Alternative, Baby

"Alternative, Baby" by Reel Big Fish is a love song of the sort that I tend to enjoy, which is to say the narrator is frustrated and self-deprecating, and the object of his affection unattainable. (Read into this what you'd like, but I'd recommend against drawing too many conclusions.) When I had a radio show, I once played a brief set of love songs for Valentine's Day, and this fit right in between "She's Actual Size" by They Might Be Giants (about a woman who the narrator must constantly remind himself is not larger than life and thus unapproachable) and "I Love a Magician" by The Dismemberment Plan (in which the girlfriend has supernatural powers and may not actually like the guy that much).

Reel Big Fish (hereafter RBF) is one of a few ska bands that became popular in the late '90s. I still find it somewhat amazing that there was a mini ska boom at the time, since the prominent horns and bouncy punk rhythms that most so-called third wave ska acts had going for them was pretty far removed from a lot of the rest of the popular rock (read: alternative (back then, anyways)) scene.¹ I was a casual fan of ska; I liked the songs on the radio, and I went and got albums by two of the bands with the biggest hits: the Mighty Mighty Bosstones (Let's Face It) and RBF (Turn the Radio Off). Later, I would branch out and get albums by other ska bands, but during my freshman year of high school those two albums were more or less the extent of my knowledge of the genre.

This means that I've had Turn the Radio Off for close to a decade now (a fact that surprises and somewhat dismays me), and I still listen to it every so often. The songs are are fun and funny. The jokier songs are more immediate, and were my favorites originally. I'm talking about songs like "Beer" (which extols the virtues of beer for smoothing over relationship problems), "She Has a Girlfriend Now", "Say 'Ten'" (which picks on the ever-popular target of vegetarians), and the hit "Sell Out" (which is nothing but the band poking fun at itself). The rest of the album is quite good as well, with the only real weak spots being "Snoop Dogg, Baby" and "S.R.". Still, by the end of any album it's easy to not be paying much attention, and that's why it took me so long to really appreciate the last two tracks, "I'll Never Be" and "Alternative, Baby".

"I'll Never Be" is a mostly understated song wherein the narrator worries that his band will never amount to anything, or worse, that he'll never amount to anything. This is a bit of a recurring theme in the album; "Everything Sucks" covers similar territory. The two are complementary; "Everything Sucks" is brash, bitter and defeated in the face of imminent failure, while "I'll Never Be" is genuinely troubled and striving ('I try I try I try I try/every day, every day'). It would be a bit of a downer to go out like that, so the band moves on to something with a little bit of swagger.

The drummer gives a quick count by hitting his sticks together, and the horns come blasting in, along with the rest of the band. It's a punchy horn line at first, well served by the rock-style guitars that start the song. They quickly shift to a ska rhythm, and the horn part becomes more fluid; it finishes as the guitars vamp a little bit, and the horns drop out to make way for the vocalist, who begins his tale. Like so many guys, our narrator is at a show and finds himself smitten with a girl in the band² (the 'alternative baby' of the title). But of course someone cool enough to be in a band is probably too cool for him. Things get a little quiet as he admits

But I don't wanna talk to you
'Cuz I know I'd just say something stupid
And I know you've got better things to do

Who can't relate to that? Okay, I'll try not to project and just say I can relate to that. But things don't stay down for long, as the chorus roars in:

Hey, little alternative girl
Don't you wanna be my friend?
You know I'm singing all my songs to you
and it's all right if you don't understand

And so it becomes clear that our narrator is in a band in part to impress the ladies. I guess that means now is as good a time as any to talk about a band I was in while I was at Case. Two people I knew through the radio station, Matt and Tim, had started a ska band, since they both loved ska.³ Once while talking to Tim I mentioned that I played piano, and he asked if I wanted to play keyboards in his band. This took me back to high school, when one of my friends had been in a ska band called the Evil Geniuses, and I had been jealous because their name was awesome and it sounded like fun and I wanted to be cool and in a band. I had to say yes. It turned out he was still in a bit of a recruitment phase, as we were adding and dropping members for a month or two after I joined, but we eventually stabilized at 9 members (I think). We got a name (Stop Laughing), played 2 shows on campus and in general had a good time.

The summer after the first year we were together everybody went home or otherwise dispersed, but we knew we wanted to play together more when we got back. Then in August, we got some exciting news. Once a semester, Case got a semi-well-known band to play a big show on campus.⁴ The upcoming fall, they had decided to bring RBF to campus. Even better, since we were known as the campus ska band, we were asked to open. Since I was at home I tried to explain to my mom why this was sort of amazing (not to mention perhaps a little undeserved), but she had never heard of RBF (unsurprisingly). "I guess we have to actually write some songs," Tim said. When we started nearly all the songs we played were covers, so we needed to write enough songs that we could do a set that was mostly our own stuff. As soon as we got back to Case we got cracking, and we managed to put together a new song just about every week for the first month and a half of the semester. During our practices it became a running joke that the keyboards were a marginal part of the band, and if I wanted to have any sort of prominence (such as a solo), I'd have to write a song myself. So I did, whence the song "Goth Baby".

I didn't realize it at the time, but "Goth Baby" is heavily influenced by "Alternative, Baby"⁵. The song is structured similarly, and lyrically fits into the mold described above, meaning the two songs resemble each other at times (especially the choruses⁶). It was fun to write and fun to play, and I probably owe a lot of that to "Alternative, Baby".

And what about the rest of "Alternative, Baby"? After the first chorus, things move forward. It seems like the narrator has made some attempt at starting a relationship, but things don't quite work out. With the couplet 'I said I was cool/but I can't lie to you' he seems to cave in to his own misgivings, an impression which the final pre-chorus reinforces:

And I don't wanna start again
'Cuz I know it'll be the same in the end
I didn't like it the first time anyway

Things don't end on a down note, however. The chorus reappears a couple of times, there's a zippy trumpet solo, and the horn line from the beginning reappears to help close out the song. There's a final blast and things end on a literal and figurative high note.

