Author Archive for Steve Landsburg

Frankly Speaking

Here’s something curious about this year’s political rhetoric: The Republican candidates claim that President Obama has made things worse, while he claims he’s made things better.

You might not think that’s a hard thing to explain. If so, I conclude that you are not Robert Frank, who keeps reminding us via his New York Times column (this one for example) that in many circumstances people care less about their absolute economic well-being than about their place in the pecking order. According to Frank, we buy big homes and fast cars not because we like big homes and fast cars, but because we like our homes and cars to be bigger and faster than our neighbors’. This in turn calls for a tax increase to tamp down that wasteful arms race.

But here’s the thing: Each of us has pretty good information on how we ourselves are doing. When politicians say the economy is doing poorly, they’re mostly informing us that other people are doing poorly. If Frank is right, we’ll consider that good news and (if we believe the news to be accurate) reward the incumbent who brought everyone else down. In other words, is Frank is right, then President Obama’s best strategy is to take credit for a disastrous economy, while his Republican opponents should argue that in fact we’re in the midst of a strong recovery.

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A Tale of Two Cities

The London subway stations have NO trash receptacles. The tracks look like this:

The New York subway stations have more trash receptacles than I can count. The tracks look like this:

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Who Expected THAT?

Suppose you go around taking extremely close-up black-and-white pictures of randomly chosen natural and unnatural objects (rocks, trees, streams, buildings, etc.). What do they look like?

Well, each one looks like a patch of varying shades of gray, of course. But do some patches arise more than others? If each of your close-ups is, say, three pixels by three pixels, Which would you expect to see more of:

This? Or this?

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What Is It Like to Talk Batty?

Sometimes I think we should license economics writers.

Thomas Nagel is a prominent philosopher (author of the provocative and widely anthologized essay What is it Like to be a Bat?) who’s just reviewed Daniel Kahneman’s new (and excellent) book in The New Republic. (Fun fact: When I stepped off an airplane at Heathrow last week, the first thing I saw was a limousine driver holding a sign that said “Daniel Kahneman”. This, incidentally, was my final issue of The New Republic, due to their criminally evil subscription practices — more on that, perhaps, later this week. ) Here is how Nagel describes what he seems to think is orthodox economic theory:

Most choices, and all economic choices, involve some uncertainty about their outcomes, and rational expectations theory, also called expected utility theory, describes a uniform standard for determining the rationality of choices under uncertainty…

The standard seems self-evident: The value of a 50 percent probability of an outcome is half the value the outcome would have if it actually occurred, and in general the value of any choice under uncertainty is dependent on the values of its possible outcomes, multiplied by their probabilities. Rationality in decision consists in making choices on the basis of `expected value’, which means picking the alternative that maximizes the sum of the products of utility and probability for all the possible outcomes. So a 10 percent chance of $1000 is better than a 50% chance of $150, an 80% chance of $100 plus a 20% chance of $10 is better than a 100 percent of $80 and so forth.

AAAAGGGHHH! Even on the Internet, it’s rare to see quite so much ignorance packed into so few words. Where to begin?

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Live From Warwick

Apparently my Saturday talk at the Warwick Economics Summit (like several of the others) will be streamed live over the Internet here. I go on at 8:55AM eastern standard time, but don’t feel like you have to set an alarm clock; there will be video available after the fact.

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Your President Hopes You’re Stupid

When an ideologically diverse roomful of economists, upon hearing the announcement of a new presidential policy, bursts into unanimous laughter, you can be pretty sure the president is trying to pull a fast one.

A couple of days ago, I happened to arrive a little late for our department’s regular Friday 10AM bagel hour, where a heated discussion of the original contraception-for-all policy was in full swing. I was able to report that I’d just heard on the radio that the president was “backing off” by transferring the mandate from employers to insurers. Hilarity ensued.

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Pro and Contra-ception

I’d been planning a blog post on the birth control mandate, but it turns out that John Cochrane has already said everything worth saying.

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Rock On

rockI don’t trust rocks. Rocks keep fooling me. They sit there looking all solid until you examine them more carefully and find out they’re mostly empty space, with a smattering of charged particles here and there. Then you look a little deeper and find out those charged particles are nothing like they first appeared. They don’t even have locations. Rocks, and their constituents, are nothing at all like they first present themselves. But at least they’re real. I think.

