September 2005 Archives

I thought Wilson's annual crop of 20+ valedictorians was indicative of rampant grade inflation and easy classes, but compared with Lewis and Clark, Wilson is brutally intense. We had our first math test today. Our overall test score is the mean of our actual score on the test taken in class and our score on a copy of the same test that we are to complete at home. We were encouraged to work in groups. This is like Marchese all over again.

I realized that I haven't yet posted about this hurricane Katrina/Rita debaucle, and it would be a very appropriate subject for an anti-Bush rant. It occurred to me though that most people reading this blog already can guess all of my opinions on this matter, so it would be redundant to confirm all of your suspicions in a long-winded rant. Let me simply say now that they are all correct. However, I have become very interested in the economics of the disaster--a much more compelling aspect than my political opinions. The Economist had a very interesting article on how the reconstruction efforts will fit in with our current economic condition and Brobdignagian debt of the federal government. Combined with the war in Iraq, I am convinced that the reconstruction effort will only further the disequilibrium of credit and debt between the US and much of the rest of the world. If this problem isn't fixed soon, a cataclysmic correction of currencies and credit seems immanent.

Ahhhh....

I played for a good 5 hours today with a small group of about seven people from PYJO at a farmers market out in some suburb. That's about at utterly exhausting as it gets, but incredibly fun.

After learning that FreeGeek gave me the wrong timeslot for my appointment, I got rather annoyed and walked across the river to the Powell's Technical Bookstore. I was killing time before I needed to meet up with my mom to eat some food, and I started reading an interesting section on electricity and relativity from an electrodynamics textbook. Although I forget a few of the exact details of the derivation, the section basically derived the electric field for a charge moving in an ideal, conducting cylinder of charge density = 0. By then using certain information about the time dilation and transverse momentum, it is possible to derive the existence of the magnetic field. While I have long known of the interconnectedness of electric and magnetic fields, this derivation was particularly elegant and gave mathematical illumination to this sometimes nebulous connection. I think it may have even restored my flagging interest in physics. At least I can glimpse a faint mirage of light at the end of the tunnel, while I monotonously recapitulate basic electrostatics yet again in class.

While English has never been my favorite subject, I will say that in my past three years of high school I have had exceptional teachers. Overall, they have been wonderfully interesting people and have provided useful feedback on work, which has allowed me to tremendously improve my writing and analytic abilities. While I may not have been smitten with each of these classes all of the time, it was typically a result of my relative lack of interest in English. However, there is a potential for my experience in English this year to break from that happy pattern. It is still too early, I think, to seriously judge the merits of the class, but based on my experiences thus far, I am skeptical.

The first characteristic of the class that I have found distasteful, is its emphasis on preparation for the AP English Lit exam. True, the class is designated "AP English", and some time should be spent preparing the student for the particular sections of the exam, but the course should not be designed according to the exam. While such a strategy can work fairly well for math and science AP courses, it is inherently flawed for humanities courses--and especially for English. The english exam is primarily an analytic examination, not a content-based test. While some information necessarily must be memorized, such as various literary terms, the test primarily judges the student's ability to analyze literature. A course that is structured specifically around this test necessarily ends up stressing exercises like writing timed analytic essays on short stories and poems in 40-60 minutes. While this is a truly important skill to develop for college, it isn't as valuable or worthwhile as carefully crafting thoughtful and detailed essays. Quality of writing is not adequately emphasized in the AP mode of instruction, nor is depth of thinking and argumentation. Today in class, for example, we read a 40-minute essay on a short story from the 2005 test. The question asked the student to discuss how literary devices were used to convey the author's purpose in a short story. It seems to me that in order to write the essay one must adequately define and defend what the author's purpose is while simultaneously showing how literary devices support that interpretation. In the example essay, the student's thesis was vague, a borderline literal interpretation, and it was poorly substantiated throughout the essay. Instead of addressing what the author's purpose truly was beyond literal facts, the test-taker harped on what attitudes and emotions the literary devices conjured up in the reader. The analysis also made several leaps of logic that were wholly unsupportable with the frame of reference of the story. It received a mark of 8 out of 9. This kind of test-specific preparation fails to actually teach the student how to do much other than simply pass the test. And passing the test is by no means indicative of any mastery of writing or literary analysis.

