Archive for the ‘Logic’ Category

Low Unpopularity

October 12, 2013 Leave a comment


[Gallup Poll]

I rarely enjoy listening to NPR Morning Edition’s host Steve Inskeep conducting interviews on political issues. More often than not, when I turn on the radio during breakfast and discover him engaged in such activity, I switch to something else. But yesterday I didn’t, and I was rewarded with an astonishing English language construction.

The segment was called Reason For Optimism? Two Sides Talking On Debt Ceiling, and it found Steve talking with NPR’s national political correspondent Mara Liasson about the government shutdown.

Three questions in, Inskeep asks, “What prompted Republicans to change course?” Liasson replies:

They were losing. They were just getting battered politically. And here’s a pretty good example of what was happening to the Republican political position. This is a new Wall Street Journal-NBC poll. By a 22 point margin the public thinks the Republican Party is more to blame for the shutdown than President Obama. That’s a bigger margin of blame than the Republicans received during the last shutdown in 1995.

The Republican Party is now at record low levels of unpopularity. Only 24 percent of people have a favorable opinion of the Republican Party. The Democrats aren’t doing much better, but at least they have a 39 percent favorable rating and they’re not dropping like the Republicans. And here’s the other thing. The president’s approval rating actually went up in this poll.

Read the opening of that second paragraph again. Yes, Mara said that the Republican Party is at record low levels of unpopularity.

I thought, oh my gosh, I have to post this. But I delayed. This morning I wrote to Language Log co-founder Mark Liberman to offer the quote as an addition to the mis-negation files that he maintains. Tonight, I sat down to write my post, only to discover that Mark was already on the case.

Categories: Language, Logic

Logicomix Again

October 7, 2009 1 comment

Two Saturdays ago, I wrote a short post about the new graphic novel Logicomix: An Epic Search for Truth, right after reading Jim Holt’s review of it in the next day’s New York Times. Now that I’ve read it, I’ll say a little more.

As noted in my earlier post, the novel tells the story of Bertrand Russell‘s failed effort to build a logical foundation for mathematics. Why math? Well, there’s the obvious reason that it’s more interesting than anything else. But more to the point, one can imagine that if there’s any hope of building a foundation for some subject– a foundation allowing us to know the truth of its statements with certainty — then the subject most likely to yield to such a construction project is mathematics. The Russell depicted in the novel (and it is a novel, based on the real Russell and his compatriots, but not a genuine biography or history) is excited in his youth by the beauty of Euclidean geometry, thrilled that logic and reason can yield truths, but disturbed that there was something missing in the foundations of the subject. At Cambridge, his disquiet grows. He observes, while courting his future wife, that “At Cambridge, no one talks about the real issues of mathematics. Like what is the nature of mathematical truth?” He adds, “If only you knew how much depends on these questions. How crucial they are!”

And she married him! How about that? I had similar interests as an undergraduate. And I wasn’t as smart as Russell. But I did know that talking about the nature of mathematical truth wasn’t a promising approach to dating. (Then again, I didn’t exactly have a lot of success with other approaches. Maybe I should have tried it.)

The novel isn’t just about logic and math. Irrationality, madness, pacifism, the limits of reason, the Vienna Circle and Nazis all play major roles. Plus, of course, it’s a graphic novel, so there are all the drawings, which I didn’t give sufficient attention the first time around, since I was so eager to follow the story. I will need to re-read it with a closer look at the artwork. Along the way, the authors get to poke a little fun at those annoyingly logical people who make normal conversation difficult. For instance, there is the imagined visit Russell and his wife pay to the great logician Gottlieb Frege in Germany some time in the 1890s. They arrive at a home and ask the fellow who is seen in the yard, trimming the hedge, “Is this Professor Frege’s house?” “No,” he replies. “This is his garden. His house is in there.” Russell asks if the professor is at home. “No, he is in the garden.” Maddening. Which gets back to the recurring theme of the interplay between logic and madness.

An important character throughout the novel, inevitably, is Alfred North Whitehead, the co-author with Russell of Principia Mathematica, the three-volume work in which they lay out their logical foundations for mathematics. But the one who steals the show — for me — is Ludwig Wittgenstein, who appears about three-fourths of the way through the book (page 223) when he arrives at Russell’s door in his Cambridge University rooms, having been sent from Germany by Frege to learn logic from Russell. Seemingly an admirer, Wittgenstein soon becomes Russell’s most powerful critic. World War I intervenes, dramatically altering both Russell and Wittgenstein. Then, as the book nears its conclusion, Kurt Gödel inevitably arrives, demolishing the dream that a proper logical foundation for mathematics can assure the existence of a proof for every true mathematical statement. One of the amusing conceits of the novel is that Gödel, who laid waste to Russell’s program, may have been the only person who ever bothered to read the Principia Mathematica in full. Yet, perhaps only by building on the Russell and Whitehead’s development of logical foundations could Gödel have developed the methods that showed the limitations of logic as a foundation for mathematics. The book can only touch on this, one of the great intellectual discoveries of the twentieth century.

The authors and artists themselves appear throughout the novel, along with a pet dog, in interludes in which they discuss the book’s issues while working or walking in Athens. All the ideas come together when they attend a local production of Aeschylus’s Oresteia Trilogy.

Math, logic, war, peace, theater, dogs. I haven’t even mentioned the failed marriages, crazed experiments in education, and messed-up children. Something for everyone.

A final note: I just noticed a link at the book’s website to a trailer, which is the youtube video I have inserted at the top of the post. Have a look. It includes an appearance by Barry Mazur, a fabulous mathematician from whom I learned algebra in my sophomore and junior years. He then became my senior thesis advisor.

Categories: Biography, Books, History, Logic, Math


September 26, 2009 Leave a comment


In looking ahead, online, at tomorrow’s NYT Sunday Book Review, I came upon Jim Holt’s review of the graphic novel Logicomix: An Epic Search for Truth, written by Apostolos Doxiadis and Christos H. Papadimitriou and illustrated by Alecos Papadatos and Annie Di Donna. I read the review, looked at some sample pages available from the review’s webpage, went to the book’s website, realized that there will be a book reading here in Seattle in two weeks, and ordered it. I have a bit of a book backlog, as usual, but I knew I would want to read this eventually, so why not just get it?

As best I can tell, the book tells the story of Bertrand Russell’s decades-long failed effort to find a logical foundation for mathematics. Along the way, other famous logicians and mathematicians appear, including Gottlieb Frege, Georg Cantor, David Hilbert, Russell’s co-author Alfred North Whitehead, and, of course, Kurt Gödel, the greatest of all logicians, hero to us all. Plus, various world events intervene. How could I resist?

Perhaps I’ll have more to say after I read it, or after I attend the book reading. If you’re skeptical that such a book might be interesting, I suggest that you read the NYT review and visit the book’s website. See too, among many choices, Rebecca Goldstein’s recent book Incompleteness: The Proof and Paradox of Kurt Gödel.

Categories: Biography, Books, History, Logic, Math