tag:blogger.com,1999:blog-115698122011-07-28T13:53:59.422-07:00calcium enriched, with lots of pulp: part of a complete breakfast<br>(mathematics, politics, ethics, physics, and other philosophical topics)Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.comBlogger731100tag:blogger.com,1999:blog-11569812.post-8784261894870872462009-12-08T20:35:00.001-08:002009-12-08T20:38:32.580-08:00

It's not like I write anything here ever.But, anyway, this is a test of LaTeXMathML. If I did it right, then $ax^2 + bx + c = 0$ iff $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Note: this works on my machine. Whether it works on yours depends on your browser, fonts, etc. In general, Internet Explorer sucks, although it does have some limited MathML support. Firefox (or Mozilla) is, of course,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-19933147511626149642009-09-30T02:01:00.000-07:002009-09-30T02:05:38.892-07:00

In this post, we find out if the instructions given here (via) really work.\frac{12 + 144 + 20 + 3\cdot \sqrt{4} }{7} + 5\cdot 11 = 9^2 + 0

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-6682181527781655572009-09-29T09:23:00.000-07:002009-09-29T09:27:35.881-07:00

As those of you who read my other blog know, I've been in Denmark this month, visiting the Center for the Topology and Quantization of Moduli Spaces, Department of Mathematical Sciences, Aarhus Universitet. I've gotten a fair amount of work done, attended a very fine Chern-Simons theory conference in Strasbourg, and met various people. But I miss Berkeley and its preponderence of interesting

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com3tag:blogger.com,1999:blog-11569812.post-35068585466652272732009-08-24T23:39:00.000-07:002009-08-25T00:05:03.120-07:00

I have a second-order differential equation on a manifold $N$, which might as well be $\R^n$. If it matters, my differential equation is the Euler-Lagrange equation for some Lagrangian $L$. I will call my differential equation $\D$, for want of a better name.Let $T \in \R$ with $T > 0$ and $Q_1, Q_2 \in N$ be given. Assume that $\gamma: [0,T] \to N$ is a solution to the boundary value problem(

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-2517526567769505842009-06-07T12:11:00.000-07:002009-06-07T12:27:49.296-07:00

This blog, as you probably have gathered, has been unused for some time. It will probably return to being unused soon. But for those of you who have it in your RSS feed, so that you are automatically alerted to new posts, I wanted to give a brief update.I am happily in graduate school at UC Berkeley, studying quantum field theory. My quals are in less than a week, so I am reading and reviewing

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-116423326960203332008-03-03T21:40:00.000-08:002008-03-03T22:20:45.984-08:00

In some of the research I'm doing, I have occasion to write expressions likeA + ABA + ABABA + ABABABA + \dots = (A^{-1} - B)^{-1}with no consideration of convergence.Although in my setting I have (multiplicative) inverses and (additive) negatives, it nonetheless becomes interesting to ask what sorts of operations we can do with just plus and times, provided that we can do such things

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-11158929819858399452008-02-12T20:18:00.000-08:002008-02-12T20:20:30.424-08:00

If you do not subscribe to the RSS feed for this blog, then you have by now stopped checking it for updates. I intend to post occasionally, but school is absorbing my mathematical thoughts, rather than writing.Since I have no extra time, I have started a new blog, sister to this one. Whereas Orange Juice Files is primarily for mathematical (and nonmathematical) essays, Local Seasoning will be a

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-50059160144813984702008-01-08T00:36:00.000-08:002008-01-12T22:27:33.525-08:00

One of the best ways to understand quantum mechanics — bear with me — is as a one-dimensional quantum field theory. No, it's not backwards, and we really should think of QM as inherently one-dimensional: there's one dimension of time. The configuration space of a particle is finite-dimensional; the size of the space of paths the particle could take — and Feynman says that a particle takes every

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-4166079523586762012007-12-27T12:51:00.000-08:002007-12-27T12:53:06.867-08:00