Only adding to my criticism is a certain difference in philosophy between my teacher and me. While I don't pretend to be an expert of anything--least of all English--I can't help but disagree with my teacher's particular notion of "multiple interpretations" of literature. Don't get me wrong, I firmly believe that literature is open to many, possibly infinite, valid interpretations, but I think that the infinity of wrong answers is vastly larger than the infinity of plausable ones. It seems to me that an argument should be based firmly in empirical evidence drawn from the text it describes, and it should encompass evidence from the entire text without conveniently "ignoring" certain sections. While there are flaws in every argument, the flaws should be minor enough that they do not pose a significant threat to the stability of the thesis. On the contrary, my teacher has stated outright that a valid interpretation "can have holes and leaps of logic, as long as they're not gaping", and can completely ignore certain sections. Thus, it seems to me that he is a firm believer that analyzing literature is not a rigorous deduction of the purposes of author and the subtextual implications of the written word, but rather an exposition on the impression and ideas that are provoked in the reader by the story and how specific components of the story elicited them. He seemed to think that the essay we read in class provided a reasonable analysis and thesis. Although I would have to reproduce the story and essay here to adequately convince you of its inferiority, I will propose that there is absolutely no way that it would pass Boly's infamous "so-what" test. Needless to say, I think I'm developing a dubious reputation for being disagreeable in that class. While Leeor, Jon, and I were getting in the car to go to Lewis and Clark, Dom drove by and shouted, "Adam, I disagree!!" And yes, I do disagree.

"The market may be getting rally for a fall rally."

--Headline from MSN Money

Although my Calculus III and Electromagnetism classes at Lewis and Clark are extremely easy, and grade inflation is even worse than at Wilson, at least the repetitive boredom of the latter is punctuated by occasional moments of hilarity. There was the time that I was helping someone with a particularly grizzly triple integral only to discover that they didn't remember what u-substitution was. There are also the times at the beginning of class when the professor turns bright red and starts yelling incoherently to capture everyone's attention. Today witnessed one of those priceless moments of humor. It is a well-known fact that physics humor far surpasses math humor in being lame, but occasionally is so bad that it's good. Consider the following joke we heard today: What do you get when you cross an elephant and a grape? Magnitude of the elephant, magnitude of the grape, sine theta. What do you get when you cross an elephant with a mountain climber? You can't do it. The mountain climber is a scaler. Bad, eh? Certainly. But when told by a balding, middle-aged man for whom telling it is exciting, you can't help but laugh. It's almost like Culpepper telling math jokes. Actually, I'm wrong. Unlike Tolsen, she doesn't have any chance of actually being funny.

"The storm's most dramatic political effects could turn out to be local. It has seriously aggravated race relations in New Orleans. Blacks tell pollsters that they are mad at Mr. Bush for the slow federal response. Whites are more inclined to blame the looters, the thugs who shot rescue boats and Mayor Nagin, who is black. A drunk white householder asks a rhetorical question: "Can you name a country run by blacks that is an example to others?" When your correspondent suggests Botswana, he roars: 'Get off my property!'"

--From "On the mend, but changed forever" in The Economist, September 17th-23rd

I spent some time today filling out college applications for my early action schools. Every school has an "office of undergraduate/college admissions", but I think that the prestigious universities having acceptance rates that are sinking into the sub-10% range should rename this department, "the office of undergraduate/college rejections". After all, that is their main function, and it would probably help prune dead wood from the applicant pool.

