| Probably not a coincidence |
[Jun. 3rd, 2009|11:18 pm] |
No spoilers.
Selene and I saw Wicked last week, finally. It was totally amazing. We've been listening to the soundtrack a lot since then, because it is also amazing. One thing struck me after a few listens though. There's this motif of sorts that interjects itself a few times throughout the soundtrack... it's not a fully-developed song exactly, just a couple lines in the same odd melody. Looking at them together, they're kindof an outline for the show. Not including the overture:
The Wizard and I: Unlimited / My future is unlimited
Defying Gravity: Unlimited / Together we're unlimited
No Good Deed: Unlimited / The damage is unlimited
For Good: I'm limited / Just look at me, I'm limited
But there was something about the melody... there's an octave jump between the first two syllables, and eventually it occurred to me that "Somewhere over the Rainbow" features that same pattern. But it doesn't stop there, they are actually note-for-note identical for seven full syllables. It's a little hard to hear, because the phrasing and meter are different (and probably the underlying key too), but listen to it (no spoilers) and convince yourself that it matches up:
| Some- | where | o- | ver | the | rain- | bow |
| Un- | li- | mi- | ted | My | fu- | ture |
Coincidence? |
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| Possibly the best wikipedia article ever |
[Apr. 20th, 2009|08:10 pm] |
The Tuck rule -- visit it now before it gets reverted to its previous, less hilarious, version.
The tuck rule or the Patriot rule is a rule in American football, currently used only by the National Football League (NFL) to help the New England Patriots win games.
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| Start spreadin' the news... |
[Apr. 19th, 2009|09:58 pm] |
Well, it's official... Selene and I are moving to New York! I accepted a job at Two Sigma Investments (where ![[info]](http://l-stat.livejournal.com/img/userinfo.gif) adereth works!) last week and Selene is going to be a Physician Assistant in the critical care unit at Montefiore Hospital in the Bronx. Whee! We are both super excited. We are planning on living in Manhattan, probably in the east part of midtown somewhere. Recommendations welcome, Selene knows the city pretty well but it's been 12 years since she lived there.
Our last day in Norfolk will be June 1st. We're going to move all of our stuff into a storage unit in MD and stay with my parents for the first week in June while Selene studies for the PANCE (chuckle). Then Selene will rock the PANCE. Then we're going to the beach! And then! A cross-country road trip! We're planning a 6 or 7 week trip starting around the end of June to drive around visiting all our friends who annoyingly don't live near us (and who we would normally get to see two or three times a year at weddings, but for some reason this year there aren't any weddings). Along the way we're going to stop at all those unlikely local restaurants with unbelievable food that we keep hearing about on the Food Network (thank you, Alton Brown, for this). And also there will be parks and camping and rafting and such. But mostly it will be for visiting people.
So here's our pretty solid itinerary as it stands now: Charlotte, Asheville, Nashville, Huntsville, Memphis, St. Louis, Boulder, Denver, Colorado Springs, Manhattan (Kansas -- couldn't resist), Salt Lake City, Boise, San Francisco, Portland and Seattle. The return trip we don't really have nailed down yet, we'll probably take a northern route through Montana then visiting St. Paul, Chicago and Cleveland and ending up in New York. We're not sure yet how much time we'll have in each city on the way back, it depends on two things: how long the front half of the trip took, and when we need to be in New York (our start dates are not set yet, and we're still trying to figure out the optimal time of the month for apartment hunting in the city).
Actually, on second thought, the front half of the trip is pretty well constrained by a wedding Salt Lake City and other factors in Seattle. So it's up to you, New York, NY. |
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| A crazy idea that doesn't work |
[Apr. 16th, 2009|09:08 am] |
Another literate Haskell post!
> import Test.QuickCheck
Yesterday I got to thinking whether that fast exponentiation function
is also a linear computation in disguise over a carefully chosen
semiring. If that worked, maybe I would be able to parallelize the
exponentiation computation over the bits of the exponent, giving one
processor half of the bits and the other processor the other half, and
combine the two results somehow.
Well, it didn't quite work out but I did come across something pretty
neat... a matrix scheme that converts a bit vector to an integer.
