Below are the 20 most recent journal entries recorded in Harry/Sniffnoy/Steve's LiveJournal:

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Saturday, November 21st, 2009
9:02 pm	Crazy combinatorial fact of the day Apparently, the number of plane partitions of n, PL(n), is equal to the number of ways of partitioning n where there are k "types" of size k. (I.e. the number of nonnegative integer solutions to x1+2x2,1+2x2,2+3x3,1+3x3,2+3x3,3+...+nxn,n=n.) Looking around a bit, I get the impression that no bijective proof of this is even currently known[0], and that this is known because McMahon proved (back nearly 100 years ago!), by rather more complicated means, that generating function for PL(n) which you can find on Wikipedia, which is pretty easy to see is the generating function for the latter sequence. This came up because I was thinking, what's the number of functions from an n-set to itself, up to permutation of the set? And it's pretty easy to see it's the latter sequence (think how number of conjugacy classes in S_n is number of partitions of n, only now instead of just cycles, you have cycles with tails). And I decide to look this up on Sloane to see if there's any nice way to write it (thinking, probably not, it's even more complicated than the partition function), and apparently this is also equal to the number of plane partitions of n. Crazy. -Harry [0]Obviously I could be very wrong about this! (Comment on this)
Friday, November 20th, 2009
3:17 am	Push your skill Take a look at this Flash game, Tower of Greed. It's a very simple design, but it's interesting. Idea is as follows: Make your way up the Tower of Greed, collect as much stuff as you can; every 5 floors there's an exit, which will end the game. But if you don't take an exit, and instead the game ends by you dying, your final score is 0 (and you get none of the in-game "trophies", and on Kongregate you'll earn no badges or cards - naturally I was at first playing it to get a second Blood Vial). So, it's just the well-known push-your-luck mechanic, except that it's not so much a game of chance. The result is that the game is very addicting. Probability says you'll screw up and die eventually - but it's not primarily a game of chance, so you feel in control, and almost always want to push further, even though this is clearly frequently wrong. This is such a simple idea that I'm sure this must have been done before, but I don't think I'd previously seen it. -Harry (Comment on this)
Tuesday, November 17th, 2009
9:35 pm	Duality failure Something from earlier I forgot to mention: So in Lie algebras we were doing classification of root systems, and of course Stembridge points out how B_n and C_n are dual to each other. He also notes how these are the root systems of o(2n+1) and sp(2n), respectively. And so Nic asks if this yields any sort of duality between o(2n+1) and sp(2n). And Stembridge says no, he doesn't know of any. That's... really disappointing. I suppose if there were such, you would also expect some sort of self-duality for the other simple Lie algebras, though I suppose it might only be nontrivial for F_4 and G_2. But seeing as apparently this doesn't work, well, uh, that's just really disappointing. I know Stembridge has said later we'll show how you can use root system information to get generators and relations - I'm surprised that doesn't yield any sort of obvious relation there, but of course I haven't yet seen how it's done. -Harry (1 Comment |Comment on this)
Saturday, November 14th, 2009
1:38 am	And the color axes don't expand why? Saw this over at Gödel's Lost Letter and P=NP: Put up just a few days ago, a claimed proof of the four-color theorem and some related stuff, no computer necessary. Anyway I figured I'd try to read through it - it's a bit hard because the author's English isn't very good - in particular, he gets articles and other determiners wrong, as well as the singular/plural distinction - which means he'll do things like say "the [something]" instead of "any [something]", which is a bit confusing; also there are typos, and at one point writing what appears to be an equality of polynomials in t, but is in fact just an equality at t=4... and his references are often to the wrong or nonexistent lemmas (did he type those in directly rather than doing it properly in TeX)? So it's a bit confusing but if you keep this in mind it's readable. Anyway I started reading through it, and I have to say, I'm totally lost at the inductive step of Theorem 4.5. The proof doesn't seem to make any sense. OK, fine, you can make the graph G_1 and all's well... and you can make G_2, and it'll be k-colorable... but, it is not at all obvious that the color axes don't expand at this step! We can connect u to V'_{m+1} while maintaining k-colorability, because the fact that u is in V^c means that there's some k-coloring that doesn't color it m+1... but it's not at all clear that it's impossible that, say, every k-coloring colors it m+1 or m+2. In which case, once you make that connection, u is not in the new graph's V^c, and you've got a problem on your hands. I thought maybe the proof would basically go through anyway, but once he got to the part with k+1-colorings, it seemed to just stop making any sense - because, well, a k+1-coloring isn't a k-coloring, so why would it obey any of the stuff we've said about k-colorings? And why would u be an axis by itself? Etc... the proof really seems to use that the color axes don't expand... do you suppose it could be fixed with some sort of strong induction? So, yeah, this doesn't make any sense to me. -Harry (3 Comments |Comment on this)
