So I was doing a practice test for the actuarial exam I'm taking tomorrow, and there was a problem that went something like:
Mike has a bowl of soup with 5 noodles in it. He reaches into the soup, takes two noodle ends, ties them together, and puts them back. Then he repeats the process 4 more times, so that all the noodle ends are tied together. If he reaches into the soup again, what's the probability that he pulls out a garland (the problem actually used this term, I remember quite clearly) with all five noodles?
The practice test described its difficulty as being 4 out of 5 stars, which is as hard as any of the problems I've encountered on the 4 practice tests I've done. Here's what happened...
If you want to try to do this problem yourself, minor spoilers (in the form of the method that didn't work) follow.
My initial response to the problem was, as it probably was for many others, "WTF?" because it seemed quite difficult to impose any kind of structure on it. In fact, it's not that hard to make some sense of it, and before long I was trying to divide the number of ways to tie the noodles into one long loop by the total number of ways to tie the noodles.
The combinatorics involved were pretty heavy. I think, but I'm not sure, that the number of ways to get a garland is 5! * 25, because you have to put the five noodles in order and then each one can be reversed in place. It may then be necessary to divide by 5 to eliminate loops that are identical but just shifted, or it might be okay to treat them as distinct if you do so for the number of ways to tie the noodles as well. Anyway it doesn't really matter, because finding that latter number is quite difficult, and I messed around with it for a while before running out of time.
If you're still working on it, the answer follows.
So I told Jenn about this problem in the car on the way to her house, and in about three minutes, she said (all quotes are paraphrased), "Well, the first time he picks an end to tie, there's only one chance in nine of making a loop and making it impossible to get a garland. If he doesn't, then it's like there's only four noodles left, because two have been combined into one."
Boom, light bulb. The rest follows by induction (in fact, when I looked later, the practice test gave the solution for n noodles). For the first tying, there's an 8/9 chance that you tie two noodles together (rather than tying one to itself, making a little loop, and making it impossible to get a garland). If you do that, then for the next tying you pick one end out, there are seven ends left to tie it to, and only one that will make a small loop and keep you from getting a garland. So there's a 6/7 chance you can keep going. And so on for the next two. So the answer is (8/9)(6/7)(4/5)(2/3); after the first four ties, you have just one long noodle and it's impossible not to make a garland. Such an elegant solution, particularly so since it can be generalized easily.
It's a cool problem. Jenn was worried that she deflated my ego by getting it when I couldn't, but I think I was stuck in a rut (and I'd just been working on other problems for two and a half hours) so I cut myself some slack and my ego remained unscathed. I did well on the practice test overall, and I'm feeling pretty confident about the exam tomorrow. And my girlfriend is really smart. <3
Oh, Christ. Another thing on the Internet that will totally consume my life if I allow it to. I'll let it describe itself:
i n f i n i t e s u m m e r THE CHALLENGE Join endurance bibliophiles from around the world in reading Infinite Jest over the summer of 2009, June 21st to September 22nd. A thousand pages1 ÷ 92 days = 75 pages a week. No sweat.
1. Plus endnotesa. a. A lot of them.
If you start now, you're a little late. But that's ok. Oh, this site, though. The essays, the advocacy, the love for my favorite author and my favorite book, auggh. And Colin Meloy wrote a fucking piece for it. Colin Meloy!
Well, eMusic's adding major labels, apparently. Hooray, I guess, but I also had this message waiting for me today:
Effective Jul 7, 2009, your plan will change to the new eMusic Plus plan which gives you 37 downloads for $14.99 every 30 days.
Currently, for the same amount of money, I get 65 downloads. Awesome, 43% less for the same price! A little more math yields the unavoidable conclusion: Fuck you, eMusic. I'll be canceling my subscription along with throngs of others who once loved you, and I hope you go under.
Longest song yet to record, hardest song yet to record, most pretentiously titled song yet, &c, &c. Three totally different parts, ack. Don't pay too much attention to the "story" because I'm pretty sure it doesn't make sense if you think about it too hard. Yes I am a woman in it.
I went back and listened to a couple of my other songs tonight and I actually thought they sounded kind of amateurish (in terms of recording quality, not necessarily songwriting) compared to this one. I must be learning something!
