Author Archive for Steve Landsburg

Puzzle Contest Update

As of now, I’ve received exactly one completely correct answer to this week’s crossword. (The submission actually contained four errors, but it was followed almost immediately by an email from the submitter with the requisite four corrections, so I’m giving full credit.) Congratulations to our frequent commenter EricK.

The contest, however, remains open. I’ll be sending free autographed books (your choice of The Big Questions, The Armchair Economist, Fair Play, or More Sex is Safer Sex) to EricK and the three runners-up, where the runners-up will be determined by some yet-to-be-determined combination of accuracy and timeliness. The contest will close on a date still to be determined, but I plan to keep it open for at least another week. Keep those submissions coming!

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Monday Puzzles

Click image to solve puzzle.

So it turns out that if you take a notion to create a crossword puzzle, put it on your blog, and include a “submit” button so that solvers can send you their answers, then — at least if your skill set is similar to mine — writing the code to make that “submit” button work will be about twice as difficult and three times as time-consuming (but perhaps also several times as educational) as actually creating the crossword puzzle. I certainly learned some hard lessons about the difference between POST and GET. But it’s done and (I think) it works.

To do the puzzle online click here. For a printable version, click here. If you do this on line and want to submit your answer, use the spiffy “Submit” button! (And do feel free to compliment the author of that button!). The clues are subject to pretty much the same rules that you’d find in, say, the London Times or the Guardian.

I will gather the submissions and eventually give proper public credit to the most accurate and fastest solvers. Feel free to submit partial solutions; it’s not impossible that nobody will solve the whole thing.

Let’s try to keep spoilers out of the comments, at least for a week or so.

I have one very geeky addendum to all this, leading to a second Monday puzzle — one that might be easy to solve for a reader or two, but most definitely not for me. Unless you’re a very particular brand of geek, you’ll probably want to stop reading right here. But:

Continue reading ‘Monday Puzzles’

Discussion Question

Imagine a world where everyone is equally risk-averse, and where there are two assets available: You can hold stock in an umbrella company, or you can hold stock in a sunscreen company. Depending on the (quite unpredictable) weather, one of these stocks is sure to gain value at 100% a year while the other is sure to lose value at 95% a year, but it’s impossible to know which is which.

Given this, the smart thing to do is to hold a balanced portfolio of the two assets and earn a comfortable 5% per year. Most people in this imaginary world are smart enough to figure this out. But a small number are stupid enough to put all their eggs in one or the other basket. Half these people are quickly wiped out; the other half become super-rich.

Now we have a society in which nobody smart is especially rich, and everyone rich is especially dumb.

Question: Does this parable contribute anything useful to understanding some aspect (obviously not all aspects!) of the wealth distribution in the world we inhabit? Discuss.

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The Coinflipper’s Dilemma

flipperThis is the story of how I came to write a little paper called The Coinflipper’s Dilemma.

When I was in high school, my English teacher must have had a free period at the time when my math class met, because every day he would march into the math class and empty his pockets on the table, whereupon my math teacher did the same. Then whoever had put down the most money scooped up everything on the table.

I am ashamed to admit that it took me until this summer to think about computing the equilibrium strategy is in that game.

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The Goldwater Standard

goldwaterFifty years ago this Labor Day weekend, the presidential campaign of 1964 got underway in earnest. It is often said that Barry Goldwater “lost the election but won the Republican party” or even “lost the election but won the future” by nudging the center of either the party or the country several notches to the right.

I don’t see it. Where is the contemporary mainstream politician — Republican or otherwise — who would repeal the 1964 Civil Rights Act, or at least those provisions (Titles II and VII) that authorize Federal regulators to override private business decisions about whom to serve and whom to hire? Where is the contemporary mainstream politician who would sell the Tennessee Valley Authority? Or end all agricultural supports? If Goldwaterism is in fact ascendant, then how did entitlement spending, as a percentage of GDP, manage to grow for most of the past 20 years — even though Republicans controlled the House of Representatives for 16 of those 20? For that matter, how is it that after all those years of Republican control, the National Endowments of the Arts and Humanities — two of the more noxious weeds to arise from the soil of the Goldwater defeat — continue to thrive?