For the last hour I read over the testimony for our first practice trial for Mock Trial team. It's going to be so much fun. I can't wait to harass some witnesses during cross-examination, although I'm not sure I will ever live up to Ian Rocker's legendary performance in that capacity, forcing multiple witnesses to cry, contradict themselves, and break down on the stand. On the other hand, I have high hopes for debate, in which I replace him as Jonathan's partner. We had better trample the entire state all the way to another first place finish in April. Leeor, beware...

SAT practice question: So what exactly do you get when you combine a budding economist, a budding physicist, a mutual love of mathematics, and one red Volvo station wagon?

Answer: Well, at the very least, it's a pretty sweet computer: a 14-inch iBook G4 purchased by Jonathan Kadish and me, to be precise. Foolish, you protest, for Apple is switching to the x86 architecture in less than a year. Ah, but we have our ways, and clever they are indeed. Just one more iBook to buy, and we're in business. If you need an iPod, I have one that's brand new in the packaging that I'll sell for $269. Meditate on it.

And in other other, depressing news:
Physics picks up, but only from a mathematical perspective: we've done a ton of triple integrals, but barely any physics of which to speak... the other classes droop down: English is utterly worthless so far and advanced chem is a little mundane and easy. Spanish is the one highlight: because I skipped a year, I'm actually feeling a little challenged and I'm learning.

I've written at least 8 pages in two languages today. Leeor has decided to pull an all-nighter. School starts tomorrow. What is wrong with this picture? Okay, so maybe Leeor is in dire straits because he procrastinates and get 100-200 pages of reading each night for Intro to Islam, and I did spend the hours of 3-8 PM in a state of absolute insanity, writing feverishly about things that I really didn't need to write about. But the point is, that this state of things is unacceptable. Unacceptable. It's like school is trying to give us ulcers or something.

If there were ever such a thing as a 19th century Russian hippy, I think that Dostoevsky would be the preemanant one. The man is all about peace, love, and God. Although, I would argue that an equally valid and, in my opinion, philosophically superior interpretation is that he does not argue for religion, but rather for the altruistic principles often associated with it that 19th century Russian nihilists loved to shun completely. His literature provides absolutely no evidence that doubt in the existance of God, and a distaste for the corruption of orthodox religion (which he, incidentally accepts--note "The Grand Inquisitor" and the preceeding chapter) necessarily implies the brand of nihilism that he vehemently argues against: the kind that sees nothing worse in killing another human than in loving another human.

"The University of Chicago is, without question, the best institution of higher learning in the entire world."

--Ron Zaraza, giving unequivocal proof that he should never be trusted.

While I'm thinking about education, it's time that paternalistically impart another story upon you. So gather round the fire, children...

I have always felt that my education has been too easy. This is not to say that it hasn't been a crapload of work, but the main challenge that I have had has merely been finding enough time to get everything done. Receiving the coveted mark of "A" has never been a problem. Long ago, I came to the conclusion that this was because I was receiving a mediocre education in an environment of grade inflation. Look at it like this: how could Ted and Leeor both have 4.0 GPAs in all of the same classes that I take if there were not rampant grade inflation in this universe? It just wouldn't be possible, you must concur.

Last spring, running out of classes in math and physics, so I applied to take classes at Reed and Lewis and Clark Colleges, where they let a certain number of high school students take one class. I was accepted at both places, but because I was stupid and blindly following this idiotic passion for math and physics, I turned down Reed. None of their math or physics classes at my level fit into my schedule, unless I wanted to retake calculus. Thankfully, Lewis and Clark let me take two classes instead of the usual one, so I could take both math and physics there. One and a half weeks into both of the classes, I am absolutely stunned. These classes are not just easy, but they are easier than high school! Bear in mind that Lewis and Clark College calls both of these course sophomore/200-level classes. I thought Zaraza's class was pretty much a walk in the park, although it required a reasonable amount of work. This physics class is also a walk in the park, covers a bunch of stuff I already know, and has about 2/3 the amount of work. Homework is even worth a whole 20% of the grade. I think it was 10% or 15% in Culpepper's class. Although Culpepper's class required absolutely no true work at all, it was actually more difficult than this math class because she was such a bad teacher that it was always ambiguous as to when the next test was. In this multivariable/vector calc class (a venerable one by L&C standards), all we have covered in 1 and a half weeks is the dot product and the cross product. That's it! That would be less than one block day of material in Fisher's class. And it's not like we're learning it from the "pure" analysis perspective either. This class is very much in the applied/computational teaching paradigm (making it even less interesting). Somehow the teacher expects to get to Green's, Stokes, and the Divergence Theorem by the end. I suppose that multivariable calculus really isn't that difficult though. I haven't talked to anyone who considers it to be particularly hard. Nevertheless, the rate at which we are progressing is highly discouraging.

