math
rallain | September 28, 2008When mowing the lawn, I like to listen to podcasts. One of my favorites is [Buzz Out Loud](http://bol.cnet.com). This weekend, I was listening to episode 817 and one of the topics of discussion was MySpace and their DRM free music stuff. [Wired](http://blog.wired.com/music/2008/09/myspace-launche.html) had a description of what they were going to do. That is not my point. The point is the claim that you could make an infinite number of playlists. How about I calculate (or estimate) the number of different playlists one could make.
First, the idea behind the idea. Calculating the number…
drorzel | September 28, 2008I'm currently reading David Foster Wallace's Everything and More: A Brief History of ∞, because his recent death made me want to read some of his stuff, and I haven't read this (which turns up on best-science-books lists) before, so it seemed like a good way to go. Reading Wallace does tend to affect my writing in a manner not necessarily to the advantage of my prose style, particularly at a time when I'm awaiting manuscript comments from my editor, whose email telling me that the comments were coming included strict instructions to break up my more complex sentences, so this may not be the…
rallain | September 16, 2008**pre-reqs:** *none*
I know who you are. I have seen you before and talked to you before. You are taking introductory physics and you are scared. Why does this have to be so difficult? It seems like there are a bazillion equations. Calm down, I will try to help. First, realize that algebra and trig are typically a pre requisite course for introductory physics. Your instructor probably expects that you have already mastered this material. Perhaps you did well in algebra (maybe you earned a B). But maybe you just worked hard and never really "got it". That is ok. There are many…
drorzel | August 20, 2008Via Swans On Tea, a ranty blog post titled Sucky Schools - How To Repair Our Education System, which takes its structure and much of its tone from Paul Lockhart's "Mathematician's Lament" (which, unfortunately, is a PDF file). I'm fond of ranty posts about education reform, but both of these kind of lose me. Lockhart, in particular, strikes me as being an excellent example of the dangers of being too attached to a subject.
He writes with great passion and at great length about the fun and creativity involved in math, which is all very nice. Unfortunately, it also leads to paragraphs like this…
drorzel | July 27, 2008A question raised in comments to yesterday's rant about humanities types looking down on people who don't know the basics of their fields, while casually dismissing math and science:
[I]t occurs to me that it would be useful if someone could determine, honestly, whether the humanities professors feel the same sense of condescension among science and engineering professors.
This is obviously not a question I can answer, but I agree that it would be good to know. So, how about it?
drorzel | July 7, 2008John Allen Paulos's Innumeracy is one of those classics of the field that I've never gotten around to reading. I've been thinking more about these sorts of issues recently, though, so when the copy I bought a few years ago turned up in our recent book-shuffling, I decided to give it a read.
Unfortunately, I probably would've been a lot more impressed had I read it when it first came out in 1988. Most of the examples used to illustrate his point that people are generally very bad with numbers are exceedingly familiar. They appear in How to Lie With Statistics, and the recent The Drunkard's…
drorzel | June 26, 2008A few days ago, some colleagues and I were discussing the year that just ended, and the curriculum in general, and the frequent lament about needing to repeat ourselves came up. Due to some quirks of our calendar, we have a lot of students taking courses out of sequence, and as a result, have to teach the same mathematical techniques in multiple classes.
On top of that, though, the students tend to say that any given technique is entirely new to them, even when they've already seen it. When that part came up, one of my colleagues said "Well, of course they do that-- I did that when I was an…
drorzel | May 29, 2008If you're reading this shortly after it's posted, you may notice ads for this book popping up in the sidebar and on top of the page. This is probably not entirely a happy coincidence-- I was offered a review copy in email from the author and his publisher, and I suspect that they had ScienceBlogs on their radar as a likely forum for web publicity.
With a title like The Drunkard's Walk, the book could be about one of two things, and the subtitle "How Randomness Rules Our Lives" pretty much rules out any Hunter S. Thompson style gonzo ranting. This is a book about probability and statistics,…
purepedantry | May 28, 2008This is cool. A computer programmer parsed the all the Wikipedia entries to find the average step length to get from any one to any other. He also found the center of Wikipedia -- the article that has the shortest average step length to any other article. The article in question is 2007.
Hat-tip: Slashdot
drorzel | May 21, 2008It's a simple question:Who do you prefer, Lorentz or Lorenz?
Chaos butterflies, or time dilation. Choose only one.
drorzel | April 29, 2008We had a talk yesterday at lunchtime from an alumnus who graduated with a physics degree, got a Ph.D. in Physics, did a couple of post-docs, and then decided to give academia a miss, and went to Wall Street where he's been a financial analyst for the last 12 years. He talked, mostly for the benefit of students, about his path to the world of finance, and what's involved in financial jobs.
