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Ups and Downs

Published
by
Steve Landsburg
on December 19, 2018
in Bad Reasoning, Economics and Puzzles
. 66 Comments

escalator_photo_2

There are two kinds of people in this world: The first kind wonders why people stand still on escalators but not on stairs. The second kind wonders what’s wrong with the first kind. After all, if you stand still on the stairs you never get anywhere.

But people of the first kind are not usually dumb. I could give you a long list of top-rate economists and mathematicians who have been stumped by this puzzle. But I could also give you a long list of equally smart people who have been stumped by why anybody thinks it’s a puzzle in the first place. It’s come up again several times recently, because I included it in Can You Outsmart an Economist? and because I talked about it on my podcast with Bob Murphy, which generated a small flurry of email from listeners. So let me try once again to explain what’s going on here.

Let’s divide this into two parts: First, what’s the right way to think about this problem? Second, why is it a problem in the first place?

Continue reading ‘Ups and Downs’

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Hypothetical Questions

Published
by
Steve Landsburg
on December 18, 2018
in Musings and Politics
. 15 Comments

Suppose, for the sake of argument, that the following three things are true:

  1. You believe, to the depths of your soul, that the future freedom, safety and prosperity of your 300 million countrymen depends critically on a construction project that would cost roughly 5 billion dollars, but that nobody else seems willing to fund.
  2. The welfare of your countrymen is one of your highest priorities. Sometimes you express this priority by calling yourself a “nationalist”.
  3. Your personal net worth is in the vicinity of 10 billion dollars.

Now my questions:

  1. Continuing to assume that all of these three things are true, what action do you take?
  2. If I observe you failing to take that action, can I reasonably infer that not all of these three things are true after all?

Click here to comment or read others’ comments.

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This is not a blog post

Published
by
Steve Landsburg
on December 16, 2018
in Humor
. 7 Comments

From the Twitter feed of my brilliant friend (and Usenet legend) Tim Pierce:

timp

CAPTCHA: Click on all the squares that are not a pipe.

Click here to comment or read others’ comments.

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Wednesday Mystery

Published
by
Steve Landsburg
on December 5, 2018
in Anecdotes and WTF?
. 9 Comments

This is a true story. The names have been changed and some personal details have been blurred by request.

In the American heartland, there lives a university professor named Fletcher. Like most university professors, Fletcher has collaborated with colleagues from around the world, including my friend Zenobia, who teaches at a college in New England. Their collaboration is relatively recent and has not yet resulted in any publications, though some of their joint work has been posted on the web.

Recently, Zenobia has started to receive (by snail mail) a number of magazines — the sort you might find in dentists’ office, like People and Working Mother — addressed to Fletcher, but at Zenobia’s home address. Fletcher purports to know nothing of how this came about, and Zenobia believes him. Moreover, a number of Fletcher’s other friends, collaborators, acquaintances and relatives have also begun to receive the same sorts of magazines with Fletcher’s name, but their own addresses, on the mailing labels.

The magazine publishers, when queried, have refused to divulge any information about who is paying for these subscriptions.

Zenobia notes that the only possible direct connection between Fletcher’s name and her own home address is that once, on the occasion of the birth of Fletcher’s first child, she used her Amazon account to send him a baby gift. However, there appears to be no similar connection between Fletcher and any of the others who are receiving magazines addressed to him.

This leaves us with two mysteries:

Continue reading ‘Wednesday Mystery’

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Bob Murphy and Me

Published
by
Steve Landsburg
on November 28, 2018
in Uncategorized
. 1 Comment

murphyshow Here is a link to my appearance on the Bob Murphy show.

Click here to comment or read others’ comments.

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Trolling

Published
by
Steve Landsburg
on November 17, 2018
in Economics and Self-Promotion
. 30 Comments

trollsA commenter in another thread wanted to talk about trolls, so I’m opening up a new post where they’ll be on topic.

The specific trolls I have in mind operate toll-booths (or troll-booths?), both of which you must pass through to get from Hereville to Thereville. The question is whether you, as a traveler, prefer to have both booths controlled by a single troll, or by separate trolls. (This is Problem 12 in Chapter 3 of Can You Outsmart an Economist?.)

(SPOILER WARNING!)

