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In the rather fanciful position below, white is to move and force checkmate in six moves:
This problem was composed by H. Lepuschutz in 1936. It is a representative of what problem composers refer to as a “logical problem.” In a logical problem, white has some sequence of moves that seems to achieve his goal very quickly. This is called his “main plan.” Sadly, black has an adequate defense to the threat. So white executes a “foreplan,” the sole purpose of which is to neutralize the defense. Then white gets back to business and executes his main plan.
Please recall that vertical files…
Back in August, I welcomed Spider the cat into my home. So how did that all work out?
That's Spider lounging in his basement room, aka the chess room. To judge from the liberal coating of cat hair, I'd say he likes that futon quite a lot. Spider's not much of a jumper, so I have no fear that he's going to jump on the table and bat the chess pieces around.
Here he is wrapped up in the mattress cover he uses as a sleeping bag. That's one of his favorite places to sleep. If he looks a bit nonplussed in this picture it's because I just woke him up.
Spider is a very timid cat, and it'…
Over at The Economist, we have this brief interview with Edward Frenkel, a mathematician at Berkeley. We met Frenkel in this post from last week. Frenkel has a new book out called Love and Math, one copy of which is currently residing on my Kindle.
One part of the interview caught my attention:
Symmetry exists without human beings to observe it. Does maths exist without human beings to observe it, like gravity? Or have we made it up in order to understand the physical world?
I argue, as others have done before me, that mathematical concepts and ideas exist objectively, outside of the…
It's finals week around here. Over the last two days I have graded just over a thousand calculus problems (many of them, let's face it, not worked out properly). So let's unwind with lighter fare tonight.
There are plenty of books and websites explaining the basics of scientific thinking. Riveting reading, certainly, but as a simple illustration of what's involved I've always liked the following piece of dialogue. It comes from Agatha Christie's novel Murder on the Links. This was the second Hercule Poirot novel (the first being The Mysterious Affair at Styles).
It will help to know…
The Bottleneck Years
by H.E. Taylor
Chapter 69
Table of Contents
Chapter 71
Chapter 70
Sunbugs, February 12, 2058
We adjusted slowly to the changes in our household. It felt funny sleeping in dad's old bed. Edie didn't say a word when I got rid of the old mattress and rearranged the room. I think she understood perfectly. The guest room became Anna's new bedroom. She was proud to have her own room, until it came to sleeping alone. It was not unusual to wake up and find her curled up beside us.
My sex life with Olivia had been boisterous and exuberant. With Edie, love making was quieter…
After posting this essay about skeptical theism last week, Michael Egnor showed up in the comments to heckle me. Egnor, if you are unfamiliar with him, is a blogger for the Discovery Institute, which does not bode well for the merits of his comment. He opened his remarks sensibly enough by conceding both that evil poses a great problem for Christians and also that he had no solution to offer. But then he went off the rails by claiming that atheists have no right to assert the problem of evil since, having rejected the existence of God, we lack an objective standard of morality from which…
Philosophy is chock-full of fantastical thought experiments. Sometimes, though, the scenario we're asked to imagine is so fantastical that it undermines the point of the experiment. From my perspective, the “Mary's Room” experiment is one such.
This thought experiment was proposed by Frank Jackson in 1982, though the basic idea for it has a far longer history. It is meant to cast doubt on materialist understandings of the mind. Here's the essence of it, as presented by Daniel Dennett (quoting Jackson) in his book Intuition Pumps and Other Tools for Thinking:
Mary is a brilliant scientist…
Friday was the last day of classes for the fall semester. We have finals this week. Then, a big pile of grading. Yuck! But then, winter break. Yay!
This semester I taught three sections of calculus. More specifically, I taught our first semester calculus course intended for students with weaker mathematical backgrounds. Essentially, we stretch the standard one-semester calculus syllabus over two semesters and use the extra time to review algebra and trigonometry.
I have taught this course a number of times, and I have yet to find a fully satisfactory way of doing it. The textbook we…
This is the first of what I hope to make a regular feature here at EvolutionBlog: A chess problem for Sunday. By “chess problem” I do not mean the sort of thing where I show you a position from an actual game and ask you to find the best line of play for one side or the other. Those are fun too, but that is not what I will be showing here. Rather, I have in mind composed positions that illustrate an attractive and pretty idea. Chess composition is an art form that uses the rules of chess as its medium.
Many chess players are disdainful of composition, since it has little to do with…
This is a movie, narrated by Jodie Foster, produced by Robert Redford, directed by Pamela Green and Jarik van Sluijs, about the first woman director ever. She made the first narrative film ever. She also invented movie stars. Oh, and the thing where you have sound? She was the first to use synchronized sound. She did a lot of things first, and no one has ever heard of her. Many of her films were destroyed, others misattributed to others. This is one of the most amazing stories of modern culture I've ever seen. Can't wait 'till the actual film comes out.
More information is here and here…
Yes, there is a connection ...
