Monthly Archive for December, 2011

Turning the Crank: The Year in Review

crankSomething about this time of year brings out the cranks. Last year at this time, Lubos Motl (along with a few others, some just confused, others just pure trolls) was disputing the simple but surprising answer to a little probability puzzle. (See first here, then here, then here, then here, then here, and finally, for an enlightening coda, here — and then for one more afterthought, here, with approximately 1000 comments altogether).

This was a tricky puzzle and of course you don’t have to be a crank to get it wrong. But the cranks distinguish themselves by a) repeating exactly the same arguments over and over and over and over and over, while ignoring the fact that those arguments have been clearly refuted; b) reacting with outrage when it’s suggested that if they make an argument with multiple implications, they don’t get to pick and choose which implications to accept; c) dismissing the relevance of definitive counterexamples (e.g. “You’ve made an argument that appears to apply to a country of any size. Let’s see if your argument works for a country with only one family.” “That’s totally beside the point! I never assumed the country had only one family!”), d) rejecting all arguments by analogy by observing that the analogy is imperfect, even when the imperfections of the analogy have no bearing on the argument; e) constantly changing the subject so as to deflect attention from arguments they can’t answer; f) constantly changing their definitions midstream so that everything they’ve been saying, even when it is self-contadictory, becomes true by definition; g) discerning a conspiracy when multiple people take the time to simplify the arguments in the (always vain) hope of penetrating the crank’s thick skull; h) substituting mockery for discourse; and i) repeating the same arguments over and over and over and over, while ignoring the fact that those arguments have been clearly refuted.

This year, instead of a small cadre of cranks, we’ve been visited by a single crank, one Yoram Bauman, who’s cluttered up a long comment thread with repeated instances of behaviors a) through i). It’s not just the flimsiness of his arguments that makes Yoram a crank; it’s the way he repeats those arguments while completely ignoring every objection, or, on those rare occasions when he takes note of those objections, dismissing them as coming from an “echo chamber”. It’s his habit of making two arguments that directly contradict each other within a single paragraph, and then getting miffed when someone points that out. It’s his substitution of mockery for debate. (Note to future commenters: It’s okay, now and then, to adopt a mocking tone when you’ve demolished someone’s argument. It’s not okay to adopt a mocking tone by way of ignoring an argument.) Above all, it’s his intense and total disdain for the process of intellectual discourse, as if this were all just a game and getting things right doesn’t matter.

Well, of course, this is just an online discussion, and whether we get things right probably doesn’t matter very much in the grand scheme of things. But most of us are here because we take pleasure in trying to understand something. Yoram’s entire purpose here seems to be to undermine that pleasure with his clownish (and possibly feigned) stupidity. He’s the guy at the party who pisses on the table for attention and then, when everyone edges away at the same time, accuses them of sheeplike subservience to social norms.

Enough of that! While the year was bookended by cranks, it was filled with other lively discussions worth remembering.

Here were the most-commented-upon posts of 2011:

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Merry Christmas

Merry Christmas. For those of you who are actually surfing the net today, you might enjoy Art Carden’s Forbes piece on how economists ruined Christmas.

Happy Holidays

I’ll probably blog very little over the next ten days or so, in recognition of the fact that most of you won’t be reading. (On the other hand, if, say, the New York Times publishes something sufficiently egregious, I might not be able to restrain myself. Meanwhile, for your holiday pleasure, here’s the Christmas column I published in Slate in 2004:

What I Like About Scrooge

scroogeHere’s what I like about Ebenezer Scrooge: His meager lodgings were dark because darkness is cheap, and barely heated because coal is not free. His dinner was gruel, which he prepared himself. Scrooge paid no man to wait on him.

Scrooge has been called ungenerous. I say that’s a bum rap. What could be more generous than keeping your lamps unlit and your plate unfilled, leaving more fuel for others to burn and more food for others to eat? Who is a more benevolent neighbor than the man who employs no servants, freeing them to wait on someone else?