Friday, November 13th, 2009
12:01 am	Playing it by bladed-boomerang-thingy I think I'm going to start switching off between Marquis and Anex, and see which I do better with. I've definitely gotten over my "oh crap how do I play this again" phase, seeing as how in the past 2 days I've played a game with Anex and won, won a game with one of my crazy counterpick[0] decks - Ubuntu with Mask (starting), Helene with Charm, Rumiko with Scroll - and played one more game with Anex and didn't die too horribly. I'm now nearly rank 27. I have to say I don't really understand how to use Anex in general - in particular, when do I want to cast Enchant Blade? None of the characters I played before can cast buffs! But this didn't stop me from winning that first game with her with a trick where I switched her in, used Chakra Slash, switched Higashi in, and won with an Open Palm that would otherwise have been too slow. And the game I played with that counterpick deck - I made like 3 intercepts with Ubuntu! Guess he's just too annoying, huh? Of course, it helps that he was playing Corny and Helene. But evidently I figured out Ubuntu quick enough to be able make predictions with him. Also, that first game I played with Anex had a funny opening. Consider this and see if you can understand why it occurred. (OK, this shouldn't be hard, as after all I'm not an Anex player and of course I understand it.) I open Anex, he opens Corny. Turn 1: I get far, he gets close. I successfully intercept him. Turn 2: We both pass. He successfully intercepts me. -Harry [0]The idea behind these was as follows: I used to just play my Marquis deck, right? So if I ended up playing someone twice in a row, they'd know my deck second game. So I figured, well, as long as there are people out there like me who will play the same deck twice in a row, I may as well make decks to coutnerpick specific characters that give my deck problems - this particular deck was meant as an anti-Vanessa deck. Of course, most people are smarter than to play the same deck twice in a row - this guy wasn't playing Vanessa the second time - but then, the theory goes, at least I'm not playing the same deck twice in a row either. (1 Comment |Comment on this)
Tuesday, November 10th, 2009
10:56 pm	Yes, it is necessary to repeat this Josh repeats to me the following joke: What is a comathematician? A device for turning cotheorems into ffee. Unrelatedly: I'm certainly still not back up to my former level, but I think I've gotten enough of a hang of the game that I may want to soon switch back to Anex from Marquis. Also unrelatedly: The house now has a copy of F-Zero GX! I have yet to play it. -Harry (Comment on this)
Saturday, November 7th, 2009
10:12 pm	How do you kill what's already dead? With mindgames, with Tafari, or in the endgame, that's how. I'd forgotten how much of a mindgame playing against MLM is. (I play MLM, sure, but he's not very common so I don't often play against him.) Kongai is always mindgamish, of course, but when you miss that intercept against MLM you really groan. "Hard to kill" is correct - unless you've got Tafari or it's endgame, you really *have* to mindgame him to kill him. So I was playing Kongai, same deck as usual[0], against a guy who was using Higashi with Totem, Zina with Girdle, and Marquis with Ring. My Higashi is killed early on, after reducing his Higashi and Zina's health to a medium amount. The rest of the game I had to dance between Rumiko and MLM - let me tell you, I got quite lucky with Rumiko managing to dodge 2 intercepts that game - and I managed to do so pretty well. While Rumiko of course kept slowly losing health, being down to a mere 3 by the end of the game, I managed to keep my MLM close to full health - but his MLM wasn't exactly shoddy either. Fortunately with Eviscerate and Ninja-port I was able to reduce his health over time, but I never managed to catch that intercept; I even got him down to one health, thought he would stay in, but nope, now he's back up at 21. Well, after a long slog - of course long, with MLM on both sides - I finally manage to reduce Zina to low enough that a Vampiric Touch would kill her. (OK, maybe her health wasn't so "medium" before. But I had a hard time getting hits on her.) Bring in MLM. Do I Vampiric Touch or intercept? Go with the Touch; if she switches out, I can kill whoever he puts in. (His Higashi was at