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!

Not much to add today. Can't wait for baseball, though. Watch both of these to prepare.

It's the 25th anniversary of the first Zelda game this year! To celebrate I provide:

EarthBound Segment 3: Twoson, because we weren't first
A new town full of strange people, new adventures and shiny things! After walking to town, Ness first rested a spell at Twoson's sleek and modern hotel (complete with upscale music) to recuperate from his travels. Journeying out into the town, we rented a bike, got a secret pizza delivery number, and made an astounding amount of cash by cornering the town's egg/chicken market. Ness also found out that Paula, the girl who had been sending him physic messages, has been kidnapped and taken to the Peaceful Rest Valley. That doesn't sound so bad; kind of relaxing actually. After investing in a few of Twoson's local, fruit-based inventors using his recently chicken-padded wallet, Ness decided to do some last minute shopping at the local market before enjoying what will no-doubt be a blissful journey to rescue a damsel in distress. Ah, to be a hero!

By and large, it was a peaceful and pleasant day for Ness. Well, aside from beating up that mob boss at Burglin Park. Meet today's villain, the head of Twoson's meager but oft-underestimated crime syndicate: Everdred.

He's slick, he's sly and he'll swindle you for all you're worth! Everdred runs the darker side of sunny Twoson, controlling its center of economy, Burglin Park. With his trademark polka-dotted pants, floral shirt and jazz-critic shades/hat combo, few dare oppose his tyrannical but generally good-natured regime. In battle he has no scruples, preferring to bite, steal and knit his brow to victory. After Ness knocks some sense into him, Everdred helps out in the search for Paula, and will be of even greater use to the party later. In the end, Everdred's the scoundrel that cares. I hear he's fond of haikus and is currently trying to get his hands on the mysterious treasure of Lair X. Aggerate...*ominous sound effect*

What? Three days in a row? You bet your beauteous buttons, Batman.

After briefly pondering the underlying linguistics, I've concluded that:
-a foamentous decision involves brazenly pouring the entire bottle of bubble bath into the tub--consequences be damned
-a gnomentous moment involves a lot of bickering shortish creatures who are generally pretty clever
-a loamentous field is great for crops and easy to excavate
-and that a tomentous library contains only the most ancient and unwieldy of books

I recently finished reading Brandon Sanderson's Way of Kings, the first book in his new series. Overall I found it an enjoyable and quick read with much of the creativity and unique worldbuilding that I have come to expect from reading several of his previous books. The entire continent on which the story takes place has the feel of a rocky tidal pool; there are retracting plants, crustaceans of all sorts and intermittent periods of diluvian danger. His signature strategy of building up to a thrilling emotional and intellectual conclusion also reared its famous head, though I might complain that he left a bit too much for the end. My other, and perhaps more damning, grievance is that I'm afraid I must accuse Sanderson of being a mediocre writer. He writes action and battles (both of which he is fond of) quite clearly and well, but often a chapter will go by with very little substance excepting plot advancement. It's as if I would have gotten just as much out of the section if I had just been told that characters A and B talked about X and Y and came to conclusion Z. Though, to be fair, the last novel I read was by one of the better pure writers in fantasy, Mr. Rothfuss. Still though, I'd say Sanderson's capacity for creative design and immersive mystery-style plotlines makes up for this weakness. And after the highstorm of revelations offered by the last 100 or so pages, I'll be sure to pick up the next installment.

Earthbound Segment #2: Of Ants and Officers
Being a hero isn't easy; saving the world ain't a piece of cake. As it so happens, Ness had to beat up a lot of things today. Some of those things were people, and some of those people were police officers. But don't judge! They were asking for it! Ness also managed to peruse the public library, enjoy the calming fluttering of a magic butterfly, purchase an unseemly amount of hamburgers (100% beef), and talk to the happiest trumpeter in the world. In other news Liar X Aggerate actually managed to unearth something this time...something sinister.
Anyway, Frank's defeat put the mayor on our side so after bashing his way through hordes of slugs, rats and antoids on the outskirts of town, Ness managed to defeat the fiendish Titanic Ant and gain access to Giant Step. There he learned the first part of some sort of melody, the inklings of which he can only begin to inkle!
Yet not all was well in Onett-ville, for upon returning to civilization Ness was accosted by an irate cop, who demanded that he appear at the local police station. After spending the night at home and receiving a strange dream calling for him to travel to Twoson (a neighboring town) our hero realized that he had no choice but to confront the roadblock-happy men in blue that compose Onett's finest.