This was terrifically interesting, and really useful. Given the way academia works, people who manage to get tenure-track faculty positions almost never have any first-hand experience of the other career…
drorzel | March 25, 2008EurekAlert provides the latest dispatch from the class war, the the form of a release headlined " Family wealth may explain differences in test scores in school-age children":
The researchers found a marked disparity in family wealth between Black and White families with young children, with White families owning more than 10 times as many assets as Black families. The study found that family wealth had a stronger association with cognitive achievement of school-aged children than that of preschoolers, and a stronger association with school-aged children's math than with their reading scores…
purepedantry | March 14, 2008It's pi day. (You know...3/14...stay with me on this...)
In honor of pi day, here are the first million digits of pi. (Not reproduced here because I don't want our tech guy to put a hit out on me.)
drorzel | March 2, 2008Technorati is working less and less well these days-- it doesn't update as often as it should, and misses links that I know are there-- but it's still good for the occasional new find. Such as Susan Beckhardt's Intrinsically Knotted, which features among other things a really nice post about mathematical games:
We're going to play a game called G(6, 3). It's a two person game, and you can go first. The rules are as follows: We start with a total of six counters, and we'll each take turns removing some of the counters-exactly one or two counters each turn. The winner is the one who takes the…
sb admin | December 17, 2007 There are many brain fitness software products available these days so when I was offered a copy of Core Learning's program Mind Builder, I agreed to check it out. It offers a series of test questions similar to America's SAT, while Mind Builder Pro is a fuller package that also incorporates IQ, career and aptitude tests intended to be "fun mental exercises." Unlike some similarly-marketed software there were no unproven claims of preventing age-related cognitive decline or improving processing speed. There were vague promises like "get smart, stay smart" and "build brain power" - whatever…
drorzel | December 14, 2007Here's where things on the Tree of SCIENCE!!! start to get more interesting, and somewhat more obscure:
Yes, that's a small wooden Christmas tree ornament hanging on our full-size Christmas tree. What's this have to do with SCIENCE!!!? Well, obviously, it represents recursion.
recursion, as you know Bob, is an extremely useful technique in computer programming, whereby you define a function in terms of itself. The classic example of this is the factorial function:
n! = 1*2*3*...*(n-1)*(n)
You can write a program to calculate the factorial of a number by defining a function f(n) that has two…
drorzel | December 12, 2007EurekAlert had a press release yesterday regarding a new study on the training of middle-school math teachers. It's not pretty:
Middle school math teachers in the United States are not as well prepared to teach this subject compared to teachers in five other countries, something that could negatively affect the U.S. as it continues to compete on an international scale.
[...]MT21 studied how well a sample of universities and teacher-training institutions prepare middle school math teachers in the U.S., South Korea, Taiwan, Germany, Bulgaria and Mexico. Specifically, 2,627 future teachers were…
drorzel | November 24, 2007It turns out that there's a Facebook group for quantum information types called the Church of the Larger Hilbert Space after a remark by John Smolin (Facebook link here), which I thought was the nerdiest thing I ever saw. Until I looked at the "Related Groups," and saw "I support the right to choose one element from each set in a collection" (here, if you have access), which is, of course, a political group for people who are Pro-(Axiom-of-)Choice. Who are, of course, opposed by "The Axiom of Life (aka Negation of Axiom of Choice)" (here). Both of those are nerdier than the Church of the…
drorzel | November 15, 2007Over at Good Math, Bad Math, Mark explains "Proof by Contradiction," a common mathematical technique that doesn't translate all that well to politics. Whenever proof techniques come up, I always think about one of the very few things I remember from my graduate class on Math Methods.
We were talking about some sort of complex analysis technique-- I don't remember what it was-- and the professor was drawing diagrams and doing contour integrals on the board to demonstrate whatever it was that he was talking about, and at one point he drifted into Proof by Invocation:
"So we integrate along this…
omnibrain | November 14, 2007David Ng from The World's Fair has decided to start another meme.... Here's the lowdown:
Anyway, this meme asks that you come up with your own scientific eponym. What's that exactly? Well, first read this excellent primer by Samuel Arbesman, which basically provides a step by step description of how to do this effectively. Then have a go at your own blog. If all goes well, I'd like to create a page at the Science Creative Quarterly, that collects (and links to) the good ones.
So onto the Higgins-Levinthal Dictum:
Also known as "the why fat smoking republicans are responsible for 9/11 number…