Now here’s what genuinely baffles me: Apparently there are people in this world (and even, occasionally, in the comments section of this blog) who haven’t the slightest doubt about the existence of rocks, galaxies, squirrels, and the rest of the physical universe, but who suddenly turn into hardcore skeptics re the existence of mathematical objects like the natural numbers. (Many of these people, I suspect, are in fact affecting skepticism because of a badly mistaken belief that it makes them look sophisticated. But that’s speculation on my part, so let’s put it aside and take their positions at face value.) I just don’t get this. Why on earth would, say, a scientist, commit to the belief that there’s a physical universe out there but not a mathematical one, when we know that our perceptions of the physical universe demand constant revision, whereas our perceptions of the mathematical universe are largely eternal. My conception of the natural numbers is very close to Euclid’s; my conception of an atom bears almost no resemblance to Demosthenes’s.

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Why Jews Don’t Farm

I’ve been a little swamped lately and my daily blogging has fallen off. Until things get back to normal, I think I’ll fill the breach by reprinting a few of my old columns from Slate. Today’s entry is on “Why Jews Don’t Farm”.

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In the 1890s, my Eastern European Jewish ancestors emigrated to an American Jewish farming community in Woodbine, N.J., where the millionaire philanthropist Baron de Hirsch provided land, tools, and training at one of the nation’s first agricultural colleges. But within a generation, the family had settled in Philadelphia where they became accountants, tailors, merchants, and eventually, lawyers and college professors.

De Hirsch had a vision of American Jews achieving economic liberation by working the land. If he’d had a better sense of history, he would have built not an agricultural college but a medical school, because for well over a millennium prior to the settlement of Woodbine, Jews had not been farmers—not in Palestine, not in the Muslim empire, not in Western Europe, not in Eastern Europe, not anywhere in the world.

You have to go back almost 2,000 years to find a time when Jews, like virtually every other identifiable group, were primarily an agricultural people. Around A.D. 200, Jews began to quit the land. By the seventh century, Jews had left their farms in large numbers to become craftsmen, artisans, merchants, and moneylenders—the only group to have given up on agriculture. Jewish participation in farming fell to about 10 percent through most of the world; even in Palestine it was only about 25 percent. Everyone else stayed on the farms.

(Even in the modern state of Israel, where agriculture has been an important component of the economy, it’s been a peculiarly capital-intensive form of agriculture, one that employed well under a quarter of the population at the height of the Kibbutz movement, and less than 3 percent of the population today.)

The obvious question is: Why? Why did Jews and only Jews take up urban occupations, and why did it happen so dramatically throughout the world? Two economic historians—Maristella Botticini (of Boston University and Universitá di Torino) and Zvi Eckstein (of Tel Aviv University and the University of Minnesota)—have recently been giving that question a lot of thought.

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Laugh of the Day

It’s been a while since I laughed out loud quite this hard.

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Where to Find Me

A few upcoming events:

I’ll be at the Warwick Economics Summit February 17-19, speaking on the 18th.

I’ll be speaking at the Adam Smith Institute in London on February 20.

On February 23, I’ll be at the off-Broadway Soho Rep Theater, moderating a panel discussion on “The Economy of Beauty” following a performance of the hot German playwright Marius von Mayenburg‘s new play The Ugly One. My fellow panelists will include the sociologist Ashley Mears, author of Pricing Beauty: The Making of a Fashion Model and a former fashion model herself.

On March 9, I’ll be speaking at the Laboratory for Laser Energetics in beautiful Rochester, New York.

I expect to be speaking at the University of Maryland on a date still to be negotiated in April or May.

And from July 29 through August 3, I’ll be giving four lectures and hobnobbing with the other participants at Cato University. (Yes, I know the link is to last year’s Cato U.; this year’s page seems not to be up yet.)

If you’re in any of those neighborhoods, do join us.

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Public Service Announcement

Monday’s post generated an unusually large number of comments that consisted of nothing but namecalling, directed in almost all cases at Paul Krugman (though in exactly one case at me). I’ve deleted all of these comments, in most cases before they were ever posted.

