Spacetime Tells Matter How to Move

Here, in honor of the hundredth anniversary of the General Theory of Relativity, is a very nice visualization:

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Family Values

Followup to last night’s debate:

Didn’t Rubio essentially disqualify himself when he said he’d prioritize his job as a parent over his job as President of the United States?

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Debate Blog

Heard only a little of the undercard, but I do have some comments on it. But I’ll add those later.

Re the main debate (I’ll add to this every twenty minutes or so till the debate is over): (Note this is live-blogging, hence not always carefully thought through).

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Sometimes you just have to take matters into your own hands.

After posting about the difficulty of finding a modern source for choosing a random city or a random river, I went ahead and created:

The Random City Server

I took the data from Maxmind’s free world cities database, but there are odd gaps in it. Although the database lists about 3.3 million cities, the population field is blank for all but about 50,000. (Most notably, that field is blank for all but two of the thousands of cities in the Republic of Korea.) My server offers up a random city from among those 50,000. I’m sure I can probably find a list of Korean cities with populations and manually tack them on to the list at some point. [Edited to add: I’ve just done that.]

Now I want to do something similar for river lengths. Does anyone know where to get the data? (No, pawing through Wikipedia’s hundreds of separate lists, for each part of the world and each letter of the alphabet, is not an option.)

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A Question About the Modern World

Suppose you want, for some reason, to find the length of a randomly chosen river or the population of a randomly chosen city.

In the old days, we all had things called “reference books”, with long lists of river lengths, city populations, etc. You could open to a random page, close your eyes, put down your finger, and there you’d have it.

But now many of us no longer own reference books. We own smartphones instead. This raises two issues:

1) I’m not sure there are online lists of river lengths or city populations that are as extensive as what you used to find in reference books. Why should there be? Nowadays, if you want to know the population of Des Moines, you just Google for Des Moines; you don’t need a site that lists the populations of thousands or tens of thousands of cities.

2) Even if there were such lists, what would be the modern equivalent of opening to a random page, closing your eyes and pointing? Scrolling for a random amount of time seems less random somehow.

So what do you do?

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Overprotective Parents, Falling Optimists, and Other Dangers

My friend and former colleague (and our occasional commenter), James Kahn, weighs in on Federal Reserve policy in a thoughtful piece over at Fox Business.

Some highlights:

Proponents of the Fed’s ZIRP (zero-interest rate policy) will quickly point out that the low inflation numbers in recent years belie any claim that policy has been too loose. In a sense they are right: Policy has not been as loose as interest rates suggest, because the Fed has been pushing forward on one lever (asset purchases) while pulling back on another (paying interest on bank reserves). With the economy’s mediocre fundamentals (those supply factors mentioned above), banks are happy to hold large reserves of cash, thus blunting the impact of the Fed’s enormous balance sheet increase.

Bernanke’s gloating about the lack of inflation is thus somewhat misplaced. The concern about losing control of inflation (in one direction or the other), has always been (or should have been), on the Fed’s ability to manage the transition back to normalcy, i.e. the unwinding of its balance sheet, the raising of interest rates, and the drawing down of bank reserves. The Fed may be able to manage all this, but so far it is just lots of rhetoric – it brags about the ability to do so while postponing actually doing it.

In other words, thoughtful critics have said all along that there’s an inflation risk associated with the (future) transition back to normal monetary policy. Less thoughtful counter-critics have claimed to refute that observation with the counter-observation that right now, inflation doesn’t seem to be a problem. Like the optimist in free fall, they figure we’re doing alright so far.

Another highlight:

Continue reading ‘Overprotective Parents, Falling Optimists, and Other Dangers’

Party of the Rich

I did not watch the debate. I chose to go to my aerial silks lesson instead.

When I got home, the debate was half over. I turned it on for about a minute, during which Marco Rubio managed to turn my stomach to the point where I just couldn’t go on.

