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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.

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

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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:

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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.

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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?

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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.

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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.

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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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Re Arizona

I realize I’m late to the party, but here are a few thoughts on Arizona Senate Bill 1062:

1) A law allowing people to pick and choose whom they want to transact with would be a very good law. Not as good as eliminating the other laws that make this law necessary, but still a big improvement over the status quo.

2) Senate bill 1062, however, was not that law. Instead it was a law allowing people to pick and choose who they want to transact with provided they have (or claim to have) a religious basis for their preference.

3) This raises the question of how we should feel about good laws that exempt only the politically favored from onerous requirements of other laws. How should we feel, for example, about a law that allows only white people, or only black people, or only Muslims, or only art history majors to practice cosmetology without a license — while continuing the status quo for everyone else?

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And for Five Points, Explain the Universe

I’m starting to prepare a midterm exam for Principles of Economics, and for inspiration I looked at an exam given by a colleague who taught this course about fifteen years ago. There I find the following question, worth 3 points out of 140:

What happened in the Great Depression?

I wonder if you lost points for failing to mention that Clark Gable won the Oscar.

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Chips off the Block

Last week, I wrote to condemn the gang of angry yahoos who have piled onto Walter Block for making a perfectly reasonable argument about slavery, involuntary association, and Civil Rights legislation. Today I write to give Walter’s argument the respect it deserves by trying to pick it apart.

It’s important to recognize that Walter wasn’t making a formal argument. Instead, he was offering a rhetorical framework to clarify some of the issues. His (informal) argument, if I understand it, comes down to essentially this:

Look. We all agree that slavery is bad. And when you think about it, pretty much all of the badness stems from its involuntary nature. This should make us wary of involuntary associations in general, and hesitant to impose them. This applies, for example, to laws that require restaurant owners to serve people they don’t want to serve.

Now I happen to be quite sympathetic to that argument (indeed, I’ve been known to make essentially the same argument myself). In fact, I’ll go further and say that I think any reasonable person ought to be at least somewhat moved by that argument. But I can see where it’s not airtight.

To see why not, let’s take a pass at formalizing this:

1) Slavery is bad.
2) For a thing to be bad, some aspect of it must be bad.
3) Slavery has no bad aspects except possibly involuntary association.
4) From 1), 2) and 3), we can deduce that involuntary association is a bad aspect of slavery.
5) From 4), we deduce that involuntary association is bad.
6) Involuntary association is an aspect of the 1964 Civil Rights Act.
7) Anything with a bad aspect is at least partially bad.
8) From 5), 6) and 7), we can deduce that the 1964 Civil Rights Act is at least partially bad.

Now let’s see where the problems are.

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Block Heads

walterblockThe righteously irrepressible Walter Block has made it his mission to defend the undefendable, but there are limits. Chattel slavery, for example, will get no defense from Walter, and he recently explained why: The central problem with slavery is that you can’t walk away from it. If it were voluntary, it wouldn’t be so bad. In Walter’s words:

The slaves could not quit. They were forced to ‘associate’ with their masters when they would have vastly preferred not to do so. Otherwise, slavery wasn’t so bad. You could pick cotton, sing songs, be fed nice gruel, etc. The only real problem was that this relationship was compulsory.

A group of Walter’s colleagues at Loyola university (who, for brevity, I will henceforth refer to as “the gang of angry yahoos”) appears to concur:

Traders in human flesh kidnapped men, women and children from the interior of the African continent and marched them in stocks to the coast. Snatched from their families, these individuals awaited an unknown but decidedly terrible future. Often for as long as three months enslaved people sailed west, shackled and mired in the feces, urine, blood and vomit of the other wretched souls on the boat….The violation of human dignity, the radical exploitation of people’s labor, the brutal violence that slaveholders utilized to maintain power, the disenfranchisement of American citizens, the destruction of familial bonds, the pervasive sexual assault and the systematic attempts to dehumanize an entire race all mark slavery as an intellectually, economically, politically and socially condemnable institution no matter how, where, or when it is practiced.