Physics is no better--if not worse. We've spent as much time getting to know everyone's name as we have learning everything else. We have covered single and multiple integration, and that is it. That's everything! One and a half weeks! The basics of multiple integration (we've only really done the basics) takes about 5 minutes to grasp: set the right limits, then integrate until you eradicate all of Leibniz's ubiquitous S's. I figured out that if I took all the right classes this year I could fulfill all of the requirements for a minor in physics at Lewis and Clark. Clearly this is a worthless program. So basically, in math I've learned what (assuming I didn't already know it, which I did) I could learn alone in about an hour or two, and in physics what I could teach myself in about 5 or 6 minutes. I've wasted ten hours in class, $40, and my $60 credit on Powells.com in exchange for about 6 minutes worth of additional knowledge and the same damn calculus book that I used (but sold) to teach myself calculus last summer. It's depressing, truly. The only consolation is that while the main Lewis and Clark library isn't fantastic, it has a collection of math books that is about 100 times better than the entire public library system, and a collection of economics books that is about 500 times better (both numbers are very accurately determined). I have full borrowing priviledges. So what do I do? That is a very interesting question. There are three things. Firstly, I'm going to do more fun things than usual this semester. Secondly, I'm going to try to get a solid foundation in the basics of real analysis. And thirdly, assuming that I can cover enough analysis on my own, I'm going to try to sweet talk Jerry Shurman into letting me take complex analysis at Reed in the spring. I'll probably fail at all three of them.

So what does this all have to do with my original point about education and the scourge of grade inflation? You can draw your own conclusions, but I see two likely ones. First, it is possible and probably quite likely that Lewis and Clark is a terrible school. College is supposed to be hard, and Lewis and Clark is definitely not. Ironically, the school seems to hold a reasonable reputation, but I cannot understand how this could possibly be. A second, nonexclusive conclusion is that perhaps my education has not not so bad or easy. Perhaps the grade inflation I have experienced is no worse than median everywhere else. Maybe my schooling really has been "hard" when compared most other places. While I find this second conclusion very unlikely, I can't deny that it is a possibility. The moral, in my opinion, is to avoid going to a crappy or even mediocre college at all costs whatsoever, and to avoid grade inflation like the plague. If the plague consumes you, at least go somewhere where you can do cool research.

Like everyone else, I've been working on finishing up my summer english assignment, and I had a few thoughts on the matter. Firstly, I can't understand why they would possibly want one to write responses in the middle of the novel. If one hasn't finished the book, it makes it can be awfully tricky to form any insightful opinions or hypotheses about the book. As a consequence, I end up leaving all the writing until the very end. Since I'm a fairly slow writer when expounding literary analysis, it becomes tedious to write 6 or 7 single-spaced pages, and I struggle to think of enough topics to discuss.

I had a much more interesting thought though. I was thinking about what I enjoy when I read, and I realized that although I enjoy good stories, I am most captivated by really interesting ideas. If this is true for other people--which it undoubtedly is--then why do people even bother writing stories to express their ideas? Why don't all of these brilliant writers write philosophy instead of hiding all of their great ideas under layers of fictional garbage? The only answer to this is that the act of obfuscating incisive ideas is a genuine and satisfying form of art for these people. This seems rather peculiar, but one can argue with art--believe me, I've tried with disastrous results. Certainly there must also be some element of demand influencing the situation as well. Philosophy is probably not enjoyed as much as good stories, so there is a higher demand for captivating fiction. Combining the two seems to make good economical sense. One can hit both markets with a single volume.