( More below the cut... ) |
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| How to compute Fib(n) in log(n) time |
[Apr. 14th, 2009|11:36 am] |
I read recently about an interesting
technique for algorithm parallelization. I decided to try my hand
at it on the simplest thing I could think of – computing the nth
Fibonacci number. You wouldn't think having two processors would
really help you (in the iterative case), since the current computation
always depends on previous results, so it would just be one processor
waiting on the other... it just doesn't seem like a naturally
parallelizable algorithm. But it turns out it is! Well, sortof. In
the end, I found that the two processors are doing exactly the same
work, so all you need is the one processor to do the work once, and
you're done -- but that's giving away the ending.
( More below the cut... ) |
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| Liebniz hates you |
[Oct. 29th, 2008|01:05 pm] |
In the best of all possible worlds, you might not exist!
But you do exist in this world. Therefore, you live in the best of all possible worlds that can accommodate you. So if the world were any better, you wouldn't be in it.
Assume for the sake of contradiction that there is someone in the world who is worse than you. If that person didn't exist, the world would be better. But then we have made the world better, without removing you. Contradiction!
Therefore, you are the worst person in the world.
Take that, Leibniz! |
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| The miracle of modern architecture that is the Baltimore Beltway |
[Oct. 24th, 2008|04:33 pm] |
First, the topologically non-trivial I-95/I-695 interchange. I saw this a few months ago on Ars Mathematica. Then the other week I was driving up I-95 North. I noticed some heavy traffic on a parallel road in the other direction... but it was on the right. Then I realized where I was. The road on the right was I-95 South. The two sides of the highway (and the intersecting highway) cross and then cross back, allowing for really short "left turn" ramps. The two crossings go over-then-under, so it's a knot of some kind.
( It's beautiful... ) |
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| Awesome Proof of the Day |
[Oct. 24th, 2008|08:59 am] |
I remembered this proof the other day, and I thought I would post it, because it is so great. Here goes:
Almost all real numbers are non-computable.
A real number is computable if you can write a program that prints out its digits (it doesn't have to terminate, but it does have to keep printing digits). So "3" is computable, and so is "3.3333...". And pi and sqrt(2) are computable too. You're probably expecting an example of a non-computable number, but I'll get there in a second. On with the proof...
A program is a finite string. There are a countably infinite number of strings of finite length. So the list of all possible programs is countably infinite. However, there are uncountably many real numbers. So all the programs in the world can't possibly cover all the real numbers, and in fact, there are uncountably many real numbers that aren't covered. (QED)
Which is great, but here's where the fun starts. Of all the uncountably many non-computable numbers, you can't name a single one. The mere act of naming a number gives you a way to compute it. You could try, "it's pi but with every 4th digit changed to a 6," but that's computable. Or, "the number whose digits are the first characters (converted to a digit somehow) of each program in the list of all possible programs, sorted lexicographically," but that's computable too.
I also tried, "the smallest real number that is greater than zero but is not zero," which might actually be computable*, and I don't think it even defines a unique real number... so it fails on both counts. What about, "the smallest non-computable number greater than zero"? This one is certainly non-computable, but I don't think there is a unique smallest non-computable number greater than zero, just like there is no largest natural number. Getting closer though.
There's the requirement that the program has to keep printing digits. If we name a number that is computed by some infinitely long procedure, such that you can't even get the first digit out without waiting for the procedure to finish, then that number would not be computable. Maybe... "the digits of pi, backwards" (e.g., 3.???...141). I don't think that's a number though. What about, "the sum of the square roots of natural numbers"? But that's a divergent series, so it doesn't define a real number. A series that converges, by definition, gives you a certain precision after so many terms, so eventually you will be able to print out some digits.
How about... the sum of an alternating sequence that hovers around 1, so you don't know whether the first digit will be a 1 or a 0**. But which sequence? It can't be a mathematically defined sequence (like the sum of alternating reciprocals, or whatever), because you can sit down with math and figure out what that number is, and then write your program to print out that number. I think it will be just as hard to name a sequence whose sum is a non-computable number as it is to name a non-computable number.
It's fun to think about non-computable numbers. They are everywhere, but so frustratingly elusive.
