January 10, 2012
Category: Mathematics
In honor of the publication of the BSB (that's the Big Sudoku Book, for those not up on the local slang), my coauthor, Laura, and I hosted a session at last week's Joint Mathematics Meetings about the mathematics of Sudoku. I gave the opening talk in the session, an overview of some interesting mathematical questions that arise naturally from thinking about Sudoku. Of course, I had a slide discussing what, until recently, was considered the biggest open problem in this area: What is the minimum number of clues a sound puzzle can have?
Of course, everyone knew the answer was 17. After all, plenty of 17-clue puzzles were known, but despite extensive computer searching no one had ever found a 16-clue puzzle. Still, since persistent failure to find a counterexample does not count as a proof, the problem was open. I had a slide in my talk saying as much.
Read on »
Posted by Jason Rosenhouse at 5:27 PM • 2 Comments
January 2, 2012
Category: Anti-Creationism
I have a general policy of not blogging when I'm on the road, but I couldn't resist poking my head up to call your attention to this article, by Paul Wallace, over at HuffPo. Follow the link to see why...
Posted by Jason Rosenhouse at 3:00 PM • 101 Comments
December 31, 2011
Category: Mathematics
Tomorrow I will observe New Year's Day by hopping into the Jasonmobile and driving to my New Jersey office. Which is to say, I will be visiting my parents. Then on Tuesday I shall hop on a train and sally forth to Boston, which is hosting the annual math extravaganza knows as the Joint Mathematics Meetings. Lots of math, lots of socializing, what's not to like? I won't be arriving back in Harrisonburg until Sunday the eigth. Alas, on Monday it's right back into the classroom for the spring semester.
Which is to say, I won't be posting anything for a little while. Now, now, let's have none of that. Show a little dignity.
The spam filters around here sometimes get a little touchy, and a lot of worthy comments end up in my spam folder. During my brief blog break, of course, I will not be checking in very often to clear out the ones that should have gone through in the first place. Sorry about that. If you keep your comments short and without links you should be OK.
So best wishes for 2012! See you in a little bit...
Posted by Jason Rosenhouse at 5:34 PM • 0 Comments
December 30, 2011
Category: Evolution
Michael Ruse has written another post about morality. Sadly, he hasn't really clarified much of anything. Throughout this discussion his position has been that there are moral facts that we come to know through non-scientific means. I have been trying to understand how he justifies either part of that, but I'm afraid I still have no idea.
He writes:
First, the complaint that since I think morality is a product of evolution through natural selection, I must therefore be using science to justify my ethical claims. I too am committing the naturalistic fallacy. Not so. Distinguish between an explanation of the origin of something and its justification. Suppose David Barash starts writing columns claiming to be the Queen of the May. We discover that this is because a group of Christian fanatics captured him and, as in The Manchurian Candidate, brainwashed him. That is the explanation for why he now thinks the way he does. It is hardly a justification of the claim--delightful though it would be, were it true--that he is in fact the Queen of the May.
Read on »
Posted by Jason Rosenhouse at 8:18 PM • 82 Comments
December 28, 2011
Category: Mathematics
Time to show you the dramatic conclusion to the story I began yesterday.
Our problem was to define the complex exponential function in a way that was consistent with everything we knew about real exponential functions. We noticed that one of the standard rules for exponents implies
\[
e^{x+iy}=e^xe^{iy}.
\]
Since we already know how to deal with the first term in that product on the right-hand side, our problem has been reduced to deciding what to do with “pure imaginary” exponents.
The key to doing that is to remember that we have a Taylor series expansion for the exponential function:
\[
e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+\dots,
\]
which is a pretty result all by itself. We have previously discussed Taylor series, so if you need a refresher course just follow the link.
Read on »
Posted by Jason Rosenhouse at 9:55 PM • 10 Comments
December 27, 2011
Category: Mathematics
Euler's identity is the equation:
\[
e^{i \pi} +1=0.
\]
If you have any taste for mathematics at all, it is hard not to smile at this. In one equation we have each of five “special” numbers (e, i, pi, 1 and 0), along with one instance of each of three basic arithmetic operations (addition, multiplication and exponentiation.) Not too shabby!
But why is the equation true? Well, the first thing to notice is that we have an imaginary number in the exponent. That means that appreciating this equation requires an understanding of how we deal with such things. Towards that end, we have the following definition:
\[
e^{i \theta}=\cos \theta+ i \sin \theta,
\]
where theta is some real number.
Read on »
Posted by Jason Rosenhouse at 9:42 PM • 21 Comments
December 26, 2011
Category: Philosophy
My earlier post on this subject was entitled “What is Scientism?” because, while I have seen the term thrown around in a number of venues, I have never been entirely sure what it means. Having had a chance now to digest some of the arguments raised in the comments, as well as the thoughts expressed at other blogs, I think it's time to go another round.
The first point I made in my earlier post was that, in the context of science/religion disputes, to be accused of scientism was to be accused of being insufficiently respectful towards religion. A perfect example of what I had in mind is this post by Ian Hutchinson. He writes:
Read on »
Posted by Jason Rosenhouse at 11:59 PM • 603 Comments
December 23, 2011
Category: Mathematics
The BSB (that's the big Sudoku book, for those not up on the local slang) is now available! It's both a math book and a puzzle book. As math book it contains a survey of some of the mathematical aspects of Sudoku puzzles. For those familiar with the BMHB, the present book is considerably less technical. A few sections are tough going, but most of it should be accessible even on a casual reading. Indeed, one of the points of the book is to use Sudoku puzzles to introduce ideas from higher mathematics.
Read on »
Posted by Jason Rosenhouse at 6:13 PM • 5 Comments
December 22, 2011
Category: Miscellaneous
This is Emily:
She sure does look comfortable, doesn't she? And why shouldn't she be? In a tour de force of inductive reasoning she figured that today would be like the previous 364 consecutive days, at least to the extent that I wouldn't even consider stuffing her into a box and bringing her out to my car.
But she was wrong.
Read on »
Posted by Jason Rosenhouse at 7:37 PM • 11 Comments
December 21, 2011
Category: Politics
You should read Ross Douthat's obnoxious eulogy for Christopher Hitchens just so you can enjoy this magnificent takedown from Charles Pierce, over at Esquire. Pierce writes:
For the sheer magnitude of its horsepucky, this column may well stand forever. Generations yet unborn will come and read it, just to stare out of the magnificent vista of presumption, self-regard, and tinpot piety the way people bring their children to look at the Grand Canyon. It takes an unusual amount of juice-box hubris to put your thoughts in a dead man's head. It takes towering presumption to put into a dead man's head your thoughts with which he would scabrously disagree. Here, we have a New York Times columnist, a god-bothering newsboy on his best day, presuming to think -- let alone speak -- for a guy who is no longer here to think or speak for himself. Ross Douthat now stands as the Pope Stephen VII of letters, digging up the recently deceased and putting his corpse on trial in Douthat's own, Colorforms version of the Cadaver Synod. I guess we can be grateful that Douthat only gums away futilely at his argument. Stephen threw the convicted remains of Pope Formosus into the Tiber. Douthat just tosses Christopher Hitchens's corpse into the shallow end of his intellect.
Pierce, if you are unfamiliar with him, is the author of a pretty good book called Idiot America: How Stupidity Became a Virtue in the Land of the Free. Well worth a read.
Also, for a more measured but equally effective reply to Douthat have a look at this post from Jean Kazez.
Posted by Jason Rosenhouse at 12:16 AM • 8 Comments