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Tipping the Scales

Former economist Paul Krugman has actually managed to get these words past an editor at the New York Times:

There is, however, one big difference between corporate persons and the likes of you and me: On current trends, we’re heading toward a world in which only the human people pay taxes.

Now I think we can be quite sure that even Paul Krugman, with his gargantuan capacity for forgetting everything he once knew, is well aware that we already live in a world where only human people pay taxes. That’s an instance of the general principle that the legal incidence of a tax does not determine its economic incidence. The corporate income tax is levied by law on corporations, but its economic effects are felt entirely by humans.

Why then, did he write this in the first place? Well, the charitable reading — and I am all in favor of charitable readings — is that all he’s saying is that the legal incidence of taxation has shifted somewhat from corporations to individuals.

But why would that be interesting? And why would it be, as Krugman seems to take for granted, a clearly bad thing? Suppose that in 1990, I received a $1 dividend and paid a 25% tax, keeping 75 cents in my pocket, while in 2014, due to a fall in corporate rates (leading to higher dividend payouts) and a rise in personal rates, I received a $1.50 dividend and paid a 50% tax, keeping 75 cents in my pocket. Who cares?

Well, perhaps there are reasons to care, involving some non-obvious incentive effect of the sort that it takes an economist to notice. Well, that, then, is where the economist comes in — his job being to explain why he thinks these things matter. In this case, I don’t offhand see the argument, but I’m perfectly happy to believe there might be one. On the other hand, if Krugman actually has an argument in mind, one wonders why he’s so reluctant to share it.

Oh, he does pay lip service to the need for an argument, but all he offers is sophistry:

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Applied Bayesianism

When I was a child, my parents took me to Atlantic City every summer. And we would always make a side trip to Longport (three towns away) to collect seashells, because my Dad said that Longport was famous for the quality of its seashells.

Last week, on a whim, my wife and I went down to Atlantic City for a few days, largely because it looked like they were having nice weather down there. In a fit of ambition, we walked the entire 16-or-so-mile roundtrip from the Steel Pier area to the far end of Longport. Along the way, I noticed no difference between the Longport seashells and the Atlantic City (or Ventnor or Margate) seashells. Moreover, we met a lifelong Longport resident (and enthusiastic civic booster) who confirmed that she had never in her life heard that there was supposed to be anything special about Longport’s seashells.

Over my lifetime, I’ve accumulated a lot of advice from my father, some of which seemed to make sense. But in light of my trip to Longport, I’m re-evaluating.

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ACT now!!

jamiewhyteIf you like The Big Questions, you really ought to know my brash and brilliant friend Jamie Whyte. After a brief but dazzling career as a philosopher at Cambridge university (he once won the prestigious Analysis prize for the best article by a philosopher under 30), Jamie distinguished himself as a management consultant, a foreign currency trader, and, via his frequent writing, an incisive and steadfast defender of rational thought and individual freedom. His little book on Crimes Against Logic delivers brilliantly on its promise to “expose the bogus arguments of politicians, priests, journalists and other serial offenders”, and his recent collection Free Thoughts (which, true to its title, you can read for free) is essential fare for anyone who cares about clarity of thought — or, because Jamie is as funny as he is brilliant, anyone who’s just looking for a good chuckle.

Now, in his most startling career twist yet, Jamie has become the leader of a political party in his native New Zealand — the ACT party, named for its forerunner, the Association of Consumers and Taxpayers. ACT stands unabashedly for individual liberty, the rule of law and the enforcement of well-defined property rights. It campaigns against corporate welfare. It’s even pro-immigration. And thanks to New Zealand’s system of proportional representation, it actually gets representatives into parliament.