Oh, it might be slightly more complicated than that. Maybe when Scrooge demands less coal for his fire, less coal ends up being mined. But that’s fine, too. Instead of digging coal for Scrooge, some would-be miner is now free to perform some other service for himself or someone else.

Dickens tells us that the Lord Mayor, in the stronghold of the mighty Mansion House, gave orders to his 50 cooks and butlers to keep Christmas as a Lord Mayor’s household should—presumably for a houseful of guests who lavishly praised his generosity. The bricks, mortar, and labor that built the Mansion House might otherwise have built housing for hundreds; Scrooge, by living in three sparse rooms, deprived no man of a home. By employing no cooks or butlers, he ensured that cooks and butlers were available to some other household where guests reveled in ignorance of their debt to Ebenezer Scrooge.

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Paging Alex Tabarrok

ip2

A mere two days after I lavished praise on Alex Tabarrok’s new book, which (among many other things) makes an eloquent case for patent reform, the U.S. Patent Office has proved that nobody’s listening by issuing patent #8,082,523 to Apple, Incorporated for a “portable electronic device with graphical user interface supporting application switching”. The abstract, in its entirety, reads as follows:

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This Particular God, at Least, Appears to Be Dead

higgsThe apparently imminent discovery of the Higgs boson by scientists at CERN will have at least one quirky side effect that appears to have gone entirely unremarked until the appearance of this blog post — it threatens to inflict fatal collateral damage to the brilliant, eccentric and infuriating Omega Point Theory proposed by the physicist Frank Tipler.

Tipler, who is not a crackpot, once published a book called The Physics of Immortality, purporting, on the basis of orthodox physics plus some plausible auxiliary assumptions, to establish the existence of an omnipotent, omniscient, omnipresent and altruistic “being” who will one day resurrect everyone who has ever lived to eternal life.

The first step toward that startling conclusion is the assumption that our descendants will not allow all life to come to an end. This in turn will require them to control the evolution of the Universe so that it doesn’t collapse in anything that human beings perceive as a finite amount of time; Tipler argues that they’ll quite plausibly have the technology to do that. But all this future tinkering with the shape of the Universe has consequences that (in a very rough sense) radiate backward and forward through time. From this and some highly technical but more-or-less standard physics, Tipler manages to conclude the existence of an Omega Point — a place where (again speaking roughly) all the information in the Universe is stored. Writing in 1994, Tipler never considered the possibility that the Omega Pont might be located in Mountain View, California. Instead, he stressed that in its omniscience, it’s something very like God.

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Launching the Innovation Renaissance

tabarroIn late 17th century England, there were no newspapers outside of London, and scarcely a printer outside of London, Cambridge and Oxford. The difficulty and expense of conveying large packets from place to place was so great that an extensive work took longer to reach Devonshire or Lancashire than it took, in Victorian times, to reach Kentucky. As a result, books and printed matter generally were largely unavailable outside of London — and London, for most rural Englishmen, might as well have been the moon.

I learned this from Macaulay’s History of England, which I just pulled up on my Kindle, which of course gives me instant — and searchable! — access to pretty much everything that’s ever been published. But the Kindle, and its brother e-readers, are more revolutionary than that. Not only do they give us easy access to existing literature; they call forth entirely new literary genres, such as the Kindle e-book, which brings to market extended essays that are too long to be magazine articles but too short to be traditional books — and are priced to sell.

All of which brings me to Alex Tabarrok’s Launching the Innovation Renaissance: A New Path to Bring Smart Ideas to Market Fast, which is both a product and a celebration of the innovation revolution, along with a recipe, or rather a set of recipes, for nurturing that revolution.

This is a great book. It’s fast-paced, fun to read, informative as hell, and it gets everything right. At first I wished I’d written it— until I realized I could never have written it half so well.