Apparently he’s all worried about American tech companies “taking advantage” of relaxed immigration laws to hire foreigners who can work more efficiently than Americans. Any firm that does this should be subjected to strict regulations on who they can hire going forward, etc. etc. And there should be a 180 day waiting period before they can hire that foreigner in the first place, etc. etc.

So let’s be clear about this: Rubio cares enormously more about American engineers than about American consumers, American investors, and low-skilled American workers, all of whom benefit from more efficient engineering. Who do you suppose is richer to begin with — the average engineer, or the average consumer/investor/low-skilled worker?

I cannot stand this stuff.

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Boys, Girls and Hot Hands

This is a post about hot hands in basketball. But first, some relevant history:

The single most controversial topic ever broached here on The Big Questions was not Obamacare, or tax policy, or the advantages of genocide, or the policy treatment of psychic harms. It was this:

The answer, of course, is that you can’t know for sure, because (for example) by some extraordinary coincidence, the last 100,000 families in a row might have gotten boys on the first try. But in expectation, what fraction of the population is female? In other words, if there were many such countries, what fraction would you expect to observe on average?

The “official” answer — the answer, for example, that Google was apparently looking for when they posed this as an interview question — is that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. Therefore the expected fraction of girls in the population is 50%.

That turns out to be wrong. It’s true that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. From this it does follow that the expected number of girls is equal to the expected number of boys. But it does not follow that the expected fraction of girls in the population is 50%. Instead, that expected fraction depends on the country size, but is always less than 50%.

If you don’t see why, I encourage you to browse the archive of relevant blog posts. If you still don’t get it, I encourage you to keep browsing. Whatever your objections might be, you’ll find them addressed somewhere in the archive. I’m not interested in relitigating this. I will, however, happily renew my offer to take $5000 bets on the matter, on the terms described here. Last time around, all takers changed their minds before putting any money on the table.

Now let’s get to the hot hands.

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On the Slaying of Dragons

The frontispiece from Differentiable Germs and Catastrophes by Theodore Brocker:

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Poison Apple

poisonappleThere are about a million reasons why I hate my iPhone, but this one pretty much sums it all up.

On my phone, I’ve got quite a few files that were not downloaded from any of my other devices. These include pictures I’ve taken with the phone itself, pdfs I’ve downloaded through the phone’s browser, etc.

Of course, I’d like to have backups of all these files. And of course Apple makes this as difficult as possible by pushing me to use its abysmal iTunes software for creating the backup.

Now here is what iTunes does: I have photo files with names like IMG_0840.jpg — which, if not terribly descriptive, is at least immediately recognizable as a photo. I have pdfs with names like Dirac.QuantumMechanics.pdf, which is a nice, easily recognizable name. I download everything to my computer via iTunes, and here is a partial directory listing of what I get:

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Bad Planning

ppIn a bid for ongoing taxpayer support, Planned Parenthood president Cecile Richards will be appearing before Congress today. It’s reported that as part of her testimony, she will admit that only 1 percent of Planned Parenthood’s affiliates currently harvest fetal tissue, and that even those affiliates charge only modest fees of $60 per tissue specimen.

Which raises the question: Why should we give money to an organization that has access to a valuable resource but can’t be bothered to sell it to the highest bidder?

When your brother-in-law is out of work, you might be inclined to help him out. When your brother-in-law is out of work, deluged with job offers, and refusing even to consider them, you’ll probably be less inclined. Planned Parenthood is that brother-in-law.

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McCloskey at Chicago

deeFor an upcoming Festschrift, I was recently asked to write an account of Dee (then Don) McCloskey‘s years as a brilliant teacher at the University of Chicago, her influence on a generation of economists, and my own enormous debts to her. This was a great pleasure to write. A draft is here.

