RE.VISIONING

Origin/Composer: Phill & Company
Year: 2004

Half our dorm watched the hilarious music video for this movie, and decided to make it kind of our unofficial dorm song and dance. Watch it. You’ll see. It’s Europop at its greatest and worst, all at the same time.

Album: Final Straw
Year: 2003

I don’t really have time to think up a good obscure song and write about it today, so I just went with this. It’s one of my favorite songs, and it kinda fits with the leaving for college thing.

Album: Silent Alarm
Year: 2005

Holy crap, gas is expensive. That’s the only reason I chose this song. The lyrics are interesting, probably with some deep meaning, but I haven’t taken the time to decipher those meanings yet. Bloc Party is an awesome band, with this song not being one of their better ones, unfortunately. I remember adding gas last week, and thought it was incredibly cheap at $2.79 at Costco. Of course, it’s still much cheaper than that of Europe and the rest of the world, so we should have nothing to complain. We should switch to hydrogen cars and harvest the fuel from the sun. Or not.

Origin/Composer: M. Salomome
Year: 2004

I first heard about this from Dustin Foley on the SUMaC group. I emailed and IM’d a bunch of people later that day about it. Then, a day later, a similar message about it came through the mn-arml list from Mitcho. What makes this song great is that its audience is pretty much only math and related majors who have taken quite a few “serious” college math classes. Most people I showed this to did not laugh much, simply because phrases like “open but too dense” doesn’t have any mathematical meaning to them. So to make this funny for everyone, I made a list of the math references in the song below:

Please visit Klein Four’s Official Site for more information about the a cappella group.

Lyrics

The path¹ of love is never smooth²
But mine’s continuous³ for you^a
You’re the upper bound⁴ in the chains⁵ of my heart
You’re my Axiom of Choice⁶, you know it’s true

But lately our relation’s⁷ not so well-defined⁸
And I just can’t function⁹ without you
I’ll prove¹⁰ my proposition¹¹ and I’m sure you’ll find
We’re a finite simple group¹² of order two¹³

I’m losing my identity¹⁴
I’m getting tensor¹⁵ every day
And without loss of generality¹⁶
I will assume that you feel the same way¹⁷

Since every time I see you, you just quotient out¹⁸
The faithful image¹⁹ that I map²⁰ into
But when we’re one-to-one²¹ you’ll see what I’m about
‘Cause we’re a finite simple group of order two

Our equivalence²² was stable²³,
A principal love bundle²⁴ sitting deep^b inside
But then you drove a wedge^c between our two-forms²⁵
Now everything is so complexified²⁶

When we first met, we simply connected²⁷
My heart was open²⁸ but too dense²⁹
Our system³⁰ was already directed³¹
To have a finite limit³², in some sense

I’m living in the kernel³³ of a rank-one map³⁴
From my domain³⁵, its image³⁶ looks so blue,
‘Cause all I see are zeroes³⁷, it’s a cruel trap^d
But we’re a finite simple group of order two

I’m not the smoothest³⁸ operator³⁹ in my class⁴⁰,
But we’re a mirror pair⁴¹, me and you,
So let’s apply forgetful functors⁴² to the past
And be a finite simple group, a finite simple group,
Let’s be a finite simple group of order two
(Oughter: “Why not three?”)^e

I’ve proved my proposition now, as you can see,
So let’s both be associative⁴³ and free⁴⁴
And by corollary⁴⁵, this shows you and I to be
Purely inseparable⁴⁶. Q. E. D.⁴⁷