After several years of turmoil, the party turned to Jamie’s leadership in February of this year. With the boundless energy that inspires awe in everyone he meets, Jamie is re-building the party and promoting a principled free-market agenda in the run-up to the September 20 general election.

actThe downside of being a principled politician — and the reason they’re almost vanishingly rare — is that it’s hard to raise funds when you won’t cater to special interests. ACT opposes both corporate welfare and legal favoritism for union members, which cuts out most of the usual big donors. Here’s where you can help, and I hope you will.

Never before (and, I expect, never again) have I encouraged my readers to support any political party with their votes, let alone their dollars. That’s because I’ve spent my adult life being seduced and abandoned by politicians who talked a good game and then caved in to expediency when the chips were down. But Jamie — and therefore ACT — is different. I know him as a friend, and I know that principles are his passion.

You can help make ACT’s vision a reality by visiting the donation page and giving generously. Remember that a New Zealand dollar is worth about 88 cents U.S., so if you’re an American, a “$100 donation” is actually $88.

A little more background on New Zealand:

Continue reading ‘ACT now!!’

Nanosteps

In a nanostep for freedom, the Supreme Court this morning protected a small number of Americans from being forced by Congress to buy contraception insurance that they do not want. In a somewhat larger step backward, that small number of Americans were not chosen randomly, but instead were selected according to the religious beliefs of their employers. Whether this bodes well for future progress remains to be considered.

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Follow the Bouncing Ball

If you want to compute the circumference of the observable universe to within, say, the width of a human hair, you’ll need to know about 35 digits of π, though this never seems to deter a certain sort of person from memorizing the first 100, 200 or 500 digits. But it turns out there’s no need to memorize anything at all! You can recover any number of digits you like from a simple little physics experiment that I just learned about, though it was invented over ten years ago by Professor Gregory Galperin of Eastern Illinois University. His lovely little paper is here.

To see how it works, start with two identical billiards lined up in front of a wall like so:

Now push Ball 2 toward Ball 1 and count the collisions: First Ball 2 collides with Ball 1 and pushes it toward the wall. (At this point Ball 2 has transferred all its momentum to Ball 1 and stops moving). Then Ball 1 collides with the wall and bounces back toward Ball 2. Then Ball 1 collides with Ball 2 and pushes it off to a far-away place. Three collisions. That tells you that π starts with a 3.

If you want more accuracy, make Ball 2 exactly 100 times as heavy as Ball 1. This time the sequence of events is a little more complicated, but it turns out there are exactly 31 collisons. That tells you that π starts with 3.1.

Or if you prefer, make Ball 2 exactly 10,000 times as heavy as Ball 1. You’ll get exactly 314 collisions. π starts with 3.14.

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The Free Marketeers

Yesterday’s brief post raised an eyebrow over a congressional candidate who manages simultaneously to call himself a “free-market economist” and to support strict controls on immigration. Here are a few more words for those who don’t quite see the problem.

First, I can imagine two possible meanings for the adjective “free-market”. Either it means you place a high value on freedom as an end in itself or it means you believe that freedom is, in general, a highly effective means to other ends you care about, like prosperity or security. I happen to be a free marketeer in both senses, though I can easily imagine being a free marketeer in either sense alone.

I see my preference for freedom as an end in itself as being similar to my preference for well done meat — you either share that preference or you don’t, and if you don’t, we’ll just have to agree to disagree — there’s no right or wrong here. One exception: If your preferences strike me as inconsistent — if, that is, you seem to make a lot of choices that indicate a strong preference for freedom while denying that freedom is terribly important to you — then I’m apt to point to that inconsistency and suggest that you might want to think a little harder about what your true preferences really are. That was the thrust of what I once tried to do in a book called Fair Play, where I suggested that the choices we make as parents often reveal values contrary to those we express in the voting booth — and that by reflecting on those choices, we might become more thoughtful voters.