Continue reading ‘Trolling’

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On Backward Induction

Published
by
Steve Landsburg
on November 12, 2018
in Economics, Humor and Logic
. 29 Comments

A Guest Post

by

William Carrington

(Note from the proprietor—I am delighted to present this guest post from my correspondent William Carrington, who might or might not have been inspired by the puzzles in Chapter Nine of Can You Outsmart an Economist?. — SL)

Like zombies and Russian spies, there are more economists among us than you might think. This can be dangerous because studies show that economists are more likely than normal people to graze their goats too long on the town commons, to rat out their co-conspirators in jailhouse interrogations, and to show up drunk on their last day at a job. This appears to be both because unethical people are drawn to economics and because economics itself teaches people to be both untrusting and untrustworthy. This feedback loop has led to the creation of famously difficult economists like John Stuart Mill and….well, it’s a long list. Like halitosis and comb-overs, the problem is worse in Washington.

Can you protect yourself against this unseen risk? Sadly, no, as economists often look all too normal and are hard to pick out from the maladjusted crowds that attend us. This is known as the identification problem in economics, and Norway’s Trygve Haavelmo was awarded a Nobel Prize for his work on this issue. Related work by Ken Arrow, also a Nobelist, proved that an infinitesimal group of economists will bollix up the welfare of an arbitrarily large population of otherwise normal people. It’s most disheartening, but I’m here to offer you a failsafe method for identifying economists. You’ll need an old refrigerator.

Continue reading ‘On Backward Induction’

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Quadratic Voting: A Pre-Primer

Published
by
Steve Landsburg
on November 5, 2018
in Economics, Policy and Politics
. 37 Comments

In honor of the forthcoming visit of Glen Weyl to the University of Rochester, I thought I’d offer a post explaining the idea behind one of Glen’s signature policy reforms: quadratic voting.

Suppose we’re going to hold a referendum on, say, whether to build a street light in our neighborhood.

The problem with giving everybody one vote is that (on both sides of the issue) some people care a lot more about that street light than others do. We’d like those who care more to get more votes.

In fact, we’d like to allocate votes proportional to each voter’s willingness to pay to influence the outcome. There are excellent reasons to think that willingness-to-pay is the right measure of “caring”. Those reasons will be evident to readers with some knowledge of welfare economics and opaque to others, but it would take us to far afield for me to get into them here. (For the record, if you’re encountering this measure for the first time, you’re almost surely raising “obvious” objections to which there are non-obvious but excellent rejoinders.) For this discussion, I’m going to take it as given that this is the right way to allocate votes.

Here’s the problem: If I allocate votes based on willingness to pay, people will simply lie. If you’re willing to pay up to $1 to prevent the street light, but know that you can get more votes by exaggerating your passion, that’s what you’ll probably do.

Okay, then. If we want to allocate votes based on willingness to pay, then we have to make people actually put some money on the table and buy their votes, thereby proving that they care. We could, for example, sell votes for $1 each. That way, people who care more will buy more votes and have more influence, as they should.

Unfortunately, that’s not good enough. If you care more about the issue than I do, you might buy more votes than I do — but there’s no reason to think you’ll buy more votes in direct proportion to your willingness to pay. Let’s suppose, for example, that the ability to cast a vote is worth $2 to you and $4 to me. Then I should get twice as many votes as you. But if votes sell for $3, I might buy quite a few, whereas you’ll buy none at all. That’s a lot more than twice as many.

So let’s try again: Instead of selling votes for a fixed dollar amount, we sell them on an increasing scale. You can buy one vote for a dollar, or two votes for four dollars, or three votes for nine dollars — and we’ll even let you buy in tiny fractions, like 1/10 of a vote for a penny. The price you pay is the square of the number of votes you buy. That’s the definition of quadratic voting.

Why the square, as opposed to the cube or the square root or the exponential? There really is something special about the square. To appreciate it, try an example: If a vote is worth, say, $8 to you, you’ll keep buying additional votes as long as you can get them for less than $8 each, and then stop. With quadratic voting, one vote costs you a dollar. You’ll take it! A second vote costs you an extra $3 (bringing the total to $4). You’ll take that too! A third vote costs you an extra $5, a fourth costs you an extra $7, and a fifth costs you an extra $9. So you’ll buy 4 votes and then stop. You can similarly check that if a vote is worth $24 to your cousin Jeter, Jeter will buy twelve votes and then stop. Jeter cares three times as much as you do, and he buys three times as many votes. And with a little calculus, you can check that if Aunt Murgatroyd’s vote is worth four or five or nine or twenty times more to her than your vote is to you, she’ll buy exactly four or five or nine or twenty times as many votes as you do. That’s exactly what we wanted. In that sense, this voting scheme works — and, except for minor variations, it’s the only scheme that works.

Continue reading ‘Quadratic Voting: A Pre-Primer’

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Glen Weyl!