Put in some good work on my song tonight after a thoroughly unproductive day. It's basically down to the bassline and drums, the most tedious parts: since I have neither a bass nor drums, I have to program them both using software that cost me a total of about $100. Indie rock music, on a budget!
I'm pretty sure the bass and drums in this song will be more complex than in any of my other songs, and I'm going to try to mix the drums up instead of just throwing together four measures and looping them for the duration of what I need. But I totally re-did the basic drum rhythm tonight and I like the new one a lot more. It's my first drum track with toms, which I really like but which never seem appropriate for my songs.
The semester's over, and now that I have a few weeks without teaching, I've had to find other ways to occupy myself, and for the most part I have had no trouble doing so. As such:
Studying for the first actuarial exam. I briefly mentioned I was considering this, and now I'm actually signed up for it and everything. I've also mentioned my disillusionment with teaching; obviously I need something to replace it, and this seems like the most viable option. The probability and statistics classes I took for my master's program, I think, actually prepared me well for it, though there's been a lot of Googling and Wikipedia to refresh my memory. My first pass through the 140 sample problems on the actuarial site yielded a 79.2% or something, which would have been very unlikely through random guessing. I'm pretty happy with that, but it did include a lot of research and consultation of notes. I have until July to make sure I can do that well or better with a time limit and no notes, and I suspect it'll involve my shelling out for a study guide of some kind. Hopefully, though, it will result in a job I can tolerate, in which case the cost of the exam and study guide will likely pale in comparison to my salary.
Dungeon Crawl: Stone Soup. I don't know how much I've mentioned that I'm a big fan of roguelikes. My brother and I used to play the shit out of Angband and its variants, using savescumming (copying save files so you can restore them when you die; death is supposed to be permanent in roguelikes) and polymorph scumming (polymorphing monsters until they become something hard, but slower than you, so you can kite them and get loads of experience) and all kinds of other distasteful munchkinism to achieve maximum character godliness.
I tried Nethack for a while but it always felt a little too surreal and bizarre for me, with too many in-jokes and extremely obscure ways to die, requiring too much dependence on spoilers.
My next roguelike obsession was ADOM, which I tried for a while at home one summer and liked a lot, but couldn't play here because it's a DOS game... until I got Boxer and got things up and running. I got pretty far in the game by extensively abusing the Improved ADOM Guidebook, but never beat it. What started driving me away was having to do the first few quests over and over again; as in any roguelike, characters die frequently, and the puppy quest and carpenter quest get really old really fast. I gave it up when I accidentally stepped onto an evil altar and a monster sacrificed me to its deity. That was just too asinine a way to die.
So now I'm onto Dungeon Crawl Stone Soup, which I think is the best-balanced roguelike I've ever come across: it's got a plethora of races and classes, each with hugely diverse play styles, but assuming you don't pick something asinine like an Ogre Conjurer, almost all can be made to work in some way. On the other hand, the game is almost never easy: every character I've played has ended up in tight spots at regular intervals, many of which ended in deaths that could have been avoided if I'd played smarter. DCSS is, however, the first roguelike I've won without savescumming, which is something of an achievement considering I've been playing different ones off and on for over a decade. Anyway, I'm going for my second win now. I suspect it'll take a while.
Songwriting, kind of. I have a song which has the basic guitar and vocal tracks pretty much recorded (though the outro is way longer than it needs to be), but I think it needs drums, and I find drum tracks very tedious to lay down. So it's kind of been on the back burner for a while. Eventually I'm sure I'll get sick of having a 75% finished song sitting around and get on that, but I'm not feeling any real urgency at the moment.
I'm putting together a medley of Mountain Goats songs (yes, my tMG obsession continues), because I'd noticed that there are a lot of lyrical themes that have been revisited several times in the huge catalog, and I thought it would be fun to try to use some similar lines in different songs as places to tie them together. Currently I have a string of bits and pieces from about 10 different songs; I'm worried that I won't really know when to stop.
I never really did a postmortem on my short little Mountain Goats cover show, but it was pretty awesome. I felt good about my performance, the audience seemed to agree, and I got some nice compliments from other performers. I do want to have another performance this summer, but I'm starting to think people might have to badger me about it.
Cooking, some. Recent exciting foods have included tom kha talay and New England clam chowder — both of which used fish broth made with real fish heads! — and two batches of scones, which it turns out are way easier to make than I'd thought.