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1. While writing this I realized that Green Day at least had the bouncy punk going for them, and they were big then.

2. Seriously, if one were ranking attractiveness on a scale from 1-10 (which of course is horribly reductive and objectifying, but, um. Everybody does it?) being in a band adds at least 1 point to one's score, possibly 2 or 3 if the band is good. Perhaps this was a contributing factor to my joining a band (about which more is coming later), but I doubt it.

3. In fact, Tim's favorite band was RBF. This is important not just because it helps make this seem like less of a digression than it is, but also for how it ties into the story of the band.

4. e.g. Jurassic 5 did a show in Fall '04.

5. My song was originally titled "My Goth Baby", which is obviously totally different. Well, it's at least not the exact same.

6. For comparison, the chorus of "Goth Baby":

I'm a happy ska guy
but when she passes me by
I wanna be sad
I want her so bad
My goth baby
Depresses me
I know that this can never be

Following the Rules

First, an apology. In my last post I implied that I would be doing a post on Cory Doctorow's stories next, and this is not that post. I still plan on writing one, but I realized last night that I had forgotten about (and hence, hadn't read) his most recent short story collection, Overclocked. Since I was planning on discussing his stories as a whole, I figured that I should probably wait until I had, in fact, read all of his stories before I did the post. Since no one actually reads this blog, this explanation is a bit superfluous, but just in case you were looking forward to such a post, now you know that you'll have to wait.


Now that we know what this post is not about, let's move on to what it is about. On Saturday I sat down and watched the whole Evil Dead trilogy. I'd heard good things, and I had already seen Army of Darkness at some point on TV, so I was interested. I dig Bruce Campbell largely because of Army of Darkness (from which the picture on the right of him as Ash comes), and Bubba Ho-tep (which is about 10 types of awesome). So I wanted to like the Evil Dead movies, and I was hoping they might even be scary. However, when all was said and done I was left feeling rather flat.

Most of my problems were with the first two movies. They weren't particularly scary, and the reason why contributed to my overall dissatisfaction with them. It comes down to something simple: they didn't follow any rules. Now, I know what you're thinking. Rules make for predictable, cliched, crappy movies. It's a good thing if a movie doesn't follow any rules, especially a horror movie, since you don't know what's coming. And I agree with you. Sort of.

See, you're talking about what I would call "rules", with quotation marks. "Rules" like the first Scream movie made fun of and deflated.

• If you say "I'll be right back," you won't.
• Your car will never start on the first try when you most need it to.¹
• Etc.

"Rules" are stupid, and are the product of unimaginative storytelling. They're not actually anything the characters have to follow (and in many cases, following these "rules" often seems supremely stupid). To their credit, the Evil Dead movies do a good job of ignoring many of these "rules". So what's my problem? What the hell are rules sans quotation marks?

Rules dictate how characters act in a story, and can't be tampered with without taking the viewer/reader out of the story. They are generally implied, which allows for some wiggle room on the writer's part ("There's nothing in the rule book that says a giraffe can't play football!"), but they shape what you, the entertainment consumer, will accept in a narrative. Let's use a simple example: If you were watching an episode of Law and Order and one of the detectives flew off a la Superman to chase a perp, you would probably shake your head and change the channel.² But if you were watching an episode of Justice League Unlimited and Superman flew off a la Superman, nothing would be amiss. The rules are different for the two shows. Crime procedurals: no flying people. Superhero stories: flying people OK. Or another example: the very notion of a deus ex machina relies on the existence of certain rules for storytelling. If there were no limits on what a character can do or what can happen in a story, then there would be no need for a term to describe a device that cheaply gets around such limits.


So back to the Evil Dead movies. The rules were really ambiguous, if not non-existent. What exactly causes one to turn into a Deadite (the main monsters, like the one pictured to the right)? It's not as simple as being bitten or touched by a Deadite or else everyone would have turned into one, and much sooner, too. In both of the first two movies, something (not shown, the camera takes its point of view) comes through the window and turns someone into a Deadite, and in Evil Dead 2, Ash gets turned into a Deadite (temporarily) after being attacked by something similar. So maybe that's it? Except several others turn into Deadites after being attacked by their newly Deadite friends, or after being killed. Plus, Ash turns into a Deadite again at one point with no provocation beyond being out in the (admittedly evil) woods. So it's not really practical to be scared about the possibility of someone turning into a Deadite, because it seems completely arbitrary.

Related to that is the question of exactly what the evil forces around the cabin can do. As I mentioned, they can definitely break through the windows of the cabin. They have some control over the interior of the cabin, as evidenced by a pretty great scene where everything (the lamp, the chair, everything) starts to laugh menacingly, which gets to Ash. But they seem stymied by the doors. Okay, this seems pretty consistent, doors are stronger than glass, after all. Except late in both movies, the Deadites break through the doors. So why did they wait? Or did the doors weaken? And in the first movie, a Deadite trapped in the cellar the whole movie suddenly breaks out in the end, no problem. Again, why the wait? So it's not really practical to be scared about the possibility of a Deadite getting into the cabin, because they will eventually, when it's least convenient.

And just how dangerous are the Deadites, anyway? In Evil Dead, one of the Deadites sits in a doorway mocking Ash for several minutes, even allowing Ash to draw a shotgun and aim it at its head, but doesn't attack until later. In Evil Dead 2 and Army of Darkness, we see scenes where Deadites do something to characters offscreen that causes a geyser of blood. We later see (in the former case) the character's skeleton, implying that his flesh was removed from his bones in a very violent manner almost instantaneously. But Ash mostly gets hit with more conventional attacks involving fingernails, biting, punching, and occasional weapon use. No instant-filet attack here. So it's not really practical to be scared about how dangerous the Deadites are, because it depends on how important of a character you are.

Do you see the recurring theme? By failing to set up rules for the Deadites, the movies make the viewer (or at least this viewer) stop caring about what's happening, because it all seems to be without rhyme or reason. There's no tension, because one can simply assume that something will attack after a certain interval, no matter what the characters do in the meantime. This means that no matter what the characters do the outcome will be the same. Why watch a movie where the characters' actions are pointless?