Published
by
Steve Landsburg
on October 29, 2018
in Events
. 4 Comments

I am delighted to announce that Glen Weyl, of Microsoft and Princeton University, will be visiting us at the University of Rochester on Tuesday, November 6 (election day!) and will speak on the topic Radical Markets: Uprooting Capitalism for a Just Society, based on the (extremely) provocative and original book of almost the same title, co-authored by Weyl and Eric Posner. The lecture is free and open to the public. The event will be held in Wegmans Hall, room 1400, and will begin promptly at 6:30PM.

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Megamillions

Published
by
Steve Landsburg
on October 20, 2018
in Book, Puzzles, Rationality and Self-Promotion
. 43 Comments

megamillions

Is it rational to play Megamillions, with the current jackpot of a billion dollars or so?

Yes and no. Here are three questions:

  1. Are you willing to pay $20 for ten MegaMillions tickets?
  2. Are you willing to pay $20 for seven weeks’ worth of immunity from fatal lightning strikes?
  3. I propose to flip a coin. Heads, you get the MegaMillions jackpot. Tails, you die. Do you want to play?

There is no irrational answer to any of these questions. Some people like to play the lottery; some don’t. Some people are safety fanatics; some aren’t. Some, but not all, love huge risks with huge potential payouts.

But there is such a thing as an irrational pattern of answers. I know there are millions who answer yes to question 1, because I see them buying tickets. I’m guessing that almost all of those people would answer no to question 2. And I’m guessing that a fair number of those would answer no to question 3 as well. Perhaps you”re one of that fair number. If so, I declare you irrational.

Ten Megamillions tickets give you about a one in thirty-million chance to win the jackpot. One in thirty-million is also pretty close to the chance you’ll be struck by lightning in the next seven weeks. If you’re willing to buy the lottery tickets but not immunity from the lightning, you’re telling me that winning the jackpot means more to you than staying alive. So you should go for the coin flip in question three. If you didn’t, I declare you irrational.

Well, so what? Some economist called you irrational. Why should you care?

You should care because this is exactly the kind of irrationality that will allow me to take all your money. Keep reading to see why.

But first, let’s acknowledge that I’ve ignored a few things, like the possibility that you’ll win one of the lesser prizes in the lottery. I’m assuming that, compared to the jackpot, those are negligible as reasons to buy a ticket. (This is consistent with the observed fact that a whole lot of people buy tickets only when the jackpot is large.) If you don’t like that assumption, we can avoid it by tweaking the numbers in the questions, in ways that I strongly suspect won’t change most people’s answers.

Now let’s get to the fun part where I take all your money. Suppose you’ve answered yes/no/no to the three questions above. Then I’ll rig up the following experiment: I fill a bag with 30 million white balls, one black ball, and one blue ball. I plan to pull a ball from the bag, but before I do, I’ll make you two offers. You can take them or leave them; it’s entirely up to you.

  • A. If you give me $20 upfront, and if I draw the blue ball, I’ll give you a billion dollars.
  • B. I’ll give you $20 upfront, provided you allow me to electrocute you if I draw the black ball.

You’ve already told me that you’d pay $20 for ten Megamillions tickets, giving you a one in thirty-million chance at roughly a billion dollars. So of course you’ll happily go for A. And you’ve already told you that it’s not worth it to you to give up $20 to avoid a one in thirty-million chance of electrocution. So of course you’ll also happily go for B.

So: You (voluntarily) give me $20 and accept my $20. So far we’re even. And, I might add, you’re very glad to be playing. You got two things and you wanted both of them.

Now the drawing. Most of the time I’ll draw a white ball, and nothing happens. But occasionally I’ll draw a blue or a black. When I do, I’ll tell you (perfectly honestly, because I’m honestly exploiting your irrationality, not trying to trick you) that I’ve drawn a non-white ball. There’s a fifty-fifty chance it’s black, in which case you will die, and a fifty-fifty chance it’s blue, in which case you win the billion. You are effectively facing the very coin flip that you told me in Question 3 that you prefer to avoid. Of course, then, you’ll gladly pay me a few bucks to call everything off. Now I’m ahead.

We might have to play this game several million times before I draw a non-white ball and take your money, but as long as you’re committed to your stated preferences, you should be willing to play several million times — or to let me set my computer to playing a virtual version for us several million times per hour. In a few hours, I’ll win some money from you. In another few hours, I’ll win more. And so on till you’re broke.

When an economist calls you irrational, it almost always means that if you follow through on your stated preferences, a sufficiently clever opponent can take all your money, leaving you smiling along the way. It’s worth being alert to such things.