I strongly encourage spirited discussion. I understand that spirited discussion can get pretty heated, and that in heated discussion people (including me) sometimes say nasty things. I prefer to keep that to a minimum, but I still allow a fair amount of it as long as the comments advance the discussion. But if your post consists of 100% pure nastiness, with no conceivable way for anybody to learn anything from it, I will usually delete it. One exception: Being very funny can compensate for a lot of nastiness, especially if it’s the kind of funny that draws the reader’s attention to a genuine flaw in someone’s reasoning. The many posts I’ve deleted over the past 48 hours were nasty without even trying to be funny.

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Wisdom from the Ivy League

Greg Mankiw’s four principles of tax reform are extraordinarily wise, and I think it’s fair to say that almost everyone who has thought hard about these issues will agree with everything he says.

I have only one quibble, and that’s that Greg is very sure we should eliminate the mortgage interest deduction in accordance with his first principle: “Broaden the Base and Lower Rates”. I think we should maybe keep it in accordance with his second principle: “Tax Consumption Rather than Income”. (Though I certainly agree that after the second principle has been implemented, it will be time for the mortgage interest deduction to go.)

How sad that so much wisdom is sure to go unheeded.

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In Which Paul Krugman Leaves Me At a Loss for Words

Okay, this one’s almost too bizarre for words. First, Paul Krugman makes an argument that ignores the existence of corporate dividends. Then, pretty much everybody in the world points out his error. Then, he admits his error, but, true to form, takes an irrelevant swipe at his critics. But in this case, the irrelevant swipe is: “Aha! You’ve just admitted that corporations pay dividends! So much for your past claims that corporations pay wages!”

Umm…Paul? They pay both. I’d lift Krugman’s own favorite dismissive phrase and say “That’s Economics 101”, but actually it’s probably standard knowledge among middle schoolers.

To review the details:

First, Krugman reposted (from the website of a left-wing advocacy group) a highly misleading chart purporting to illustrate the federal tax burdens borne by various income groups. The chart accounts for payroll and income taxes, but omits corporate taxes, thereby making the burden on high-income tax payers appear substantially smaller than it is, because corporate taxes reduce dividends which are disporportionately paid to high-income taxpayers.

Next, he got called on it by lots and lots of people, including, for example, Greg Mankiw.

Next, Krugman acknowledged his error. But, as always, he did so with the least possible grace, suggesting that his critics, by virtue of pointing out Krugman’s mistake, have somehow undermined their own principles.

In particular, his position is that by acknowledging that corporate profits benefit shareholders, “conservatives” have undermined their own ability to claim that corporations benefit anyone other than shareholders (e.g. workers). He relies, in other words, on the cockamamie notion that if something is good for group A, it can’t possibly also be good for group B.

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Mitt Romney’s Taxes

Mitt Romney says his tax rate is “probably around 15%”. It’s not clear what he means by that (marginal rate? average rate? federal rate? federal-plus-state-plus-local rate?) but the New York Times is quick to point out that he’s a beneficiary of the “fact” that investment income is taxed at a much lower rate than wages and salaries, leaving him with a lower percentage tax burden than the working-stiffs he employs.

For at least the eighth time on this blog, I want to point out that this widely believed “fact” is not true.

To understand Mitt Romney’s tax burden, you have to compare him to his doppelganger Timm Romney, who lives on a planet with no taxes. In the year (say) 2000, Mitt and Timm both earned (say) a million dollars. Timm invested his million dollars, saw it double over the past decade or so, and cashed out his investment this year, leaving him with two million dollars. Mitt, by contrast, paid 35% tax in 2000, leaving him with $650,000. He invested it, saw it double, and cashed out last year, paying 15% tax on the $650,000 capital gain. That leaves him $1,202,500, which is about 60% of what Timm’s got. In other words, the tax system costs Mitt almost 40% of his income.

By contrast, people on our planet without investment income collect their wages, pay 35% in taxes, and spend what’s left. The tax system costs them 35%, while it costs Mitt almost 40%. In other words, people with investment income bear a higher tax burden, as a percentage of their income, than anyone else — and that’s before you even start accounting for the taxes on dividends, interest, corporate income and inheritance.

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On the Road Again

I’m traveling for the next week, and will probably not be on the net much. I’ll blog if anything catches my fancy, but most likely you won’t see me for at least a few days.