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Ask Not What the Church Can Do For You; Ask What You Can Do For the Church

Pope Francis is coming to New York, and Cardinal Timothy Dolan is disturbed about ticket-scalping:

“Tickets for events with Pope Francis are distributed free [via lottery] for a reason — to enable as many New Yorkers as possible, including those of modest means, to be able to participate in the Holy Father’s visit to New York,” Cardinal Dolan, the archbishop of New York, said in a statement. “To attempt to resell the tickets and profit from his time in New York goes against everything Pope Francis stands for.”

So according to Cardinal Dolan, “everything Pope Francis stands for” consists of the proposition that for New Yorkers of modest means, nothing should take precedence over turning out to see Pope Francis — not groceries, not medicine, not car repairs, not any of the other things that people can buy with the proceeds from selling their tickets.

I doubt that Pope Francis is quite as egomaniacal as the Cardinal paints him. But apparently the Cardinal himself would rather see poor people cheering for the Pope than improving their lives.

Nature or Nurture?

My sister snapped this picture of my Dad and me sitting on a couch:

No, this wasn’t posed. It’s just how we happened to be sitting.

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Are You Smarter Than Google? — Part Three

To review the bidding:

Two days ago I posed a puzzle about 10 pirates dividing 100 coins.

Yesterday, I presented what appears to be an airtight argument that the coins must be divided 96-0-1-0-1-0-1-0-1-0.

But yesterday I also told you that the “airtight argument” is in fact not airtight, and that other outcomes are possible. I challenged you to find another possible outcome, and to pinpoint the gap in the “airtight argument”.

Our commenter Xan rose to the occasion. (Incidentally, his website looks pretty interesting.) Here’s his solution:

Continue reading ‘Are You Smarter Than Google? — Part Three’

Are You Smarter Than Google? — Part Two

treasureToday I’ll offer the “official” solution to yesterday’s puzzle — that is, the solution that Google has apparently expected from its job candidates. This is also the solution I gave when I first saw the puzzle, and the solution I usually get from my best students, and the solution given yesterday by some astute commenters.

But this solution has a gaping hole in it. Can you find it?

Continue reading ‘Are You Smarter Than Google? — Part Two’

Are You Smarter Than Google?

pirateI’m not sure where this problem originated. I heard it first from John Conley, and have often assigned it to my classes. Google has used it to weed out job candidates. The answer that Google expects is the same answer I gave John Conley, and the answer I usually get from my best students. That answer is wrong. (Long time readers might feel a sense of deja vu.)

Can you get it right?

Here’s the problem:

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Minimum Logic, Part 2

Yesterday’s post touched on several related points, and I’m afraid the most important one got buried near the end, so I want to repeat it:

1) In the presence of an effective minimum wage, all benefits of the earned income tax credit are transferred to employers. This is, as they say, a matter of Economics 101. (Edited to add: As Bennett Haselton points out in comments, I should have said “dissipated”, not “transferred to employers”. The point remains that the benefits don’t go to the workers, which, for this discussion, is what matters.)

2) Paul Krugman argues that we should have an effective minimum wage in order to prevent some of the benefits of the earned income tax credit from being transferred to employers.

In this context, it should be remembered that Krugman ordinarily reserves his deepest scorn for those who, according to Krugman, willfully ignore the lessons of Economics 101.

Let’s review the argument for 1), with reference to the graph below. In the presence of, say, a $5-an-hour minimum wage, employers will hire 1000 workers. Because more than 1000 people want to work, employers can extract extra concessions in the form of reduced on-the-job-training, shorter breaks, and harsher working conditions. They can get away with exactly $1-an-hour’s worth of this, because even at an effective wage of $4, there are still 1000 people willing to work.

Edited to add: I am assuming that these concessions are of relatively little value to employers (otherwise they wouldn’t have waited for the EITC to demand them!), so that the quantity of labor demanded does not change.