If you thought this was fun, you should take the ten-question Irrationality Test in Chapter Six of Can You Outsmart an Economist?. Come back to the blog and let me know how you did.

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Where I’ll Be

Published
by
Steve Landsburg
on October 12, 2018
in Events and Personal
. 6 Comments

This Monday (October 15), I’ll be in at Webber International University in Babson Park, Florida, talking on the subject “What Do the Rich Owe to the Poor?”. The talk is at 7pm in the Yentes Conference Center. Please join us if you’re in the area!

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Errata

Published
by
Steve Landsburg
on October 1, 2018
in Books, Oops and Personal
. 14 Comments

Somewhere on my shelves, there is a math book with a page very like the following:

I know this because I remember seeing it (or at least I think I do), but I can’t quite remember which book it’s in.

Fortunately, I didn’t try to steal this joke for Can You Outsmart an Economist?, because it turns out there’s an actual erratum in the main text. It comes in Chapter 16 where a series of problems leads the reader to discover the basics of option pricing. The arithmetic in those problems is all correct, except for one thing: In order to keep the math easy, I assumed an interest rate of 50%. But with an interest rate that high (and given the other assumptions in the chapter), nobody would be mucking around with buying options in the first place; we’d all just be putting our money in the bank and getting rich in a hurry.

So what I should have done is assumed an interest rate of 20%. If you’ve got a copy of the book, you should pencil in the following changes:

Continue reading ‘Errata‘

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Can You Outsmart an Economist?

Published
by
Steve Landsburg
on September 25, 2018
in Books, Cool Stuff, Economics and Personal
. 22 Comments

Can You Outsmart an Economist?

100+ Puzzles to Train Your Brain

My new book is now on sale! Readers of this blog will recognize some but not nearly all of these 100+ puzzles (146, actually, by my count). If you’ve enjoyed my puzzle posts, you’ll probably enjoy these extended discussions of some past puzzles, and the many more that are entirely new. Most of these puzzles are designed to teach important lessons about economics, broadly defined to encompass all purposeful human behavior. All of them are also designed to be fun.

Once you’ve had a look, please don’t hesitate to share your opinions right here on the blog — or better yet (especially if your opinions are positive!) don’t hesitate to share them on Amazon or on Goodreads.

Or, if you’d prefer to taste the milk before you buy the cow, here is the introduction, absolutely free of charge.

You can read a few advance reviews here. And remember, the more copies you buy, the sooner I’ll write the sequel.

Click here to comment or read others’ comments.

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Efficient Tariffs

Published
by
Steve Landsburg
on September 23, 2018
in Economics and Policy
. 14 Comments

You’re a policymaker in a country where people buy widgets that are produced both at home and abroad. You can set (separate) excise tax rates on domestic production and imports. (The tax on imports is, of course, what we usually call a tariff.) What tax rates should you set?

The Economics 101 answer makes two assumptions:

1. You care only about the economic welfare of your citizens (and not at all about foreigners).

2. You can’t affect foreign prices (i.e. your country is a negligible portion of the world market for widgets). The fancy way to say this is that the supply of imports is perfectly elastic.

From these assumptions, it follows that both tax rates should be zero. In fact, we can relax assumption 1) and allow you to care as much as you want about the welfare of foreigners; the conclusion doesn’t change.

But suppose we relax these assumptions in a different way:

1A. You care about both the economic welfare of your citizens and (separately) about the tax revenue earned by your government. (I continue to assume, however, that you don’t care about foreigners.)

2A. The foreign supply curve might not be perfectly elastic. Contrary to the Economics 101 assumption, this gives you some market power that you might want to exploit. (I continue to assume, though, that you take the foreign supply curve as given. In particular, this means that your policies do not affect foreign tax rates, so I am assuming away things like retaliatory tariffs.)

Now what’s your best policy? I can’t answer that because you have two competing goals (economic welfare and tax revenue) and I don’t know how much weight you put on one versus the other. But surely if I can show you that Policy A delivers on both goals better than Policy B, you’ll want to reject Policy B. The existence of Policy A leads me to call Policy B inefficient, and surely you’ll want to reject any inefficient policy.

So which pairs of tax rates are efficient?

Continue reading ‘Efficient Tariffs’

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Kavanaugh v. Thomas

Published
by
Steve Landsburg
on September 20, 2018
in Current Events and Politics
. 32 Comments

I keep hearing that the matter of Brett Kavanaugh is “just like Clarence Thomas and Anita Hill all over again”.

Seriously?