*An alternative (and probably better) definition of a computable number is one where you can write a terminating program to print out its first n digits, where n is an arbitrary parameter. So the program that prints out n digits of the smallest number greater than zero would just print "." and then n 0s.
**You can further relax the definition so that the program has to print a number within a given epsilon of the number in question, and then terminate. So that gets around the problem with the series that hovers around 1... it doesn't matter if the first digit is correct, as long as you get within epsilon. |
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| If you lose to the Rams, they kick you out of the league! |
[Oct. 15th, 2008|09:28 am] |
Well, we had a fun trip, even though they lost. It was Selene's first visit to FedExField, but not her first Redskins game -- WAS@SEA playoff game in 2005! That one was great... We were living in Seattle, and around game 16 or 17 we realized, if the Redskins make the playoffs, and win the wildcard round, and the Giants win, and some other team does something, then the Redskins come HERE for the divisional round! It totally happened, and we totally went. And they totally lost. But this time it was nice to be around 90,000 other Redskins fans.
It was a great game. My cousin Rachael and her husband had her dad's marching band tickets, her sister Stacey and her boyfriend had their dad's season tickets, and we had their brother's marching band tickets. So we tailgated and found seats together during the game.
The Rams' first-quarter fumble on their own 4 and subsequent TD by Portis happened in our end zone. The rest of the game we were screaming our heads off for the defense, and standing there in shock at all the fumbles the offense committed. It was a rough loss, but here are some things that are great: 1. Portis leads the league in rushing, 2. Dallas and the Giants also lost, 3. we got a new punter, and 4. Shaun Alexander is now a Redskin!
Click through for the rest of the pics...
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| The crucial anti-decided voter contingent |
[Oct. 14th, 2008|12:02 pm] |
This weekend, in the car, heading up to DC:
ME: I thought of another reason why I shouldn't vote.
SELENE: You're still going to vote though, right?
ME: Well...
SELENE: I don't want to hear it unless you promise you will vote. This is an academic exercise only.
ME: Okay, I promise I will vote.
SELENE: Good.
ME: ... for a third party!
SELENE: Doh!!
I love this argument because it sidesteps the morality issue (what if everyone did the same thing... then the third party would win?) and the tie-breaking fantasy (if a candidate loses by a single vote... you can blame anyone who also didn't vote for them), and reduces the wasted-vote argument to a matter of preference (you're throwing your vote away! ... so you think I should instead vote for whoever you want me to vote for?), while setting up the following argument:
ME: So... what's the difference between voting for a third party and not voting?
SELENE: You are not a nice husband.
The best part is that I am a (lower-case-l) libertarian at heart, so I could even implement this plan and still be voting my conscience. Or not-voting my conscience.
Selene did point out one major difference between the two: your responsibility as a citizen to vote. I objected to this abstract notion of responsibility, arguing that it should not be grammatically possible to say "responsibility" without specifying to whom you are responsible (like saying "the cat is under" without saying what it is under), that is, who will be adversely impacted if you fail to meet your responsibility. But she was happy leaving it abstract. I'm pretty sure that's what our disagreement boils down to. So I'm happy that we've identified that.
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| The trouble with "combined" records |
[Oct. 2nd, 2008|04:44 pm] |
The other day I made the claim that the Redskins' remaining non-division opponents are a combined 9-20. Actually, at the time they were 8-19, since BAL@PIT on Monday night hadn't happened yet, but I thought it was safe to assume that one of them would win and the other would lose. That got me thinking, why should I include that game at all? If one team has to win and one team has to lose, doesn't that artificially push their combined average towards 50%?
So today I sat down and figured out the implications of excluding those games for the 8 teams in question: BAL, CIN, CLE, DET, PIT, SEA, STL, SF
The following 8 games took place between members of this group through Week 4:
BAL-CIN
BAL-CLE
BAL-PIT
CLE-CIN
CLE-PIT
DET-SF
SEA-STL
SEA-SF
The group is a combined 8-8 against itself (clearly). So their adjusted combined record is now a whopping 1-12. The one non-group win comes courtesy of PIT over HOU in Week 1.