Now let’s add a $3-an-hour earned income tax credit, which shifts the labor supply curve to the dashed position. Ordinarily, this would lead to a lower equilibrium wage, transferring some of the benefits of the EITC to employers. But in the presence of the $5 minimum, wages can’t drop, and employment remains fixed at 1000, though now even more people want to work, allowing employers to impose even harsher conditions until the effective wage drops to $1 an hour (the wage at which there are still 1000 people willing to work). This process transfers all the benefits of the EITC away from the workers.

Continue reading ‘Minimum Logic, Part 2′

Minimum Logic

The question is often raised: “Why would you ever want to raise the minimum wage when you could raise the earned income tax credit instead?”. In other words, if you’ve got a choice between two ways to increase the effective wage rate, why would you choose the one that reduces employment over the one that increases employment?

Paul Krugman has an answer. He’s argued on numerous occasions that the EITC and the minimum wage are complements, not substitutes — that is, each makes the other more effective. So, according to Krugman, once you’ve raised the EITC, the case for a minimum wage hike becomes stronger, not weaker.

Here’s his argument: When you raise the EITC, more people enter the labor market. The increased supply of labor tends to drive wages down, which transfers some of the benefit from the workers you intended to help to the employers and/or consumers who you presumably care about less. To prevent this perverse consequence, one needs a hike in the minimum wage.

The other day, a colleague (who I’m not naming because I’m not sure whether he’d want to be quoted) pointed out that this argument makes not a shred of sense. Here’s why: Any effective minimum wage (that is, any minimum wage set above the wage rate that would prevail in an unregulated market) suffices to do the job Krugman wants it to do. At best, then, Krugman has made an argument for having some minimum wage, not a case for raising it.

Here’s the picture:

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Innumeracy Watch

Did Stanford university surgeons fail first grade arithmetic? Or do they just assume the rest of us did?

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Dear Old Golden Rule Days

ssyShortly before I started Kindergarten, my mother purchased a book called “Steven’s School Years”, with pockets to store my report cards and school projects, and questionnaires for me to fill out at the end of each school year.

I was not diligent about filling in the questionnaires, and they remain mostly blank. But had I been forced to, I wonder how I would have answered the following question, which was to be answered annually at the end of Grades 1,2,3,4,5, and 6:

(According to my mother, my ambition at age three was to be an electric drill, and sometime after that a rabbit. No other records of my early career inclinations seem to have survived.)

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Seeing Things Differently

Can humans learn to see in more than three dimensions?

What follows is highly speculative (and therefore possibly nonsense), but bear with me. (Or, if you prefer, don’t.)

First, let’s think about how humans learn to see in more than two dimensions. Your visual cortex (at least as I understand it) is pretty much two-dimensional, but apparently your brain is pretty adept at converting two dimensions worth of information into a three-dimensional picture of the world around you.

To accomplish that feat, your brain employs (at least) two tricks. First, it can infer an object’s depth (by which I mean its distance in front of you) from the angle between it and your two pupils:

Second, your brain can infer an object’s depth from the size of the accommodation reflex (change in lens shape, pupillary contraction, etc) needed to focus on it.

Ordinarily, these two methods pretty much agree, and your brain uses that answer to construct its map of the world.

But suppose I could surgically adjust your eyes in a way that breaks that agreement. For example, the angle-method might continue to work just as it does now, but I’d disrupt the accommodation reflex so that your pupils now contract by an amount that depends not on the distance to an object but on, say, its redness, or its squareness, or even just varies randomly. Better yet, suppose I could do this at a very early age, when your brain is still learning how to process visual signals.

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The Ashley Madison Test of College Faculty Cluelessness

Science marches on. Recent developments have made it possible to answer the age-old question: What percentage of your college faculty used their work email addresses to establish accounts at Ashley Madison?

In a sample of 33 highly ranked colleges, the answer ranges from a low of 1.6% at Oberlin to a pretty much unbelievable 22.6% at the University of Minnesota. (The full rankings appear at the bottom of this post.)