Point the First: Clarence Thomas stood accused of boorishness. Brett Kavanaugh stands accused of violent attempted rape. If all the accusations against Thomas were true, he deserved an elbow to the ribs. If the accusations against Kavanaugh are true, he should probably be in jail.

To suggest that there is even a rough equivalence here is sheer madness.

Continue reading ‘Kavanaugh v. Thomas’

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Quick Thoughts on Kavanaugh

Published
by
Steve Landsburg
on September 17, 2018
in Current Events
. 29 Comments

First: Neither you nor I know who’s telling the truth, who’s honestly misremembering, who’s dissembling, and who’s doing some combination of all three. But if we want to think about what should happen next in the real world, it pays to think first about what should happen next in a hypothetical world where we can somehow be sure that Professor Ford’s account is 100% accurate. In that world, we need to ask this question: Should a night of bad behavior at age 17 be punished by a career derailment at age 53 (assuming there’s been no punishment in the interim)?

The answer, of course, depends on the benefits and costs of that punishment.

First the benefits: Punishments are beneficial when they deter other bad behavior. So we should embrace this punishment only insofar as we believe that some future 17 year old boy will be deterred from committing sexual assualt by the prospect of a career derailment 35 years down the line. How big is that deterrent effect? Not only do I have no idea; I also have no idea how to start forming an idea. That is, I can’t think of any good empirical strategy for measuring such a deterrent effect. We have good data on the deterrent effect of imprisonment, of capital punishment, and of fines — but not, as far as I know, on the deterrent effect of long-delayed career consequences. (I’ll be very glad if any reader can prove me wrong about this.) I do, however, have a guess. My guess is that for boys of the social milieu that Kavanaugh came from, this effect could loom pretty large. True, no 17 year old really expects to be nominated to the Supreme Court some day, but plenty of 17 year olds at prep schools have lavish dreams of future success, and seem to care quite a bit about preserving that future. If my guess is right, the benefits of killing this nomination might be pretty big.

Continue reading ‘Quick Thoughts on Kavanaugh’

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Public Service Announcement

Published
by
Steve Landsburg
on August 29, 2018
in Personal and Recommendations
. 22 Comments

Having recently dealt with some of the same customer service issues at both Vanguard and Fidelity, I can make these recommendations with confidence:

1) Keep your money at Vanguard.

2) If you’ve made the unfortunate mistake of keeping some of your money at Fidelity and you ever need customer service, and if your customer service representative turns out to be named Cameron Marcil, hang up immediately and try again.

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In the Matter of Sarah Jeong

Published
by
Steve Landsburg
on August 6, 2018
in Bad Reasoning, Current Events and Journalism
. 16 Comments

Two decades after hiring Paul Krugman, the New York Times has doubled down by hiring the venomous Sarah Jeong, whose old tweets include the following rhetorical question:

Are white people genetically disposed to burn faster in the sun, thus logically being only fit to live underground like groveling goblins?

According to Jeong’s supporters, the tweet needs to be read in context — it was, you see, intended as a parody of Andrew Sullivan’s audacious piece in New York magazine, advocating research — or at least opposing the suppression of research — into racial differences in IQ.

I’m all for parody. I’m all for taking other people’s logic (and my own!), pushing it to its limits, seeing where it leads, and thereby calling attention to its weaknesses. And I am outraged when authors engaged in this enterprise are taken out of context. If I say “X”, and if “Y” is both analogous to X and clearly outrageous, then Sarah Jeong or anyone else ought to be able to tweet “Y” by way of making fun of me, without having to face down a gang of yahoos accusing her of believing “Y”.

But that’s not what this is about. Because — and here is the crux of the matter — the analogue to

Are some races genetically disposed to be less intelligent than others?

is

Are white people genetically disposed to burn faster in the sun?

which is not at all the same thing as

Are white people genetically disposed to burn faster in the sun, thus logically being only fit to live underground like groveling goblins?

The problem here is not that Sarah Jeong believes white people are fit only to live underground like groveling goblins. (I feel pretty confident, in fact, that she believes no such thing.) The problem here is that she is attempting to refute Andrew Sullivan’s logic by writing down an analogy (so far so good) and then, having done so, tacking on the phrase “being only fit to live underground like groveling goblins”, which in no way reflects anything Andrew Sullivan said, and which Sarah Jeong pulled out of her ass.

Continue reading ‘In the Matter of Sarah Jeong’

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Monday Solution

Published
by
Steve Landsburg
on July 30, 2018
in Logic, Math and Puzzles
. 14 Comments

The answer to Friday’s puzzle is YES. If I am a logic machine who only states what I can prove, and if I say “If I can prove there is no God, then there is no God”, it does follow that I can prove there is no God.