On the other hand, if you doubt that freedom is an effective means toward prosperity, then I’m pretty sure you’re just wrong, and that if you thought about it harder you’d change your mind. A lot of my other writing has tried to explain how to think about it harder, and to demonstrate that this is a subject where hard thinking can be fun.

Now I’m not sure in which sense our congressional candidate considers himself a free marketeer, but surely if you’re a free marketeer in either sense, you’ll tend to endorse statements like these:

Continue reading ‘The Free Marketeers’

Annals of Self-Contradiction

The central policy issue in this race has become Cantor’s absolute determination to pass an amnesty bill. Cantor is the No. 1 cheerleader in Congress for amnesty [for illegal immigrants]. This is not the Republican way to fix our economy and labor markets.

  — David Brat, congressional candidate and self-described “free market economist”

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Veterans Affairs

Suppose you’ve just joined the army and expect to serve for, oh, say, four years before returning to civilian life.

Which would you rather have when you get out: a lifetime-guaranteed annual check for $7500 (adjusted each year for inflation) or a package of VA benefits?

To help you decide: The VA benefits include payments of anywhere from about $100 a month to almost $3000 a month in the unlikely event that you are partially or fully disabled, a pension on the order of $15,000 a year in the more unlikely event that you are both disabled and poverty-stricken (rising to more like $20,000 a year if you need regular aid and attendance), educational benefits under the GI bill, and health care of whatever quality the government chooses to provide.

Me, I’d take the guaranteed $7500-a-year in a heartbeat. If that’s the typical response, then it’s hard to see why we have a Veteran’s Administration in the first place, seeing as how the VA’s annual budget would just about cover those payments.

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On Piketty and Capital

Important disclaimer: I have not read Thomas Piketty‘s book on Capital in the Twenty-First Century, and therefore cannot possibly have given it a fair reading.

I do, however, trust Per Krusell and Tony Smith to have given it a fair reading, because Krusell and Smith have long track records as diligent and thoughtful scholars. And their analysis appears to devastate both Piketty’s model and his prediction that income inequality is destined to grow explosively over time.

Here’s why:

All of Piketty’s predictions depend on his assumptions about how much people save. The simplest respectable model (that is, a model that economists generally feel comfortable using for many purposes, and which fits fairly well with observations) says that we save a fixed percentage of our incomes — say 30%. (There are also more sophisticated models in which this percentage can change as economic conditions change.)

Piketty, by contrast, assumes that our net saving is a fixed percentage of our net incomes, where “net” means “after subtracting depreciation of our assets”. That’s a very different assumption, and, according to Krusell and Smith, not at all a plausible one. It’s implausible first because it has extremely odd implications. Most notably, it implies (though this is not immediately obvious) that if economic growth slows to zero, we will eventually choose to save 100% of our incomes(!!). Beyond that, Krusell and Smith argue in considerable detail that, compared to the more traditional models, Piketty’s does a poor job of fitting the last seventy years’ worth of data.

According to Krusell and Smith, Piketty demonstrates correctly that under his assumptions, slowing economic growth must lead to massive inequality over time. But under the far more plausible assumptions found in modern textbooks and modern research papers, that conclusion goes away. In fact, after substituting those assumptions, Piketty’s arguments yield something like the opposite conclusion — as growth slows down, changes in inequality become pretty much negligible.

If this analysis is right — and given the identities of the authors I’ll be very surprised if it’s wrong — then there appears to be very little reason to buy into Piketty’s story. That doesn’t mean he’s wasted his time. We learn a lot by making a variety of different assumptions and figuring out where they lead us, even when the assumptions are ultimately unsupportable. But a serious intellectual exercise is not the same thing as a serious prediction.

The Rising Tide

So the Obama administration has released a climate forecast, according to which Miami could be under water by the end of the century. Apparently we’re supposed to be very concerned about that.

