math
esiegel | April 15, 2009Yesterday, after a long day, my wife and I settled in for some time to chill out, and turned on the TV. Although I'd never watch it on my own, I know my wife is a fan of watching The Biggest Loser, so I joined her for an episode last night. And to be completely fair, I think it's a wonderful thing to help make people conscious about their bodies, their diet, their lifestyle, and how to have the life they want. The results of the people who succeed at this are truly spectacular.
They're doing "couples" this season; there are mother-daughter teams, father-son, husband-wife, sisters, best…
drorzel | April 7, 2009Via Matt Yglesias, a new CBS/ New York Times Poll has been released, accompanied by quite possibly the stupidest graphics ever. The pseudo-pie-chart at right is one of three, all of which have the same glaring flaw as this one.
Somebody really ought to lose their job for this. There's just no excuse for putting out "pie charts" that are this incompetent.
Sadly, this probably went through two or three people before hitting the web, and nobody noticed. It's hard to think of a better example of how deeply innumeracy has penetrated the media.
bioephemera | April 3, 2009At 3quarksdaily, Sam Kean has an interesting essay on the future of theoretical mathematics, whether computers capable of generating proofs will supplant human mathematicians, and what that will mean for the "beauty" of math:
There's general consensus that really genius-level mathematics is beautiful--purely and uncorruptedly beautiful, the way colored light is, or angels. More particularly, it's regarded as beautiful in a way that science is not. With a few exceptions--Einstein's theories of relativity, string theory, maybe Newton and Darwin--no matter how much science impresses people, it…
drorzel | March 24, 2009One of the NCAA pools I'm in has a copy of Obama's bracket entered, and the last I checked, I'm a couple of games up on him. This means I'm as qualified as anyone else to offer a plan to fix the financial crisis, and I have just the plan we need.
On the question of the AIG bonuses, I'm pretty much in agreement with the people who say that it's not worth making too much fuss over less than a tenth of a percent of the total bailout funding they're received. Passing laws to punish specific individuals is a lousy precedent, and it's not worth corrupting our principles for such a pittance. Let the…
bioephemera | March 17, 2009I know I've typed out some howlers in my day, so I say this with all due humility. But this post over at iO9 had me rolling on the floor last night:
Paul Murtaugh, a statistician at Corvallis' Oregon State University, claims that our carbon legacy isn't just limited to our own emissions, but 50% of our children's (The other parent gets the other 50%). And 25% of their children's, and so on, and so on. He arrived at this estimate using math: Murtaugh used UN population projections, which say that after 2050, birth rates in all countries will be 1.85 children per woman, on average. Then he took…
drorzel | March 17, 2009Nobody is ever going to mistake me for Edward Tufte, but whenever I run across a chart like this one:
(from Matt Yglesias, who got it from Justin Fox where it was merely one of many equally horrible plots), I find myself distracted from the actual point of the graph by the awfulness of the presentation.
I mean, look at this thing. The numerical labels for the horizontal axis are up at the top, rather than at the bottom where they usually go. The label that states what's actually plotted on that axis is down at the bottom of the graph, where it appears to be just a stray bit of text labelling…
bioephemera | March 12, 2009The Pi Day bill went up for a vote today and passed 391-10. Now Congressman Jason Chaffetz explains (via Twitter, natch) why he dared vote against the hallowed number:
Fie, fie! No Yes PeCan Pi for you, Representative Chaffetz (R-Utah)! But kudos for a creative excuse.
drorzel | March 6, 2009Over at Unqualified Offerings, Thoreau is bemused by his students' reaction to unusual numbers:
[I]t is fascinating how we condition people to be used to numbers in a certain range, and as soon as a number is either very big or very small it becomes disconcerting. On one level, I'm glad that they are able to do the conversion and that they at least realize that numbers need to be checked. I've had people happily measure the dimensions of an object in millimeters, get their conversion to meters wrong, and cheerfully tell me that their tiny metal cylinder has a volume of 27 cubic meters. At…
rallain | February 28, 2009This idea comes from my friend Thomas. His son is like mine in that they both think LEGO are awesome, and they are correct. For some reason, Thomas decided to calculate the price per piece of LEGO in each set. To promote repeatability, I decided to do this also. Looking at the catalog at LEGO.com, I can get both the price of each set and how many pieces it has. Just a note, I looked at almost all of the Star Wars LEGO series and some other select themes. I didn't include any sets that had been marked down in price. I will put the first plot on down below, maybe this would be a good…
drorzel | February 8, 2009Williams has long held a dominant position in a number of categories of blogging: Dan Drezner on economics and politics, Marc Lynch on the Middle East, Ethan Zuckerman on the developing world and really cool conferences, Derek Catsam on history and Red Sox fandom, yours truly on canine physics. And I'm sure I'm forgetting several people.