Once again, it was our commenter Leo who got this first (in Friday’s comment thread, graciously rot-13’d).

As with Thursday’s solution to Wednesday’s puzzle, there are two key relevant background facts:

A) An inconsistent system can prove anything.

B) A sufficiently complex consistent system cannot prove its own consistency. (This is Godel’s second incompleteness theorem.)

Here’s the logic:

1) I’ve asserted that “if I can prove there is no God, then there is no God”. We know that I assert only things that I can prove. Therefore I can prove this assertion.

2) That means I can also prove the equivalent assertion that “if there is a God, I cannot prove otherwise”.

3) Therefore, if I take my axioms and add the axiom “There is a God”, then I can prove that there is something I cannot prove.

4) Therefore, if I take my axioms and add the axiom “There is a God”, then I can prove that my axiom system is consistent (by Background Fact A.)

5) Therefore, if I take my axioms and add the axiom “There is a God”, my axiom system is inconsistent. (Because only an inconsistent system can prove its own consistency — that is, Background Fact B.)

6) Therefore the statement “There is a God” must contradict my axiom system.

7) This can happen only if my axiom system is able to prove that “There is no God”.

So yes, I can prove there is no God.

Continue reading ‘Monday Solution’

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Friday Puzzle

Published
by
Steve Landsburg
on July 27, 2018
in Puzzles
. 10 Comments

A followup to Wednesday’s puzzle:

The assumptions are the same as on Wednesday:

I am basically a logic machine. There are certain axioms that I believe, and I never say anything out loud unless it can be deduced from those axioms via the rules of logic. (Fortunately, I can talk about many things, because my axioms include everything from the usual axioms for arithmetic to a rich set of beliefs about ontology, ethics, psychology, and everything else I care about.)

Now I’ve found myself in a whole new imaginary conversation with the same old imaginary Bob Murphy. This time I found myself saying out loud that “If I can prove there is no God, then surely there is no God.”

The Puzzle: Can I in fact prove there is no God?

Solution forthcoming on Monday.

Click here to comment or read others’ comments.

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Thursday Solution

Published
by
Steve Landsburg
on July 26, 2018
in Math and Puzzles
. 38 Comments

Here are the answers to yesterday’s puzzle. The first correct solution came from our commenter Leo (comment #18 on yesterday’s post).

The assumptions of the problem were: Everything I say out loud can be deduced from my axioms. My axioms include the ordinary axioms for arithmetic, among other things. And I recently said out loud that “I cannot prove that God does not exist”.

The questions were: Can I prove there is no God? Can I prove there is a God? And is there enough information her to determine whether there actually is a God?

The answers are yes, yes and no: Yes, I can prove there is no God. Yes, I can also prove there is a God. And no, you can’t use any of this to determine whether there is a God.

To explain, I’ll use the phrase “logical system” to refer to a system of axioms sufficiently strong to talk about basic arithmetic (and perhaps a whole lot of other things), together with the usual logical rules of inference. It’s given in the problem statement that I am a logical system.

Here are two background facts about logical systems:

A. An inconsistent logical system can prove anything at all. That’s because it’s tautological that if P is self-contradictory, then any statement of the form “P implies Q” is valid. If I’m inconsistent, that means I can prove at least one statement (call it P) that’s self-contradictory. Then if I want to prove, say, that the moon is made of green cheese, I note that:

  • I can prove P
  • It’s tautological that “P implies the moon is made of green cheese”
  • Therefore I can conclude by modus ponens that the moon is made of green cheese.

B. No consistent logical system can prove its own consistency. This is Godel’s celebrated Second Incompleteness Theorem.

Now here’s the argument:

Continue reading ‘Thursday Solution’

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Down on the Farms

Published
by
Steve Landsburg
on July 25, 2018
in Current Events, Policy and Politics
. 30 Comments

Suppose there’s a guy in your neighborhood who routinely harasses strangers on the street, calling them ugly names, maybe threatening them with violence, but always stopping short of anything that’s actually illegal.

You consider this bad behavior, so you work to pass some laws that will discourage it. Maybe you criminalize the behavior; maybe you tax it.

The new laws turn out to be somewhat effective. The guy tones it down. He still harasses people, but only half as much.

Question: Do we owe this guy something? Should the taxpayers cut him a check so he won’t feel so bad about having to rein himself in?

I’m going to go out on a limb and guess that most of you will answer “no”.