At this point it's probably easy to accuse me of overanalyzing these movies. I should just enjoy the fast pacing of the trilogy, and the slapsticky aspects of the later two. But it's hard to enjoy a movie where I don't care what happens, no matter how stylishly whatever it is does happen. Army of Darkness suffers the least from these problems, and so is the one I enjoyed the most. In fact, before seeing the first two and noticing these things, I liked AoD better, because I didn't notice the few times these problems did appear.³ I didn't set out to pick these movies apart, and I didn't devote any extraordinary mental effort to finding these problems. They are obvious and grating.

Good stories follow internal rules. These can be pretty loose; in Gravity's Rainbow, for example, all manner of absurd things occur, including a pie fight taking place in midair between a hot air balloon and a plane, but within the framework presented, this is fine. Even tight rules can allow for good stories. John Carpenter's The Thing has very simple rules.

• The Thing can look like anyone.
• Every cell of the Thing will do whatever it can to survive, and replicate to the best of its ability.
• Fire will kill the Thing.

That's pretty much everything you need to know about the main menace of the movie, and it's everything the characters know. In all instances, the Thing follows these rules. And yet these simple rules make for a movie about which it is pretty much required to use the words "tension" and "paranoia" when reviewing it. I held my breath several times when watching that movie, I gasped, and most importantly, I was completely absorbed.

When characters follow the rules it allows one to get into the story and to understand why the characters are acting the way they are. When there are no rules, or the rules are broken, you're not shocked or delighted like you might be when the "rules" are broken. You're confused and all of a sudden all-too-aware of the artifice of the whole venture. This is definitely not a good thing.

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1. Evil Dead kinda does this one, as there is a scene where a car will not start until after several tries, but there is no imminent danger present, so I'll give it a pass.

2. This channel would almost inevitably also be showing Law and Order, though.

3. AoD is really an action-comedy, and a very slapsticky one at that. It's easy to miss the inconsistencies at first, because here they are almost always in the service of some gag or another.

Everything and More: A Review, I Suppose

This summer, with no job to speak of, I'm finding myself with a lot of time on my hands. This is not something I'm used to, but I'm somehow managing. I've been doing some light reading, going through books at a good clip. At this point, I've read most of Cory Doctorow's novels (still have his short stories to go), and I'll probably write another post about those once I make it through them all. Today, though, I'm writing about the book Everything and More: A Compact History of Infinity, by David Foster Wallace.

A couple of things to start off: First, David Foster Wallace is best known (to me, at least) as the author of Infinite Jest, a massive novel about addiction, consumption, family, tennis, and a few other things besides. It plays hard with narrative form, toying with chronology and containing about 100 pages of endnotes which are crucial to the story and must be read. I really enjoyed it, and it even got me watching tennis (although I mostly just watch the majors). Second, the book is about the mathematical development of infinity, from the Greeks to Georg Cantor, the mathematician who discovered/created most of the important proofs related to infinity that allow mathematicians to work with infinite sets in meaningful ways. So, a book about math by an author I dig? Of course I picked it up. These two things (i.e. the book's author and subject) likely will not motivate you as strongly as they did me, so I am attempting to add one more reason to that list with a positive review.

The book's content is strong, with a good overview of the development of infinity and how various problems of interest over the years spurred mathematicians to deal with (or in many cases, ignore) infinity and related concepts¹, and how prevailing attitudes towards the infinite affected these developments². So it's not just math; you get a good helping of history and philosophy as well. In this way it is similar to the book Zero: The Biography of a Dangerous Idea. I didn't like that book very much, though; it read too much like a series of magazine articles that sought to hype their subject material unrealistically. I can only stomach so many statements about the terrible power of the Void, i.e. zero. Anyway, this book is better, and less worried about the importance of its central concept (even though it is important).

And the math isn't too bad. The book was written with a reader in mind who had done well in high school math, but didn't necessarily do math in college. I would say that if you have taken a first-semester calculus course, you definitely have enough math background to read this book. Even if you haven't, as long as your eyes don't completely glaze over when somebody mentions math, you can read this book with a little effort. I mean, Zeno's Paradox is the problem given the most time in this book, and I'm pretty sure I saw that explained in a Meg Ryan movie once. Not that I watch Meg Ryan movies. Damn.

Of course, this very reduction in complexity to make the book more palatable to the general reader can be somewhat frustrating to someone who is familiar with the math being discussed. It can seem that important details are being glossed over; still, one gets the impressions that such decisions were made carefully after much tweaking to see which details could be pared down. Wallace acknowledges this glossing in at least one example, so he's not unaware. Overall, the math comes off well (most importantly, Cantor's diagonalization proof, central to his results on the relative size of certain infinities, and related proofs are presented well), but I did find the discussion of Cantor's work on the Uniqueness Theorem for Trig Series³ to be murky. (To be fair, part of this is undoubtedly my tendency to confuse sequences and series; there is a difference.)

But what makes the book great is Wallace's style. It's conversational, humorous, and knowledgeable. It reads like a series of entertaining lectures by a cool professor given to small asides and allusions to interesting facts that he just doesn't have time to cover. Wallace spins off footnotes like nobody's business⁴, and this is often where he sneaks the funniest remarks. He's not shy with parenthetical remarks, either. I would often count 3 right parentheses at the end of a sentence, meaning he had doubly nested parenthetical statements. It was the first time I could think of prose that reminded me of LISP in any way. In short, it's written in the sort of focused but cross-referenced (so to speak) style I like.

So, if you're curious about infinity, and want to read a book that traces it from the Greeks and Zeno to roughly the present day, I recommend this one. If someone ever told you to read the book Zero: A Biography..., read this one instead. And hey, I'll probably have another post up in a week or two about some fiction, if that's more your thing.

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1: Good example here: the creation of calculus to deal with a wide variety of physical problems. Calculus requires one to use infinitely small quantities, but there was about a century of hand-waving about these before mathematicians figured out exactly why they could do math using such quantities.

