Just a quick school update

Tomorrow (Monday the 30th) is my first day of classes here at Stony Brook. Now, I only have one class, as it turns out, but it also promises to be a really good one.

People always say that, especially as a graduate student, you shouldn't necessarily take a course because of the topic, or because you feel like you "have to,"  but because of the professor. They say you should ask around the department, find out who the coolest teachers are, and then just sign up for whatever they're teaching. Well, here's one such guy:

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∫ Finally, a math puzzle I can use!

After much thought, I've hit upon a math puzzle that will work for my friend's little neighbor, the aspiring mathematician. Actually, I'm going to give her a two-part puzzle: a more straightforward version of the "littler math puzzle"  posted below, and this little guy that I came up with yesterday while exploring the behavioral sciences building. Incidentally, why do "people scientists"  and "medical scientists" always have such nicer buildings than "hard scientists?"

Anyway, here's the puzzle:

Most small numbers are pretty close to a prime number. For example, the number 22 isn't prime, but if I just change the second 2 into a 9, then it is (because 29 is prime). Similarly, 310 isn't prime, but 313 is. So it seems like often, all I have to do is change one digit in a number and I can make it into a prime number.

Unfortunately, that's not true for ALL numbers. There are some numbers that can't be made into a prime number just by changing one (and only one) digit. The question is, what is the smallest of these numbers?

Answer and explanation below the fold, as always.

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If America wants to be like Rome, we have to start paying our athletes more

That's the message I take from this post by Peter Struck, a professor at U Penn who writes a blog about interesting things from history. Struck is writing in response to the news a year or so ago that Tiger Woods has become the first athlete to earn $1 billion in the course of his career. For comparison, he points us to the charioteers of ancient Rome, who were apparently the absolute hottest attraction in the Roman entertainment scene.

No, this is not a picture of Gaius Appuleius Diocles.

The hottest of the hot, a Spaniard named Gaius Appuleius Diocles, apparently earned so much money that after his retirement--at age 42--a monument was erected to immortalize the staggering amount of his collective winnings. As Struck writes:

His total take home amounted to five times the earnings of the highest paid provincial governors over a similar period—enough to provide grain for the entire city of Rome for one year, or to pay all the ordinary soldiers of the Roman Army at the height of its imperial reach for a fifth of a year. By today’s standards that last figure, assuming the apt comparison is what it takes to pay the wages of the American armed forces for the same period, would cash out to about $15 billion. Even without his dalliances, it is doubtful Tiger could have matched it.

I'm a little skeptical of Struck's strategy for translating Diocles' earnings, as it seems to me there are a lot of variables about the size and cost of the armed forces that are uncontrolled for. I think in terms of comparing him to modern athletes, a better strategy might be to ask what percentile of earners he fell into against the percentile rank of Woods and the like. But whatever his actual  "adjusted" salary turned out to be, its pretty clear it would have been far more than what our average athlete makes today. I think it's even possible that by this metric, he would project out to have made a lot more than $15 billion, quite a feat given the fact that the general public in this day and age probably has a lot more disposable income to put into seeing athletic competitions than the amount that was available when just a few wealthy statesmen were organizing these things.

In other words, the next time someone tells you that the US is on its way to becoming "just a modern Roman empire,"  make sure to include in your rebuttal the fact that we aren't yet nearly obsessed enough with sport.

Mark Wahlberg and an eggplant teach me to enjoy action flicks

I watched "Shooter" last night while I made eggplant curry. The curry turned out really well--turns out the missing ingredient last time I made it was coconut milk-- but the really interesting part of the evening was the experience I had watching the movie. By most accounts, "Shooter" was a pretty bad movie, or at least pretty mediocre, but I really enjoyed it. And I think the reason was, I wasn't really paying attention.

I'm not trying to rip on the movie. I've always believed that the so-called "mindless action flick" was a perfectly defensible art form. It's just like I always appreciated the music of folks like Justin Timberlake and the Black Eyed Peas. I think they're geniuses: they are legitimately some of the best in the world at crafting catchy beats, hooks, and melodies. You just can't go to them expecting depth and introspection. That would be foolish. You go to them when you need to be emotionally manipulated by music on a deep level. And I'm not so snobby as to think there's anything wrong with that on any level. Sometimes you need to be tricked into feeling happy, sad, hopeful, whatever. We do this all the time by turning to friends, starting leading conversations, et cetera. So there's no reason to feel bad doing it with music.

For some reason, though, I've always had trouble letting movies do this to me.
Action films in particular get on my nerves when they try to provoke an emotional response. They always try really hard to get me to have a gut-level, testosterone laced level of support for the hero, and they often try to get me to join in on the his righteous anger against whatever evildoers he's battling, too. And for some reason, even though I know the trick to enjoying such movies is not to expect any deep revelations about the state of humanity, and not to expect any magical, arts camera work, et cetera, I always manage to get angry at the shallowness of the movie.

