(Saturday, May 10, 2003)
The Mathematica equivalent of a skipping record. (It got the right answer though.) Aaron, I thought you might appreciate learning about improper dumps and how to integrate them.
Tax day. I wonder if any great physics had ever been discovered while trying to decipher the Massachusetts tax code. Last night, there were two major activities among the first year grad students: a) an all-night battle with Mathematica to tease out the solutions to an optics problem, and b) a vigorous debate about the morality of claiming stipend money as non-taxable income versus wages.
Neither problem was solved to anyone's satisfaction.
Lately, I've been getting a slew of emails asking me to update my website. I don't know why they continue to do this since most of my updates consist of me apologizing for not updating. That's not very fun to read, is it? So in order to give you all something to think about, I'll actually pose a type of high energy meta-physics problem.
At it's most fundamental, is the universe infinite or finite?
This is a question that my dad has asked me many times in the past few weeks. (Rhetorical question to the reader: If my *dad* doesn't expect me to update my website, then why should you?) I'll give you my way of answering the infinite/finite question, and I hope at least some of you will disagree. (It would be an infinitely boring universe if everyone believed the same thing.)
Let's start with the real numbers. There are an infinite number of real numbers just as there are an infinite number of integers, but in essence all real numbers have the same properties, so if you see one real number you've seen them all. So even though there are an infinite number of real numbers, we have a finite (namely one) number of names for the real numbers. In fact, there is a mathematical theorem that says that if it looks like a real number, smells like a real number, and quacks like a duck, then it's a real number of ducks. So we have in essence reduced the infinite to the finite by giving it an unambiguous name.
Similarly, if you've seen one electron, you've seen them all, so we've also reduced a very large number (the number of electrons in the universe) to a single name (the electron). If we say that the universe goes to infinity in the x-direction, the y-direction, and the z-direction, then we have really reduced the infinite extent of the universe to the names x, y, and z. In this way, we've taken control of the infinite by assigning it properties that we understand (and sweeping the rest under the rug). Of course, in physics, there is much disagreement about the names that we should use, and just because we call something an electron doesn't mean that we understand everything there is to know about electrons. But assuming that we had a complete picture of the universe, I claim that everything about the universe would be reducible to a finite number of descriptive names.
You might counter that there might be an infinite number of names, to which I would say that often in physics, we assign meta-names to infinite collections of names. (Temperature is a meta-name for the infinite number of ways that your thermometer might read 36 degrees. It certainly casts away a lot of interesting information, but it leaves us with a quantitative measure of what we mean by "hot".) In my mind, the only true infinity would be an infinite tower of nested infinite collections of infinities, but if the universe were indeed such a tower, then physics would only be able to tell us about the ground floor.
(Tuesday, February 24, 2003)
I recently received the following threat from a highly suspicious source.
From: Aaron K Thaler <athaler@***.edu>As you can see, to avoid becoming the victim of fratricide, I only let a week go by before "bowing to the needs," as it were, of my maniacal wombmate. (Ok, weren't not twins so that doesn't even make any sense. Also, the joke is only one step away from the idiotic pun-par-excellence, "womb with a view." I should be ashamed of myself.)
In other news, I have moved to a new office in the attic of the physics department. It's quite nice for an attic and I have a skylight all to myself. I'll take a picture of it at some point and post it along with a couple of nice shots from the recent anti-war march in New York.
Ok, brother-dude. Are you happy now with my pathetic little update? Did it "make your day?" Are you going to "tell all your friends about it?" Perhaps you'll even decide to start your own weblog so I might actually get some PEACE AND QUIET AROUND HERE.
The time of weddings has passed (though I've unearthed evidence of the groom's prior transgressions). We have now entered the prime year of 2003 (= 2003 x 1). Harvard is on a strange academic calendar, thus even in the month of January, I await the final exams of Fall semester.
Not that I'm studying too hard. All of the exams are open-book 48 hour take homes, so I figure the best I can do is vaguely flip through my notes and get a lot of sleep. And I'll need sleep, because between each exam, I have but 24 hours to recover. You can see my schedule for details.
Well, the pencils are sharpened and the scrap paper is stacked high, so wish me luck! (Also, for you physicists out there, ask me about my wacko theory of "momentum relativity" that I "discovered" while studying for stat mech.) And once exams are over, I'll have a week off to do what I wish. Any one want a grad student to decorate their living room? I'd make a fine couch coverer.