Thank you, football gods! Easiest non-division schedule ever! Now just... don't screw it up. |
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| Hail, Victory |
[Sep. 29th, 2008|09:02 am] |
I think they start calling it a rivalry when the worse team coming into a given game is more likely to pull off a win. Witness the 1989 season when the Cowboys finished 1-15... you can guess who that 1 was.
After the win last night, the Redskins are 5 for the last 7 meetings of the two teams, each win in dramatic fashion:
- 2005 @ DAL - Santana Moss catches two 50+ yard touchdowns in the last 4 minutes. Final score 14-13.
- 2005 @ WAS - Redskins dominate the first half 28-0, final score 35-7. This is the 3rd game of 5 must-win games to make the playoffs (they did).
- 2006 @ WAS - A bright spot in a disappointing 5-11 season. Redskins block the would-be game-winning field goal and Sean Taylor returns it 20 yards as time expires. A facemask penalty brings the Redskins in field goal range and extends the game by one untimed down. Redskins win 22-19.
- 2007 @ WAS - Week 17 win-and-you're-in situation at home vs Dallas. Dallas is already in the playoffs and doesn't try very hard. But still. Final score 27-6.
- 2008 @ DAL - Final meeting of the two teams at Texas Stadium, where the Redskins are 1-12. Dallas comes in with the best offense in the league. Washington is widely considered the worst team in the (albeit very tough) NFC East (which, btw, is 8-1 vs non-division opponents -- thanks Philly). Defense shuts down TO and Barber, Redskins win 26-24.
This does not sound like the Redskins I know at all:
- Only team in the NFL with 0 offensive turnovers (I just jinxed it)
- Leads the NFL with +6 turnover ratio
- Rookie backup free safety Chris Horton leads the team with 3 interceptions and a fumble recovery
- Have outscored opponents 27-7 in the 4th quarter this year
Remaining non-division opponents (Rams, Browns, Lions, Steelers, Seahawks, Ravens, Bengals, 49ers) are a combined 9-20 after week 4, assuming the Steelers and Ravens don't tie tonight. Things are looking good for the NFC East... it's a shame they can't all make the playoffs.
Finally, there's nothing like seeing your favorite players acting like regular people. Here are Chris Cooley, Jason Campbell, Fred Smoot, Santana Moss and Mike Sellers drafting their fantasy football teams. Smoot is by far the most hilarious. Seriously, watch it, it had Selene rolling on the floor.
Update: The Redskins account for half of Tony Romo's losses as a starter. He is 1-3 against the Redskins and 22-6 against everyone else. |
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| Tufte would approve |
[Aug. 28th, 2008|09:53 am] |
Which body parts are sung about the most?
No suprise in the Hip-Hop category. What a great chart though!
And this comment made me chuckle:And a lot of the time the word "ass" isn't really being used to refer to the behind; instead it's used in phrases like "leave your ass dead" or "I'm a Southern ass star" (which does not mean that he's an ass star from the South). |
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| In Soviet Russia, hole bores YOU!! |
[Aug. 25th, 2008|10:38 am] |
Could this technically be called the boringest job in the world?
Also, choice quote:"The Soviet Union has always been more consistent in carrying out large-scale studies of the structure and regularities of the evolution of the continental crust than other countries," he wrote. "This is a deeply rooted tradition in our country, and it is still very much alive." Yes: gymnastics, borscht, and large-scale studies of the structure and regularities of the evolution of the continental crust. |
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| I am not a gamer |
[Aug. 25th, 2008|09:07 am] |
I finished Braid last night. What a beautiful, mind-twisting game. And I think it might have been... the first video game I've ever finished in my entire life (see title of post).
I'm glad video games have moved away from this "die 3 times and you have to start over from the very beginning" paradigm. And you know what else is great? Downloadable demos. |
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| Etymology note of the day |
[Aug. 13th, 2008|08:51 am] |
The word outrage, a loan-word from French, carries a connotation of anger in English whereas in French it does not. This is because English speakers parse it out-rage, and it's the rage part that lends it that extra meaning. However, in French, there is no out morpheme, so French speakers parse it outr-age instead, correctly identifying outre (beyond) as the root and -age as the abstract-nounifying suffix (not a technical term).
