jrosenhouse | June 20, 2011We mathematician types like solving polynomial equations. The simplest such equations are the linear ones, meaning that the variable appears to the exponent one. They have the general form:
\[
ax+b=0.
\]
If you remember anything at all from your basic algebra classes, then you know that this is readily solved by bringing the b to the other side and dividing by a. We obtain
\[
x=\frac{-b}{a}.
\]
Of course, we are assuming here that a is not zero, but let's not be overly pedantic. We can think of this as “the linear formula,” since it can be used to solve any linear equation we might…
jrosenhouse | June 17, 2011I spend a lot of my free time reading, one result of which is a long list of rhetorical pet peeves. Little phrases and expressions that, for me at least, immediately make the writer look like an amateur.
Starting a sentence with “Uhm” or “Hmmmm,” for example. This is an especially common one among blog writers. It's a silly and cliched way of suggesting that your opponent has not merely made a weak argument, but has actually said something unhinged and foolish. In the early days of blogs this might have been a clever way of achieving a conversational tone, but now it's so overused it just…
jrosenhouse | June 15, 2011Chris Mooney has has a new article in The American Prospect about the Republican war on expertise. There are a lot of interesting nuggets, but Chris somehow manages to avoid making the really obvious point.
First, let's set the tone:
Increasingly, the parties are divided over expertise--with much more of it residing among liberals and Democrats, and with liberals and Democrats much more aligned with the views of scientists and scholars. More fundamentally, the parties are increasingly divided over reality itself: over what is actually true, not only about hard science but also social…
jrosenhouse | June 14, 2011Some encouraging news:
Baptisms in the Southern Baptist Convention, the nation's largest Protestant denomination, have dipped to their lowest point in 60 years, according to a new report.
Last year, there were 332,321 baptisms in the church, which is 17,416 less than 2009, according to the report from Nashville-based LifeWay Christian Resources. There was only one baptism for every 48 Southern Baptists in the country in 2010. Sixty years ago, there one baptism per every 19 church members. In eight out of 10 years, the number of baptisms performed have declined.
Skipping ahead:
Church…
jrosenhouse | June 14, 2011Over at The American Prospect, Paul Waldman has a helpful rundown of the views of the Republican Presidential candidates on religion. Here's a sample:
But if you're a Republican voter looking for the most devout candidate, you've got yourself an embarrassment of riches. There's Tim Pawlenty, who left the Catholic church for an evangelical megachurch in Minnesota. He and his wife were married by their pastor Leith Anderson, who is now the president of the American Association of Evangelicals. Pawlenty's campaign book is peppered with dozens of quotes from the Bible. There's Michele Bachman,…
jrosenhouse | June 7, 2011We New Atheist types are used to having hyperbolic claims leveled against us. A while back author Ron Rosenbaum, writing at Slate, wrote “And some of them [the New Atheists] can behave as intolerantly to heretics who deviate from their unproven orthodoxy as the most unbending religious Inquisitor.” Clearly so. The most unbending religious Inquisitors were in the habit of torturing and imprisoning those with whom they disagreed. The NA's write books and give public presentations in which they express their views. The comparison is obvious.
More recently, we have Michael Ruse proclaiming…
jrosenhouse | June 3, 2011So, I went to the midnight show of the new X-Men movie yesterday. Short review: Wowee wow wow! What a great movie! Best comic book movie in quite a while, and since there have been several good ones that's really saying something. Longer review below the fold. Only minor spoilers ahead, but if you truly want to know nothing about the film going in then it might be best to stop reading now.
The X-Men are a bit of a hole in my comic book education. A while back I worked my way through the first volume of The Essential X-Men, which collected some of the original 1960's comics, but that's…
jrosenhouse | June 2, 2011That's the title of a new paper from Elaine Ecklund and Elizabeth Long, published in the academic journal Sociology of Religion. I'm playing catch-up here, since other bloggers have already discussed this paper, but why should they have all the fun?
But first, a story. Many years ago, when I was home from college over a summer break, I was sitting in Palmer Square in Princeton, NJ. I was enjoying my lunch from Hoagie Haven, which my Princeton-based readers will tell you is the finest sandwich shop on the planet. On the table in front of me was a chess magazine and an ice-cold bottle of…
jrosenhouse | May 31, 2011Truly there is no end to the vapid inanity the HuffPo Religion section will post. Our latest example comes from David Lose, in an essay titled, “Has Atheism Become a Religion?” Want to take bets on whether the answer is “No”?
I don't recall who first said it, but it has been wisely noted that if atheism is a religion then not collecting stamps is a hobby. That ought to be the end of things, but Lose encourages us not to dismiss the question out of hand. He then presents four lines of evidence. Let's have a look.
1) As recently reported in the New York Times, military personnel who…
jrosenhouse | May 25, 2011It hasn't been the best week for Israel. President Obama gives a perfectly sensible speech saying publicly what everyone already knows, and the vile right-wing noise-machine presents it as “throwing Israel under the bus.” As Jeffrey Goldberg explains, Netanyahu seems hell-bent on a course that seems so obviously suicidal that you have to wonder what he could possibly be thinking.
