Greetings! How fares it for those of you who aren't me? I arbitrarily presume that is goes well. Despite the elimination of the Rays, baseball has been pretty good in that the Yankees/Phillies World Series has been averted in stunning fashion, with neither team even reaching their respective league championship. Honestly, I'm cool with any of the remaining teams.

A few news items piqued my interest this week, so I'll be a bit unorthodox and discuss them.

The 2011 Nobel Prize in Physics was given out last week to three astrophysicists for the discovery that our universe is expanding. Something called Dark Energy is to blame, and while this might sound bizarre and enigmatic to you, I assure you that it is far more baffling to Physicists. It is currently postulated that 73% of the universe consists of this mystery material, and we know next to nothing about it. I would go as far to say as that it is currently the biggest unanswered question that science has about the universe, and hence the discovery of the question is well worth the highest award the community has to offer. Note that google image searching Dark Energy is pretty funny.

After hundreds of years the greatest minds of humanity have managed to learn a little bit about 4% of the universe! Hopefully our progress will accelerate along with the universe's expansion 

I'm sure you also heard that Steve Jobs died. The man worked for Atari, Pixar, and Macintosh and was one of the most creative and influential businessmen in American history. Countless facets of our lives would be radically different had he not been who he was and done what he did. Much more has been written, so I need not elaborate. Great man.

But now to the maths. Most know that Pi is the famous ratio of a circle's circumference to its diameter. So if you were marooned on a desert island with nothing but a circle, a ruler, and the foolish idea to waste your precious energy, you would probably be able to estimate Pi's value fairly well from a few quick measurements. But imagine if things were much worse: What if after failing to pay your cyber-taxes in the 23rd century you were recruited into a astro-debtor's program as a planet-to-planet needle salesmen and forced onto an artificial gravity-enhanced, oak-planked vessel launched into the far reaches of the universe and after a fairly nondescript voyage through the vast, inky blackness between galaxies your ship's computer accidently lost its data for Pi in an ill-advised gamble with the onboard coffee maker and you had no choice but to enter a new value that would, depending on your accuracy, either send you hurtling into a black hole or safely on your way into the lucrative business-bosom of Thread-Star VI. This problem (or one without some of the extraneous details I may have added for dramatic effect) troubled the Comte de Buffon in the 18th century. Given a set of parallel lines and a needle, he showed the you can actually come up with an experimental calculation for Pi. Here's how to solve the famous problem of Buffon's Needle:

Suppose I randomly drop a needle of length L onto a set of parallel lines a width d (where d > L) apart as indicated in the above diagram. There are only two free parameters given this situation, the perpendicular distance x from the center of the needle to the nearest line, and theta, the acute angle between the needle and the aforementioned perpendicular. From these constraints we know that the possible values for x range from 0 to d/2 and the possible values for our angle range from 0 to Pi/2. Since all values for each variable are equally possible within these bounds, my probability density functions for each will be uniform. Calling them A and B and normalizing (ensuring that the sum of all probabilities is one) gives:

Now we need only integrate over the relevant parameter-space to determine the odds that the needle will cross a line. A bit of geometry shows that this will happen whenever half the length of the needle times the cosine of the angle it makes with the perpendicular is greater than the distance to the nearest line. Hence the probability that a randomly dropped needle will cross a line is given by:

So, if your needle happens to be the exact same length as your line spacing, the odds the needle will cross a line are 2/Pi or about 64%. Hence, given enough free time you could drop a whole bunch of needles, come up with a percentage of your own, and experimentally calculate Pi!

Using a very similar process, I also solved the problem for the tiled case below (again for a,b > L).

The problems works out in a very similar manner (although one does need to be a bit careful about adding probabilities), and in the end you find that given the above geometry the odds that a needle crosses any of the lines when dropped is:

Of course, the savvy statistician will recognize this as the probability of crossing one of the horizontal lines plus the probability of crossing one of the vertical lines minus the probability of doing both. Note further that in the case of a or b going to infinity we re-derive our Buffon case. Finally, we see that if a=b=L (the happy situation that you have square tiling and your needle has the same length as the tiles), then the odds of the needle crossing a line are 3/Pi, or about 95%. 

I want to emphasize that all the above calculations were done assuming that the length of the needle was less than or equal to the lengths between lines. The results are not valid otherwise and in fact things get a bit ugly in that case. Another way to muck things up is to carry out this calculation for a grid of equilateral triangles! I wouldn't advise it though...the math gets very messy. After all, nature abhors the triangle.

A quick villain for your viewing pleasure. Today I bring you one of the main antagonists from Tale Spin (of the holy trinity including Darkwing Duck and Duck Tales). He is the Air Pirate Don Karnage.