I got these percentages by counting the number of unique email addresses ending with, say, “” in the leaked Ashley Madison database, and dividing by the number of Harvard faculty, as reported by the college either on its website or in its Common Data Set filings.

The methodology, is, of course, fraught with peril. First, the majority of academic email addresses belong not to faculty, but to students. But it seems like a good guess that faculty (by virtue of their average age) are both far more likely than students to be trolling Ashley Madison, and far more likely than students to be clueless about acquiring anonymous email addresses. Besides, a quick spotcheck of the email addresses in the Ashley Madison database does indeed confirm that most of them (at least in one small but random sample) belong to faculty members.

There are also, of course, staff, and the staff-to-faculty ratio probably varies a lot from school to school, so weeding out the staff could change the relative rankings quite a bit. But again, my (still small but still random) sample continues to indicate that these are mostly faculty members.

A far more important issue might arise from the fact that some universities have multiple campuses. It’s possible, for example, that the 657 email addresses in Minnesota’s numerator came from many campuses, while the 2913 facuty in their denominator represents only the main campus. This will tend to inflate the rankings of the big state schools, and might account for the appearance of Minnesota, Virginia, Michigan and Cornell at the top — suggesting that if the numbers were crunched more carefully, the prize might go to Liberty University. If I were going to use these rankings for anything important, I’d give this issue a harder look.

One might also note that anybody can type anybody else’s email address into Ashley Madison, but I’m inclined to discount the importance of that, because it’s hard for me to see what the motive would be (except, perhaps, as part of a campaign to flood someone’s email box with unwanted replies).

With those caveats, feel free to use these rankings as a measure of your college faculty’s average cluelessness, at least when it comes to maintaining anonymity over the Internet.

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Politics As Usual

paulTo me, the biggest disappointment of this camapaign season has been Rand Paul. I’m sure there will be others.

I just saw Senator Paul on Fox News, where he made four substantive statements, one nonsensical, one innumerate, one economically illiterate, and one evasive to the point of dishonesty.

On the subject of collecting cellphone data without warrants, the host posed a hypothetical situation where a foreign terrorist is identified and we want to know which Americans he’s been talking to for the past six months. Paul’s answer: Get a warrant. The problem, of course, is that not even the US government, even newly armed with a warrant, is powerful enough to gather calling data that vanished into the ether six months ago. When the host pointed this out, Senator Paul ignored it.

On the subject of his tax plan, when presented with estimates that he’d be cutting taxes by 3% for the poor and by 13% for the rich, the senator could either have denied those numbers or defended them. Instead, he patiently explained that if you cut everyone’s taxes by 10%, then of course the rich will get bigger cuts (in absolute terms) than the poor. True, but to think that this was in any way relevant to the question requires a complete abandonment of all knowledge of arithmetic.

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So apparently I screwed up last night and posted many of my second-debate comments in the first-debate thread. And apparently this confused some readers, who gave up and went away. Others followed my lead and posted their own comments to the wrong thread.

I’ve gone ahead and moved all second-debate-relevant comments off the first-debate thread and onto the second-debate thread. Sorry for all the confusion. I’m sure there will be plenty more opportunities to share your thoughts about these guys.

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The Second Debate in Real Time

This thread is your opportunity to post comments on the second (9PM eastern time) Repbulican candidates’ debate, in real time as the debate occurs. I might or might not find the stomach to participate.

Keep in mind the guidelines I posted yesterday:

I will have zero tolerance for comments that contribute nothing to the enterprise. In other words, anything of the form “Ha ha! I knew so-and-so was an idiot” will be deleted as soon as they appear. Ideally, all comments will contain food for thought. Bonus points for pointing out subtle self-contradictions. If you insist on posting pure insults, they should at least be hilarious.

Now have at it.

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The First Debate in Real Time

This thread is your opportunity to post comments on the first (5PM) Repbulican candidates’ debate, in real time as the debate occurs. I might or might not find the stomach to participate.