Math References

¹ Path: Basically the set of points that can be described by a function, or the curve along which a path integral is taken.
² Smooth: A function that can be differentiated infinitely many times.
³ Continuous: A function without “breaks.”
⁴ Upper Bound: The upper bound is a value that can sometimes be calculated to determine the maximum possible value of a certain solution.
⁵ Chain: A totally ordered set in set theory.
⁶ Axiom of Choice: An axiom of set theory stating, in the vernacular, that one can choose an element from each set in a set of sets.
⁷ Relation: A definition relating two or more mathematical objects.
⁸ Well-defined: Mathematically defined in a logical way from base axioms, and without ambiguity.
⁹ Function: Everyone should be able to get this joke 😀
¹⁰ Prove: Logically establishing a statement to be true from previous axioms and proven statements.
¹¹ Proposition: A conjecture.
¹² Finite Simple Group: Umm…these three words take a lot to explain. Well, a group is a mathematical concept that combines a set of objects together with an operation, along with three axioms. Then, you can look at symmetries and other cool stuff in that object called a group. A finite group is simply one that has a finite set of objects defined within it. A simple group, in plain English, is the most basic type of group, similar to the prime numbers in the natural numbers.
¹³ Order Two: The order is the number of elements in a group. A simple finite group of order two is very interesting in that it is the smallest prime cyclic group, with some interesting properties.
¹⁴ Identity: A value e, such that axa^-1=e
¹⁵ Tensor: A geometric entity describing a certain space.
¹⁶ Without Loss of Generality: Often abbreviated “WLOG,” this is often used in proofs to (correctly) substitute a simpler, equivalent special case for the general case to be proven.
¹⁷ An example of a bad use of WLOG. 😀
¹⁸ Quotient Out: In a quotient group, a specific type of simple finite group, certain values are said to be “quotient out” to create the group.
¹⁹ Image: The resultant figure after a mathematical tranformation.
²⁰ Map: A function that takes each value in an object and corresponds it with another value.
²¹ One-to-One: For each x, there is one f(x), and for each f(x), there is one x.
²² Equivalence: A binary relation that is transitive, reflexive, and symmetric.
²³ Stable: A polynomial in which all the roots lie in the left half-plane, or in the open unit disc.
²⁴ Principal bundle: I know this is math, but I have no idea what it means. Check Mathworld or Wikipedia or something.
²⁵ Two-forms: Another one I don’t know.
²⁶ Complexified: A vector space that has been extended to the complex numbers.
²⁷ Simply connected: In plain terms, an object that is in one piece, and without any “holes” or “loops.”
²⁸ Open: An interval that does not include the end-point.
²⁹ Dense: Basically, a set that there are infinitely many values between any two values in the set.
³⁰ System: A group of equations to be solved simultaneously.
³¹ Directed: In graph theory, a graph where the edges have specific directions.
³² Finite limit: A limit is something in calculus…and a finite limit is a limit that is finite.
³³ Kernel: There’re a lot of definitions. Check Wikipedia.
³⁴ Rank-one map: In linear algebra, the number of rows or columns that are linearly independent.
³⁵ Domain: The “input” of a function.
³⁶ Image: I think I’ve done this already…yep. Check number 19.
³⁷ Zeroes: The roots of a function, or just the number zero.
³⁸ Smoothest: Check number 2.
³⁹ Operator: A symbol that defines a specific relationship between mathematical objects.
⁴⁰ Class: Any group of set with a certain distinguishable trait.
⁴¹ Mirror Pair: The paired point in a reflection. Or in physics, the anti-particle or supersymmetric particle of a particle.
⁴² Functors: Don’t know. Check Mathworld or Wikipedia.
⁴³ Associative. The property that, with three values a, b, and c, and operator ^, (a^b)^c=a^(b^c). Associativity is one of the axioms of groups.
⁴⁴ Free: A variable that is not dependent.
⁴⁵ Corollary: A result or statement that comes obviously from a statement that has just been proven.
⁴⁶ Purely inseperable: ???
⁴⁷ Q.E.D.: Quod Erat Demonstrandum, or “Which was to be demonstrated” in Latin. It is often used at the end of proofs as a completion.

Perhaps a Math Reference

^a You: Maybe a play on the letter u, which is often used in calculus?
^b Deep: A theorem that has many implications and goes to a core of mathematics.
^c Wedge: A mathematical shape–a triagular prism.
^d Trap: Just sounds like it could be mathy.
^e “Why not three?” Obviously, many of the propositions in this song would be false if the finite simple group became of order three. Also, this hints at a three-some. I won’t go into what that means, if you’re a poor confused soul

Year: 2004

Jason Mraz didn’t learn guitar until he was 18! Kinda like me! Except that I started at 17. His debut album, Waiting For My Rocket to Come hit double platinum, and his current album, Mr. A-Z (haha, very nice wordplay (Note: “Wordplay” is also his first single from the album)), is also doing quite well. I tried to get tickets to his concert last year at the U, but the tickets sold out way too fast. His songs are amazing in the way that they have lyrics comparable to great folk songs and a beat and pronunciation comparable to great rappers. And while his lyrics often fill many pages, they always make sense, or contain tons of puns and jokes in there.

Almost every Jason Mraz song could be a song of the week, but in the light of his new album, I chose this for one reason. Notice in the lyrics that the word “words” is repeated many many times. Now if you took Wally’s English class through Hamlet, or if you saw Branaugh’s Hamlet, you know that Hamlet says “words, words, WORDS!” to Polonius while feigning insanity. Right after that class (or during it, rather), I wondered whether Mraz knew of this Hamlet line when he wrote the song. I just don’t think it’s a coincidence that in the 4th paragraph/stanza, the word “words” is used three times, just like in Hamlet, and the song ends with

And I just can’t resist including this song, too, as a kind of bonus, since the title reminds me of me playing frisbee on the heliconia team. So, I present, “Geek in the Pink” from his album “Mr. A-Z.”