pretty low health by this point.) It works; he has to put someone else in. And he puts in the Marquis! Oy oy oy... but why would he do that? What advantage could he possibly get by bringing in the Marquis now? I can see only one: INTERCEPT TIME! His Marquis *finally* dies and he concedes. (Though, I figure with a bit of luck he still could have won that... maybe quite a bit of luck... well, I never concede, so I suppose I shouldn't comment on such things.) And as a result, I won a Deadly Poison, of all things! Unrelated things: I have been reading a bit of Less Wrong, even if not actually, you know, attempting to use its suggestions, because that would take work; but it's interesting stuff so I've been reading it. And so when the other day I was to introduce to my class the use of radians for angle measure, I made sure to tell them, that radians may seem like a strange unit; but reality is never strange, so if radians seem strange to us, it is not because radians are strange, but because we are strange. I'm not sure if that had the effect I intended. :) Also news I saw there: The fixing of the LHC has been stalled again (if only for a few days) due to a piece of bread apparently dropped in there by a bird. Also unrelatedly: I finally managed to go to GYGO's game night... only to find nobody there. :-/ "Yeah, we tend to get more people on Thursdays." OK, let's hope I have time to go some Thursday... Also unrelatedly: Filters in general topology. They make sense. Somehow, before today, I never sat down and took an hour to understand them. Now I feel really silly. -Harry [0]That's Marquis with Phylactery, Higashi with Insignia, Rumiko with Scroll. (4 Comments |Comment on this)
Tuesday, November 3rd, 2009
2:46 am	More on naming things People seem to agree that the "Artin-Schreier theorem" is a statement about real closed fields. They don't seem to agree on which statement about them it is. Wikipedia gives this name to the statement that every ordered field has a unique real closure; Keith Conrad gives this name to the statement that any field F whose algebraic closure is finite over F, must be real closed. (A "blurb" of his on it is one of the first results on Google for "Artin-Schreier".) Also: Artin-Schreier extensions aren't something I actually know anything about, but it just seems funny to me that they're significant enough in their own right to get this name, while it looks like the reason Artin and Schreier originally looked at them is because they're a problem case in proving their namesake theorem (er, the one Keith Conrad calls by that name). -Harry (Comment on this)
Monday, November 2nd, 2009
2:50 am	From the annals of terrible terminology Hey, you want to confuse people? How about instead of saying "intermediate value theorem", you say "Weierstrass Nullstellensatz"? ADDENDUM: Actually, I suppose some context might be in order. I was looking through an old algebra book and there was a proof of Sturm's Theorem, and it referred to something called the "Weierstrass Nullstellensatz". What the hell does the Nullstellensatz have to do with Sturm's Theorem, I wondered? Turns out it's a (presumably quite old) name for the intermediate value theorem. What a terrible and misleading (though technically sensible) name! (2 Comments |Comment on this)
12:24 am	But I have to say I'd still prefer to actually be able to look things up more easily Looking things up on Google Books can be rather interesting when a few key pages are omitted and you have to figure out those parts yourself... (Thought: Couldn't I just find what I'm looking for in the library? Yes, but, uh, somehow I didn't think of that until now. :-/ ) (Comment on this)
Saturday, October 31st, 2009
4:48 am	You know what's better than a Valkyrie's Charm? That's right: Two Valkyrie's Charms. (You were going to say an item *other* than Valkyrie's Charm? Surely not!) ...OK, so my current deck uses all of zero Amazons, but still. Having two Valkyrie's Charms could come in handy. (Actually, one of my old counterpick decks used both Helene and Anex, so I updated it to use both Charms. Whether it'll ever actually see play, who knows.) That's right, I'm not using my Anex deck still - remember, the reason I started using it previously was not because I thought Anex fit in better on the whole (though perhaps she does; certainly, without context, I'd say Anex is better than Marquis, but context is of course everything), but because I decided that Marquis was terrible in the metagame at the time - and, well, I haven't been playing again long enough to get any real feel for the current metagame. Until I get more info, I'm sticking with Marquis. It is annoying how hard it is to get multiples of items. When I started playing, I thought it very strange that you can use multiples of items, but they're quite hard to obtain, and, well, I still do. One of the ideas of Kongai, I thought, was that while you can buy cards with money, it shouldn't be too hard to collect them all anyway. But collecting multiples