2: Another good example: The Greeks as a culture didn't have a concept of infinity (or zero), and this was part of they reason they didn't manage to create calculus about 2 millenia before it ultimately came about. At least one Greek mathematician, Eudoxus, had the right idea, just no way to even acknowledge the infinities involved.

3: Don't worry if that sounds crazy, it's the hardest math in the entire book. It's not typical.

4: A device I'm rather fond of, clearly.

Panopticon

After I received my first paycheck from my summer job, I went out and bought a CD, my first in a few months. I picked up Panopticon, by Isis. It wasn't the first Isis album I'd heard; I bought The Red Sea a while back and liked it quite a bit. It is grandiose and abrasive and punishing. Maybe it's just the title of the record (and that of their 2nd most recent album, Oceanic), but it reminds me of a hostile ocean, inspiring fear and awe as giant waves of guitar, thundering drums, and acrid vocals crashed down in my ears. The only respite was a few samples from a David Lynch project, including a desperate recitation of some William Blake. It's a good listen if you're in the mood to be dazed and a little scared by your music.

5 years (and 5 releases) went by between The Red Sea and Panopticon, and the sound has changed. Compositions are calmer, more drawn out, and include more electronic bits. This is not necessarily a bad thing. Occasionally you may hear Isis called "post-metal", as in "post-rock" with metal touches, and Panopticon earns this title much more than The Red Sea, which had more in common with Neurosis than Godspeed You Black Emperor. Now songs begin with meandering guitar lines that become powerful chords; the "angry bear" vocals of previous albums are much rarer. There are still moments when the guitars threaten to crush you, holding you down for the drum hits to pummel you, but overall the album is a more atmospheric affair. Not indistinct or lazy, no. But where The Red Sea was an exhausting trip through hostile waters, Panopticon calms down long enough for you to get your bearings, and decide that you have no idea where the hell you are, but it's dark, and you'd rather be home. Then it shows its teeth.

But it's not just Isis's sound that can be considered artsy (if you believe that metal must be fast). Isis has certain lyrical fixations throughout their albums. As mentioned previously, the ocean comes up frequently. They also often refer to a central female figure, occasionally identified with a tower. It is this theme that gets a nod on Panopticon. It turns out that panopticon isn't just a cool word. Back in the early 19th century, Jeremy Bentham¹ tried his hand at prison reform. His design was simple. A circular prison, with cells whose doors faced the center and windows faced outwards. In the center, there was a giant watchtower².



The design hinged on two complementary principles. The prisoner can always be seen, not only from the watchtower but also by other prisoners across the circle, backlit by light coming in their windows. The guards in the central tower can never be seen, their presence hidden by blinds and the like. So as far as the prisoners know, they are always being watched. This leads to better behavior, and paradoxically allows the prison to have guards watching less often.

Bentham had high hopes for his design, but it's not best known as a practical prison layout. Instead, it is as an idea that it has proven to resonate strongest. It gained most of its notoriety when Michael Foucalt focused his attention on it, in Discipline and Punish. As I understand it, he argued that the Panopticon structure was a sort of ultimate version of hierarchy, with one (always unseen) party being able to exert control at all times over the other (always observed) party. Read more here. Later social theorists have pointed out that the modern prevalence of surveillance technology allows for a Panopticon-type social structure to be put into place (to be fair, George Orwell totally saw this coming). There's a lot to be said for this idea; surveillance cameras are pandemic (moreso in England, that den of brutes and thieves). Head over to Google Maps and you can see satellite images of just about anywhere on earth, generally of pretty high resolution. I can, in fact, see my house from here³.

Isis is full of smart guys, and they know all this stuff. I haven't mentioned these things completely randomly; the liner notes contain quotes from Bentham and Foucalt, as well as one regarding new technology. Not to mention the album art is composed entirely of satellite images. And hey, here's some lyrics from the song Backlit:

Always object
Never subject
...
Always upon you, light never ceases
Lost from yourself, light never ceases
Thousands of eyes, gaze never ceases
Light is upon you, life in you ceases

If the idea of a total surveillance society seems far-fetched, then you underestimate the incentive governments, corporations, extortionists, and Hollywood have to get you on camera. If the idea of a total surveillance society seems like a reality to you, then you should cut back on coffee and watching Enemy of the State. The big question is, quis custodiet ipsos custodes⁴? In the Panopticon, no one does. And it is this secrecy that is so threatening. I'm sure we can all think of some secrets that have come to light recently that made us feel the "unequal gaze".


Just saying. And the answer to the big question is obviously, "the people". Well, that's the idea, anyways. Here's hoping that continues to more or less work out for us.

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1. Fun fact: Jeremy Bentham had himself stuffed, and his corpse "attended" board meetings from time to time at the college he founded.
2. See? It's a tower.
3. Here being my computer, of course.
4. Who watches the watchmen? Sorry, not trying to be fancy, it just sounds cool. Also it's in one of my favorite comics, Watchmen.

The Imaginary, the Hyperbolic, and Mathematics

Ah. This post is going to be a long one. But then, I haven't really done a short one yet. What follows is the final paper that I wrote for my Philosophy of Mathematics class. It makes reference to all the readings we were given in that class, so it moves around a bit, but that should just serve to keep it interesting, right?

The conclusion is more or less what I believe about mathematics. The practicality of mathematics is often vastly overstated, and yet there is something that I find fulfilling about it. Over Spring Break I read A Mathematician's Apology, by G.H. Hardy, and since then, I have come to agree more and more that mathematics is a field concerned mostly with aesthetics. When dealing with messy fractions involving square roots and the like, one often calls the result ugly; certain proofs are called elegant almost without fail. I have a textbook which compares spectral theorem to a symphony. The language of beauty is tied into mathematics more deeply than most realize.

