tag:blogger.com,1999:blog-115698122015-09-16T08:50:03.328-07:00The Orange Juice Filescalcium 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.comBlogger73125tag:blogger.com,1999:blog-11569812.post-8784261894870872462009-12-08T20:35:00.001-08:002009-12-08T20:38:32.580-08:00Another TestIt'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-19933147511626149642009-09-30T02:01:00.000-07:002009-09-30T02:05:38.892-07:00A testIn 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 + 0Theohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-6682181527781655572009-09-29T09:23:00.000-07:002009-09-29T09:27:35.881-07:00What the Hell is a Feynman Diagram?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-35068585466652272732009-08-24T23:39:00.000-07:002009-08-25T00:05:03.120-07:00Differential Equations Bleg. Or: In which we find out who uses an RSS reader.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-2517526567769505842009-06-07T12:11:00.000-07:002009-06-07T12:27:49.296-07:00In which we find out who uses RSSThis 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 reviewingTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com1tag:blogger.com,1999:blog-11569812.post-116423326960203332008-03-03T21:40:00.000-08:002008-03-03T22:20:45.984-08:00From products of infinite sums to subtraction and divisionIn 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-11158929819858399452008-02-12T20:18:00.000-08:002008-02-12T20:20:30.424-08:00New BlogIf 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 aTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-50059160144813984702008-01-08T00:36:00.000-08:002008-01-12T22:27:33.525-08:00A composition law for discrete-time QMOne 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 everyTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-4166079523586762012007-12-27T12:51:00.000-08:002007-12-27T12:53:06.867-08:00On Presidential PrimariesOne 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-81421336743146097772007-12-13T15:11:00.000-08:002007-12-13T15:13:16.359-08:00Linear Differential EquationsIn 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-55553337042943767992007-10-14T01:49:00.000-07:002007-10-14T01:56:15.103-07:00Divergent Series take 1The 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-81065873908909578742007-09-30T13:26:00.000-07:002007-09-30T13:54:18.288-07:00Whole 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-13048857730047132552007-09-16T11:56:00.000-07:002009-06-26T10:10:38.182-07:00Partial FractionsI 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-16156947148903452412007-09-14T22:27:00.000-07:002007-09-14T22:39:22.503-07:00Lavender and AppleThis 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-63624995495198558302007-09-13T21:43:00.000-07:002007-09-14T16:50:35.430-07:00IntegrationThis 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-20129821940362032862007-09-03T11:52:00.001-07:002007-09-03T17:22:50.399-07:00Don't tell the departmentI'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"I'm not a scientist."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-44850024041667618792007-07-29T10:41:00.001-07:002007-07-29T11:24:36.395-07:00Day 3: What is Electric Charge?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-64256253248951629202007-07-28T11:13:00.000-07:002007-07-28T11:41:01.415-07:00Another day of QM Topics: A Finite Hidden-Variables ModelThis 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 callTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-31534091424408982672007-07-27T22:34:00.000-07:002007-07-27T23:18:35.382-07:00Quantum Mechanics in Pictures, or How I spent my summer vacationAfter 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, andTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.com0tag:blogger.com,1999:blog-11569812.post-48192611388611380322007-07-18T11:14:00.000-07:002007-07-21T03:45:47.668-07:00The problem of timeOne 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-41914168079984915282007-06-30T21:49:00.000-07:002007-06-30T22:24:08.933-07:00Marie Antoinette was right!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-56651779432463163352007-06-25T15:24:00.000-07:002007-06-26T00:13:00.408-07:00A note on ultrafilters and voting.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-57871403852746368302007-06-19T18:25:00.000-07:002007-06-19T20:36:25.229-07:00MoneyIt 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-40411363386327641662007-06-10T01:43:00.000-07:002007-06-10T01:47:58.228-07:00Categories, trees, and polyhedraHere'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.com0