So everybody’s on the same side, here, right? Surely nobody believes the slaves were voluntarily snatched from their families, shackled and mired in waste, sexually assaulted and all the rest. All the bad stuff was involuntary and — this being the whole point — was possible only because it was involuntary. That’s a concept with broad applicability. One could, for example, say the same about Auschwitz. Nobody would have much minded the torture and the gas chambers if there had been an opt-out provision. And this is a useful observation, if one is attempting to argue that involuntary associations are the root of much evil.

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The View From Olympus

Correct me if I’m wrong here:

1) In Russia, there is a law against so-called “gay propaganda”. Reasonable people (including me) consider this a regrettable curtailment of liberty. Some of those reasonable people also believe that it contributes to a culture in which violent acts against gay people are condoned or encouraged. This, if true, is sickening.

2) In Russia, there is also a law requiring most male citizens to serve at least a year in the military. Reasonable people (including me) consider this a regrettable curtailment of liberty. It is widely reported that conscripts are routinely subject to violent hazing that has been characterized as rising to the level of torture. News reports suggest that hundreds of conscripts die every year as a result of this hazing. This, if true, is sickening.

3) Conscription affects far more people than the anti-propaganda laws. In most cases, it also affects them far more severely. (If you doubt this, try asking your friends which they’d prefer: avoiding public discussions of homosexuality or serving a year in the Russian military.) Conscription is therefore, on both counts, the (far) greater outrage.

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Style Versus Content

Paul Krugman pauses to wonder why he’s been characterized as immoderate when — according to him — “there’s not a lot of air between my views and those of, say, staff economists at the Fed.” His conclusion: “What was radical, if you like, was my style, not my content.”

Bingo. Krugman’s detachment from mainstream economics is indeed a matter more of style than of content. But one symptom of that detachment is his failure to recognize that style is all that matters. Economics is most valuable not as a repository of received truths, but as a way of thinking — a way of thinking that has proved itself extraordinarily valuable as a bulwark against nonsense and claptrap. It’s that way of thinking — the style of economics — that Krugman so often and so depressingly abandons.

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Truth In Advertising

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State of the Union

I’m leaving this one up to my readers. What was the most egregious moment?

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Thursday Solution

Wednesday Puzzle

(Source omitted to discourage Googling; acknowledgements will come next week).

You have a sealed lockbox about a cubic yard in volume, containing $100,000 in hundred dollar bills. Your balance scale tells you that the box (with the money inside) weighs 100 pounds. You give the box to your friend Al, who flies it to the moon, while you, along with your balance scale, follow in a separate vehicle. Upon arrival, you retrieve the sealed box, put it on the balance scale and verify that it still weighs 100 pounds. You then give the box to your friend Barb, who loads it into her all-terrain vehicle and drives it to your moonbase, with you following along, again in a separate vehicle. When you get to the moonbase, Barb returns your lockbox. You open it and it’s empty.

Who stole your money, Al or Barb?

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Blinded By Prejudice?

I’ve been reading about the passage of the 1957 Civil Rights Bill, which, in its original form, banned racial segregation in theaters, restaurants and hotels (though by the time it was passed, almost all of the content had been stripped out). There’s a part of this history that makes no sense to me and I’m wondering if someone can explain it.

Remember first that this was at a time when several southern states enforced laws that mandated segregation in theaters, restaurants and hotels.

It was also at a time when, as I understand it, the outcome of the legislative battle was very much in doubt, so that each side feared the worst and was eager to compromise. Supporters weren’t sure they could beat a filibuster, which meant the bill might never even come to a vote. Opponents feared a filibuster might be beaten and the bill passed without amendments.

Lyndon Johnson, the majority leader of the Senate, wanted above all else to avoid a major fight, and was eager to facilitate any compromise both sides could agree on. He floated several compromise proposals and actively solicited others, from legislators, attorneys, and everyone else he could think of.