A romantic adventurer, man of accented eloquent and no-good thieving scoundrel of the skies, Don Karnage is a villain not soon to be forgotten. He menaces merchants and pilfers pilots around the humorously named Cape Suzette, looking to score a quick buck aboard his flagship, the Iron Vulture. While he's not the nicest guy and certainly not the smartest, the  pirate captain sometimes turns friend and helps out Baloo, the hero of the show. Among his arsenal of weaknesses are his bumbling crew, startling vanity and incredible overconfidence. His personal fighter plane is pretty sweet though. 

Today's post has only one purpose. That purpose is to tell a tale about baseball; it is a tale of greed and power, a tale of underdogs and comebacks. The end was only just written, but it needs no editing.

In the spirit of my blog, let me start with the villain, the 2011 Boston Red Sox.

The Red Sox are quickly becoming a team as obnoxious and as hated as the New York Yankees. They buy up all the best players and have an air of entitlement about them that can be smelled from the other side of the country (trust me, I know). At the start of September, with less than a month of baseball to play, the Red Sox had a titanic and seemingly impenetrable nine game lead on their closet competitor for a spot into the playoffs, the Tampa Bay Rays.

The Rays are the first of this story's two heroes, an up-and-coming team whose salary is less than a quarter of Boston's. Beaten down in the AL East (baseball's infamously strongest division) since coming into existence, over the past few years they've begun to thrive on homegrown talent, good pitching and solid, all-around baseball. But nine games was surely far too many for even the scrappiest of teams to make up in the course of one short month, right?

Yet Red Sox somehow began to fade; Tampa was catching up quickly. But analysts were not worried. After all, Boston had six games at the end of the season against the Baltimore Orioles, a team that, at times, can hardly remember what sport it is supposed to be playing.

So it fell to the oft-inept Orioles to be the second heroic group in this magical tale. Perhaps they were sick of being looked down on or maybe it was some kindred spirit they saw in Tampa, but despite being woefully out of contention Baltimore caught fire and played evenly with, nay, outplayed the desperate, title-seeking Red Sox during their many encounters at the season's end. Before you could say "legendary chokers," it was September 28th, last night, the final day of the season. The Red Sox and Rays were tied for the wild card. Whichever team won their last game and saw the other defeated would be headed for the playoffs and a shot at the championship. It was do-or-die; the tension was palpable.

Tampa was matched up against the Yankees, the top team in the American League. Boston was again pitted against the suddenly-ignited Orioles. However, the Red Sox had a literal ace up their sleeves, Jon Lester was on the mound, a man who was a perfect 14-0 against Baltimore in his career. Despite their recent troubles, Boston appeared to be in the superior position.

Indeed, things went quite badly for our heroes at first. Perhaps as bad as can be. After a heart-crippling grand slam from the Yanks and several other miscue-filled innings, Tampa found itself down 7-0 in the eighth, a positively impossible situation. Meanwhile, Baltimore was playing its heart out but losing 2-3 to Boston in the middle of a prolonged rain delay. The weather seemed portentious of something, but at the time it could not be said of what.

It was then that the first miracle happened.

Tampa Bay, having been shut out for seven innings against the Yankees, suddenly tore free and, led by a three run blast by the face of their franchise, Evan Longoria, scored six runs in the eighth inning, leaving them down by a single, oh-so-scorable run heading into the ninth. Yet that final inning, surely the last inning of their season, started with disaster and the Rays saw themselves facing the final out of the game. Tampa Bay's skipper, the savvy Joe Maddon did not despair and pinch hit Dan Johnson, a man hitting .108 and who hadn't hit a home run since April. What did he do? Well, what could he do? He smacked one of the most ludicrous and dramatic home runs I've ever seen and sent the game into extra innings.

Hundreds of miles to the north, the skies cleared over Baltimore.

Play resumed and the Orioles and Red Sox continued their titanic clash even as the Rays and Yankees took their game beyond the ninth in Tampa Bay. The night burned on as the pitchers hurled and the hitters lashed but none of the four teams could make a dent. Yet no such unstable system can long remain in equilibrium, and as the Orioles entered the bottom of the ninth down a run, things appeared grim.

Jonathan Papelbon, the famous Boston closer, took the mound. Adam Jones struck out swinging. Mark Reynolds struck out swinging. Suddenly the Orioles were left with but one out in their season. But then by some great feat of will the next two Orioles hitters, first Chris Davis and second Nolan Reimold, smashed balls all the way to the wall for doubles, bringing the score level and leaving Reimold, the winning run, in scoring position. Camden Yards was going wild, roaring in September night and at once believing in the impossible.