One of the crimes of our current electoral system — the United States picks its President in about as undemocratic a method imaginable — is that the same four million people pick the candidates for both major parties every year.Wikipedia lists the fifty states' and six non-state U.S. territories' populations, based on official estimates by the U.S. Census Bureau. In light of next month's

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-81421336743146097772007-12-13T15:11:00.000-08:002007-12-13T15:13:16.359-08:00

In the calculus class I'm TAing, we spent some time learning how "the method of undetermined coefficients" could be used to solve linear differential equations. I have never taken a first-year differential equations class, so although I'd solved many differential equations this way, I had never really though about such methods with any real theory. My goal in this entry is to describe the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-55553337042943767992007-10-14T01:49:00.000-07:002007-10-14T01:56:15.103-07:00

The following talk is significantly too long. Some parenthetical remarks are easy enough to excise, but what else should I drop?The talk is available here (pdf). I will give it on Thursday at "Many Cheerful Facts", a brown-bag student-organized talk series in which different graduate students present general-audience material: if you know the subject already, you won't learn anything in the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-81065873908909578742007-09-30T13:26:00.000-07:002007-09-30T13:54:18.288-07:00

Whole grains, it bears repeating, are tasty and nutritious. They cook easily, but many take a fair amount of time. Whole grains are processed and sold dried: before eating, they must be boiled in (potentially salted or flavored) water. Most grains should be combined with a prescribed amount of water in a pot with a well-fitting lid, brought to a boil, and simmered covered for a prescribed

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-13048857730047132552007-09-16T11:56:00.000-07:002009-06-26T10:10:38.182-07:00

I really am taking my own classes, and thinking about my own mathematics. But so far my classes have discussed supermathematics, which is cool but to which I have nothing so far to add, and classical (Lagrangian and Hamiltonian) mechanics, which I had intended to blog about last year. Perhaps I will some day write about such stuff; for now, I'd like to tell you about another topic we've been

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-16156947148903452412007-09-14T22:27:00.000-07:002007-09-14T22:39:22.503-07:00

This article is also posted (semi)permanently on my recipe files under the same title.I was very concerned when I saw this month's They Go Really Well Together: Apples aren't in season! I thought. It's the start of September. We're still eating peaches and tomatoes. I had not contributed to any of the previous TGRWTs: one was inconveniently timed, and most included ingredients I was not a fan

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com3tag:blogger.com,1999:blog-11569812.post-63624995495198558302007-09-13T21:43:00.000-07:002007-09-14T16:50:35.430-07:00

This semester I am a graduate-student instructor for Math 1B — the second half of a first-year calculus sequence. Students attend large three hours a week of lectures with 400 classmates, and also have three hours of GSI-led "section". We get remarkable freedom with our classes: I write my own quizzes and worksheets, and plan my own material. I spend a lot of my time with "big picture"

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-20129821940362032862007-09-03T11:52:00.001-07:002007-09-03T17:22:50.399-07:00

I've been spending so much more time thinking about food than about mathematics. I had promised myself that math, the lowest-priority of my three main passions (with cooking and dancing) last year, would move to first in graduate school. So far it's second only because I haven't been dancing in months.Is it a bad sign that I'm already fantasizing about dropping out and starting a restaurant or

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com6tag:blogger.com,1999:blog-11569812.post-21372066291063752992007-08-10T19:00:00.000-07:002007-08-10T19:53:50.337-07:00

Gov. Bill Richardson (D-New Mexico) has been receiving a lot of criticism for botching a question from Melissa Etheridge at Thursday's lgbt-themed Democratic forum. I would like to provide my views.I haven't watched most of the forum. In the "botched" clip, Richardson is clearly exhausted and fumbling --- he later apologized, explaining that he just fly from New Hampshire. But the question

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-44850024041667618792007-07-29T10:41:00.001-07:002007-07-29T11:24:36.395-07:00

The third and final day of my Topics in QM class was harder and more advanced, and had the distinct disadvantage of not being based on a particular paper. The goal was to explain electric charge from a QM/QFT point of view; to get there, we had to discuss momentum, wave functions, etc. To wit:How can you describe position of a particle? Need three numbers. What three numbers? Depend on my

