano and I kept bumping her with my elbow. After the class I wanted to tell her that I was sorry, so I went up to her and just hugged her." "Oh, Mom," I said, "I bet she didn't take that very well." "No," said my mom, laughing, "she ran away. I chased after her to try to explain, but..." We laugh about this for a little while, and then she turns to me and says, a little accusingly, "Why don't I ever get to see your friends any more? You never bring them home." At this point, after struggling for a moment with confusing layers of reality and dream, I remember the real reason. Mom isn't just ailing. "Mom," I say gently, "don't you remember? You died." I'm not sure if I realized at this point that it was a dream, but for whatever reason, I accepted that I was able to meet my mom occasionally, but it was clearly impossible to bring anyone else with me. She seems even more confused by the layers than I am, and is silent, re-realizing that she is dead now. I want to ask her if she gets to meet anyone else ... somehow I had thought that she would have the company of other dead people, but now I realize that this is perhaps not true. But my mother is very confused now, and I can't ask the question clearly. Instead, I wake up. (In real life my beliefs about the afterlife are not anywhere near so simple, and I certainly have no belief that we can communicate with the dead in dreams.) (Comment on this)
Sunday, June 10th, 2007
10:33 pm	Chapter 34 On April 1, I wrote about 1100 words of the beginning of Chapter 34, and today I finally convinced myself to finish the chapter. I really have some sort of psychological block about it, and I have to get over it. I think I know what it is, but I don't feel like explaining it all to you guys now; next time I'll try to get my thoughts in order and psychoanalyze myself, in case anybody's interested. Anyway, Chapter 34 has 1,947 words, and the total is now 60,810. Edgar Rice Burroughs's A Princess of Mars is about 66,000 words long, and though it is a short novel it is not pathologically short, so I think I am definitely approaching respectable novel length. If only I manage to keep writing. (1 Comment |Comment on this)
Saturday, May 12th, 2007
12:10 pm	11 nodes, and an example of proof technique Yesterday I thought I had settled the case of 11 nodes, and I thought I'd describe how I went about it to satisfy jokermage's request for my proof technique. It is quite simple, but a bit tedious. ( The gory details ) (4 Comments |Comment on this)
Friday, May 11th, 2007
10:28 am	9 and 10 nodes This morning on the bus to work, I settled the cases for 9 and 10 nodes. Only a little diligence was required to show that 14 links could not be placed among 9 nodes without creating a square. It took a little longer to settle the case of 10 nodes. I had an example with 15 links: the pentagon adorned with five triangular "ears". This looks just like the classic five-pointed star, or pentagram. And I had shown that one could not put more than 17 links. This left the possibility that examples existed with 16 or 17 links. It was easy to eliminate 17. I thought it would be easy to eliminate 16 too. But instead (drumroll) I found an example with 16 links! I was very surprised. I can't draw pretty pictures like jokermage, but I can describe the arrangement so you can draw it. We know we can put 6 links on 5 nodes, in the "bowtie" arrangement. Do this twice, so that you have two bowties; this accounts for 12 links. Now, sew together the two bowties by connecting the outer corners. This can be done in two ways; one is obviously wrong (it creates squares), but the other works! Another way to describe this configuration: Create an octagon of 8 nodes and 8 links. Number the nodes clockwise from 1 to 8. Now we add two more nodes. One is connected to octagon nodes 1, 2, 5, and 6; the other hooks up to the remaining octagon nodes, which are 3, 4, 7, and 8. It's quite pretty! So here are my results so far: Number of nodes Maximum number of links 1 0 2 1 3 3 4 4 5 6 6 7 7 9 8 11 9 13 10 16 (3 Comments |Comment on this)
8:05 am	7 and 8 nodes I posted a couple of days ago about the following problem: establish as many links as possible among a given collection of nodes, subject to the constraint that no four nodes are linked in a "square". At that time I knew that for 1, 2, 3, 4, 5, and 6 nodes, the maximum number of links was, respectively, 0, 1, 3, 4, 6, 7. For 7 nodes I knew I could get 9 links, but thought I might be able to get 10. For 8 nodes, I knew I could get 11 but thought 12 might be possible. Since that post, I have shown that 9 and 11 are in fact the best that can be done. Number of nodes Number of links Example known Proven limit 1 0 2 1 3 3 4 4 5 6 6 7 7 9 8 11 9 13 14 10 15 17 At this point, I expect that for 9 and 10 nodes, 13 and 15 respectively are the best possible, but I have only proven that I can't do better than 14 and 17 respectively. (2 Comments |Comment on this)
Thursday, May 10th, 2007