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Alas, Poor Yoram

crazyskullThis just in: The study of physics makes people less compassionate. Data show that when cornered at a party by the inventor of a perpetual motion machine, physics majors are particularly unlikely to offer positive encouragement.

Also, the study of history leads to closed-mindedness. After taking an American history course, students become considerably less open to the idea that Millard Fillmore might have been Abraham Lincoln’s vice president.

Meanwhile, the study of chemistry makes people less ambitious. Chemistry students are particularly unwilling to invest in lead-to-gold conversion kits, even when they are conveniently offered over the Internet.

Geology students are just plain nasty. Among all majors, they are the least likely to participate in coordinated meditation exercises for the prevention of earthquakes — even when the organizers estimate that hundreds of thousands of lives might be at stake.

And economics majors are so greedy that they are particularly unlikely to donate to left-wing interest groups that seek to undermine capitalism.

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The Big Surprise

Back in the 1930′s, Kurt Godel proved two amazing facts about arithmetic: First, there are true statements in arithmetic that can’t be proven. Second, the consistency of arithmetic can’t be proven (at least not without recourse to logical methods that are on shakier ground than arithmetic itself).

Yesterday, I showed you Gregory Chaitin’s remarkably simple proof, of Godel’s first theorem. Today, I’ll show you Shira Kritchman and Ron Raz’s remarkably simple (and very recent) proof of Godel’s second theorem. If you work through this argument, you will, I think, have no trouble seeing how it was inspired by the paradox of the surprise examination.

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Berry Interesting

confiture and ingredientsToday, I’m going to give you a short, simple proof of Godel’s First Incompleteness Theorem — the one that says there are true statements in arithmetic that can’t be proven. The proof is due to Gregory Chaitin, and it is far far simpler than Godel’s original proof. A bright high-schooler can grasp it instantly. And it’s wonderfully concrete. At the end, we’ll have an infinite list of statements, all easy to understand, and none of them provable — but almost all of them true (though we won’t know which ones).

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A Tale of Three Paradoxes

This is a tale of three paradoxes and why they matter.

  • First, the ancient Liar Paradox: “This sentence is false”. If this sentence is true, it must be false. If it’s false, it must be true.
  • Next, the century-old Berry Paradox: Call a phrase “short” if it contains fewer than 13 words. The English language contains a finite number of words, and hence a finite number of short phrases. Hence there must be some natural numbers that can’t be described by any short phrase. Among these natural numbers, there must be a smallest. What is that natural number? Why, it’s the smallest natural number that can’t be described by any short phrase, of course. Except that this number is in fact described by the short phrase in boldface.
  • Finally, the more modern Paradox of the Surprise Examination (or the Unexpected Hanging), which we discussed yesterday.

The paradoxes are slippery, because they are stated in the imprecise language of English. But each of them has inspired a precise mathematical counterpart that is central to a brilliant argument in mathematical logic.

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The Surprise Exam, and More Surprises

surpriseexamIf you’re the sort of person who reads this blog, you’re likely to be familiar with the paradox of the unexpected hanging, which has been floating around since 1943 but achieved popular notoriety around 1969 through the writing of Martin Gardner. But you’re less likely to be aware that the unexpected hanging plays a central role in a wonderful new piece of serious mathematics related to algorithmic complexity, Godel’s theorems, and the gap between truth and provability.

The unexpected hanging might as well be a surprise examination, and that’s the form in which I present this paradox to my students every year: In a class that meets every weekday morning, the professor announces that there will be an exam one day next week, but that students won’t know exactly which day until the exams are handed out.

The students, of course, immediately start trying to guess the day of the exam. One student (call him Bob) observes that the quiz can’t be on Friday — because if it is, the students will know that by Thursday afternoon. After all, if Monday, Tuesday, Wednesday and Thursday mornings have all passed by, only Friday remains. A Friday exam can’t be a surprise exam.