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-64256253248951629202007-07-28T11:13:00.000-07:002007-07-28T11:41:01.415-07:00

This material is from R. Spekkens In defense of the epistemic view of quantum states: a toy theory.Heisenberg says you can't have complete knowledge of position and momentum. This is a theorem in traditional QM "wavefunction" model. We will take this as axiomatic: you can't have complete info.Important conceptual point: At any given time, system is in definite classical state, which I will call

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-31534091424408982672007-07-27T22:34:00.000-07:002007-07-27T23:18:35.382-07:00

After a two-week camping trip, I visited Canada/USA Mathcamp for one week. While there, I studiously avoided any Harry Potter spoilers (upon returning home, I dutifully took a one-day break from the rest of life to read the book), offered an evening activity focused on mind-body-movement-partnering exercises called "Learn to Fly", and hung out with some of the best people on the planet. Oh, and

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-48192611388611380322007-07-18T11:14:00.000-07:002007-07-21T03:45:47.668-07:00

One of my campers asked me about the problem of Time: why is it different from space, why can't there be hidden time dimensions.Here's my response; please comment with corrections/additions:The problem of Time is a very difficult one, and you've asked some deep questions, many of which do not yet have good answers. I'll answer bits of them, but my answers will be necessarily incomplete.First of

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-41914168079984915282007-06-30T21:49:00.000-07:002007-06-30T22:24:08.933-07:00

Or, rather, Marie-Therese was, when she encouraged the commoners to eat rich, expensive desserts. I recently procured a copy of Rose Levy Beranbaum's The Cake Bible, a book I highly recommend. Ultimately, I hope to try every cake she suggests; over the last two weeks, I began that project with the first five of her recipes, in order, and also a few of her cakes later on. We've had almost one

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-56651779432463163352007-06-25T15:24:00.000-07:002007-06-26T00:13:00.408-07:00

Terence Tao has a very nice discussion of ultrafilters in his most recent post. In his comment thread, I posed two problems (and provided an embarrassingly incorrect solution to one of them), which I will repeat here; then I'll write about another aspect of Tao's post.Problem (1): Construct (with Axiom of Choice, of course) a bounded sequence and an ultrafilter so that the sequence has no large

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-57871403852746368302007-06-19T18:25:00.000-07:002007-06-19T20:36:25.229-07:00

It takes a lot of money to run a Presidential campaign. In 2000, Bush raised and spent a little under two hundred million dollars; Gore only got 150 million (Center for Responsive Politics). In 2004, each of the major candidates raised and spent between three and four hundred million dollars. For the 2008 race, so far Clinton has raised the most money (36 million, ibid.) and Obama is next (

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-40411363386327641662007-06-10T01:43:00.000-07:002007-06-10T01:47:58.228-07:00

Here's a Zome Tool exercise that y'all can try your hand at, and then I'll tell you some of the category theory behind it, and why I was thinking of it. Build a solid with six pentagonal faces and three quadrilateral faces.  By Euler's formula, then, there are 14 vertices, all necessarily trivalent.  I want this figure to be as "regular" as possible: so two of those 14 vertices should be where

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-31886643967146784702007-05-30T00:16:00.000-07:002007-05-30T00:57:15.475-07:00

Any computer user knows that, form time to time, a piece of software gets stuck, "crashing" into an endless loop of calculations, and making the computer unable to perform any other tasks. If a human user notices the computer in such a state, she will usually try to abort the task, sometimes simply by restarting the computer. Because getting into infinite tasks can drastically curtail a

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-17662771098601196362007-05-13T00:13:00.000-07:002007-05-14T23:42:15.403-07:00

If any physicist asked to use any particular function, I would never begrudge it of her. Absolutely, if a particular mathematics is useful in calculating something about the world, by all means take advantage of it. But over the entire history of humanity we will never write down even countably many functions, and it's unlikely that any physical theory will ever require more than countably many

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-43829699579483989992007-05-12T17:11:00.000-07:002007-05-12T18:01:01.843-07:00