Here’s why I ask:

The President of the United States believes that under current circumstances, much international trade is a bad thing and ought to be discouraged. Unfortunately, there’s a bunch of farmers out there who have been behaving very badly (i.e. trading with foreigners) and the law hasn’t done much to stop them. So the President has expanded the scope of the law to punish this bad behavior via tariffs. And then he’s turned right around and announced a plan to compensate the bad guys.

Continue reading ‘Down on the Farms’

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Wednesday Puzzle

Published
by
Steve Landsburg
on July 25, 2018
in Puzzles
. 21 Comments

Here’s what you should know about me: I am basically a logic machine. There are certain axioms that I believe, and I never say anything out loud unless it can be deduced from those axioms via the rules of logic. (Fortunately, I can talk about many things, because my axioms include everything from the usual axioms for arithmetic to a rich set of beliefs about ontology, ethics, psychology, and everything else I care about.)

Here’s what else you should know: Last night, in the course of an imaginary chat with an imaginary Bob Murphy, I found myself admitting out loud that “I cannot prove that there is no God.”

First Puzzle: Can I in fact prove that there is no God?

Second Puzzle: Can I prove that there is a God?

Third Puzzle: Based on the information given, can you determine whether there is a God?

I’ll answer tomorrow, or in a few days depending on how the comments play out.

Click here to comment or read others’ comments.

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The Elephant in the Brain

Published
by
Steve Landsburg
on July 17, 2018
in Books
. 14 Comments

elephantI haven’t been blogging much lately, but John Lanchester’s boneheaded review of Robin Hanson and Kevin Simler’s The Elephant in the Brain seemed to demand a response. But I see that Robin himself has saved me the trouble with his devastating refutation here.

This does remind me that I never fulfilled my intention to review the The Elephant myself. This fell through the cracks because I’d accumulated substantial notes while reading it, lost my notes, decided to search for them before reviewing, and then sort of fell temporarily out of the blogosphere for a while. But it is a genuinely terrific book; my lost notes contain a long list of minor quibbles, but the bottom line is that I learned a lot (about others and about myself) and had a lot of fun along the way. There was never a moment when I wanted to put this book down.

The book, for those who have somehow managed not to hear about it, is about the hidden motives for human behavior — the motives we hide from each other, and the motives we hide from ourselves. The table of contents promises to enlighten us about how hidden motives drive our body language, laughter, conversation, and our choices in consumption, art, charity, education, medicine, religion and politics — and the book delivers on those promises with a heady mix of sparkling logic and striking evidence. There are plenty of fun facts you’ll be repeating at cocktail parties, and plenty of deep insights that will make you smarter forever.

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Letter from an Infantryman

Published
by
Steve Landsburg
on July 8, 2018
in Outrage, Personal and Tragedy
. 11 Comments

armydad

I found this among my father’s papers. He wrote it as a 20-year old infantryman who had been in combat for about six months.

I am struck by the eloquence, and doubly struck that he managed to be eloquent in the medium of pen-and-ink, with no copy/paste/delete and not even any crossouts:

Monday, Jan. 8 (1945)

Dear Mother and Dad:

Well, the new year has arrived and with it, sadly enough, have come no great changes. The war is still being fought, I and millions of other boys are still several thousands of miles away from home and our loved ones, and it almost seems as if there will never be an end to this useless, heart-breaking, killing war.

Whether a man is German, American, or French, he looks just the same when he is wounded, dying or dead. The battlefield bullet is a great leveler; it can make the biggest man very small or the weakest man a hero, but in this war most of the heroes are dead.

We who are actively engaged in defeating the enemy would not hesitate to lay down our arms and surrender if we thought that the people who make the peace will fail to make it permanent. The mere thought that our comrades may have died for nothing, that we may have a brief pause from this war so that we can raise sons to fight another war would cause us many sleepless nights. The last thing one dying soldier said to me was that he was dying on the battlefield so that his son would not.

I may sound very bitter and full of resentment and frankly I am. This war should have been averted in 1918 and the ensuing years, but instead of preventing war, the American people actually encouraged it by ignoring everything that was going on around them. For the sake of all the men who have gone through this hell, we must not let this happen again. We must not have allowed so many of our boys to have died in vain.

I can’t possibly express the resentment these boys feel when they hear about these “Victory in Europe Celebrations”, and when they hear about the lotteries that are held to determine the date of the European victory. Here their own sons are being killed, maimed and crippled for life, and they trouble themselves with such trivial tripe. What is the matter with the American public? Is it entirely aloof to this war?