7:06 am	Browser annoyance du jour I use FireFox as my usual Web browser. Now, I am a little more mouse-averse than most computer geeks, preferring to keep both hands on the keyboard. So when I want to scroll the browser, I usually use the Page Up/Page Down keys (when reading long texts). But sometimes I want to scroll more smoothly, so I use the up and down arrow keys. Rather than tap-tap-tap, I hold the key down to make it auto-repeat, as the content rolls by. But when an inline YouTube video happens to roll under the mouse, the arrow keys stop working. Somehow, the YouTube content steals the usual functionality of the arrow keys. I have no idea what, if anything, YouTube expects me to use the arrow keys for. I do know that it is impolite to suddenly disrupt the user interface of the containing application (my browser) when I have made no overt selection gesture that might license such a power-grab. To resolve the problem I have to take my hand off the keyboard and roll the pointer off the YouTube content; then the arrow keys take up their normal function again. I blame this entirely on FireFox. It should never delegate UI functions to web content without a specific, overt gesture of selection from the user. This is a special case of a much more pervasive problem, where browsers are much too ready to hand off user-interface events to arbitrary, unvetted chunks of JavaScript code that have come in from god knows where. The fact that I loaded your web page is not sufficient license for usurping the normal function of my console. (Comment on this)
Wednesday, May 9th, 2007
10:22 pm	A math problem that I've been falling asleep to I've been making myself drowsy in the evenings with a problem in graph theory. I haven't done any research on it, so it's quite possible that the solution is well-known. If you know the answer, don't tell me! I want to work on it myself for a while. Suppose you have a crowd of people, let's say 41 of them, just to pick a number at random. Among these 41 people, some pairs are friends, and some pairs aren't. We are interested, for this problem, in the number of pairs who are friends. In principle, among 41 people, there could be anywhere between zero pairs of friends (if they are all antisocial) and 820 pairs (if everybody likes everybody else). (Why 820? Well, if each of the 41 people liked all of the 40 others, that would be 41 times 40, or 1640 "likings". Each friendship pair accounts for two "likings", so there must be 820 pairs.) But now, we throw in a constraint. Let's suppose we happen to know that in the whole crowd, there is no clique of three people who all like each other. In other words, if Fred is friends with both Pam and Ivan, then we know that Pam and Ivan are not friends. The question is: what is the highest possible number of friendship pairs that can exist in this crowd, subject to the constraint that no three people are mutual friends? Now, I must confess that this problem is not the one that I think about at night. The problem I just sketched is a simpler version, and one that I happen to already know the answer to. I was thinking about it a few days ago, though, and I realized that there is a closely-related problem that I've never seen discussed. Suppose that we don't forbid mutually-friendly trios. Instead, we forbid cycles of length four. Please forgive the jargon. I mean, if Pam and Fred are friends, and so are Fred and Ivan, and so are Ivan and Chris, than we may be assured that Pam and Chris are not friends. We have relaxed the "triangle" constraint, and substituted a "rectangle" constraint instead. For the "triangle", problem, I know a rule for producing a maximally-friendly crowd (highest possible number of friendships) for any size crowd, and I can prove that the rule is correct. For the "quadrilateral" problem, however, I know the answer for sure only up to about seven people. For eight people, I know how to pack in eleven friendships, but I am not certain that I can't squeeze in a twelfth and still avoid the forbidden four-sided cycle of friendships. Perhaps I will be able to come up with a rule and prove it correct. I would love my readers to speculate about the problem in the comments. But please, if you already know the answer, don't spoil my fun. (Yes, I know where to look in Mathematical Reviews to see if anyone has worked on this.) By the way, for the forbidden-triangle problem, with 41 people the answer is that the maximum is 420 friendships. See if you can figure out the rule for arbitrary-sized crowds. (8 Comments |Comment on this)
Saturday, May 5th, 2007
5:07 pm	Fourth run of 2007 24 laps in 60:55, for a new second best. Geez, I could do this with Twitter. I should come up with something more interesting to post about. (2 Comments |Comment on this)
Saturday, April 28th, 2007
1:39 pm	Third run of 2007 24 laps in 61:27, a minute or so slower than last week. It was fine weather. The soccer kids were screaming and having a blast on Liberty Field. An ice cream truck played the A part of "Turkey in the Straw" incessantly. I had some stiffness in my abs and left glute. I should record that sort of thing more often, so I can see if it moves around between muscle groups or if I have perennial problems with the same ones. (Comment on this)
Monday, April 23rd, 2007
9:13 am	Second run of 2007 Today felt like a much more respectable effort; the heart monitor didn't zone out as much, and I ran at a consistent pace. And now the winter's work really shows: 24 laps in 60:20. This is my best track performance for as long as I've been keeping records. The track miles must be longer than the treadmill miles, but not by all that much. 24 laps is presumably 6 miles, and I've been doing 6.8 or better on the treadmill. Perhaps it's the innermost lane that is exactly a quarter mile, and my extra 12% is due to the fact that I run in lane 4, which I've regarded as "my lane" since I started running at Bartley Track. I only have to shave off another twenty seconds to reach my next milestone of 24 laps in less than an hour. (1 Comment |Comment on this)