This has made a lot of my friends angry to no end. So many of them got a huge rush out of "Quantum of Solace," but I was busy being mad that it didn't live up to the emotional complexity of "Casino Royale." A good number of them managed to get a kick out of the fight sequences in "G.I. Joe," whereas I couldn't get over the fact that it contains some of the most unrealistic science, most incoherent plot "twists," and most densely-packed clichés of all time.

Well now I've learned the trick, courtesy of Mark Wahlberg.

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∫ Things I learned from teaching undergraduates: Tennis Ball Topspin Edition

The Youtube clip above shows Roger Federer hitting a topspin forehand in slow motion. The ball is moving too fast after he hits it for you to be able to see the direction of its spin, but you can tell pretty clearly from the motion of his racket that he's hitting a little bit beneath the ball and then sliding the racket upwards along the backside of the ball at the same time as he follows through. The result is the the ball will be spinning with what tennis players call "Topspin."  It's a rotation where the ball the top of the ball is moving in the same direction as the ball is flying, and the bottom of the ball is moving the opposite way.

Topspin is a huge deal. Part of the reason Roger Federer is so good is that he hits with 2,500 RPM of topspin, which is more than either Pete Sampras or Andre Agassi (only Rafael Nadal hits with more, although it's been argued that he actually hits with too much!)

Now, like anyone who's ever taken a tennis lesson, I know tennis reasons the pros hit most of their shots with topspin. Coach after coach after coach has told me over the years that there are basically two principal reasons: first, a ball with topspin will "kick" upwards when it bounces (I think it's pretty easy to see why) and that can make it harder for your opponent to hit, because they wind up having to hit it up around their ears. But then there's this second reason: Topspin is supposed to make the ball "drop" sooner, meaning you can hit it higher over the net and still get it to land inside the court. Being able to hit higher  in turn means you have less chance of hitting it into the net, and it means that you can hit it a little harder. Seems like a good deal all around.


But one thing I definitely did not know until a couple of days ago is why topspin causes the ball to move like this. After all, why would spinning make a ball want to fall downward faster? It's not like it makes it any heavier.

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My first research job offer. Sort of.

I was at a departmental welcome barbecue (yes, physicists can have social events!) and I wound up talking to Chan Kee Jung, a professor here at Stony Brook who's well known in the world of neutrino physics (he headed up the experiment that first showed evidence of neutrino oscillation, but that's another story). When I first saw him, however, I had no idea who it was, because as far as I could tell, it was just some big, stocky Korean with a pony tail, a Hawaiian shirt and a hotdog in each hand, talking to a handful of physics students about why a follow-through is important if you want to punch someone.

I crashed the conversation and discovered that Dr. Jung teaches a course called "The physics of sports" for nonscience students at Stony Brook. As the rest of the students wandered off to have another go at the mango salsa, he and I wound up having a one on one conversation, during which we talked about everything from the spin of tennis balls to the sweet spot of a baseball bat (thank you, COMAP competition!) I also found out we cheer for a lot of the same teams in college basketball.

Next thing I know, Dr. Jung was asking me to be a TA for his Physics of Sports class (I get the impression that the guy who's supposed to do it didn't know much about sports). I told him I'd look into it and see if it would work with my schedule (I've since found out it won't) and I decided to try to steer the conversation towards his current neutrino research, which is a really cool project called T2K, in which a neutrino beam detected on one sideof Japan is detected and studied 300 miles away, on the other side. We had a fun conversation about that, too, and then suddenly, he was suggesting that I should join his research group and come with them to Japan this summer.

I have to say, I was pretty flattered, except for the obvious fact that his favorite thing about me was that I liked Duke and knew the rules of soccer. So it seems the sad fact is this: after all the time I've spent honing my interview skills and my professional persona so that I can appear like a promising job applicant, it turns out the real trick is to get your future employer a beer and a couple of Brooklyn-style hotdogs, and start chatting him up about his favorite sports teams.

A non-math puzzle

Here's a puzzle of a different sort:

It's been a while since I wrote one of these, but I think I'm getting better at it. It's still not up to NYT standards, but I'm making progress. And more importantly, I'm getting faster at it. The first crossword I ever wrote took me pretty much an entire summer. I finished this one in a week and a half, partly thanks to the fact that I'm now using some software to do the grid-setup and to keep track of the numbers and clues. Anyhow, here's the puzzle, have at it. I think it should be about equivalent to a hard Tuesday Times puzzle, but it may be a little harder than that.