is damn annoying even if you *do* go buying cards. Actually, I've been looking at some of the balance changes intended for Kongai 2.0; apparently, the current plan is that Valkyrie's Charm is going to give only +1 speed instead of +2 speed. I have to say, even if the Charm is overpowered, it's going to be quite disappointing to see it the old Charm go... Evidently I haven't forgotten *too* much, my rank's been holding steadily in the 24-25-26 range, though I still don't think I'm as good as I was before. I once made it to rank 29, let's not forget; but right now there's no way I'm making it that high anytime soon. Speaking of rank, does anyone know what's up with those two guys who have somehow made rank 50? I can't find any information on them, but it seems pretty obvious gustavocola at least has to have cheated, right? Ah, I see looking it up, cheating has happened before and the people involved have been penalized. So, presumably whoever is responsible for that sort of thing, whoever they might be, will take care of it... Totally unrelatedly: Today I saw a man with an eyepatch walking by the math building. For a moment I wondered what Paul Sally was doing here, before realizing that that was most certainly not him... -Harry (Comment on this)
Saturday, October 24th, 2009
11:31 pm	Another episode of "Harry records amusing whiteboards" I go down to dinner last night, hear angry music coming from the kitchen, and see written upon the whiteboard: Room #113 Dinner ⇒ PISSED ↑ + Corrie ♥ Derek is pissed Corrie is pissed Yann is fuckin' pissed 1) Angry meetballs 2) Annoyed spaghetti 3) Violent pineapple cake (Who said "soup"?) FUCK YOU! (They had tried to make a pineapple cake, but it didn't quite come out right, and so one of them (probably Yann, who wrote the whiteboard too...) stuck a sign in it reading "Don't eat me, I am a disgusting SOUP.") -Harry (Comment on this)
8:17 pm	So after reading a bunch of the stuff on Less Wrong... ...I've noticed that Eliezer Yudkowsky sounds a lot like Youlian to me. Current Mood: noting nothing substantial (Comment on this)
Friday, October 23rd, 2009
12:45 am	Can anyone explain this statement? See this part of the Wikipedia article on Robinson arithmetic (a weaker version of Peano arithmetic). OK, that's kind of neat; if you expand it out, this amounts to saying that (z+2)(x+y)=(z+2)z, and since we're in the whole numbers here, z+2≠0, x+y=z. But... how can you use this as a definition of addition, when multiplication is specified (not exactly "defined") in terms of addition in the first place? Without x(Sy)=xy+x, all you have regarding multiplication is x0=0, not really much to go on. If somehow that statement implied that x(Sy)=xy+x, you could then check x+0=x, x+Sy=S(x+y); but *none* of those seem to follow because the LHS is a product, the RHS is a successor, and without either addition to work with, or x(Sy)=xy+x, there doesn't seem to be *anything* you can do to turn one into the other! (Then there's the whole problem of checking uniqueness...) So... this doesn't seem to make a lot of sense to me. Unrelatedly: My uchicago email is still getting lots of email from various schools asking me to apply there. Mostly this is just annoying, but today there was a funny one: I got an email from Michigan asking me to apply! (Of course, it wasn't from the math department. But still.) -Harry (1 Comment |Comment on this)
Wednesday, October 21st, 2009
5:16 am	OK, I just played my first *real* game of Kongai since I stopped It was against someone of rank 23. (Recall, I was rank 25 when I stopped.) I won it. So, not a bad start. Tangentially, apparently we have a copy of Guilty Gear XX ^ Core. ...yeah, I get the idea there's no way I'm going to be able to learn to play that game... Totally unrelatedly, I now have set up my "website" on Michigan's servers too (and there's even a link to there from my name in the math department's grad student directory). But also tangentially I notice that the MacLab back in Chicago has new computers now. Yay. I should probably copy over my stuff from there at some point... -Harry (Comment on this)
Sunday, October 18th, 2009
3:52 am	Things not related to alternate forms of the triangle inequality Or to any particular topic. Because things related to alternate forms of the triangle inequality was two posts ago. (I found a counterexample to the normed vector space idea, btw. Obviously that is there and not here.) The other day I saw a dead squirrel that had its guts partially extruded. I have to wonder, was it killed in such a manner as to force them out, or had something pulled them out so it could eat them? I now have an R3 Deadly Poison, so - until the expansion comes out anyway - I now have one of every Kongai card. (Quite a long way from having 3 of each item, mind you.) But the irony is I haven't actually played since that unranked game last week. I didn't go to game night this night either - had to do laundry. But apparently we get Monday and Tuesday off this coming week - "fall