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If you asked an average person to describe mathematics, they would likely respond by saying that mathematics is the study of numbers. Some might remember to mention geometry, a topic most don’t deal with beyond one class in high school. Although this is a limited view of mathematics, it’s not wrong. And how hard can numbers be? Or plane geometry, for that matter? While some may say that they are not mathematically inclined, most people will tell you that they know what a number is, and they certainly know how shapes work. So 22/7, or the square root of 2? Definitely numbers. And two straight lines side by side will obviously never meet. Then what about the square root of -1? Is that a number? And what about hyperbolic geometry? Is it useful, or simply a warped version of what is real? Mathematical constructs like these raise questions about the very nature of mathematics.

The square root of -1, more commonly referred to as i, gives one pause. The term “square root” highlights the difficulty. The square root of 2 is the length of a side of a square with area 2. The square root of -1, then, is the length of a side of a square with area -1. Such a square makes absolutely no physical sense, which is why i is often called the imaginary number.

Is mathematics concerned with physical reality, though? This discussion goes back quite a ways. Plato, in his Republic, discussed mathematics at some length. At one point, Socrates says in reference to geometers (the mathematicians of their day), “They talk of squaring, applying, adding, and the like; whereas, in fact, the entire subject is practiced for the sake of acquiring knowledge.” (Book VII, 527a-b) So the physical impossibility of i is of no concern to mathematicians. Earlier in the Republic, Socrates takes the geometers to task for using physical objects (specifically, “the animals around us, every plant, and the whole class of manufactured things” (Book VI, 510a)) as images on which they base their studies. But no such physical object exists for i. Instead, one might say that when dealing with i, mathematicians are using other numbers as images. In the same way that geometers make arguments about squares and diagonals, drawing inspiration from the imperfect squares and lines that they see in nature, a mathematician might make an argument for the existence of i by looking at more conventional numbers. -1 is really not that different from 2. They are both integers. So if 2 has a square root, than why wouldn’t -1? This is how the square root of 2 acts as an image for i. When dealing with i, one must work completely through reason, and although still falling short of dialectic, one is still operating in the third portion of Socrates’ divided line, referred to as thought, well into the intelligible section of the line[1]. It is ironic that such numbers are called imaginary, when it is the lowly first section of the line that is referred to as imagination.

Although the concept of i has been around for centuries, it was ignored and disparaged for quite some time. Leonard Euler put in a lot of work to make i respectable. He receives the credit for introducing the notation of i for the square root of -1, and the famous equation e^iπ+1=0 bears his name. Starting in the 19^th century, mathematicians began to discover a number of surprising properties of functions involving i. This was part of a general movement in mathematics, mainly spurred by developments in geometry (which I will return to shortly), toward increased rigor and examining the foundations of mathematics. The question inevitably arose: What is mathematics? Kant classified mathematics as a synthesis of a priori knowledge with knowledge from the content of specific experience. In response, Dedekind, Frege, Russell, and Whitehead attempted to show that mathematics (in Dedekind’s case, just arithmetic) is entirely based on a priori knowledge: that is, that it is entirely analytic and concerned only with pure logic. This school of thought is known as logicism and is, at least initially, an attractive explanation of what mathematics is and with what it is concerned.

Of course, i fits into all of this. If anything, the existence and study of i in mathematics would seem to provide an excellent counterexample to Kant’s argument that mathematics is synthetic a priori, for there is no specific experience from which one might get the concept of i. As stated earlier, no squares have area -1. How could a field of study that deals with such a concept be synthetic? Then again, as also stated earlier, one might draw the concept of i from previous experience with other square roots by simply generalizing to the non-physical. I have studied no Kant (unfortunately), but I imagine something known through this type of mental experience is still considered a posteriori knowledge.

Still, the logicists have a trick or two up their sleeves to talk about i in terms of pure logic. It requires only a rather simple argument to show that all numbers involving i (called complex numbers) can be represented by 2 real numbers, and any operations you can perform with complex numbers are the same as certain operations on those 2 real numbers. So if the real numbers can be said to be purely logical construction, it follows trivially that i, and indeed all complex numbers, are also purely logical constructions. But there’s the rub; it has turned out to be subtly and maddeningly difficult to give a logical formulation of the real numbers. By the time one has arrived at such a construction, its definition has enough conditions on what a number is that it seems far from a priori knowledge. And Gödel’s Incompleteness Theorem brings into question whether looking at mathematics only in terms of logic is even useful. After all, one could derive a statement whose truth is undecidable from its axioms. This is a grave limitation that naturally leads to the assertion that math is more than just logic, for good or ill. So although i has risen to be as respected as the other numbers, it turns out that this is only so far up. It would seem that even as unreal a concept as i must be taken to be known only through experience, albeit experience of a very particular sort.

All this focus on number has led us away from the other branch of mathematics, dealing with shape. Geometry has been intensely studied at least since the time of the Greeks. It is geometers that Plato alternately criticized for basing their studies on unshakeable, physically-based hypotheses, and lauded for working by means of pure thought when making their arguments. Later, probably at least in part as a response to Plato, Euclid would attempt to lay down a set of axioms and postulates from which the important geometric theorems of his day could be logically derived. Many of these were uncontroversial, perhaps because they fell into the trap of using the perceived behavior of physical objects as their basis. It seems clear from experience that “a straight line may be drawn from any one point to any other point” (Euclid’s Elements, Book 1, Postulate 1), or “The whole is greater than its part” (Book 1, Axiom 9). But one axiom stood out as being different from the others, and caused a great deal more concern among mathematicians. Euclid’s parallel line postulate can be stated in many different ways, most commonly as, “Given a point and a line, there is exactly one line through that point that will never intersect the given line,” although this is not the form found in the Elements. Though this postulate was fiercely debated, and to some seemed that it should be somehow derivable from the other axioms, it was shown much later to be indispensable when dealing with Euclidean geometry. In fact, if one removed the parallel postulate, he or she would end up with a completely alien system of geometry, one in which nearly everything diverges from everything else, given enough time. This system is called hyperbolic geometry, and given a point and a line, there are multiple lines through that point that will never meet the given line. To many, it sounds ridiculous. However, it has been shown that all of Euclid’s other axioms work just fine in hyperbolic geometry. There is even a simple model of hyperbolic geometry, a circular plane with its border at infinity, and straight lines drawn as circular arcs that cross the border at a right angle. But as simple as this model is, it seems absurd, and a little lonely. Everything ends up infinitely far away from everything else.