The number of blogging fields with prominent Eph contributions has increased this week, with the entire Williams math department making the jump into blogging. It's a bold move, but math blogging has always been more respectable than other types.
At this…
drorzel | February 5, 2009Having mentioned this a few times in course reports, I thought I'd throw out a link to my lecture notes (PDF) on complex numbers. This is the one-class whirlwind review of complex numbers from defining i to Euler's theorem about complex exponentials.
To answer a slightly incredulous question from a commenter, this is necessary because the math department does not teach about complex numbers exponentials (edited to correct an inadvertent slur against the math department) in the calculus sequence, and the only math prerequisites for the sophomore modern physics class I'm teaching are calculus…
drorzel | February 1, 2009Theorem:
The set of students who can learn the material of a course without attending lectures or working homework problems is always smaller than the set of students who think they can learn the material of a course without attending lectures or doing homework problems.
Years of intense study have so far failed to produce a counterexample to this theorem, but no airtight formal proof has yet been devised, either. The closest attempt attempts to prove it by assuming the opposite, and finding a contradiction, arguing that were the set of students who think they can learn without homework of…
drorzel | January 19, 2009Back in the "Uncomfortable Questions" thread, Thony C suggested that I should do running updates on the course I'm teaching now. I meant to get to this sooner, but last weekend's bout with norovirus kind of got in the way...
I like the idea, though, so below the fold are a bunch of comments on the classes I've had thus far this term:
Class 1: Introduction to Relativity. I do a quick recap of the two classical physics classes that are pre-requisites for my class, showing the various conservation laws, and Maxwell's equations. I then set up a version of the problem that led to relativity,…
drorzel | January 5, 2009Rebecca Goldstein's Incompleteness: The Proof and Paradox of Kurt Gödel is another book in the Great Discoveries series of short books by noted authors about important moments in the history of science, and the people behind them. Previous volumes include Everything and More and A Force of Nature, both of which were excellent in their own way, and Incompleteness fits right in there with them.
As the subtitle makes clear, this is a book about Kurt Gödel's famous Incompleteness Theorem, which shows that any formal logical system complex enough to describe arithmetic must allow the formation of…
drorzel | November 17, 2008There's a link in today's links dump to a post from Pictures of Numbers, a rarely-updated blog on the visual presentation of data (via Swans On Tea, I think). There's some really good stuff there about how to make graphs that are easy to read and interpret.
I would like to dissent mildly from one of their points, in the Better Axes post, specifically the advice about not starting at zero. In many cases, this is good advice, but like most rules of thumb, it shouldn't be followed too closely.
Take, for example, this post from one of my metastable xenon papers:
A strict application of the…
awild | November 15, 2008Sometimes, it's best not to interject statistics into your personal life.
h/t Podblack Cat
drorzel | October 28, 2008The closing narrative of the McCain campaign is apparently going to be "Obama's a pinko commie socialist who wants to raise your taxes," which means it's time for all good liberals to bust out the graphs to show why this is false. Well, graph, singular. You know the one:
I don't remember who first posted it (I got it here), but it's been everywhere this campaign. It shows a head-to-head comparison of the consequences of the McCain and Obama tax plans for various income groups.
I hate this graphic.
Not because of the information it contains, mind-- that's fine. I hate this graph because it…
drorzel | October 14, 2008Via Physics and Physicists, a breathtaking blog at the Washington Post proudly proclaiming the author's ignorance of algebra:
I am told that algebra is everywhere - it's in my iPod, beneath the spreadsheet that calculates my car payments, in every corner of my building. This idea freaks me out because I just can't see it. I sent out a query on my blog last week asking, Who among us in the real world uses algebra? Can you explain how it works?
This is exactly the sort of intellectual innumeracy I have ranted about countless times. The whole concept of the blog (subtitled "A year reliving high…
drorzel | October 8, 2008
A Colbert Report re-run about the financial crisis has just ended, so I turn the tv off, grab my jacket and the leash, and head out for a walk with the dog. She's oddly pensive as we head up the street. After a little while, she stops and asks, "What was that all about?"
"All what?"
"All that 'crisis' and 'bailout' stuff. It sounds scary."
"Well, a bunch of banks made a bunch of really bad loans, and people have lost a lot of money."
"I got that," she says. "I may be a dog, but I'm not stupid. I'm asking how they lost a lot of money."
"Well, it's complicated, but I'll try to explain. Let's…
drorzel | October 5, 2008The best way-- really, the only way-- to sum up David Foster Wallace's Everything and More: A Brief History of ∞ is by quoting a bit from it. This comes from the middle part of the book, after a discussion of Fourier series, in one of the "If You're Interested" digressions from the main discussion:
(IYI There was a similar problem involving Fourier Integrals about which all we have to know is that they're special kinds of 'closed-form' solutions to partial differential equations which, again, Fourier claims work for any arbitrary functions and which do indeed seem to-- work, that is-- being…