In Master of the Senate, the third in his three-volume biography of Lyndon Johnson, Robert Caro describes a vast number of compromises that failed before the passage of the final successful compromise.

Now here’s what astonishes me: Here you had all these lawyers and politicians, desperately trying to find a creative compromise — and yet, as far as I can tell, nobody ever proposed the compromise that seems (to me) to be obvious. The Republicans and northerners wanted mandatory integration. The southerners wanted to maintain mandatory segregation. The obvious compromise, I should think, would be to have neither — the northerners agree not to pass a federal law, and the southerners agree to repeal some state laws.

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Walter Oi, 1929 – 2013

A long time ago, when I had just started teaching at the University of Rochester, a blind man marched into my office, adopted a commanding stance, and announced in a booming voice that “it takes 150 condoms to prevent one birth in India”. Then he turned on his heels and marched out, leaving me to wonder what he had divided into what to get that number.

That’s what it was like working with Walter Oi, who died peacefully in his sleep on Christmas Eve after a long illness. Walter loved odd facts, and he loved to share them. It was Walter who told me that when all frozen pies had 12 inch diameters, apple was the most popular flavor — but when 7 inch pies came on the market, apple immediately fell to something like fifth place. His explanation: When you’re buying a 12 inch pie, the whole family has to agree on a flavor, and apple wins because it’s everyone’s second choice. With 7 inch pies, family members each get their pick, and almost nobody chooses apple.

Walter loved facts so much that he sometimes invented new ones, because the world could always use more. One day he walked into the department coffee room and announced that “A one hundred pound man and a three hundred pound man have exactly the same quantity of blood.” When this was met with considerable skepticism, Walter responded as he always responded to skepticism — by repeating himself more forcefully: “A one hundred pound man and a three hundred pound man have EXACTLY the same quantity of blood”.

In those pre-Internet days, some of us owned a device called an “encyclopedia”, which was sort of like a hardcopy printout of Wikipedia, but with fewer Simpsons references. A couple of my more enterprising colleagues went home and checked their encyclopedias that night, and came back the next morning to report that according to authoritative sources, a man’s blood volume is roughly proportional to his body weight. Walter’s response: “Nope. A one hundred pound man and a three hundred pound man have EXACTLY the same quantity of blood.”

If you watched carefully and didn’t blink, you might have caught him suppressing a smile.

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Thursday Solution

Tuesday Puzzle

Here I have a well shuffled deck of 52 cards, half of them red and half of them black. I plan to slowly turn the cards face up, one at a time. You can raise your hand at any point — either just before I turn over the first card, or the second, or the third, et cetera. When you raise your hand, you win a prize if the next card I turn over is red.

What’s your strategy?

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MegaOdds

In case you’re thinking of running out for a MegaMillions lottery ticket in the few hours left before tonight’s drawing: If you drive one mile to buy your ticket, your chance of being involved in a fatal accident on the way is about 8 times as great as your chance of winning the jackpot.

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Vocabulary Lesson

So…Democrats want to increase federal spending. Republicans supposedly want to decrease federal spending. The “compromise” is to increase federal spending by $45 billion.

I do not think the word “compromise” means what these people seem to think it means.

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Blast from the Past

With minimum wages in the news, one of my old posts on the subject has been getting a lot of hits lately. Unfortunately that post is quite long and the key points come near the end — past the point where I suspect a lot of people might stop reading. So here I’m excerpting what I consider the main ideas:

1. If we’re going to transfer income to low-wage workers, it’s both fundamentally unfair and politically unwise to put the entire burden of that transfer on a relatively small segment of the population (namely the owners and customers of businesses that employ a lot of low-wage workers). The right thing, given that we’re going to make this transfer, is to fund it as broadly as possible — say through an increase in the Earned Income Tax Credit, which comes out of general tax revenues.