It was inquiry into alternate geometries such as these that helped lead to serious discussion of the nature of mathematics. In dealing with such geometries, it was shown that any theorem that could be deduced from its axioms should hold in any accurate model of those axioms. This lent itself to a logicist view of mathematics, because so long as the axioms of geometry could be considered pure logic, all of its theorems were deduced through pure logic, and so geometry itself could be considered purely logical. This ran into the same problem as the logicist view of numbers, namely, the Incompleteness Theorem. Other schools of thought arose in the late 19^th and early 20^th centuries as well. One, formalism, is in many ways similar to logicism, and so will not be discussed in this paper. But the third major school of thought, intuitionism, has serious differences from the other two. It seems to be a complete restructuring of mathematics that leaves behind some of the most important tools in mathematics to arrive at new and novel ideas.

Intuitionists believe that mathematics deals solely with mental constructions based on intuition. Based on this belief, they reject the Law of the Excluded Middle, which holds that if something is not not true, then it is true. An intuitionist would respond that by showing that something is not not true, one has not shown any construction in which it is true, so how can one draw such a conclusion? This thinking led to a radical reconstruction of analysis and logic, albeit one that appears in many ways limited and, ironically, counter-intuitive. What would an intuitionist make of the hyperbolic plane? A better question might be, what would an intuitionist make of the parallel postulate? It is doubtful that they would hold it in high regard. Although it is simple to construct two lines with a common perpendicular, an intuitionist would likely scoff at the claim that all the perpendiculars between those two lines are now common. Such a thing is not able to be shown, because it deals with an infinite number of perpendiculars. Or when dealing with Euclid’s original statement of the parallel postulate, one can certainly show where two lines that meet on a straight line at less than two right angles meet using trigonometric functions. But an intuitionist would challenge the thought that you can tell whether or not lines meet at a right angle. If one measures the angle between the two to be 90.0000^o, it still cannot be said with certainty that it’s a right angle, because it could really be 90.00001⁰. So an intuitionist would not hesitate to throw out the parallel postulate, opening the door for hyperbolic geometry. It seems likely, however, that an intuitionist would also not hesitate to throw out quite a bit more. Any theorem in hyperbolic geometry proven by contradiction would be thrown out. Any proof that uses such a theorem would be thrown out. Precious little remains of geometry after an intuitionist has his or her way.

The hyperbolic plane and the number i both turn our focus to the unbelievable in mathematics. Their existence seems nothing more than useless mathematic abstraction, separated from reality. An intuitionist would say that mathematics is wholly based on our intuitions about reality, and although intuitionism is largely dissatisfactory to many mathematicians, if the intuitionists are wrong, then what is mathematics if it is not concerned with reality? Some would say it is concerned only with logic, but this view does not hold up to close scrutiny. Others reduce mathematics further, to simple operations on strings of symbols, but this seems to ignore the power of mathematics. Plato described mathematics as reasoning from assumptions, and few would argue with that. It is still a good description, and it is by working logically from simple assumptions that surprising results like the properties of i and non-Euclidean geometries have been discovered. But what good is such reasoning? Although Plato found the assumptions mathematicians made appalling, he still recognized that mathematicians worked through pure reason, and in doing so, turn their minds toward what he termed the Good, by which all truth and beauty is illuminated. Ultimately, mathematics is the pursuit of the Good through logic, with help from a few extra-logical assumptions. From as simple a set as possible of first principles, mathematicians work toward beauty and truth. By working with concepts like i and the hyperbolic plane which are far removed from the physical world, mathematicians come to deal more completely in pure thought, moving ever closer to that goal.

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[1] Does this mean Plato would have favored complex analysis over real analysis?

On Persistence

Persistence of Time

It's generally agreed that thrash metal as a genre is dominated by four bands: Metallica, Megadeth, Slayer, and Anthrax. These bands are, at the very least, the most successful thrash groups. Artistically, they brought different things to the thrash metal party. Metallica wasn't afraid to show off some prog rock along with speed metal in their influences, and created some fairly complex metal. And Dave Mustaine, who formed Megadeth after being kicked out of Metallica, decided that anything Metallica could do, he could do harder, faster, and more technically. Because of this (somewhat one-sided) rivalry, Metallica and Megadeth charted similar territory with their music. Slayer was darker. Dealing with Satan, murder, the Holocaust, or anything else horrific, they used simpler riffs played faster and louder to create a visceral sound. Really, Slayer is as close to death metal as you can come without the growling vocals necessary for genre membership.

Which brings us to Anthrax. How do they fit in? After working my way through the classic albums of three of the Big Four (Metallica's Master of Puppets¹, Megadeth's Rust in Peace, and Slayer's Reign in Blood), I decided that it was time to complete the tetrafecta² and find out. After consulting a few sources, I picked up Persistence of Time, which is considered by many to be Anthrax's best album. I listened to it and was dismayed.

The music in Persistence of Time isn't particularly fast. For a thrash album, that's a rather damning statement. In fact, the album drags on horribly. Persistence of Time turns out to be an appropriate name for the album; as you listen, each second of every song seems to last longer than it should, a strange dilation of time that makes you wonder how only one hour has passed when the album finishes. It seems like three times that, hours spent feeling your energy wane to nothing. But it's not just the speed. The riffs are all limp, having no power and incapable of holding your attention. The album bores me. Listening to it was a chore, and I hope to never do so again.

1. I prefer ...And Justice for All, myself, but that's a minority opinion.
2. What, were you thinking "quadfecta", or "quadrafecta", or something like that? Nuh-uh, dude.

Persistence of Memory

Persistence of Memory is Salvador Dalí's best known work, and the painting most people think of when they hear the term "surrealism". It features a barren landscape with few landmarks, and four clocks that appear to be melting. It's a striking image to be sure, one that has worked its way into our culture, and with it, the idea of surrealism.