After bashing this way through a handful of henchmen, Ness came face to face with our second featured EarthBound villain: Captain Strong.

Captain Strong is a suburban police force legend. Overseeing the peace and quiet in the sparsely populated, law-abiding Onett for years, while at the same time maintaining the roadblock labyrinth that put his town on the map, nothing gets by his super-keen constabulary senses! In combat he is lethal; Captain Strong prefers to rely on devastating submission holds, but when taxed he will unleash his Super-Ultra Mambo-Tango-Foxtrot Martial Arts, at which point law-breaking becomes impossible and bone-breaking becomes certain. Luckily he befriends Ness after being impressed by his bat-wielding prowess and determination and agrees to let our hero journey to Twoson.

The first day of classes went pretty well. It looks like I'll be waking up early a lot this quarter, but that does mean I'll be done with most time-sensitive things by 4ish or earlier each day, meaning I will have evenings to watch Orioles games and do homework. In other news, I'm teaching Physics 7C again, so magnets and birefringence ahoy!

But the best news is that none of the Sushi crew teach on Monday nights! Hence, tonight will be delicious.

What? Mathematics? Yes, yes. Here it is. The cosine and sine of an angle theta can be defined respectively as the x and y components of a vector (oriented an angle theta above the horizontal) from the origin to the unit circle centered at the origin. That might sound complicated, but you might recall that it's as simple as drawing a triangle and finding the blue and red distances in the diagram below.

Note that the total distance (in yellow) from the origin to the circle is always 1 since the radius of the unit circle is one by definition. This, when combined with the pythagorean theorem, gives rise to the famous trigonometric identity cos^2 + sin^2 = 1.

This simple definition led me to think: why a circle? My next thought was, "why can't I define functions in the same way with different shapes," and that is when the madness began. For you see, the cosine and sine functions are so nice due to the beautiful uniformity of the circle. My functions will have none of this niceness, and will require several additional stipulations in their definitions. 

I now define the Poly_n and Gon_n functions of theta as the x and y components respectively of the vector (with an angle theta above the x axis) going from the origin to the regular n-gon centered at the origin whose side length is such that the distance to any vertex from the origin is one. Another caveat to this definition is that I mandate that all polygons be oriented such that below the x-axis a side of the polygon be parallel to that same axis. To make this more clear, let's check out what Poly₃ and Gon₃ look like:

Since a regular 3-gon is more commonly referred to as an equilateral triangle, you'll note that creating this diagram from my definition was pretty simple; Poly₃ has taken the place of cosine and Gon₃ has taken the place of sine. Note however that we lose the ability to label the yellow distance as one; in fact, it will only be one at the vertices. In addition, the Poly and Gon functions will be piecewise because of the sharp edges. Let's quickly take a look at the the Poly₄ and Gon₄ functions:

Though my simple colored lines look similar, you'll note that these functions will have a completely different form to them than those before. In fact, I hesitate to do more at the moment because they're just so darn ugly. Plotting the functions themselves would be terrible thanks to the jagged shape of polygons, in fact anything I do with them would have to start from basic geometry or with the niceness of sine and cosine. Possible future directions for this include finding the yellow distance and naming it something, finding the form of a few of the piecewise functions using geometry and writing them as a Fourier series of sines and cosines and ultimately finding the power series expansions for them. This could lead to finding some "useful" identities and maybe even derivative relations. Sadly, I can think of absolutely no use for this formulation. The one nice thing I can say about the Poly_n and Gon_n functions is that in the limit as n goes to infinity, they blessedly become cosine and sine! That's it for this adventure into strange maths: join us next time when I discuss approximations in all their vague glory.

EarthBound Segment #1: I'm Onett!
My playthrough of EarthBound has begun! I had planned on posting some of my favorite quotes from each segment, however after eagerly cataloguing each of the game's first dozen or so lines, I realized the futility involved. EarthBound's script is simply one of the most beautiful ever crafted. Each sentence uttered, each sign read delights the mind with its marvelous oddity. It really must be experienced directly.
Anyway, let's dive right in! After learning of Giygas's threat to the universe from Buzz Buzz (who was quickly and tragically smote by the fiendish Larda Minch), Ness realized that he needs to gather the Earth's Eight Melodies, as well as three comrades in order to save the world! Based in Onett, he's told that the first melody is nearby, at the location known only as Giant Step. After a new day dawned Ness's first steps were to:
-Explore Onett and its penchant for roadblocks (they're going for the world record!), mayoral propaganda (by the esteemed B.H. Pirkle) and social revolutions (the Fresh Breeze Movement wants to clean up the town!)
-Talk to local billboardsmen, treasure hunter and vagabond Liar X. Aggerate who survived a meteor impact because he eats lots of garlic. Apparently he has something he wants to show Ness later...but only when he's alone...
-Purchase some handy equipment and grab the Mr. Baseball hat from the secret hideout
-Get his first smash attack and revel in the bone-crushing 16-bit sound effect
-Be ambushed by an eccentric, but mysteriously wise photographer in front of his house