The games had that had begun at 7:00 entered their fifth hours and clocks struck midnight on the East Coast.

Robert Andino, last of the Baltimore Orioles, strode up to the plate. He had slain the Boston closer just recently, but surely he couldn't duplicate the feat. He was quickly down in the count. Papelbon readied and threw his final pitch.

Just before that fateful toss, Gary Thorne, the Orioles play-by-play commentator noted, "the Baseball Gods are laughing now." Oh how right he was. Robert Andino lined the pitch into left field, Noland Reimold crossed the plate and the Orioles, with nothing but pride on the line, had somehow come back and defeated the Boston Red Sox!

But this is not the end of the story. Oh no. The Rays still had to win their game to ensure their victory over Boston. Back in Tampa, even as their own BJ Upton struck out in the bottom of the 12th, the Rays fans were going wild. They had just heard the news: mighty Boston had fallen to the Orioles. It's said that those in attendance could feel that the tides had turned, that their beyond-improbable victory was now a thing of certainty. And who came up the to plate next but Mr. Tampa Bay, Evan Longoria, looking to end things once and for all. And just as reasonably as Chip Hilton scores the winning touchdown or as a baseball team loses a nine game lead in the space of a month, he swung his bat and sent the ball hurtling over the fences, Tampa Bay into the playoffs and the reeling Red Sox into the history books.

* * *

Has all that ludicrousness sunk in yet? Well too bad that's only half the story. The Atlanta Braves were leading the in National League Wild Card by eight and a half games at the beginning of September. Somehow they ALSO managed to be overtaken by the team behind them (the Cardinals) causing a race that ALSO came down to the last game of the season which they ALSO lost by falling in the THIRTEENTH inning. Unbelievable. Marvelous. Baseball.

I have returned. 

The summer was a good one. I spent a good portion of it wandering. In particular I visited Sequoia National Park with my parents, enjoyed an epic trek across the Oregon Dunes with a friend, hung out in New Jersey with some bros and visited the trees and beaches of the California coast with my brother and cousin. I read books, played games and was twice thwarted by a Snowy Plover. Oh, also there was physics; I managed to survive preparing for and taking the Physics Preliminary Test given to all graduate students here after their first year. I'll find out if I passed in the next few days, though I'm not really worried.

Having time to read for pleasure was a strange situation to be in and one that I abused quite  thoroughly. Highlights from the summer include Snow Crash and Neuromancer from the cyber-punk genre,  George R.R. Martin's new tome, Shades of Grey, and the first handful of the Dresden Files.

I played a good amount of Starcraft 2 and more recently Civilization 5. Both involve intricate tactics and the latter is delightfully reminiscent of Settlers of Catan.

Behold the beauty (but only if you really want to)

Speaking of the Civilization series, perhaps the single coolest part of any of its iterations are the absolutely breathtaking wonder videos from the second game (there's too many great ones to link, sorry). The sense of accomplishment and power they instill has yet to be equalled.

Classes have started up here again, but I now find myself solely on the student end of the teacher-student spectrum. I work in the lab in the mornings and attend classes in the afternoons. It's a pleasant sort of situation, especially compared to the hectic madness that best describes my first year graduate student experience.

So yeah, the blog is back in business. You'll notice we have new pictures on the sidebar! I hope to update again before the weekend is over with some thoughts on geometric probability. Yeah. Get excited. For now though it's time to bring back The Blog of Many Thing's time-honored tradition of villainy. I watched the Phantom Tollbooth recently and it reminded me very quickly how much I loved this particular fellow. If you've ever had a professor who required you to agonize over the tiniest minutia or a boss who forced you to sink time into wasteful tasks then you already know the power of today's villain: the Terrible Trivium!

The Phantom Tollbooth is rife with metaphorical characters, but my favorite is the spiffy gentlemen pictured above. The Terrible Trivium is a demon who lives atop the Mountains of Ignorance. He attempts to befriend travelers in that harsh environment and wile them into completing pointless and time-consuming deeds for him. Sound innocent enough? Say that when you're stuck spending eternity factoring 20-digit integers or turning a boulder into sand using only a sewing needle! He has the tongue of Saruman and dresses like a gentlemen. The reason behind his mysterious lack of neck or wrists can only be guessed at; though I'd avoid doing so as it's probably the Trivium's plan to make you waste time in that manner. His parting cry, along with his hilarious annunciation, will always comes to mind when I abandon any particularly menial piece of labor: "Come back, come back! There are so many things to take away, and things to bring back! Come back, there are so many useless things yet to do!"