Still, there has been one piece of good news for Israel this week. We now have an official challenger for the World Chess Championship, and he is Boris Gelfand, formerly of Belarus, but now an Israeli citizen…
jrosenhouse | May 23, 2011Jerry Coyne calls our attention to this abstract, from a recent issue of Proceedings of the National Academy of Sciences:
We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato-Levine, and Arf invariants. We also define higher-order Sato-Levine and Arf invariants and show that these…
jrosenhouse | May 23, 2011The BECB, that is. (That's the big evolution/creationism book, for those not up on the local slang.) Many years ago, my thesis adviser, exasperated that I was “putting the finishing touches” on my thesis for about two straight months, told me heatedly that at some point you have to stop revising and just hand in the damn thing. So I took that to heart. Each time I proofread the BECB I found something new to fiddle with, but at some point you just have to say that enough is enough. It's as good as it's ever going to get. So I sent it off to my editor this morning.
Of course, it will be a…
jrosenhouse | May 16, 2011Update, May 17, 2:35 pm: Many thanks to Jerry Coyne for clearing up the question of Richard Dawkins's views on human inevitability in evolution. As I thought, Dawkins does not hold the view Ruse attributed to him. Coyne has Dawkins's response to Ruse's piece, so follow the link and go have a look.
It's been all book, all the time around here. The first draft of the BECB (that's the big evolution/creation book) has benefited mightily from the heroic efforts of a number of proofreaders, but this has meant a certain amount of rewriting to produce the second draft. I'm putting the finishing…
jrosenhouse | May 9, 2011In last week's post we discussed perfect numbers. These were numbers, like 6, 28 and 496, that are equal to the sums of their proper divisors. We referred to Euler's formula, which claims that every even perfect number has the form
\[
2^{p-1} \left(2^p-1 \right),
\]
where the term in parentheses is prime. As we discussed last week, the term in parentheses is known as a Mersenne prime, which entails that the exponent p is prime as well.
Our goal this week is to prove this formula. This is a very beautiful proof, in my view. It has tremendous flow, by which I mean that there is no one…
jrosenhouse | May 7, 2011Except for the part about getting up early on a Saturday, I've always kind of liked graduation. Quite a few of our graduating majors have had several courses with me, so it was nice to be able to congratulate them and meet their families. And since our stadium here is currently under construction, we have temporarily dispensed with the big, everyone-in-one-place ceremony in favor of a series of smaller productions, one for each college within the university. That gets the whole thing down to just under an hour, which seems like a good length.
And since I'm up at this hour anyway I might…
jrosenhouse | May 6, 2011Time for a quick quiz. Who here finished all his grading today and, with the exception of scraping his carcass out of bed tomorrow morning to go to graduation, has now officially started his summer break? If you answered me, you're right! So let's get caught up on some blogging.
We start on a light note. Ever wondered who the most accurate political prognosticator is? Well, according to this study, it's Paul Krugman. Surprise! In fact, here are the top six: Krugman, Maureen Dowd, Ed Rendell, Chuck Schumer, Kathleen Parker and Nancy Pelosi. Notice anything? Except for Parker, all of…
jrosenhouse | May 2, 2011In last week's post, we discussed Mersenne primes. These were primes of the form:
\[
2^p-1, \phantom{x} \textrm{where} \phantom{x} p \phantom{x} \textrm{is prime.}
\]
I mentioned that such primes are relevant to the problem of finding perfect numbers. So how about we flesh that out?
Let's define a function that takes in positive integers and records the sum of their divisors. We shall denote this function with the Greek letter sigma, so that
\[
\sigma(n)=\sum_{d|n} d = \phantom{x} \textrm{the sum of the divisors of} \phantom{x} n.
\]
Here are some sample values:
\[
\sigma(3)=1+3=4…
jrosenhouse | May 1, 2011Writing in The New York Times, Dave Eggers and Ninive Clements Calegari bring some blessed common sense to the subject of teacher salaries:
WHEN we don't get the results we want in our military endeavors, we don't blame the soldiers. We don't say, “It's these lazy soldiers and their bloated benefits plans! That's why we haven't done better in Afghanistan!” No, if the results aren't there, we blame the planners. We blame the generals, the secretary of defense, the Joint Chiefs of Staff. No one contemplates blaming the men and women fighting every day in the trenches for little pay and scant…
jrosenhouse | April 29, 2011Today is the last day of classes around here, meaning that I am just too darn happy to work up the righteous indignation needed for a proper blog post. So your homework is to go read this excellent essay from Russell Blackford. It is mostly directed at the recent chest-thumping of Michael Ruse, but also addresses some other issues as well. I especially appreciated this part:
For Ruse, the whole point seems to be that a bright line must be drawn between religion and science, but this is not merely simplistic, misleading and wrong - though it is all of those. It is impossible.
Whatever we…