Polling data, a year and a half before the election, has almost no information in it. Then again, neither do those talking heads, and folks like me don't know anything either, and that's never stopped me from spouting ideas. So:RealClearPolitics reports that, at present, Giuliani wins the GOP nomination (he's at 28% nationally; McCain is next at 20%; McCain, though, wins Iowa and New Hampshire,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-560297116973800622007-02-12T13:46:00.000-08:002007-02-12T13:46:05.637-08:00

I apologize for being so absent from the blogosphere. My computer died — it moved from epileptic through comatose to completely blind — in January, and since then I've been spending maybe ten minutes a day on the internet. I'm not taking classes, so my math exposure consists mostly of reading (I'm currently enjoying Hartry Fields' Science Without Numbers); instead, my time is consumed by an

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1165388144688628902006-12-05T21:41:00.000-08:002006-12-22T01:30:38.683-08:00

Today's* ODEs class was rather amazing. In standard Yasha style, the topics darted around (he once explained that "It is impossible to be lost in my class. Because topic changes every two minutes, so if you are lost, you won't be lost."): a taste of KM theory, a dash of geodesics on ellipsoids, and a little infinite-dimensional Hamiltonian systems.It is this last discussion that I found rather

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1163305222038798962006-11-11T19:12:00.000-08:002006-12-05T18:11:25.936-08:00

A long time ago, in a 2n-dimensional symplectic manifold M, with form \omega_{\mu\nu} (and dual form \omega^{\mu\nu}), far, far away...Prologue: Our hero, a young Hamiltonian H: M\to\R, defines a "hamiltonian flow" via a vector field (X_H)^\nu = dH_\mu \omega^{\mu\nu}. We can understand H as, for instance, the total energy, and M as the phase space. H has a friend, G, which is preserved by the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1163123876176356512006-11-09T16:55:00.000-08:002006-12-05T16:37:15.050-08:00

I seem to have fallen way behind in writing about my classes. In particular, it may be a while yet before I do any quantum mechanics; I'm more excited by my classical geometry. But perhaps I will move into the quantum world soon. I almost understand it.In the last few weeks, my classes have defined forms and fields, integration, chains, Lie groups, and Riemannian manifolds; quantum fields,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1161586354866124992006-10-22T17:32:00.000-07:002006-10-22T23:52:34.956-07:00

Since I'm behind in my series of posts on fields, quantum or otherwise, I will instead talk today about some linear algebra, and not define most of my terms.The category Vect of vector spaces (over generic field \R = "real numbers") nicely generalizes the category Set of sets. Indeed, there is a "forgetful" functor in which each set forgets that it has a basis. Yes, that's the direction I mean.

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1160527638280237172006-10-10T17:06:00.000-07:002006-10-11T13:58:24.940-07:00

Voice-over: "Last time, on Blogging My Classes, Blogging My Fields,"Screen flashes with images of surfaces and atlases. Main character says something cliche (but stunning because of the background music) about the definition of the manifold. Then screen switches to the final scene: The Scalar Bundle.Voice-over: "And now, the continuation."Classically, the tangent bundle T(M) to a manifold M was

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-1160419559395511842006-10-09T11:31:00.000-07:002006-10-09T13:54:47.886-07:00

I think I might like to spend some time thinking about definitions in mathematical physics. What is a quantum field, for instance? Physicists usually give a slightly incoherent answer: a quantum field is a quantum particle at every point, just like a field is a number at every point. You ask them to unpack this a bit, and some might remember that there may be global — what the physicists call

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1158395438252606942006-09-16T01:30:00.000-07:002006-09-16T01:30:38.266-07:00

Pacifism is something I've struggled with since at least mid high school. When the President started making waves about Iraq, the American Left moved strongly towards an isolationist/pacifist stance, and although I was nervous about the occasional paleoconservative philosophy, I was already on the bandwagon, having felt that the President's hasty response in Afghanistan was poorly executed,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1157270225463237062006-09-02T22:15:00.000-07:002006-09-03T00:57:05.510-07:00