Perhaps I don’t sound like a twenty-year-old kid anymore, but I’ve seen things that I shall never forget, ghastly things that I shudder to think about. I think that a just punishment for any of these “Victory in Europe Celebration” planners would be to pick up a soldier’s boot on a battlefield and find the foot still in it, or sweat out just one artillery barrage. If they could just realize what is going on they would spend all their spare time praying for the safety of their boys and thanking God that America has been spared everything but an army.

Aside from being a little angry, I’m feeling fine. I’ve received several of your packages and everything is swell. I know that God has been answering your prayers, and he will continue to watch over me.

Love, Norman

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End of an Era

Published
by
Steve Landsburg
on July 8, 2018
in Personal
. 20 Comments

dad2
Norman Landsburg (1924-2018), a survivor of the worst ravages of the Great Depression, a survivor of the trenches in France, where he landed in the wake of the Normandy invasion (and, according to what I think I’ve just learned while going through his papers, was awarded two bronze stars that he never once mentioned to his wife of 68 years or any of his three children), who transcended a series of hard knocks that would have led many to despair and struggled every day, often against mighty odds, to make a better life for his family, succumbed tonight to complications from Alzheimer’s disease.

His bullheadedness was his greatest vice and his greatest virtue. I owe him a couple of good slaps upside the head (not that I ever got one from him, but he deserves them anyway) and eternal gratitude for the way he eased my setting forth and filled my world with possibilities. Neither debt will ever be paid.

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The Case Against The Case Against Education

Published
by
Steve Landsburg
on April 27, 2018
in Uncategorized
. 34 Comments

I am quite unqualified to review Bryan Caplan’s blockbuster The Case Against Education, by virtue of the fact that I have not (yet) found time to read all of it. But I think I have a pretty good idea what’s in it, and an even better idea of what others are saying is in it. So this will be a review not of Bryan’s book, but of the various paraphrases that are floating around the internet. Those paraphrases might or might not be accurate representations of Bryan’s thinking, but they deserve to be treated as arguments in their own right. So this will be a review of those arguments.

Continue reading ‘The Case Against The Case Against Education’

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Hanushek Tonight

Published
by
Steve Landsburg
on April 23, 2018
in Events
. 2 Comments

With apologies for the late notice: Eric Hanushek of Stanford University, the great pioneer in the applications of economics to evaluating educational policies, will speaking tonight in Wegmans Hall, room 1400, on the University of Rochester campus. The general public is invited.

Title: Can we put a Price on Student Achievement? Financial Returns for Academic Success

The event will begin promptly at 6:30PM. The general public is welcome.

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Where I’ll Be

Published
by
Steve Landsburg
on March 14, 2018
in Events, Math, Personal, Philosophy and Religion
. 4 Comments

I’ll be speaking this Saturday at the Freethought Festival in Madison, Wisconsin (follow the link to register!) on the topic “Truth, Provability and the Fabric of the Universe”. I’ll be glad to see you there.

Click here to comment or read others’ comments.

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Like the Groundhog, He Emerges

Published
by
Steve Landsburg
on February 24, 2018
in Outrage and Personal
. 33 Comments

Regular readers of this blog will have noticed by now that my blogging has been mostly dormant for a while. This is partly because I’ve been working on multiple book projects (e.g. this one), partly because I felt so disillusioned after the outcome of the election season, and partly because I’ve felt like I’ve already said much of what I have to say. But sometimes you can’t resist.

This is the City Mattress store on Monroe Avenue in Brighton, New York:

My wife recently wanted to buy a mattress, drove by the store, and noticed that there were no hours posted in the window. The next day, she guessed at the opening time, happened to get it right, went into the store, and mentioned to the friendly manager that it would be nice if they could post their hours. The manager agreed that being able to post their hours would be very nice indeed, but that the town of Brighton had forbidden them to do so on the grounds that it would “make the store look like a sub shop”.

Question 1: Please study the picture above. How probable do you think it is that you’d mistake it for a sub shop? (Your answer should be a number between 0% and 100%).

Question 1A: By how much would your answer to Question 1 change if this store had its hours posted in the window?

Question 2: If you did happen to mistake this store for a sub shop, how much damage would you feel you’d incurred? (Your answer should be the number of dollars you’d have to lose to feel equivalently damaged.)

Incidentally, the lack of an hours sign inconveniences not only people like my wife, who wasn’t sure when to show up. The manager mentioned that every night at closing time, they have to turn away new arrivals who, due to the lack of a sign, were unaware of the store hours.

The Brighton Town Supervisor is Mr. William Moehle. This is a picture of his house:

Continue reading ‘Like the Groundhog, He Emerges’

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