To put this in perspective, we’ve currently got about 140,000,000 square miles of ocean on this planet — about 71.066% of the earth’s surface. Add Miami’s 35 square miles and that goes up to 71.066007%. You could add all of South Florida and barely notice the difference.

Here’s what Jeff Goodell of Rolling Stone says about that:

Of course, South Florida is not the only place that will be devastated by sea-level rise. London, Boston, New York and Shanghai are all vulnerable, as are low-lying underdeveloped nations like Bangladesh. But South Florida is uniquely screwed, in part because about 75 percent of the 5.5 million people in South Florida live along the coast.

What Mr. Goodell appears to overlook is that of the 5.5 million people now living in South Florida, approximately zero will be alive a hundred years from now, and those that are will presumably have had the sense to move inland well before the water reaches their breastbones.

Continue reading ‘The Rising Tide’

Something to Celebrate

Here’s a key lesson of economics: Trade is good, but trade with people very unlike yourself is even better. I’m a teacher who eats beef, drives a car and lives in a house. I don’t need other teachers so much as I need students, ranchers, autoworkers and architects. If your neighbors love gardening as much as you hate it, you’ll find it easy to hire a gardener. If it’s the other way around, you’ll do well in the gardening business.

The lesson spills over beyond the markets for goods and services. We learn new ways of thinking and new ways of living from people who think and live differently than ourselves.

We thrive on diversity — diversity of skills, diversity of interests, diversity of lifestyles, diversity of religious and political outlooks, diversity of culinary and artistic tastes, diversity of lifestyles, and, lest we forget, diversity of income. Capitalists need workers and workers need capitalists. A wealthy factory owner won’t stay wealthy for long if here’s nobody to work the assembly lines. A middle-class assembly line worker won’t be middle-class for long if there’s nobody building factories.

Let us then celebrate diversity, not try to extinguish it. And let’s not forget that diversity of income — or, if you prefer, “income inequality” — is just as much a blessing as diversity of skills, preferences, cultural outlooks, and ways of living.

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Housing Problems

Josh Barro observes that home ownership is a really bad investment strategy insofar as it involves putting an awful lot of eggs in one basket — indeed, for many people it involves putting more eggs than they’ve got in one basket, since the mortgage market allows you to sink more than your entire net worth into a single house.

In fact, it’s even worse than Josh says. If your house is located anywhere near your workplace (in other words, if you’re almost anyone) then a local economic downturn can devastate your home value at exactly the same time that it’s costing you your job. That’s a whole lot of unnecessary risk.

As Josh acknowledges, that doesn’t mean you shouldn’t own a house; it just means you shouldn’t fool yourself into thinking it’s a wise investment.

But Dan McLaughlin at the Federalist isn’t satisfied:

Economists … should never make the mistake of ignoring consumer behavior they regard as irrational…What Barro should have asked himself (as any real economist should) before declaring that vast numbers of homebuyers and homeowners have been acting irrationally for millenia in buying their own homes is: what are they getting out of it that my analysis is missing?

I enthusiastically endorse the sentiment that when we observe “inexplicable” behavior, our first instinct should be to ask “What am I missing?”. But Barro at least tried to do that — he pointed to “a sense of security” and the desire to customize one’s residence. I agree with McLaughlin’s assessment that these are pretty weak answers, but unfortunately McLaughlin’s own “answers” are even weaker. According to McLaughlin, we own houses because we don’t like to move, and he elaborates at length on the reasons why —- moving is expensive, it means adjusting to new neighborhoods, uprooting your family, etc. etc.

The thing is, though, none of this is a reason to own rather than rent. You could accomplish all of the above with a 99-year lease (binding for the landlord but not for the tenant) which would give you all the residential stability of home ownership while transferring the risk to a professional landlord with diversified holdings.

So why do people buy houses? Offhand, I can think of three answers:

Continue reading ‘Housing Problems’

Social Accounting

We’ve had a very long recent thread about the social costs and benefits of high frequency trading, where I’ve apparently managed to confuse a number of readers by switching back and forth, according to the convenience of the moment, between two different, but perfectly legitimate, social accounting systems.