EDIT: There will be a special baseball edition tomorrow to detail what was the greatest and most unpredictable night in baseball wildcard history!

This, my friends, is POST NUMBER 50. In celebration I shall do exactly nothing more than mention the semi-historic event. Well, actually I think I'll post Wikipedia's article on the number 50, just because its articles about random numbers are generally hilarious.

Fifty: when ordering the natural numbers by magnitude, it comes before 51 and after 49 according to Wikipedia 

Classes go well and continue to consume more time than Augustus Gloop does chocolate. My current bill of fare is special relativity and radiation in Electricity and Magnetism, quantum statistics in Statistical Mechanics and the dreaded second quantization in Quantum Mechanics. Also, I'm teaching about electric fields in my introductory class. Fields are a very interesting physical formulation; the thought that an object's very presence alters the universe around it is still quite jarring. And then there's gravity that is even more weird. Why is mass only positive? Why should inertial mass be the same as gravitational mass? Our universe has some strange rules...

I plan to discuss birefringence as soon as we get to the polarization of light waves, which should be shortly. Good times right?

I've been factoring integer terms in some of my many equations lately. It began because of integrals like this, and it remains entertaining to juggle physics all the while knowing that you have precisely 17 two's and eight 3's and two 5's in your mathematical arsenal. I've been doing a lot with counting lately too. In energy space, phase space, real space and sometimes with Multinomial coefficients. I just found out that you can use geometric series to find the area of fractals, for example the Koch Snowflake, created by the intimidating mathematician below.

Helge Von Kosh; he makes delicate crystals of infinite ice

In reading about finding the area of fractals, I stumbled across Archimedes' Quadrature of the Parabola, a work in which he found the area under the famous shape by the method of a geometric series. I can't even begin to understand how ridiculously intelligent this guy must have been.

Enough about such things! The Orioles continue to play decent baseball. Certainly they could (and should) hit a little better, and the pitching should likewise step up, but overall this assembladge of humans actually looks like it could plausibly be called a team. Vlad sadly got his first walk of the season, so his streak of 115 a bats without one came to an end. The record was just 150 or so, so he did pretty well, all things considered. We've lost the first two to the Rays this weekend, but I think we will be redeemed tomorrow. Mother's Day bats ahoy!

I've stalled in my EarthBound playing due to classes and Portal 2 coming out. I'll talk more about that next time, which will hopefully be pretty soon. Other negligible news items include planned camping and baseball trips (separately of course).

Last week and this week exposed me to my first Bollywood movie: Lagaan (the title refers to some kind of harvest tax, not that other Lagann). It's about ragtag band of dancing villagers who have to set aside their differences to fight against their true enemy: the crumpet-scoffing, doily-using, tax-taxing Brits! Of course, fighting them physically is out of the question, and so the movie is all about playing a game of cricket with the province's taxes on the line! One of the songs serves as the training montage too. It's pretty good actually (I really want to try playing cricket now), but quite long. Anyway, today's villain is the Captain of the British cricket team and the troops in the area: Captain Russell!

Captain Russell is a pompous blowhard, racist elitist and morally bankrupt human being. In short, the perfect villain. He struts about the British cantonment with his pristine uniform and daggerlike sideburns ordering his lackeys to and fro, sneering superior smiles with his puckered lips at any who dare look his way. He's actually also pretty clever, but he uses his cunning only to be even more underhanded and bastardly than otherwise possible. Even when playing a game of cricket he doesn't hesitate to send spies into the enemy ranks, order his players to cause deliberate injuries and trick children into making mistakes. To recap, Throughout the movie Russell is trying, for the sake of his own ego, to starve to death an entire province of villages, and he goes about it by the most British, unscrupulous and downright deceitful ways imaginable. Truly a man to be remembered.

The Orioles have finally started looking like the Orioles unfortunately. Perhaps after they escape this horrendously difficult part of the schedule they can start playing better again. I'm having the most fun watching Vlad at bat and on the bases at the moment. His hilariously aggressive and straightforward approach makes me laugh every time. My friend and I postulated that should he become a third base coach he would demand that every baserunner steal home (moreso, his secret sign for such action would simply to be stare his player in the eyes and point to home plate demandingly).

You might have noticed that it's been a while since I last posted. Well, that's what happens when the quarter really ramps up to speed. I'm truly in the thick of things now. Between learning more about magnetic materials for this summer, evaluating 144 ladder operator expectation values, computing volumes in 3N-dimensional phase space (they're the same as surface areas, by the way), determining the quality factor of a resonant cavity and explaining total internal reflection to my 60 students, I've had little time for leisurely typesmanship. Of course, that only covers what I've done in the last 24 hours. I have midterms for the next two weeks and have to grade next week, so yeah...don't expect it to be blog central around here anytime soon.