Keep in mind the guidelines I posted yesterday:

I will have zero tolerance for comments that contribute nothing to the enterprise. In other words, anything of the form “Ha ha! I knew so-and-so was an idiot” will be deleted as soon as they appear. Ideally, all comments will contain food for thought. Bonus points for pointing out subtle self-contradictions. If you insist on posting pure insults, they should at least be hilarious.

Now have at it.

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Goin’ To the Candidates’ Debate

I might regret this, but…..

Thursday evening (August 6) there will be two debates among the Republican candidates for president, the first beginning at 5PM eastern time and the second at 9PM eastern time.

Shortly before each debate, I plan to open a thread and invite readers to post comments in real time as the debates progress. Each thread will appear on this site ten minutes before the debate’s starting time.

I will have zero tolerance for comments that contribute nothing to the enterprise. In other words, anything of the form “Ha ha! I knew so-and-so was an idiot” will be deleted as soon as it appears. Ideally, all comments will contain food for thought. Bonus points for pointing out subtle self-contradictions. If you insist on posting pure insults, they should at least be hilarious.

I might or might not join the fray myself.

The first post will appear slightly before 5 and the second shortly before 9. I am heading out now to stock up on junk food.

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This Would Be a Great Illustration of Comparative Advantage if It Weren’t Such a Great Illustration of Absolute Advantage

diracPaul A.M. Dirac was a pioneer of quantum mechanics and quantum field theory. His work pervades all of modern physics. He was, by almost all accounts, one of the top 10 physicists of all time, and by many accounts one of the top 2 physicists of the 20th century. And he’s one of my personal heroes.

When Dirac was awarded the Nobel prize in 1933, he was asked to say a few words at the banquet that kicks off the multi-day Nobel celebration — and chose, against tradition, to speak about a subject other than physics. Here is Paul Dirac on the source of all our economic problems:

I should like to suggest to you that the cause of all the economic troubles is that we have an economic system which tries to maintain an equality of value between two things, which it would be better to recognise from the beginning as of unequal value. These two things are the receipt of a certain single payment (say 100 crowns) and the receipt of a regular income (say 3 crowns a year) through all eternity. The course of events is continually showing that the second of these is more highly valued than the first. The shortage of buyers, which the world is suffering from, is readily understood, not as due to people not wishing to obtain possession of goods, but as people being unwilling to part with something which might earn a regular income in exchange for those goods. May I ask you to trace out for yourselves how all the obscurities become clear, if one assumes from the beginning that a regular income is worth incomparably more, in fact infinitely more, in the mathematical sense, than any single payment? In doing so I think you would then get a better insight into the way in which a physical theory is fitted in with the facts than you could get from studying popular books on physics.

True to form, then, Dirac set an agenda that others scurried to follow — the agenda in this case being the exploitation of the Nobel prize as a license to spout economic gibberish. Almost a century later, his program continues to flourish.

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What’s Fair is Fair

Suppose you’ve got 1000 students to assign to two schools, each with 500 slots available. Everyone prefers the Good School to the Bad School. Which of the following is a fair way to decide who goes where?

Method A: Give each student a coin to flip and count on the Law of Large Numbers to insure that just about exactly 500 will flip heads. Those students go to the Good School.

Method B: Randomly assign each student to one of two groups. Then flip a single coin to determine which group goes to the Good School.

Method C: After taking note of the fact that, coincidentally, exactly half the students are white and half are black, flip a single coin to determine which race goes to the Good School.

Method D: Assign all the white students to the Good School.

(There’s also of course Method D-prime, where you assign all the black students to the Good School, but I don’t think we need to consider this one separately.)

I ask this question because economists have been very involved with the design of school-allocation mechanisms, particularly in Boston, and one of the things they worry about is fairness. So it seems important to stop and think about what fairness means in this context.

Continue reading ‘What’s Fair is Fair’