A more thoughtful student (call her Carol) observes that this means the quiz must be on one of Monday, Tuesday, Wednesday or Thursday — and that if it’s on Thursday, they’ll know that by Wednesday night. After all, Friday’s ruled out, so if Monday, Tuesday and Wednesday have passed by, then only Thursday remains. That rules out a surprise exam on Thursday.

Another student (call him Ted) observes that thanks to Bob and Carol, we know the exam must be on one of the first three days of the week — which means that if it’s not on Monday or Tuesday, it must be on Wednesday. Therefore if it’s on Wednesday, they’ll know this by Tuesday night. Scratch Wednesday from the list of possibilities.

Now Ted’s girlfriend Alice points out that the exam can’t be on Tuesday either. Whereupon Bob concludes that the exam must be on Monday. But wait a minute! Carol points out that if they know the exam will be on Monday, it can’t be a surprise. Therefore no surprise exam is possible.

The students, relieved, decide not to study. But they’re awfully surprised when they show up in class the following Tuesday and the professor hands out an exam.

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Defying Gravity

Last weekend, while I was in Boston, my fellow aerial arts students put on a show!

I’d have been there if I could have. Thankfully, we live in an age of instant video, so I still get to see the highlights. Congratulations to Caitlin, Celeste, Chris, Erika, Jacki, Maddie, Maia, Mairi, and Maya for a job beautifully done. You can leave compliments for them here or at the YouTube page. Or both!

Here’s proof (which I’ve posted before) that I can do something similar. But maybe not quite as gracefully as some of these other people:

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The Price of a Haircut

Yesterday I had the pleasure of attending a very good talk by Yale’s Gary Gorton on the origins of the financial crisis.

Gorton’s story is that this was a bank run, not substantially different from the bank runs that have always plagued capitalist economies. In this case, the run took place in the repo market, which is an unregulated (and largely unmonitored) industry roughly equal in size to the standard banking industry. The repo market serves large institutions (e.g. Fidelity Investments or state governments) with a lot of cash on hand that they want to stash in an interest-bearing account for a day or two. So Fidelity deposits, say, a half-billion dollars at, say, Bear Stearns, just as you might deposit five hundred dollars at your local bank. One difference, though, is that your account at your local bank is insured, whereas Fidelity’s account at Bear Stearns is not — so Fidelity, unlike you, demands collateral for its deposit. Bear Stearns complies by handing over a half-billion dollars worth of bonds, of which Fidelity takes physical possession. The next morning, Fidelity withdraws its money and returns the bonds.

The problem comes in when rumors begin to spread that some bonds might be riskier than they appear, and Fidelity starts to worry that maybe Bear Stearns is picking particularly risky bonds to hand over. Therefore Fidelity demands more than a half-billion in bonds to guarantee its half-billion dollar deposit. If there’s, say, a 10% discrepancy between the deposit and the collateral, we say that Bear Stearns has taken a half-billion dollar haircut.

Because Bear Stearns has a fixed quantity of bonds on hand, and because all of its depositors are demanding haircuts, Bear Stearns can now accept fewer deposits than before. This means that Bear Stearns has less cash on hand. This makes depositors even more worried about the security of their deposits, which means they demand larger haircuts. The effects snowball until Bear Stearns collapses. Like so:

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Quote of the Day

You do not examine legislation in light of the benefits it will convey if properly administered, but in light of the wrongs it would do and the harms it would cause if improperly administered.

—Lyndon Johnson

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Surprises

Travel and other projects have kept me absent for a couple of weeks, but I’m hoping to be back on a regular blogging schedule very soon now. Meanwhile, here is the video of the Gosnell Lecture that I recently gave at the Rochester Institute of Technology, titled “More Sex is Safer Sex and Other Surprises”.

One of the surprises turned out to be that the audiovisual equipment didn’t work, so I didn’t get to show my prepared slides. But I think things went pretty well anyway.

Slightly higher quality video is here.

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