I stopped playing today after defeating EarthBound's first real villain (Starman Jr....well, he just doesn't quite cut it as far as villainy goes), Frank Fly.

First of all you'll need his battle music. Got that funky beat playing? Alright, now you're grovin' to Frank's style. Frank is the leader of the Sharks, Onett's local ruffian gang. Ness finds that if he can defeat Frank, thus quelling the hoodlums on the streets, the mayor of Onett will give him the access to Giant Step that he desires. Frank fights dirty: he uses knives against a kid (then again, Ness does have a baseball bat), talks trash and retreats to his robot, Frankenstien Mark II when things are looking dangerous. Once conquered though, Frank acknowledges Ness's strength, and will support his struggles for the rest of the game! Frank Fly, as it turns out, is one cool guy.

We'll it's been a while. And (but?) for good reason. Last week was finals, yet I'll say no more on such a subject since few reading this have the patience or physical background necessary to care or understand what I would have to say on the matter.

Let us instead discuss how I spent my week off from physics: by camping. Perhaps as eager as I to get away from Davis for a few days, I enlisted the aid of a few of my friends to journey with me to Jedidiath Smith Campground, located in the far north of California's Redwood Park. I'll try to find some pictures, but for now I will have to use English to convey my description of our adventures. The drive was pleasant and scenic: on the way up we had sun and our eyes feasted on titanic redwoods, quaint towns and calm waters, but on the way down we were assaulted by snow, furious seas and mist-shrouded peaks reminiscent of the Scottish Highlands. The stay itself will certainly be one to be remembered. In short we drove though a tree, were attacked by the ocean, skipped rocks at a riverside, huddled around some smoldering logs that could occasionally have been classified as a fire, opposed the wind (Greg) himself to gain purchase on a lighthouse's rocky outcropping, told tales, ate foods and played a game of discovery, settlement and trade while cowering within our flimsy canvas stronghold from the sky's incessant and bone-chilling assault on our lives. I can't wait to go again.

I've decided just this morning to start playing EarthBound, king of games. I think I'll update the blog frequently with my progress and with EarthBound villains. Given that this coming week is but the first of the term, and that homeworks won't be due until much later, I think I should be able to entirely ensconce myself within the game's enchantingly eccentric embrace before reality attempts to pry me loose with its petty needs and cruel demands. To whet your whistles I give you now its awesome (and I do mean it in the literal, awe-inducing sense) title screen:

And now for a random assortment of announcements. First, at the request of a certain Dr. Science, I will be providing Strange Maths in the next post. Second, I find myself really wanting to try steak tartare; it seems quite tasty. Third, I will be, yet again, postponing my fantasy novel reviews. I've now consumed Brandon Sanderson's The Way of Kings, but will speak of it at a later date.

I've watched quite a few movies lately, but only one has a villain who is both worthy of being included on the blog and whose label as a evil force doesn't completely spoil the plot of the film. So I bid you now to cower beneath the sleazy, conniving power of Gordon Gekko's smile!

Before I even begin talking about what a great villain this guy is, let's just take a moment to look at him. Look at his slicked-back, sinister hair enhancing the reptilian image created by the name Gekko. Look at his shifty, plotting eyes that never quite seem to look at your own. But most of all look at that grin. That malevolent, bemused smirk that wants nothing more than to bite the head off of anything that gets in its way. This my friends is the face of a villain. Antagonist of the film Wall Street, Gordon Gekko is a ludicrously wealthy but morally bankrupt investor who will stop at nothing to increase his fortune. During his speech at a shareholder's meeting midway through the film you would swear greed personified walks the earth in his exorbitantly priced, black shoes. He seeks to bring those around him into his corrupt fold, chews them up and spits them back out once he has what he needs. This man is truly villainous.