2. I used the phrase “fundamentally unfair and politically unwise”. I’ll expand on both points, starting with fairness. When we collectively want a whole lot of 18-year olds to form an army, do we put the entire burden of that desire on people who happen to be 18 years old, by conscripting them at zero wage? Or do we think it’s fairer for those of us who enjoy the protections of that army to bear the cost through the tax system? When we collectively want to convert farmland to parkland, do we put the entire burden of that desire on people who happen to own farms, by taking their land without compensation? Or do we think it’s fairer for potential park-goers to pay for that land through the tax system? When we collectively want to raise the wages of unskilled workers, should we put the entire burden of that desire on those who happen to employ unskilled workers? Or is it fairer for those who have collectively made this decision to share the burden?

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Minimum Insight

Paul Krugman argues that:

  1. Hiking the minimum wage has little or no adverse effect on employment
  2. and therefore

  3. A minimum-wage increase would help low-paid workers, with few adverse side effects

.

In other words, Krugman, not for the first time, is peddling the sort of claptrap that few of us would accept from a college freshman.

The first point — that hiking the minimum wage has little effect on employment — is an empirical one. Not all smart observers agree with Krugman’s reading of the data, but many do — so for the sake of argument, let’s assume he’s right about that.

The question now is: How the hell do you get from point 1 to point 2? Answer: Only by forgetting the most basic principle of economics, which is that things have to add up. If the minimum wage has no effect on employment, then it’s basically a pure transfer of resources. Which means that the costs and the benefits are equal. The only way there can be “few adverse side effects” —- i.e. few costs — is if there are few benefits. Our job as economists is to make sure people understand such things.

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Elbow Catch

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This Day in History

Fifty years ago today at 1:30 PM eastern standard time, a minor tragedy took the life of President John F. Kennedy. A little over an hour later, a major tragedy ensued, as Lyndon B. Johnson was sworn in to replace him.

If there is such a thing as evil, it lived in Lyndon Johnson, whose life was one long obsession with the accumulation and exercise of power. His biographer Robert Caro relates how, in college, Johnson engineered, by intimidation and deceit, a takeover of the Student Council partly so that he could, apparently for sport, force the removal of talented and hardworking students from the editorships of campus publications, replacing them with non-entities and reveling in the tragic aftermath as ousted incumbents (who had received small but urgently needed stipends for their work) were forced through financial hardship to drop out of school.

It was downhill from there. As President, Johnson presided over a misbegotten war in Southeast Asia — a whirlpool of destruction fed with lives and treasure — and an equally misbegotten “War on Poverty” that too often became a war on economic freedom, the only effective antidote to poverty the world has ever known.

The War on Poverty might have been more accurately termed a war to consolidate Johnson’s influence. Poor rural families got grants and loans to expand their farms — provided they stayed on the farms, where Johnson needed their votes. Job training, educational programs, small business loans — all were available as long as you lived your life in a way that suited Lyndon Johnson’s purposes.

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A Little Knowledge is A Dangerous Thing

Sent by a reader:


(Click to enlarge.)

Some questions for the economics students:

  • Which vertical line segment illustrates the carbon tax revenue?
  • Which vertical line segment illustrates the compensation paid by the government?
  • Where does the difference come from?
  • What difference would it make if you changed the axis labels from “Polluting Products” and “Non-Polluting Products” to “Watermelon” and “All Things That Are Not Watermelon”?

Answers below.

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False Imprisonment

The frequently insightful and usually accurate Megan McArdle gets this part quite completely wrong in her latest Bloomberg column about ObamaCare:

Democratic politicians and insurers are locked in a prisoner’s dilemma. In this classic game-theory case, you and a professional associate are both arrested for theft. If neither of you talks, then you’ll probably get off. But if just one of you talks, then the person who talks will get a reduced sentence, while the other person has the book thrown at them. If you both talk, then both of you go to jail for a long time. The equilibrium is for both of you to talk, just in case the other guy does .

I sincerely hope that anyone who’s ever taken my Principles of Economics course — or for that matter, any Principles of Economics course — can explain to McArdle how wrong this is, and why.

Exercise for the reader: To what extent, if at all, does this howler undermine the larger point of McArdle’s column?

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