Many people think that surrealism as a movement solely focused on presenting the strange and unreal. However, its goals were better defined than that. Surrealism sought to create an art of the subconscious, to reproduce the logic of dreams in art. And at this, I tend to think that it fails. I am, of course, no expert. My knowledge is limited to the collections of a handful of museums that I have been to. But allow me to use Persistence of Memory as an example. Never have I had a dream that presented to me an image similar to the "soft clocks" of that picture. Dalí­ paintings contain images that are completely outside the realm of my experience. Their logic is that of a mad painter, not of a sleeping individual.

Certainly, though, I know what is meant by "dream logic". My dreams are in no way a perfect mirror of reality. Strange things are often accepted at face value, and people and places are connected in unlikely ways. I remember one dream that I had in which I was allergic to color. Nothing about this struck me as odd; I simply spent as much time in the dark as possible. And I'm not the only one who has had a dream in which the front door to your house leads to a building across town. At which point you simply make note that you won't have to mow the lawn this week, seeing as how it no longer exists, and continue on your way. Yet these ideas are absurd while awake. If Dalí, Magritte, and the rest fail to capture this distinctive view of reality, then is there anyone who does?

Yes. Of course yes. There are too many artists out there for there not to exist such a thing. In fact, I'm sure that there are more good examples of dream logic in art than I could ever possibly know about. So I'll just use this space to talk about two of my favorite examples.

The first example would be the episode of Buffy the Vampire Slayer titled "Restless". In it, we see into the dreams of Willow, Xander, Giles, and Buffy. Xander's segment in particular seems very dreamlike: his insecurities have a central role, and all paths seem to eventually lead him to his parents' basement, even if he was just on a playground or driving. Add in a touch of sex (two women make out, off screen, and Buffy's mom is strangely...forward), and you have a bona fide dream.

Second, we have the excellent webcomic A Lesson is Learned, but the Damage is Irreversible. Each strip is its own self-contained vignette, and each seems to take place in a world where things work in ways that they probably (definitely) shouldn't. Certain strips hit the perfect note: bullets that only pierce the flesh of your one true love, philosophical Yeti, and Satan marrying your mom. The art works exactly as it needs to: Panels flow into one another as required by the events in the comic, pulling off some excellent visual effects that create meaning beyond the text. Such excellence truly is something of a dream, because it's too great to exist in the real world.

Persistence of Vision

Persistence of vision is the name given to a physiological phenomenon of the retina. Well, sort of. Some people use the term to refer to the process by which one appears to see motion when images are flashed in quick succession (e.g. in movies). This is incorrect, and kind of complicated³. And honestly, the phenomenon I'm going to talk about is actually called something else nowadays (to avoid confusion); something along the lines of "afterimage", depending on who you ask.

You see, when you look at something, your retina keeps a part of the image for some time after the stimulus is removed. The most obvious example of this is the red and green dots that float around in your field of vision after a flash goes off. This happens essentially because your retina is tired. The chemicals in your retina that move around to create the sensation of color, they take a little time to build back up sometimes. This is a simplification, and probably wrong in some way. If you're really interested, you should do some research. Joseph-Antoine Plateau did some research of his own on the subject back in the mid 19th century. At one point, he stared at the sun for twenty-five seconds; this eventually led to blindness.

It's kind of poetic, actually. He stared at the sun so long that it was scarred on his retina, giving his sight for his science, and carrying the mark with him for the rest of his life.

3. If you want details, check out this link.

Persistence

persistence: Continuance of an effect after the cause is removed.
The American Heritage Dictionary of the English Language, Fourth Edition

Nothing persists; not really. Not in the above sense, anyway. Ask Ozymandias.

Actually, that's not fair. Oz stuck around for longer than we credit him. We still look upon his (or at the very least, Shelley's) works and despair. Not for the same reasons as we might have originally, I suppose. It's a paradox: We despair that we no longer despair. Because if even mighty Ozymandias can be laid low be time, then we certainly will be as well. But eventually we'll forget even that we've forgotten Ozymandias.

This is all very basic stuff: mortality, temporality, entropy. It's the way the universe runs. At the very least, it's the way this universe runs; some might say there are others where such things don't exist⁴. Which brings us to infinity. What a trip, eh? It goes on forever. Which is cool.

Well, I'm not going to tackle that stuff here. I'm underqualified, and it doesn't make for good blog reading⁵. I tried writing some fiction on the theme of persistence for this section of the post, but it was all horror, and either lost the theme or sucked or would make me sound way too creepy. So instead you get this. But it's up for the world to see now, so it can stop kicking about the back of my brain. Thus, a persistent idea sees the light of day, in which it will eventually wither. And if that sounds really harsh, then a) you must have really liked the post, and b) you totally were not paying attention to the last part.

4. Plato, I'm looking at you. And the Christians too, I guess.
5. Not like an excerpt from a news article and a snarky comment, no way!

A Treatise on Sir Mix-A-Lot's "Baby Got Back"

I. Wherein the Author Discusses the Cultural Impact
of Sir Mix-A-Lot's Magnum Opus

Released in 1992 on the Def American label, Sir Mix-A-Lot's third album, Mack Daddy, contained a song that would become a cultural touchstone for a generation. That song was "Baby Got Back". It spent four weeks at number one on the Billboard charts, and ended up as the year's second-biggest single, behind Boyz II Men's "End of the Road". But the song has more power than it's sales hint at.

At the time, there was much consternation and discussion over the song's message. Sir Mix-A-Lot deftly touched upon issues of race and sex in a manner so flippant as to dismiss any criticisms. Did his song objectify women or empower them? The video provided some clues, but for the most part, was inscrutable. Were the flashing words an effort to unconsciously indoctrinate the viewer into a world of large butts? And what of the flying fruits? Sir Mix-A-Lot sent the world a cryptogram, and in the giant yellow mounds, we all saw asses.