I found that in the footnotes to How to Read the Bible, which I am totally glad I read. (Right now I am wishing that the relative pronoun in English had number, so you would know that "which" refers to the footnotes and not the book. Although I am also totally glad I read the book.) For the interested, Appendix 1: Apologetics and "Biblical Criticism Lite" has been published online, if you want to get a sense for the book. |
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| Obamulke |
[Jul. 25th, 2008|10:37 pm] |
Funny story, that's actually a yarmulke from my cousin Aaron's wedding a couple weeks ago. Apparently one of Obama's interns is a friend of Aaron's in-laws and was at the wedding. When Obama visited Yad Vashem in Israel, someone suggested that he wear a kippah, and he just happened to have it in his pocket. |
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| Can you fix my computer? |
[Jul. 24th, 2008|09:00 am] |
When I was a junior in high school, I performed a miracle.
One day in class I was talking with my friend Ann (who I had a crush on at the time, but that's only marginally important in this story), and somehow the subject of computers came up. And immediately: "Ooh, you know about computers?!" -- at which point I'm thinking, oh, she thinks I'm cool for knowing about computers (I would soon learn not to think this) -- and then, inevitably: "Can you fix my computer? I can't get on the Internet." (She probably actually said "World Wide Web" or "AOL" given that this happened in 1996.)
I said sure, but really I knew nothing about computers. I could program my way around an Apple II, but my family had only had The Internet ourselves for a few months. I was fully expecting to go in there and not know what I was doing and just have to give up -- I hadn't yet learned about the potential for making things worse.
So I went over to her house, and she showed me the computer and I sat down. My first (and only) idea was to try to connect their dialup. She said MSN was their service provider, so I asked what their email address was (which was what you used to sign into dialup in 1996). She said: "so and so at MSN dot com dot." Me: "Dot com dot? Not just... dot com?" (thus illustrating the extent of my knowledge about the Internet). Ann: "Yeah, MSN dot com dot. It was in the letter they gave us." Me: "Are you sure it wasn't just at the end of the sentence?" Ann: "I think so." I didn't press the point, but I was certain that "MSN dot com dot" would constitute a malformed address -- a belief I held until just today.
Then I asked what the password was, and she had no idea -- it didn't seem like she even knew what passwords were, to begin with. Ann retreats to the other room to watch TV while I "work." So great. I'm out of ideas, if I don't have the password I don't have a chance of fixing "the Internet," and I'm going to look stupid in front of this girl I have a crush on. So I start poking around the desk, not really knowing what I was looking for, and eventually I come across a scrap of paper with some writing on it that in some way looked like it might be someone's password. So I tried it. The modem seemed to connect, so I held my breath and started up IE, and MSN.com totally started loading.
So what reminded me of all this was the whole "MSN dot com dot" thing, an oblique reference to which I came across on this ridiculous page on cross-site scripting vulnerabilities (search for "absolute DNS" on the page) -- ridiculous because of the sheer number and variety of attack vectors, and the susceptibility of most browsers and server-side filters for untrusted content.
That page, in turn, I found via recommendation from the stackoverflow podcast, which is fully great. It's Joel Spolsky (who puts the "Joel" in Joel on Software) and Jeff Atwood (from Coding Horror, which I do not read regularly), who are working on a software project together -- well really it's just Jeff who's doing the coding and Joel who's advising and consulting. They live on opposite coasts, so every week they talk on the phone for an hour about the project, about software and the business of software in general, and just general stuff. And they record their phone conversation and that's the podcast. It's pretty cool, because it's like the phone conversations I have with my friends, only they (well, Joel) is really really smart. Yeah, so I don't really like Jeff that much. He's got this philistine attitude about learning C, and has resisted Joel's advice in a few cases where I think Joel is totally right. But that's the thing (and they even talk about this principle in one episode), in order for you to enjoy listening to a show like this, you have to like one guy and hate the other guy, so you're sitting there rooting for the one guy (in my case, Joel) to stick it to the other guy (Jeff), and it's interesting. If you like both of them, it's kindof boring. |
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