In case you need it, or if you find a place I made a mistake, you can check the solution below the fold:

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A playlist for the week

The theme for this, the first of what I hope will be many "playlists for the weeks to come" is "Cover versions that surpassed the original. Here's the playlist; some comments on each song below. 

Note, by the way, that I've intentionally omitted a bunch of songs which are "technically" covers, but whose original version is obscure or tremendously overshadowed. These are interesting in their own right, and may be the subject of a future playlist (admit it: you had no idea Quiet Riot didn't write "Come On Feel the Noise.") But that's not what concerns me here: I'm interested in bands who boldly dared to record new versions of songs that were already popular-- and somehow managed to raise the bar. Alright, enough chat. Give it a listen. A warning, one or two swear words appear.

Long, rambling, stream-of-consciousness style commentary on the songs and why I picked them below the fold. Also, a bonus track!

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∫ A littler math puzzle

I was still working on coming up with a puzzle for my friend's neighbor and I came up with this little guy, which I think is easier than the previous one, and also easier to explain. I haven't decided if I'm going to use it yet, but either way, it's a nice little puzzle so I wanted to share it with someone. Lucky you!

So here's the puzzle: Jill walks into her math classroom at the end of the school day to find Jack sitting sullenly at one of the desks. "What's the matter?" she asks.

"I'm gonna fail my math class," says Jack. "The teacher told me I could do this extra credit problem for him to get my grade up to a C-, but now I'll never be able to solve it and it's not my fault."

"What do you mean?" asks Jill, sympathetically.

"I mean, he told me to start with 1 and then start adding the odd numbers together in order on my calculator, you know, like 1+3+5+7 = 16, and so on. And then he said ' If you tell me what the first nine-digit number you can make just by adding together odd numbers in order is I'll round your grade up to a 70.0%.'"

"So what's the problem?" asks Jill, feeling annoyed that all she gets in this dialogue are questions.

"The problem is, I sat here for an hour adding together odd numbers on my calculator, but then I realized that my calculator can only display eight digits at a time anyway. So I'll never be able to figure it out!"

"Don't be silly!" said Jill, finally using a declarative. "I know what the first nine-digit number you can make by adding up consecutive odd numbers is."


And the question, of course, is "What is it?" Answer below the fold.

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Glenn Beck and double standards

This time I just have a short thought to share. I don't want to be too partisan, and I admit I haven't actually dug through the old news reports, but I'm just surprised no one else seems to be complaining about this. Am I the only one who thinks that, while its really not such a big deal where or when Glenn Beck wants to hold a rally, the real hypocrisy is what he's calling it? I mean, maybe trying to piggyback off the emotion MLK invokes is a little tacky, but who's surprised that Glenn Beck (just like Ed Schultz and other punditainment hosts) is playing with people's emotions in tacky ways? What really ticks me off isn't anything that Beck's doing, its what everyone else ISN'T doing. It seems to me that if any, literally any left-of-center political figure wanted to hold an event and said it was about "Restoring America's Honor,"  he or she would be flayed alive by conservative pundits/bloggers/facebookists. And Sarah Palin's twitter feed would read "Enuff w/ liberals unpatriotic H8! I Didnt kno USA had become DIShonorable?! If U hate it here u can MOVE 2 FRANCE!"

I don't think I'm just wildly speculating; I recall just this kind of talk helping to take down John Kerry and dragging Michelle Obama into a mini-scandal as well. Personally, I remember a few years back having a hard time expressing my earnestly held opinion that president Bush's policies had  deeply damaged America's moral standing in the world. I was worried that if I ever said anything like that, the rest of my opinions would be written off as those of an "America Hater." And yet no one is questioning Glenn Beck's patriotism just because he happens to think that Obama and the democrats have damaged America's honor. Why? Because right-wingers are automatically patriotic. 

I hate double standards like that. And to be fair, they happen in both directions. I  happen to think that democrats get away with shamelessly raking in the dough from huge corporations and then turning around and cutting them huge breaks in regulatory policies. Why? Because the left is automatically against big-business. And while we're at it, why does everyone think Ken Salazar is doing a good job as Secretary of the Interior? Is it just because democrats are automatically good at the environment? The whole thing just really ticks me off. Good thing bloggers are automatically not required to offer constructive solutions and are just entitled to complain about the political status quo.

∫ I learned from teaching undergraduates: Mass Spectrometry Edition

During TA training at Stony Brook this week, one of the things they had us do was perform one of the lab experiments taught in the freshman lab courses and give a presentation on it as though we were explaining it to our students. I was assigned a lab about measuring the charge-to-mass ratio of the electron, which was a pretty slick lab in and of itself. But along the way I also learned something new about how mass spectrometry works, and I learned that phasers might just be electron beams fired in a fluorescent gas. But first things first.