Categories, best described with commutative diagrams, allow for truly non-linear thinking, and yet they are usually defined linearly, similar to the way groups are usually introduced. This almost makes sense: morphisms, as one-dimensional objects, are about the most natural thing to compose linearly. And yet the power of category theory comes from the non-linear diagrams people draw, showing

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1157090472257672362006-08-31T22:57:00.000-07:002006-08-31T23:01:12.266-07:00

Today's headlines in the New York Times:Lockheed Martin got another government contract.Bush said something he said last week too.Folks post stuff online.Someone in Chicago wants to be mayor.No news is good news?

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1156836492401286632006-08-28T23:13:00.000-07:002006-08-29T00:30:12.706-07:00

While looking out the window at a rainy Newark Airport and waiting for a very delayed flight, I found myself standing next to a young boy — perhaps five or six — eating a large roll of bread. I struck up a conversation, and we were soon joined by his older brother — six or seven. I let the conversation go wherever it wandered, and learned quite a lot: that their father is a pilot; that the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1155802567865812482006-08-17T01:06:00.000-07:002006-08-17T01:17:13.003-07:00

I'm taking the GREs tomorrow (today), so instead of sleeping I'm avoiding looking up the rules and instructions. To do well on tests, it's best to go in knowing the structure of both the individual questions and the test as a whole. I don't yet, because I've been procrastinating with such useful time-sinks as listening to all of these pieces (link from the most excellent TWF234, about math and

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1155196068130083062006-08-09T23:41:00.000-07:002006-08-10T00:47:48.466-07:00

I'm in the progress of writing up what I understand about tensors, defining them from scratch, using only intuition and Penrose's graphical notation. Eventually, perhaps I will write a version of my notes for Wikipedia, since their current article on the subject is laughably bad. I first read about them in this post by jao at physics musings; I had started reading Penrose's most recent book,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1154072915937665772006-07-28T00:46:00.000-07:002006-07-28T00:48:35.956-07:00

Although I've been a Mathcamp JC, I've carefully stayed away from any talk financial. I've certainly been around, so perhaps have more knowledge than most, but I'm pretty sure that any numerics I might quote are, to within my level of accuracy, publicly available.Mathcamp tuition for the five-week summer hovers around $3000; half of this goes to the university for room and board. (For

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1152164588781589722006-07-05T19:15:00.000-07:002006-07-05T22:43:08.826-07:00

When I went off to college, my mother strongly encouraged me not to get a credit card. I have a debit/atm card, no debt, and no credit either. Sometime, probably at the end of the summer, I'll sign up for one of those air miles cards, and put all sorts of notes-to-self in my calendar about how much to spend, and when to pay it off, and when to cancel. I need the credit history, because it

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1136443459649414452006-01-05T12:56:00.000-08:002006-01-05T12:58:58.206-08:00

In november I discussed two famous proofs of the infinitude of primes, arguing that the two proofs are essentially the same. I'd like to play that game again, with a more complicated theorem.Theorem (Brouwer in two dimensions) Any continuous map $f:D\to D$ from the disk into itself must have a fixed point.Proof 1 (Algebraic) Assume the contrary. Let $S$ be the circle, and $h:S\to D$ be the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com4tag:blogger.com,1999:blog-11569812.post-1135751445992323912005-12-27T22:08:00.000-08:002005-12-27T22:33:48.126-08:00

It makes me sick that this (Boston Globe) is still news. Or even still an issue. But the article doesn't really help. Sure, it mentions that "the responsibility for this lab-vs.-life conflict lies with institutions" and that "[t]he primary barrier, they say, is the conflict between lab and family under the grueling demands of today's academic culture." And, sure, it pays lip service to what I

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1135548670075161972005-12-25T11:35:00.000-08:002005-12-25T14:11:10.163-08:00