To clarify matters, let’s forget for the moment about high frequency trading and look at something simpler — innovation in the IT industry, where it’s clear that profit-maximization can easily lead to too much innovation. I’ll do the accounting both ways to make it clear that both ways are right.

First, the assumptions:

Alice has developed a word processor, which she sells online. It costs her $5000 a year to maintain a server, where you can download a copy for $1000. She sells 100 copies a year, and therefore collects $100,000 in revenue. Most of the consuemrs who buy those copies value them at more than their price. In fact, the total value of those 100 copies to the consumers is $200,000.

Bob has an idea for a word processor that’s a little better than Alice’s, so that each consumer would be willing to pay $10 more for Bob’s than for Alice’s.

If Bob develops his word processor, how much can Alice charge for hers? Because her word processor is inferior to Bob’s, she’s got to undercut his price by $10 in order to maintain any customers at all. So if Bob charges $600, Alice charges $590. But then Bob can steal all of Alice’s customers by lowering his price to $599.99, whereupon Alice must lower her price to $589.99, whereupon Bob steals all her customers by lowering his price another penny….and the race to the bottom is on. But Alice’s price cannot fall below $50, because then she wouldn’t earn enough to cover her server costs. So Alice, who is smart enough to foresee all this, gives up and cedes the market to Bob.

Once Bob has the market to himself, he doesn’t have to worry about re-entry by Alice, because they both know perfectly well that the instant she renews her server contract, the race to the bottom will be back on and she’ll have spent $5000 for nothing.

Now if Bob sells his word processor for $1000, it’s he instead of Alice who earns $100,000 a year in revenue and therefore (after subtracting the server cost) $95,000 in profit. He weighs this against the $80,000 cost of developing his word processor and takes the plunge.

I claim that Bob’s decision is privately wise (i.e. wise from Bob’s point of view) and socially foolish (i.e. it reduces social welfare, defined as the total dollar value of all the gains to consumers and producers). We can calculate the costs and benefits of Bob’s decision in either of two equally legitimate ways. Because they are equally legitimate, they lead to the same bottom line: Bob’s private benefit exceeds his private cost by $15,000 (which is why he plunges ahead), while the social cost exceeds the social benefit by $79,000 (which is why we wish he wouldn’t).

Continue reading ‘Social Accounting’

Flying Robot Rockstars

With a hat-tip to our occasional commenter Alan Wexelblat…..flying robots making music!!! (Best viewed fullscreen; click in the lower right corner.)

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Flashback

Last week, I posted video of my talk to the undergraduate math students on truth, provability and the fabric of the universe — and heard from several readers who requested that I post it in a non-flash format.

My readers’ wish is my command. Here is the file for download in an m4v format.

This is relatively low resolution. The best viewing is still the flash version here.

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High Frequency Rentseeking

Spread Networks recently spent $300 million to build a fiberoptic cable that will let Wall Street traders shave .003 seconds off their execution times.

What’s the social value of that cable? If you can shave .003 seconds off the time it takes to execute a trade, how much good have you done the world?

Clearly, the full value of the cable resides in its ability to get things done faster. So start with a vast overestimate: Suppose the entire economy is on hold waiting for that trade to be completed. Then, thanks to the cable, we can all get on with our lives .003 seconds sooner and produce an extra .003 seconds worth of output.

In a $15-trillion-a-year economy, that comes to about $1500.

If we assume, more realistically, that just 1/1000 of the economy is hanging fire waiting for this one trade, the social contribution of a .003-second speedup is roughly $1.50. I’m confident it’s even more realistic to replace that 1/1000 with 1/1,000,000 . That gets us down to about an eighth of a cent.

But chances are you’d be willing to pay a hell of a lot more than an eighth of a cent for that extra speed, which is why Spread Networks is willing to pour $300 million into this thing, and why, quite generally, we should expect there to be more invested in such projects than they return in social value.