The Imperial Japanese of World War II and the Nazi Germans of the same era held one thing in common: You were with them or you were nothing. Non-Japanese prisoners were treated very poorly. The lives of non Japanese who did not swear allegiance to the emperor were not valued at all. For instance, when the Japanese exited Manila near the end of the war, they killed hundreds of thousands of Philippine people. The Nazi's slaughtered millions of Russian prisoners, those they considered "unfit" or otherwise different from them, and of course, attempted to…
Over at HuffPo, Jeff Schweitzer serves up a cri de couer against religion. He writes:
Many factors have brought us to this sad state of affairs, but we can no longer ignore the 600 pound gorilla and trumpeting elephants in the room: religion is killing us. While our kids are being taught that god created gravity, children in Zaire are learning about Newton and Einstein. As children in Lichtenstein are being taught about the warping of space-time, American kids are learning that "people who do not believe in god" are incapable of understanding gravity.
Preach it!
American religiosity has…
The Linux Journal Readers' Choice Awards are out with the current issue. Let's talk about some of them.
The number one distribution was, as usual Ubuntu. But, Ubuntu only got 16 percent, with Debian coming in second at 14.1 percent. So, one could say that Debian is strong since Ubuntu is based on Debian. One could also say that Ubuntu is surprisingly weak. One would think it would be higher. One possibility is that Linux Journal readers are pretty hard core, and might often eschew Ubuntu for other distributions that cause more pain. Face it. Real Linux users like to wear hair shirts.
I…
Around here it's the last day of classes for the fall semester. Yay! So how about we mark the occasion with some math humor.
Over at HuffPo, math teacher Ben Orlin contrasts actual headlines with what they would say if people were more mathematically savvy. Some examples:
Our World: Market Rebounds after Assurances from Fed Chair
Mathematically Literate World: Market Rebounds after Regression to the Mean
Our World: Firm's Meteoric Rise Explained by Daring Strategy, Bold Leadership
Mathematically Literate World: Firm's Meteoric Rise Explained by Good Luck, Selection Bias
Our World: Gas…
Ikea’s typhoon rescue relief outguns China’s. Nope. Not surprised that their government does not care much.
China Ends One-Child Policy.
“Viking-age” ‘gold men’ unearthed in Sweden”. Actually, a bit older than the Vikings...
When the workload grows too huge, I recommend a solution found in Terry Pratchett’s Pyramids. The pyramid engineer creates a time loop so different temporal versions of him can work in parallel. Literally “an army of me”.
The Welsh language must be perfect for writing sagas about ancient heroes battling it out.
Creepy White Guys and Asian Women” *shudders in disgust…
Rereading my post from Monday, I see there was one aspect of Vincent Torley's post that I neglected to address. Recall that Torley was at pains to explain why God might be innocent of the charge of hypocrisy, for demanding that we behave in ways that He does not Himself practice. Torley made two suggestions in that regard, and in Monday's post I gave reasons for thinking that those suggestions do not solve the problem.
Perhaps aware of the inadequacies of his arguments, Torley tries another gambit:
It appears that Loftus's argument from evil, like Dr. Sean Carroll's, is a powerful prima…
In Tuesday's post I started discussing this essay (PDF format), by mathematician Doron Zeilberger. I wholeheartedly seconded the sentiments from the first part of the essay, in which he lamented the generally poor state of mathematical communication.
But I'm a little skeptical of this part:
The purpose of mathematical research should be the increase of mathematical knowledge, broadly defined. We should not be tied up with the antiquated notions of alleged “rigor”. A new philosophy of and attitude toward mathematics is developing, called “experimental math” (though it is derided by most of…
It occurs to me that many of you may not know this because you don't live in the Twin Cities or are not Facebook Friends of the Mayor of Minneapolis, but the guy is very funny and creative and produces a lot of poetry, especially this time of year.
In Minneapolis, there is an arcane system of plowing snow that I will not even attempt to explain. (I come from New York and Boston where the system for removing snow from the city streets makes perfect sense.) The point is, if you mess up they tow your car to a sort of automotive dungeon and it costs a lot of money to get it back.
So, when…
Back in 2009, Chris Mooney, together with Sheril Kirshenbaum, wrote a book called Unscientific America. It purported to explain the origins of America's current antipathy toward science, and to make suggestions for what we might do about it. It created something of a stir in the science blogosphere. I was one of many folks who found the book disappointing, for reasons I explained in a lengthy, three part review (Part One, Part Two, Part Three). I pulled my punches somewhat, partly because at one time Mooney and Kirshenbaum were my colleagues here at ScienceBlogs, and partly because I was…
In an opinion piece for the New York Daily News, published in July 2012, mathematician Edward Frenkel and school superintendent Robert Ross write:
This Fourth of July will forever be remembered in the history of science as the day when the discovery of the Higgs boson was announced. The last remaining elementary particle among those predicted by the Standard Model of three forces of nature finally revealed itself through painstakingly assembled data of billions of collisions at the Large Hadron Collider, the most sophisticated machine ever built by humans.
But one important aspect of this…