jrosenhouse | September 14, 2010Via Jerry Coyne I have just come across this op-ed, from the USA Today, by Chris Mooney. The title: “Spirituality Can Bridge Science-Religion Divide” My initial reaction: No it can't!
Mooney's argument is a standard one:
Across the Western world -- including the United States -- traditional religion is in decline, even as there has been a surge of interest in “spirituality.” What's more, the latter concept is increasingly being redefined in our culture so that it refers to something very much separable from, and potentially broader than, religious faith.
Nowadays, unlike in prior…
jrosenhouse | September 13, 2010Time for the big finale! We now have all the pieces in place to establish the divergence of the sum of the reciprocals of the primes.
Recall that we have the Euler product expansion of the harmonic series:
\[
\sum_{n=1}^\infty \frac{1}{n}= \prod_p \left( \frac{1}{1-\frac{1}{p}} \right)
\]
We noted that this formula was really just a consequence of the fundamental theorem of arithmetic.
This is definite progress, since we now have a product indexed over the primes. To convert that to a sum over the primes we simply take the natural logarithm of both sides:
\[
\ln \sum_{n=1}^\infty \…
jrosenhouse | September 9, 2010Over at Huffington Post, Denis Alexander hawks his new book Biology and Ideology: From Descartes to Darwin, coedited by Ronald Numbers. It features an essay by Alister McGrath entitled, “Evolutionary Biology in Recent Atheist Apologetics.” McGrath, if you are unfamiliar with him, is a Christian apologist whose most recent book is a defense of the notion of heresy. It features a foreword from Rick Warren, who writes, "We know that truth is eternal and unchanging. If it's true, it's not new.” Charming. Somehow McGrath is not someone I trust to lecture me about the perils of ideology.…
jrosenhouse | September 8, 2010Here's an interesting article from The Washington Post. It's title? “For Math Students, Self-Esteem Might Not Equal High Scores.”
It is difficult to get through a day in an American school without hearing maxims such as these: “To succeed, you must believe in yourself,” and “To teach, you must relate the subject to the lives of students.”
But the Brookings Institution is reporting today that countries such as the United States that embrace self-esteem, joy and real-world relevance in learning mathematics are lagging behind others that don't promote all that self-regard.
Consider Korea and…
jrosenhouse | September 7, 2010As part of my research for my book on evolution and creationism, I have been reading a lot of books and articles about how to read the Bible. From this reading I have learned a great deal, but I also find certain things a bit puzzling.
For example, consider the book Reading the Bible Again for the First Time: Taking the Bible Seriously but not Literally, by Marcus Borg, published in 2001. According to the back of the book, Borg is a professor of religion and culture at Oregon State University.
For obvious reasons I was especially interested in what Borg had to say about Genesis. Early in…
jrosenhouse | September 6, 2010It is time to continue our quest to prove that the sum of the reciprocals of the primes diverges. We have one more ingredient to put into place. I am referring to the notion of a Taylor series. The idea is this: Some functions, like those from trigonometry, are difficult to evaluate precisely. It would be nice to be able to approximate them via some other, more manageable, function. And since polynomials are the most manageable functions there are, why not try one of them?
So, let f(x) be a smooth function we wish to approximate. For simplicity, let us assume that we seek a polynomial…
jrosenhouse | September 6, 2010Recently i have been browsing through a book called What About Darwin?, which is a collection of quotations from various worthies regarding -- surprise! -- Charles Darwin. One that jumped out at me was a statement from Calvin Coolidge. This is from a letter he wrote to his father:
I see [Oliver Wendell] Holmes [Sr] is dead, the Autocrat of the Breakfast table on whom the years sat so lightly and who had only just declared that he was 85 years young. No one but [William] Gladstone is left of those great men that were born in 1809. Darwin is gone, the great expounder of evolution, a…
jrosenhouse | August 26, 2010With classes set to start on Monday I am not in the mood for heavy fare. So how about some entertainment blogging!
Like all sensible people I am a big fan of the James Bond movies. That none of them, let's face it, are actually all that good, does not affect my inability to change the channel when I notice that one is on. I used to feel strongly that Roger Moore was the best Bond, but that is partly because, given my age, he was the first Bond I encountered. Lately I have moved on to a more ecumenical approach that recognized the strengths and weaknesses of all the Bonds (including…
jrosenhouse | August 25, 2010P. Z. Myers had heart surgery yesterday, to implant a few stents. It was all very worrisome, but since he is already back to yelling at HuffPo it seems that things will work out OK.
Best wishes for a speedy recovery, P. Z.
jrosenhouse | August 23, 2010We begin with a joke. What's a logarithm? It's a birth control method for lumberjacks. Hahahahaha! Believe it or not, one of my high school math teachers taught me that.
Actually, logarithms are a computational tool for turning products into sums. They are defined as follows.
\[
\log_a b=x \textrm{ if and only if } a^x=b.