The basic equation of motion of a Newtonian particle in one dimension acting under a potential energy $V(x)$ is$$ \frac{\d^2}{\d t^2}q(t) = \frac{1}{m}\frac{\d}{\d x}V(x) $$where $q(t)$ is the position (measured in $x$) of the particle at time $t$, and the left hand side is evaluated at $x=q$. (I tend to write $\d$ for $\partial$ --- my TeX files always start with \def\d\partial.) This equation

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1135152678066760822005-12-20T22:49:00.000-08:002005-12-21T00:17:31.513-08:00

John Jones, over at the USDCMDP, recently posted a stinging critique of Intelligent Design, as well as a thorough recap of the events leading to the Dover, PA, creationism trial. No, Jones is not a liberal blogger. John E. Jones III is the U.S. District Judge for the Middle District of Pennsylvania, a Republican nominated by George W. Bush and confirmed unanimously by the Senate, and he

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-1134890688492743742005-12-18T01:18:00.000-08:002005-12-18T01:19:16.023-08:00

It's been, oh, probably ten years since I last read C.S. Lewis' The Chronicles of Narnia — I did read all of them, some more than once, and enjoyed about half — more recently, I've read many reviews and discussions of the new film and the old books. I'd like to respond to a few published thoughts, and record a few of my own (with the caveat that my memory for the original texts is patchy at best

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com4tag:blogger.com,1999:blog-11569812.post-1133077468244024412005-11-26T22:17:00.000-08:002005-11-26T23:44:28.256-08:00

I would like to write about this article in The New York Times and this book, which I'm currently reading. But I have little directly to say, beyond that I think y'all should read both of them.The two pieces report on practices of polygamy and rape, the article in poverty-stricken northeast Africa, the book in Fundamentalist Mormon communities in North America. Both discuss the horrors of the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1132738220401714622005-11-23T00:16:00.000-08:002005-11-23T01:56:03.536-08:00

Some day, I hope, I'll get the chance to be a mentor at Mathcamp. In the meantime, I've started accumulating classes I'd like to teach. All are, not entirely unsurprisingly given my interests, motivated by physics.Order-of-Magnitude PhysicsI'm taking a course this quarter for first-year physics grad students called "Back of the Envelop Physics". It comprises a ten-week review of undergraduate

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com5tag:blogger.com,1999:blog-11569812.post-1132481217863189152005-11-20T01:48:00.000-08:002005-11-20T02:06:57.876-08:00

Congress reduces its oversight role: Since Clinton, a change in focusThis is what the media should be doing. Keeping the government honest. Acting as gadfly. Pointing out when politicians fail to do their jobs.Also in the news, The New York Times a few days ago reported that Some Judges Criticize Court Nominee on Civil Rights.

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1132478916494927582005-11-20T01:24:00.000-08:002005-11-20T01:30:31.320-08:00

I've started reading Speaking Natalie, a blog by a friend of mine, fairly regularly. Eric is an amazing writer; what I enjoy most about his blog is that he presents an amazingly different world-view from mine. Eric understands his life in terms of God — he writes, for instance, that "God called me to Stanford" and that "I was not born into the warrior caste either, but Jesus treats me that way.

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1131438809573939842005-11-07T23:52:00.001-08:002005-11-08T00:33:29.576-08:00

There's a classic "topological" proof of the infinitude of primes given by Fürstenberg:Consider the an unusual topology on \Z in which our basic open sets are both-ways-infinite arithmetic progressions (i.e. sets of the form \{ ... , c-d, c, c+d, c+2d , ... \}). It's clear the the intersection of two (and hence finitely many) basic opens is a basic open (or empty), and in general any open set is

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-1127032854365742292005-09-18T01:40:00.000-07:002005-09-18T01:40:54.823-07:00

Antimeta recently mentioned two famous paradoxes, those of Sleeping Beauty and the Unexpected Examination. I'd like to briefly record some thoughts on the former of these — nothing, I'm sure, that hasn't been said already, but more for posterity's sake — a longer post on the latter problem will hopefully be coming soon.In the classic Sleeping Beauty problem, Beauty, a brilliant mathematician,

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1126759683394316382005-09-14T21:48:00.000-07:002005-09-19T13:59:46.386-07:00