Did you know Moonbows existed? What about Absolute Hot? I learned of these things just this week. Though the best news of the week was that the entirely of this manga has finally been translated into english. There is but one applicable reply:

EarthBound Segment 5: Quote's a plenty!
Ness and Paula, united and ready to kick some butt made their way back to Twoson and with the help of Everdred and the World's Greatest Bluesmen, the Runaway Five, managed to journey to the next town, aptly named Threed. Unfortunately the town is swarming with ghosts and zombies. After being captured their only hope was a third boy, Jeff, located in the snowy country of Winters. Hearing their plea, Jeff rushed to their rescue in UFO known as the Sky Runner. Along the way he had the help of a legendary monster, a monkey who loves to blow bubbles and his genius father, Dr. Andonuts. Remember how I said I wanted to post great quotes? Here's fewer than half of the ones I really liked from this section of the game (not even including hilarious battle antics):
"Money, that's what I want. Money, that's what is hot. Money, that's what I want. Money, it's what we ain't got 'cept freedom, freedom, freedom is what we've really sought!"
"Tessie may unexpectedly be living in the woods. I personally think so."
"By combining my skills and Dr. Andonuts intelligence, I can become Dungeon Man, the first combination of human and dungeon in history."
"Hey sidewalk, get out of my way!"
"But you'll never run out, 'cause it's a super jumbo pack!"
"Would you like a donut? Well, I was only offering."
"Watch for falling materials! ...Brick Road" (What follows can only be described as the most appropriate fanfare in the history of surprise photography)
"This Bulletin Board greets you this evening. All is well, Good Night."


I expect to play some soccer tomorrow and probably watch Aladdin. Sadly (or perhaps gloriously), this guy has already appeared on the blog in all his malicious elegance. Have no fear though! For today's villain is another of the Disney greats, Ursula.

She's a vile, plotting witch whose flamboyant personality is complemented by her knowing grin and the depths of her unfathomably cold gaze. The only question is if you will you first be ensnared by her sinister plots or her sinuous tentacles. There's little more to say here, but frankly, if you haven't experienced what she has to offer already than you're nothing more than a Poor Unfortunate Soul!

The Orioles are currently undefeated and winning the AL East. Yes, in baseball. Yes, the Baltimore Orioles. No, it's not April Fools Day anymore. Look, I have this picture to prove it:

So far we've had great pitching, excellent defense and timely hitting. What more could one ask for? A season with a winning record. That's what I ask for. There are good omens though, apparently. The last time the Orioles started a season 3-0 was in 1997 (yeah 14 years ago), the same year that we last made it to the playoffs and had a non-losing record.

This coming week marks the first of the quarter during which I will have to deal with homework for every class and teach twice as well. I've been a bit uneasy without being constantly inundated and flanked from all sides by responsibilities, but this should kick things into high gear again. I'll probably not be able to watch many Orioles games, but I'll survive by virtue of sushi and soccer alone if I have to.

EarthBound Segment 4: The Color Blue
It turns out that the Peaceful Rest Valley was named by a madman. Far from the scenic stroll promised by its name, Ness's journey though the Valley was fraught with peril at every step. He was hounded by explosive trees, UFOs that spread the common cold, and parachuting photographers (I'll get a video of this guy later). With the help of Apple Kid's ingenious invention, the Pencil Eraser, Ness finally arrived at Happy Happy Village, the location of the kidnapped Paula. Unfortunately names continued to betray and deceive as the town's moniker failed completely to convey the fact that it was filled with insane cultists bent on painting the entire world blue for the betterment of humanity.

After fighting my way past hordes of cultists Ness found Paula locked tight in a mountain cabin. See can't get out, but leaves Ness with the Franklin Badge and word that the leader of the blue-fanatics has the key. Minutes later I stand before this man, Mr. Carpainter.

A strange man by all accounts, he gives his all to "end your pitiful game!" Mr. Carpainter stands at the heart of Happy-Happyism, the religious movement bent on painting the world blue. Moreso, he possesses the power to call down lightening on those who defy him. Thanks to Paula's warning, Ness can easily knock some sense into this old geezer since the Franklin Badge contains the power to deflect electrical blasts right back to their source! Yet it's what's behind Mr. Carpainter that is especially troubling...a shining statue that seems eerily familiar to Ness...and why is it that Paula was the target of his madness? Can that really be a coincidence? These questions and more will be answered next time, on EarthBound!