But still, it seems strange that in the elementary K-12 education, there is an overwhelming emphasis put on literature, and almost none put on pure philosophy. This is especially true considering that the primary goal of much of the study of literature is to "de-obfuscate" the hidden philosophical ideas in fiction. But rather than discussing, arguing, and testing the validity of these philosophical ideas, the study of literature only extracts them and lays them on the table with a nifty bag of tricks involving pattern recognition. It's rather like performing integration by hand. It itself is not actually compelling unless you're somehow odd or sadistic.

That brings me to my final point, that the emphasis in the humanities in K-12 education is put in very bad places. Contrary to what people say, literary analysis is not actually useful. Sure it teaches you how to gather evidence and form an argument, but debating philosophy does the exact same thing and involves a much deeper level of analysis and inquiry. Instead of mechanically pointing out occurances of the word "red" and linking them to Curly's impending murder of that obnoxious woman on the farm in Sophomore english class, why don't we argue about things like moral systems and whether or not they are fundamentally flawed. At least that would require debating ideas, instead of wasting so much time trying to deduce the implications of mechanical literary constructions like symbols and themes. Clearly my opinion is highly biased. I don't think that literary analysis doesn't have its valid place in an elementary education, it just seems to be given the sole focus in the humanities. I'm a strong proponent of requiring 3 years of english and at least 1 year of philosophy. But instead we are left without any philosophy even available, and a way too much literature to be balanced.

In the mathematics of one's elementary K-12 education there are a revolting number of fundamental assumptions that one is taught to make, by virtue of the fact that the student is not taught to think about math but rather only to use it as a tool. Even if one did stop to question the very fundamental ideas of numbers, there would be no one capable of answering any really good questions or proving any interesting theorems. In my very limited experience, these fundamental questions turn out to be extremely interesting and lead to very beautiful explanations of what numbers really are. I was so excited when I read this one that I have to relate it to the reader.

First we must ask the question, what is a real number? No one really stops to explain what they actually are. Sure, teachers will say that they are the set of all rational and irrational numbers, where rational numbers are those numbers that can be written as fractions and irrational numbers are anything else. But that doesn't really tell much about what a real number actually is? How can I even know they exist? It seems to be an awfully heinous and unrealistic complication to make numbers that can't be written as fractions and go on indefinitely. Well, maybe this method won't really "prove" the existance of real numbers so much as define their existance, but it's pretty amazingly cool. So here it is, sans set notation because that isn't really fully available in the character map.

Theoretically, anyone should be able to understand this, there's no opaque shroud of obfuscatory notation in the way. It's pure logic. But just so everyone can understand that this is cool, I should say a few things. Sets are bunches of things--usually numbers--basically arranged in a list. If a set 1 is a subset of set 2, then all of the elements of set 1 are also elements set 2. The union of two sets is another set containing all the elements from both sets. The intersection of two sets is another set containing the elements in common between both sets. An empty set is a set containing nothing.

Define a "cut" (a Dedekind cut, to be more specific) of sets A and B, where A and B are subsets of the set of rational numbers so that:
1.) The union of A and B = the set of rational numbers, A is not an empty set, B is not an empty set, and the intersection of A and B is an empty set.
2.) If a is an element of A, and b is an element of B, then a < b.
and
3.) A contains no largest element.

A real number is thus defined as a cut in the set of rational numbers.

Think about it. It's cool. It basically defines the set of real numbers as the set of rational numbers plus all the infinitely numerous and infinitely small gaps in between the rational numbers. It's like having an infinite string that has been cut in a bizillion places and defining the real numbers as the string and all the space from the cuts in between. Maybe that doesn't give much more insight into real numbers, but you have to admit that it's just a little bit exciting.