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Social Notes From All Over


(Click picture to enlarge)

The undergraduate Finance and Economics Council here at the University of Rochester held an event at my house last week, which included pizza, informal chat with professors, a rationality test (out of 31 students, exactly one scored a perfect 5 and one scored a perfect zero), a selfie shot or two, and some time on the aerial silks, where three students were brave enough to go up in the air — and each of them accomplished more in under ten minutes than I accomplished in my first ten weeks. The evidence:


Demo Lance Floto
Front Salto Dive
_________________________________________________________

Juan Bernardo Tobar
Front Salto Dive
Lev Bokeria
Crossback Straddle

Thanks to Council president Shucen Wu for making this happen, to Zach Taylor for the video, and to everyone who participated. We should do this again.

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Truth, Provability and the Fabric of the Universe

Here is my talk to the University of Rochester’s Society of Undergraduate Math Students on “Truth, Provability and the Fabric of the Universe”. The audience was great, and except for a couple of slips of the tongue (like “Sir William of Ockham” for “William of Ockham”), I thought it went very well.

Get the Flash Player to see this content.

(Click the lower right hand corner to view fullscreen, or click here for higher quality video).

Faithful readers will recognize multiple themes from the book The Big Questions, and from numerous past blog posts, including:

Continue reading ‘Truth, Provability and the Fabric of the Universe’

Krugman Versus Keynes

Remember Paul Krugman? You know, the guy who thinks we’re so deep in a liquidity trap that pretty much all spending is good spending, even if it’s socially wasteful?

Well, here’s something odd. That very same Paul Krugman is outraged to the core by expenditures on fiberoptic cables to support high frequency trading — expenditures that I happen to agree represent a giant social waste.

“We’re giving huge sums to the financial industry for little or nothing in return”, gripes the very same Krugman who thought it was a swell idea to stimulate the economy through hundreds of billions in government spending, whether or not we got anything in return.

It’s true that Keynesian economists have reasons to believe that wasteful spending is sometimes good. But honest Keynesian economists tend to acknowledge that those reasons apply equally well to both private and public spending.

Krugman’s view, apparently, is that, at least in the current climate, wasteful spending is good as long as you’re spending taxpayer’s money, but bad if you’re spending your own money. That’s not Keynesianism. It’s just crankiness.

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Homer Nods

Well, nobody’s perfect.

When it comes to skewering bad reasoning — and making the right arguments crystal clear — Don Boudreaux is usually about as close to perfect as anyone gets. But this time I believe he’s committed a gaffe of his own.

In a column on the minimum wage, Don writes:

Suppose that I invent and use a machine to steal $15,000 every year from each of 500,000 poor Americans, with the $7.5 billion being transferred into my Swiss bank account. After skimming off a few hundred million bucks to cover processing and handling expenses, I share the bulk of these proceeds with about 16.5 million friends…Am I acting immorally? Most people would answer “yes”…

By way of context, a CBO study forecasts that raising the minimum wage to $10.10 per hour will cause 500,000 workers to lose their $15,000-a-year jobs, while raising the pay of 16.5 million others.

But Don’s analogy fails, because taking someone’s $15,000-a-year job is not the same thing as taking someone’s $15,000. I think it’s a fair guess that most minimum wage workers dislike their jobs. So losing one of those jobs has an upside, which has to be weighed against the downside of not getting paid. On balance, losing that $15,000-a-year job might be no more painful than losing, say, $5000 a year.

The right version of Don’s analogy, then, goes more like this:

Continue reading ‘Homer Nods’

The Arithmetic of Wage Gaps

Mark Perry and Andrew Biggs argue in the Wall Street Journal that

These gender-disparity claims [the claims that women are paid 23% less than men for the same work] are also economically illogical. If women were paid 77 cents on the dollar, a profit-oriented firm could dramatically cut labor costs by replacing male employees with females. Progressives assume that businesses nickel-and-dime suppliers, customers, consultants, anyone with whom they come into contact — yet ignore a great opportunity to reduce wages by 23% [by hiring women instead of men].