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∫ A little math puzzle

A week or two ago an eighth grade girl who lived down the street from one of my good friends told me how much she liked math; I told her that I would send her a math puzzle and leave a little prize with my friend that she could claim if she solved it.

Actually, the first thing I told her was that she could have the prize if she figured out what perfect numbers were and described them to me. I figured she would consult an encyclopedia or her math teacher, but she proceeded to text "what is a perfect number" to ChaCha and read me the answer verbatim. So I called her a cheater and then resolved to come up with a puzzle she couldn't just look up the answer to.

Anyway, while I was walking to the grocery store the other day, the following little puzzle occurred to me. Unfortunately, I'm worried its a little too easy, since you can get the answer without really knowing what's going on, so it's not going to work as a puzzle form the little mathematician. But I liked it enough I wanted to put it someplace. Don't worry, its pretty easy, but it's based on something kind of neat that I didn't personally realize until the other day. Here goes:

The king's royal mathematician is about to retire, and he has to name a successor. He has two students, both with excellent marks on their exams and both of whom have shown real promise as mathematicians and as mental calculators. Thus, the old man announces a test: In the presence of the king and his court, he will write a 5-digit number on a piece of parchment and place the parchment on the table before the two students. Whichever one of them can be the first to correctly tell the king what the first (one's place) digit in the square of the number on the parchment is will be the new royal mathematician. However, to prevent them both from simply blurting out a guess (with a one-in-ten shot at winning), anyone who answers wrongly will be executed.

When the day of the test arrives the old man takes his quill pen, dips it in the bottle of ink, and carefully writes down his number of choice. Then, to ensure everything is fair, he squares the number himself, whispers the answer in the king's ear and turns around to place the parchment on the table and begin the test. However, just then the mathematician clutches at his chest, and falls over on the table, dead of a heart attack. As he falls, he knocks over the ink bottle, spilling it across the parchment and obscuring everything except the one's-place digit of the number he had written, which is a 7.

"Sire," says the first student, "I know the answer." He announces it to the court and the king nods in amazement.

The question is, what did he say, and, given that his life was on the line, how could he be so sure?

Answer and explanation is below the fold

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A note about the integrals

Occasionally blog posts will show up with with titles like these:

∫ A Little Math Puzzle

Or

∫∫∫∫Why I Love Parseval's Theorem

I intend the integral symbols (the things that look like this "∫") to be a warning that the post contains some technical math or science. The number of integrals indicates the dimensionality of the underlying metric space. Er, sorry, in this context it indicates the level of background knowledge I think you will need to get anything useful from the post. Incidentally, the bad joke above is a weed-out joke. If you understood it well enough to groan, then you can consider yourself weeded out from reading the rest of this post and just keep reading the rest of the blog with impunity ;-)

If you didn't, good for you! And thank you for helping me prove that I have friends who are real people. However, if you still want to read the blog, just use the integral symbols as warning signs. They'll let you know how much heavy thinking you're in for.

Note that, within the post, there may be separate sections that have more technical information than the post as a whole. In keeping with the above description, I'll always mark a multi-part post with the value of the easiest section, because you can still get something out of the post even if you might find reading the whole thing to be a bit taxing. When possible, I'll separately mark the technical sections inside the article.

The general guidelines I'll use are:

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Welcome to WLOG: The personal explanation

Welcome to WLOG: The personal explanation
Okay, so I just told you a why, from a technical standpoint, this is called the WLOG blog. The explanation was basically this: I like math and physics, conveniently, there's this acronym "WLOG" that gets used a lot in math and physics, and the name "WLOGblog" sounds funny. I think that about sums it up.

Really, though there's a second reason, which is probably just as dorky but at least not as nerdy. And that's this: I'm starting this blog just as I'm simultaneously starting graduate school, in pursuit of a Ph.D. in physics, and as you might imagine, that requires a lot of specialization. In fact, in this day and age, getting an advanced degree in any field of study is going to really narrow your outlook on the world, as Matt Might so effectively demonstrates in his Illustrated guide to a Ph.D.

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∫ Welcome to WLOG Blog: the technical explanation

"Hello. What on earth is a WLOG blog?"

"Hello, it's nice to meet you. And I'm glad you asked."

There are basically two reasons why this is called the WLOG blog, a technical one and a personal one. I'll cover the technical one here, and we'll have to get to the personal one in a subsequent post.

Basically, WLOG is an acronym that pops up from time to time in a mathematical proof, and it stands for "Without Loss Of Generality." I know what you're asking yourself right now: "What on earth does that mean, and who in the world gave mathematicians the right to use prepositions in their acronyms?" Well I can only answer the first question, so here goes.

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