Perhaps the peak of Sir Mix-A-Lot's success was when he received the 1993 Grammy Award for Best Rap Solo Performance. He was never able to follow up on his biggest hits, despite efforts such as Chief Boot Knocka and Return of the Bumpasaurus. Some might look at such a story and declare the good Sir a one-hit wonder, doomed to be an answer to a Trivial Pursuit question and a segment on I Love the '90s.

Of course, for a time, the song was all of these things. But it had made its mark on the malleable minds of the children of the early '90s. Although many so-called "novelty" songs from that period are only remembered with a knowing chuckle and delight in their kitsch factor, something about "Baby Got Back" was so powerful that it was remembered fondly in a completely unironic way. And admiration brings imitation.

The most basic form of imitation in the musical world is the cover. And there is at least one cover of "Baby Got Back" out there. More fascinating are those who have used the song as a jumping-off point for their own expression. One of the most infamous examples of this is "Baby Got Book", which takes the sexualized beat and form of "Baby Got Back" and recontextualizes it as a Christian hymn. A personal favorite is the reimagining of the song as a piece of 16th-18th century prose poetry¹, which shows the tender heart at the center of the song. An excerpt:

If one were to express one's feelings about the quality, shape, and – to be blunt – size of the area of anatomy belonging to those of the fairer sex, an area that I will forthwith call to question, and if that aforementioned "one" were indeed myself, then I would have to hastily bring it to any curious party's attention that this desired area of discussion, the hindquarters to speak it quickly, could – and yes should – be likened closer to a giraffe than a lap dog, closer to a behemoth than a deer tick. On this matter, no utterance of falsehood shall ever pass my lips.

Every cultural movement has a dark side, however. The obesity epidemic in this country may be traced back to Sir Mix-A-Lot's glamourization of a larger female; his original message may have been for a woman to "pack much back" without increasing her risk of diabetes or hypertension, but over the years, this crucial need for moderation has been lost. This provides a sobering example of the power an artist has over the public. Thus far, the controversial Mix-A-Lot/obesity link has not been proven, but it certainly warrants study.

1. This site has been down as of late. I would recommend consulting Google's cache if this is still the case.

II. Wherein the Author Discusses the Current
Whereabouts of Sir Mix-A-Lot

Sir Mix-A-Lot was born Anthony Ray on August 12, 1963, in Seattle, Washington. Upon reaching adulthood, he had a strong interest in hip-hop. Unfortunately, Seattle had no hip-hop scene to speak of at the time, so he was forced to create one from whole cloth. He created his own record label and worked to promote himself. All of this work paid off, and he was signed to Def American Records.

His first two albums were successes that have since been forgotten, as the massive presence of "Baby Got Back" prevents one from looking further back in his career. But both albums went platinum and performed well on the charts. Then he released Mack Daddy, and it proved to be a cultural watershed moment, as detailed in the first section of this post.

Since 1993, Mr. Ray has been active in the musical world, as well as the newspaper world for a brief stint as an advice columnist. He has released 3 solo albums (as previously alluded to), as well as involving himself with a few collaborative projects. The most exciting of these was SUbSET, a collaboration between Mr. Ray and The Presidents of the United States of America. The similarity of their two careers is striking: Both are Seattle artists who achieved one-hit wonder status and found themselves unable to regain the spotlight, despite continuing to produce music. Unfortunately, no music from this collaboration was ever officially released. Diligent searchers may be able to find SUbSET songs on their preferred file-sharing service, but then again, they might not.

As our cultural fascination with "Baby Got Back" has remained strong throughout the years, Mr. Ray has often been asked to appear on television programs to discuss his work. Many of these shows focus on his one-hit wonder status. Occasionally, it is more of a "Where Are They Now?" production, something I find a bit insulting. It is as though mainstream culture sends a search party for former celebrities drowning in a sea of obscurity, fishes them out for all to see, and promptly tosses them back into the waters.

III. Wherein the Author Begins to Ramble,
And Loses Focus

Another of Sir Mix-A-Lot's collaborations was a song on the Judgement Night soundtrack, entitled "Freak Momma", which was done with Mudhoney, a Seattle "grunge" band. The Judgement Night soundtrack was full of such collaborations, pairing rappers with rockers. To Sir Mix-A-Lot, this sort of thing was old hat: On his first album, released in 1988, he did a cover of Black Sabbath's "Iron Man" with the Seattle metal band Metal Church. It could be said that this sort of thinking led to Korn, Limp Bizkit and any other rap metal band, but let's not put the blame for something like that squarely on Sir Mix-A-Lot's head. It was bound to happen, and just because he beat the trend does not make him responsible. Besides, "let he who is without a Korn album cast the first stone", or something like that.²

I do like the idea of collaborative soundtracks. One of my favorite albums is the original soundtrack to Spawn: the Movie. Its central conceit was slightly different than Judgement Night's: Instead of pairing rappers and rockers, it put metalheads and electronic artists together, with excellent results. Best known is probably Filter and the Crystal Method doing "(Can't You) Trip Like I Do", essentially a metal remix of "Trip Like I Do" from the Crystal Method's Vegas. The most brilliant combination was Slayer and Atari Teenage Riot, probably the two most aggressive bands in their respective genres. "(No Remorse) I Wanna Die" combined the high-BPM, male-female yelling attack of ATR with the extreme thrashing guitars and murderous intent of Slayer. Perfect for a movie about a CIA assassin who dies, goes to Hell, and agrees to lead Satan's armies against Heaven if he gets to go back to Earth to see his wife first.

At this point, I could start a lengthy discussion of movie adaptations of comics, or Todd McFarlane's low-level douchebag-ness, but I seem to have completely lost the thread of the post, so I'll stop. Which is probably for the best.

2. Yes, I do own Follow the Leader. And I still enjoy the first two-thirds or so, although the end drags (somewhat intentionally, I think). While their music has been somewhat uninspired (read: it tends to sound the same) as of late, they are starting to lash out at the major record companies in very public ways. See their "Y'all Want a Single" and "Twisted Transistor" videos for what I'm talking about. Hopefully, some MTV watching kids see these videos and have a small epiphany regarding the ways that major corporations manipulate bands' images to sell records. But probably not.