\]
The thing on the left is read, “Log to the base a of b.” It can be thought of as the power to which a must be raised to obtain b
Two simple examples are
\[
\log_2 32 =5 \phantom{xxx} \textrm{and} \phantom{xxx} \log_7 49=2.
\]
What do we mean when we say that…
jrosenhouse | August 22, 2010For the past few days I have been intending to do a big post about the proposed “Ground Zero Mosque,” in which I would gather up and comment on what various other people had said. Alas, I have not had time for that. So let me instead just do a quick post.
I have no problem whatsoever with the proposed cultural center (it's not a mosque for heaven's sake, though it would not change my opinion if it was). They have an absolute right to build it, and if they decide to exercise that right it will be a complete non-story as far as I am concerned. Of course, as an anti-religion kind of guy I do…
jrosenhouse | August 17, 2010And speaking of evidence for God, here's Matt Rossano putting forth an interesting idea:
Now this may seem too whimsical to be taken seriously, but the important point is this: however one envisions convincing scientific evidence of God, let's suppose we've got it. Let's further suppose that this god is pretty much the god we all expected to find -- not Aristotle's reclusive thought-contemplating-itself god or Plato's disappointingly limited Demiurge, but the “golden rule,” Ten Commandments kind of god with whom we are all pretty familiar. This God is now on the same footing as gravity,…
jrosenhouse | August 16, 2010Monday Math is off this week. School starts in just two more weeks, and I have been making a last push to have as much of my books done as I can before it does. Cuts into my blogging time, alas.
Which is a shame, since there is plenty of fodder. For example, Peter Enns has a new essay up over at Huff Po. It's title is “Atheists Are Believers, Too” I suspect that everyone reading this could reconstruct Enns' argument from that title alone.. Still, let's consider the specifics.
Things start off well with this:
Christians sometimes claim to be certain about spiritual matters. This can be…
jrosenhouse | August 12, 2010That's the Big Monty Hall Book for those unfamiliar with the local slang. The review appeared in the May issue of The American Statistician, not freely available online, alas. The author was Michael Sherman of Texas A & M University. Here's the opening:
Jason Rosenhouse states on the last page of his book that he encountered much “incredulity” at writing a “whole book” on the “Monty Hall problem.” I confess that I was one of the incredulous upon picking up this book. After reading it, however, I have quite a different view.
And just what is this new view of which he speaks?…
jrosenhouse | August 8, 2010In this week's edition of Monday Math we look at what I regard as one of the prettiest equations in number theory. Here it is:
\[
\sum_{n=1}^\infty \frac{1}{n^s} = \prod_p \left( \frac{1}{1-\frac{1}{p^s}}\right)
\]
Doesn't it just make your heart go pitter-pat?
You are probably familiar with the big sigma notation for sums. The big pi indicates an infinite product. In this case the product is indexed over the primes. In other words, the product contains one factor for each prime.
There is something very counter-intuitive in this equation, which is a large part of why I find it so…
jrosenhouse | August 8, 2010By now you have no doubt heard that a federal judge in California has struck down Proposition Eight, a voter referendum that outlawed gay marriage. Go here for a quick summary of the basic facts.
I have not had a chance yet to read the entire decision, and I do not intend to attempt a legal analysis of its merits. I am very happy about it, of course, as should anyone who cares about basic justice and the rights of homosexuals. There were two things that struck me, however, upon hearing the news of the judge's decision.
First, as I mentioned in this post, a few weeks ago I spent an…
jrosenhouse | August 4, 2010The second good post comes from Frank Schaeffer, making an argument that usually gets you dismissed as a village atheist. Here's the set-up:
There is a verse in Timothy that says that all Scripture is for our edification. This verse, not the many Bible stories of the many killings “ordained by God,” is the scariest verse in the Bible.
In Timothy (3:16) we read; “All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness.”
The “all Scripture” being spoken of is the Old Testament. The New Testament was just being…
jrosenhouse | August 4, 2010I can't quite believe I am writing this, but the HuffPo religion section actually has not one, but two, good posts up. The first is from Victor Stenger talking about some of the daffier misapplications of quantum mechanics. It makes a nice follow-up to Monday's post about Michael Shermer's essay.
In short, a physical object isn't either a particle or a wave. These are just two alternative descriptions of the same object. You do not have to measure one property or the other exclusively. Observing a beam of light with appropriate apparatus, you find that localized photons are always present…
jrosenhouse | August 3, 2010Here's Rod Dreher giving lectures about civility:
What is it with science-oriented advocates who consider contempt a virtue? Who, exactly, do they think they are going to persuade? (You could say the same thing about sneering political bloggers, sneering religious bloggers, and, well, sneerers in all forms of public discourse, inasmuch as sneering seems to be a popular pose these days.) Most of us are tempted to sneer every now and then (I certainly am guilty of this), but some of these people adopt sneering as a basic intellectual stance to the world.
Here's Rod Dreher hectoring Anne Rice…