Well, first of all, even if we take the gender disparity claims at face value, this doesn’t add up to an opportunity to reduce wages by 23%. Only about half the work force is female, so the average firm, if it replaced all of its men with women earning 23% less, would reduce its wage bill by only about 11.5%.

Beyond that, the Perry/Biggs argument appears to founder on the observation that lazy and incompetent managers do in fact manage to ignore profit opportunities all the time. Why, then, is it so hard to imagine that they’re ignoring this one?

Fortunately, I’m here to fill the gap —- by figuring out just how big a profit opportunity we’re talking about.

Continue reading ‘The Arithmetic of Wage Gaps’

The Talker of the Town

tillyOnce upon a time, the New Yorker took special pride in its famously scrupulous fact-checking department. Nowadays, they’ve apparently stopped caring whether the pieces they publish are even remotely plausible, let alone true.

Thus, writing about the Affordable Care Act in the current issue, Jeffrey Toobin is able to report that “it’s clear that the law is helping a lot of Americans” because, among other things, “more than a hundred million people have received preventive-care services, like mammograms and flu shots, at no cost!!!!!!!!!!!!!!!!!!!!!!!!!!!” (Emphasis added.)

Now surely nobody at the New Yorker, right down to the greenest intern, can possibly believe that it is possible to provide a mammogram or a flu shot at no cost. The statement is so ridiculous that one has to believe either that it was intended as some sort of parody (a reading which the context does not support) or that Toobin meant to say something entirely different. But what?

Continue reading ‘The Talker of the Town’

Many Many Worlds

tegmarkMax Tegmark is a professor of physics at MIT, a major force in the development of modern cosmology, a lively expositor, and the force behind what he calls the Mathematical Universe Hypothesis — a vision of the Universe as a purely mathematical object. Readers of The Big Questions will be aware that this is a vision I wholeheartedly embrace.

Tegmark’s new book Our Mathematical Universe is really several books intertwined, including:

  1. A brisk tour of the Universe as it’s understood by mainstream cosmologists, touching on many of the major insights of the past 2000 years, beginning with how Aristarchos figured out the size of the moon, and emphasizing the extraordinary pace of recent progress. In just a few years, cosmologists have gone from arguing over whether the Universe is 10 billion or 20 billion years old to arguing over whether it’s 13.7 or 13.8.

    Continue reading ‘Many Many Worlds’

A Pi-Day Treat

In 1706, the British astronomer John Machin calculated π to 100 digits (by hand of course). His trick was to notice that π = 16A – 4B where A and B are given by

If you’re computing by hand, this is an excellent discovery, because the series for A involves a lot of divisions by 5, which are a lot easier to calculate than, say, divisions by 7, and the series for B converges very fast, so just a few terms buys you a whole lot of accuracy. (Try using, say, just the first four terms of A and just the first term of B to see what I mean.)

Machin’s 100 digits were a substantial improvement over the 72 digits obtained just a little earlier by Abraham Sharp, using the far less efficient series

In 1729, a Frenchman named de Lagny got all the way to 127 digits, but, in the words of the scientist/engineer/philosopher/historian Petr Beckmann (of whom more later), de Lagny “sweated these digits out by Sharp’s series, and so exhibited more computational stamina than mathematical wits.”

Machin’s methods were ingenious, but no more ingenious — and certainly no more striking — than John Wallis’s 1655 discovery that


which still looks awesome to me after decades of familiarity.

Continue reading ‘A Pi-Day Treat’

Quantum Games

The Society of Undergraduate Math Students here at Rochester asked me to give an elementary talk on quantum game theory last week. I’m posting video of the first (non-technical) half of that talk. I’ll post the second (more technical) half after I get around to editing out the embarrassing mistake I made near the very end.

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