What bothers me most about a new apostolic visitation, reported in the New York Times, is not the increased authoritarianism. Sure, it's troubling any time an organization looks like it's about to purge quite a few members, especially when the purge sorts people not on, say, competence, but on dimensions of identity on which I think one should not discriminate. (In this case, the Church is

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1126119401016580372005-09-07T11:55:00.000-07:002005-09-07T11:56:41.023-07:00

Dear Governor Kulongoski,I would like to voice my support for the California Religious Freedom and Civil Marriage Protection Act, AB 849, which passed the Assembly yesterday in a close 41-39 vote. When you next see the California Governor, please give him my love or ire depending on whether he stands up for equality (and, incidentally, for what he has indicated he actually believes) or bows to

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1124144521754355962005-08-15T15:01:00.000-07:002005-08-15T15:23:38.220-07:00

The Boston Globe Magazine Sunday ran a detailed article by Niel Swidey on some of the research on What Makes People Gay. I haven't seen most of the research — I'm suspicious of much of it, but more as a knee-jerk reaction than for real reasons — and so refer you to the relatively reasoned article. I did want to point out that the media these days has come to consensus: "gay" is the preferred

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1119508284475493442005-06-22T23:30:00.000-07:002005-06-22T23:31:24.496-07:00

The cover story this week in The New York Times Magazine is about the "culture war" over gay marriage, and specifically on the religious conservatives who are fueling the battle. It's an interesting article, and I suggest you read it. It might remind you that the front-line anti-gay-marriage activists are real, thoughtful, intelligent people, who are doing what they think is right. It might

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-1118387283620265722005-06-10T00:08:00.000-07:002005-06-10T00:08:03.623-07:00

The Onion asks exactly that in a recent editorial: Well, I Guess That Genocide In Sudan Must've Worked Itself Out On Its OwnSome of my friends continue to work to end the Darfur genocide, although I, sadly, have not been actively supporting them, since, as The Onion points out, there is not political momentum. They continue to call for Stanford to divest from Sudan — this is part of a larger

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1118377627316463872005-06-09T21:27:00.000-07:002005-06-09T21:27:07.330-07:00

Supposedly I can now post entries here from my Dashboard (that wonderful device in Mac OS X.4). I wonder what this entry will look like.

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1118295021473715782005-06-08T22:27:00.000-07:002005-06-08T22:30:46.206-07:00

We're concerned about the effort [within the public schools] to capture youth through indoctrination into the homosexual lifestyle. Students are a captive audience, and they are being targeted by groups with that as an agenda.Mathew D. Staver, president and general counsel of the conservative advocacy group Liberty Counsel, quoted in a 9 June article in The New York Times.

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-1117605200115727112005-05-31T22:08:00.000-07:002005-06-22T23:37:51.446-07:00

My eleven-year-old sister not too long ago was listening to a discussion between my mom and me about a certain genderqueer college student back home who had received hate mail from a conservative group on campus. She asked why they would do that. I gave her an honest but a little flip answer, and she pressed the issue. She was not asking a rhetorical question. She seriously wanted to

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1117096299408660982005-05-26T01:00:00.000-07:002005-06-08T22:34:04.526-07:00

So much political bullshit recently, so much to explain why it's bad. But I still have a week or two more of term, so such essays will have to wait. Hold me to writing on some of this, though:Benevolent sexism and the military: Restricting what jobs women may hold in the military should be illegal, not required by law (women, like gays and rich kids, are already restricted from certain posts;

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1116143096741648732005-05-15T00:11:00.000-07:002005-05-15T00:44:56.746-07:00

Let's say, for a moment, that it's a few years from now, and the moderate former New York City mayor Rudolf Giuliani is about to wrap up the Republican nomination for President. What should the Democrats do? Granted, I'm not sure the Republicans will nominate someone that moderate, but conservative televangelist Pat Robertson says he likes him, so it's possible. And we should have a game

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1114330414640731292005-04-24T01:10:00.000-07:002005-04-24T01:13:34.643-07:00