Biking, at least once; my mom and I went on a 44-mile bike ride in rural Wisconsin this Saturday. It was a nice ride, though it would have been better if we'd brought food because there was fuck-all in terms of any kind of convenience store or gas station along the way. We didn't die, though.
It bears mentioning, though it doesn't really fit into the list above, that I'm still devotedly in love with Jenn. She had a two-week vacation in Ireland and Scotland in the beginning of the month and I'm glad she's back.
See, Jenn always has to drive over here if she wants to see me. So yesterday afternoon, instead, I biked out to Maple Grove (red) to see her, and this morning (orange) I biked back. It came to a little over 30 miles each way and I'm a bit wiped but not too bad. It was super awesome to do a longer ride, even better to do two back to back, and even better-er that I had an actual destination to reach rather than just doing a 30-mile loop. Saw some beautiful parts of the Cities and surrounding areas that I'd never seen before, and re-affirmed my conviction that they are a pretty damn decent place to bike. Click the picture to pop over to Flickr and see the super! exciting! annotations! with trip highlights.
This Friday, March 27th, 9 pm. 21+. $4. THAT'S FOUR FREAKING DOLLARS. Featuring eight or more people (including me) playing three to five Mountain Goats songs each. C'MON.
One time my friend got pretty blazed and drunk and we were standing outside a house and few people came out and started a campfire. My friend began cheering them on by shouting things like "FUCK YEAH! FIRE!" and "BURN THAT SHIT!" and "SET THAT SHIT ON FIRE!" When I told him he was being kind of an ass he turned to them and said, semi-obnoxiously, "Hey, man, sorry for partying," as though to say, "Just because you're not partying means that I have to put my completely great partying on low heat? That is mega bullshit, but whatev, chief."
Ever since the phrase "Sorry for partying" has become an arbitrary expression of moral and drunken superiority among my pals. If you do something crazy like shit on a pit bull, well, "Sorry for partying," and you are completely in the right. Vomit pants buttons all over a passed out cheerleader at a baby shower? Sorry for partying. Snort a line of organic honey and get three chicks and a dude pregnant? Sorry for partying. Slam some weed in some everclear and pound some hoot juice and wind up freezing up the Jumbotron at a Knicks game? Sorry for partying.
Okay, I feel like I should be spreading the word about this early.
There's going to be a show at the Turf Club later this month (tentatively planned for Friday the 27th, I believe) in which a bunch of people will play Mountain Goats songs. I found out about this today, and as of today there is also a high probability that I will be one of those people.
Save the date. This will be my first public performance and I'd love to have some support for it!
Who the fuck elected these people? Why do they have anything to do with making laws in this country? Why, in fact, are they doing anything other than standing on street corners shouting at people and smelling bad?
It'd been kicking around in about 95% recorded state for quite a while till I finally got around to polishing off that last 5% a few weeks ago. But then it had to sit on my hard drive for a while so I could listen to it with a fresh ear and confirm that there are no horribly embarrassingly rough edges in it still. As with all my songs with more than two tracks, there are places where it gets a little dodgy in terms of the timing or something but I'm managing to choke back my perfectionism enough to just put the damn thing out.
The working title was "Fucking Thermodynamics," and I decided to stick with it even though it kind of gives away the lyrical conceit.
I recorded each of the three main guitar melody lines in it about eight zillion times before I got a take that I reluctantly deemed good enough. They're still kind of rough around the edges. Sometimes a dude just has to confront the fact that he will never be a very good lead guitarist.
Still, I'm happy with the song, and I'm glad I futzed around with it and decided to write an electric guitar overdub. It pushes it slightly beyond standard dude-with-a-guitar fare. Into dude-with-two-guitars fare.
The vocal is perfunctory. If any singers are reading this and would like to do me one better, let me know. It would be rad if you were willing to record your own singing along to it, and I'll probably be willing to swap out my vocals for yours and re-up the song that way. Wouldn't that be cool? Everything's already written for you, even. I can send you the lyrics. All you have to do is sing better than me.
Agh. Black Milk, I surrender. This track is about to make me fall in love with hip-hop again, to start saying things like "ill" and "dope" despite my extreme whiteness. Holy moly listen to that fucking snare. Aaaaargh.
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