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Off the Deep End

Paul Krugman argues that success in business is not, by itself, a qualification for making wise economic policy, and I agree. But then he goes all looney-tunes on us:

A businessman can slash his workforce in half, produce about the same as before, and be considered a big success; an economy that does the same plunges into depression, and ends up not being able to sell its goods.

So according to Krugman, it’s better for you and your spouse to earn $40,000 each than for one of you to earn $80,000 while the other stays home with the kids. I wonder how many two-earner families would agree with him.

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How to Fix Everything

Here is how I answered that question in Jamaica:

(Slightly higher quality video here.)

Edited to add: There were apparently some problems with the video stalling somewhere around the one-hour mark (during the post-talk question period.) I believe this is fixed now.

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Debt: The Never-Ending Topic

Don Boudreaux, who as always merits careful attention, attempts to mediate among me, Paul Krugman, Bob Murphy and Nick Rowe on the subject of the public debt. His title is “Let’s not Talk Past Each Other on the Burden-of-Public-Debt Issue”. Indeed, I think that to a very large extent we are all saying exactly the same thing (as you’d expect, because we’re all good at thinking about this kind of stuff, and really, it’s not that hard), but disagreeing about where the emphasis should lie. So let me sum up the major points here. (For background see here, here, here, and the links therefrom.) I think it would be great if Bob, Nick, Don and Paul would let us know, by number, which of these points (if any) they disagree with:

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Debt Again

I hadn’t intended this to be national debt week here at The Big Questions, but when you get into a back-and-forth with a guy as compulsively readable as Bob Murphy, you milk it for all it’s worth.

Murphy objects to formulations along the lines of “government debt is not a burden because we owe it to ourselves” and offers a parable that he thinks illustrates all the key issues. I agree that his parable illustrates all the key issues, so let’s review it — and see what it really illustrates.

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You, Your Grandchildren, and the Public Debt

Nick Rowe, applauded by such luminaries as Don Boudreaux and Bob Murphy, argues that, contrary to folks like Paul Krugman and yours truly, government debt is too a burden on our grandchildren, unless you believe in Ricardian Equivalence.

I want to explain what that means, and why it’s wrong.

To make sure we’re all talking about the same thing, I’m going to adopt all of Nick’s assumptions, most critically that all taxes are lump sum. I’ll come back at the end and say a little more about why this obviously false assumption is the right assumption to make.

Now: Suppose the government borrows money to finance a tax cut. That makes us feel richer. We therefore buy and consume more stuff, which leaves less stuff for our grandchildren to consume. (Nick tells a very nice detailed story about how this might play out across generations; I applaud that kind of detail, but it’s not important for this response.) Government debt is therefore a burden to our grandchildren.

Unless! If we — the current generation — foresee all this, and care about our grandchildren, we’ll choose to (in effect) undo what the government has done by saving our tax cuts and giving them as gifts to our grandchildren (presumably as part of their inheritance). This restores every generation’s consumption to the original status quo.

Ricardian Equivalence is the economist’s jargon for the assertion that we will foresee all of this, and will care about our grandchildren, and therefore will give them our tax cuts as gifts. Nick Rowe’s claim is that unless you make the very strong assumption that Ricardian equivalence holds, government debt enriches us at the expense of our grandchildren.

Here’s why that’s wrong: Continue reading ‘You, Your Grandchildren, and the Public Debt’

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Actually, We Owe It All to Ourselves

Paul Krugman has a very good column on government debt and why it doesn’t matter nearly as much as many people believe. There’s just one spot in the column where I think Krugman misses the point, and therefore makes a weaker case than he could have made. He writes:

U.S. debt is, to a large extent, money we owe to ourselves.

It’s true that foreigners now hold large claims on the United States, including a fair amount of government debt. But every dollar’s worth of foreign claims on America is matched by 89 cents’ worth of U.S. claims on foreigners. And because foreigners tend to put their U.S. investments into safe, low-yield assets, America actually earns more from its assets abroad than it pays to foreign investors. If your image is of a nation that’s already deep in hock to the Chinese, you’ve been misinformed. Nor are we heading rapidly in that direction.

All true, but all beside the point. Even if 100% of U.S. debt were held by foreigners, and even if Americans had no offsetting claims on foreigners whatsoever, the U.S. debt would still be money we owe to ourselves.

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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.

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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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