One of the publications and commentators that I regularly read online is the New York Times' Public Editor, an ombudsperson and "reader's representative". This Sunday's column is on the Times' coverage of the Israel-Palestine conflict. It's nice, if not particularly deep; I'm hoping that he discusses soon the more newsworthy issue of the Times' coverage of the Pope. To this end I sent him the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1113528968436607232005-04-14T17:41:00.000-07:002005-04-14T18:36:08.436-07:00

I would like to direct your attention to two recent writings by other people on gender and sexism.(1) In an editorial in The Register-Guard, Sandra Morgen and Linda Basch argue that Bush's tax cuts are specifically unfair to women.(2) Like most e-mail lists, that of my house at school had a flury of e-mails when Harvard President Summers made his inflamatory comments about women in math and

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1112582075548454502005-04-03T19:03:00.000-07:002005-04-03T19:34:48.746-07:00

I would like to direct your attention to Galois, a New York-based mathematician who blogs about same-sex marriage. In particular, his most recent post, titled Encourage, Not Just Permit, Same-Sex Marriage raises some good points. I think, however, that it is not radical enough. Gabriel continues to focus more on individual health than on broad trends in gender and sexuality in society, and in

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1112173241065914372005-03-30T00:57:00.000-08:002005-03-31T10:31:49.080-08:00

As reported in The New York Times:The Supreme Court ruled 5-4 on Tuesday that Title IX protects those who bring sex discrimination complaints, even if they are not directly discriminated against in the usual sense (story and opinion (pdf)). Justice O'Connor wrote for the majority, joined by Justices Stevens, Souter, Ginsberg, and Breyer; Justice Thomas' dissent was joined by Justices Kennedy and

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1112171318077396122005-03-30T00:27:00.000-08:002005-03-30T00:29:04.633-08:00

The Colorado State Supreme Court Monday upheld a lower court's ruling, reversing the 1995 sentence of Robert Harlan who was convicted of raping and murdering one woman and crippling another. He had been sentenced to death; the Supreme Court found that the jury's deliberations were problematic, and changed his sentence to life in prison without parole.In general I support courts who reverse

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1111986044025147002005-03-27T20:58:00.000-08:002005-03-27T21:00:44.040-08:00

Scientific inquiry generally asks questions that fall into two broad categories: (i) Describe the world we live in, and (ii) List all possible worlds. These questions can, of course, inform each other --- an answer to (i) better be on the list in (ii), and if (ii) only ends up finding one possible world, then that better be the answer to (i) --- and different disciplines specialize in one or the

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com2tag:blogger.com,1999:blog-11569812.post-1111955753581912112005-03-27T12:20:00.000-08:002005-03-27T12:53:13.060-08:00

While I work on a longer essay on philosophy and physics, I leave you with two recent opinion pieces.One is a spot-on op-ed from the Washington Post, which I saw in my local paper this morning, on Town of Castle Rock, Colo. vs. Jessica Gonzales, a case before the Supreme Court asking whether the Castle Rock police violated the 14th Ammendment when they ignored Gonzales' legitimate concerns over

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1111308074653430172005-03-20T00:39:00.000-08:002005-03-20T00:41:14.663-08:00

On Wednesday, Judge George Greer, a compassionate conservative in Tampa, FL, ordered Terri Schiavo's feeding tube removed; doctors removed the tube Friday. Judge Greer has overseen the Schiavo case since 1998 --- due to a potassium deficiency probably caused by an eating disorder, her heart stopped briefly and she suffered severe brain damage in 1990, and has been incapacitated since --- and has

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-1111301299393781582005-03-19T22:48:00.000-08:002005-03-19T22:48:19.396-08:00

A new blog is always an adventure, or at least a gamble, or maybe a new blog is just a question. A number of questions, not entirely unrelated: Will it be any good? Will the writer ever post anything? What will the posts be about? And what the hell does the title mean?I hope the answers to the first two questions are yes and yes, respectively, and I'm pretty sure the third's answer includes

Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0