break" - and due to exams last week, I'll have hardly any grading to do this coming week. So, yay, I finally get some sort of rest. (Had I known about the break, perhaps I could have taken the time to pay a visit to Chicago? Probably not, I still have other work to do.) I had a dream last night, where I was visiting Nick and he took me to a mostly-empty arcade named "Alter Kacker"[0] where he showed me a game called "Canoe Racing"[3], which had nothing to do with racing canoes. Rather, you traveled down some sort of sewer, backwards, I guess in some sort of boat (a canoe?), the point being to go as far as possible, and the obstacles to this being... unclear? Until the 9th and 10th levels, where the tunnel went entirely underwater for periods of time, and you had to hold your breath (actually hold your breath, not just in the game). Unsurprisingly this being a dream the game/reality distinction was pretty blurred. I know I could look around (i.e. by actually turning my head) and see what was behind me, which was important for timing when to start holding my breath, but I think had I failed to hold my breath I would have died only in the game. Regardless, I made it through. The point of this being... my subconscious is terrible at inventing video games? So of course when I came here to Ann Arbor I took the sign Liz Goetz had made for me for my room[4], but I never put it up. Now I wonder if it would actually be appropriate anymore. Naturally I still don't shower very often, but there's not a big selection of food here - whatever's for dinner, I eat - and not having sweets around (barring soda) means I actually find myself eating apples for snacks. It's kind of scary. The "Harry only eats brown food" running joke may be meeting its end. -Harry [0]Literally, Yiddish for "old shit", corresponds to English "old fart". In fact the only reason I know this is because of TVTropes. At the time I misremembered it as German, though maybe it means that in German too, I don't know. [3]Or "Canoe Races", or something similar. [4]For those who haven't seen it, its text is as follows. In the original, each sentence is a different color (which is what the "those represented here" comment is referring to). There are also several additions that various people have made - I'll mark these with varying types of brackets. [] is for Ginny, <> is for Ian, and {} is for I don't know who but I think it was probably Wai Lee. Dear {AW}Harry Altman: Please take your vitamins. <Shower! Please! 2x/Week!> They are good for you. [And drink more tea!] And eat food that is not colored a shade of brown. (Skittles don't count.) Acceptable non-brown colors include, but are not limited to, those represented here. [Carrots, oanges, spinach, etc.] This is green. So is lettuce. Love (♥), Tufts Haus. (And yes, the sentece "This is green" is green.) (Comment on this)
Wednesday, October 14th, 2009
10:27 pm	Well, I guess Youlian was right about Lindsay, sort of She's been put on referral for uncooperative behavior for repeatedly making whatever room she's in unlivable for her roommate. I remember when I was a first-year Frank joked "If anyone moves in with me, I'll pee on their bed"[0], but she appears to be doing that seriously. (Er, I don't mean she's literally peeing on people's beds. Just the spirit of it.) We'll see what happens. -Harry [0]For the record, the school eventually put Felipe in his room, and no, Frank most certainly did not pee on his bed! (Comment on this)
2:35 am	I decided to look up why "non-Archimedean" is unambiguous And apparently proving basic facts about absolute values is all about amplification tricks. ...I have to say, for such a crazy-seeming fact - that if N (or Fp, as appropriate) is bounded, the absolute value is automatically an ultrametric - the proof is amazingly simple. I think I'd rather not go into the ridiculous approach I was trying... (9 Comments |Comment on this)
Tuesday, October 13th, 2009
11:50 pm	2-color ...you know, I think I just don't find free-for-all Smash that fun anymore. Today was I think probably the first day I just sat down and played Smash for an hour, and I think it's largely because Kyle wasn't around for a while, it seems, and without him we were always playing free-for-all and I just kind of got bored with it. So... things are getting better? -Harry (Comment on this)
7:18 pm	Three unrelated statements 1. So actually the new RvB series (Recreation) is pretty good, and yeah, it's back to essentially comedy[0]. Though I'm not sure how easily followable what plot there is is if you haven't seen Reconstruction. 2. I recently discovered http://lesswrong.com/ . I get the idea that sometime (not now, certainly!) I've got a lot of reading to do... 3. I only today realized I could get a printout of all my students' pictures and names. D'oh. Well that'll certainly make them easier to remember... -Harry [0]Not that I didn't like Reconstruction, but the attempt to be somehow serious seemed kind of ridiculous at times. (Comment on this)