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December 12, 2011

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Paul Krugman: Depression and Democracy

Posted: 12 Dec 2011 12:33 AM PST

Severe recessions -- depressions -- have effects that go beyond economics:

Depression and Democracy, by Paul Krugman, Commentary, NY Times: It's time to start calling the current situation what it is: a depression. True, it's not a full replay of the Great Depression, but that's cold comfort. Unemployment in both America and Europe remains disastrously high. Leaders and institutions are increasingly discredited. And democratic values are under siege.
On that last point, I am not being alarmist. ... Let's talk, in particular, about what's happening in Europe... First of all, the crisis of the euro is killing the European dream. The shared currency, which was supposed to bind nations together, has instead created an atmosphere of bitter acrimony.
Specifically, demands for ever-harsher austerity, with no offsetting effort to foster growth, have ... failed as economic policy...; a Europe-wide recession now looks likely even if the immediate threat of financial crisis is contained. And they have created immense anger, with many Europeans furious at what is perceived, fairly or unfairly (or actually a bit of both), as a heavy-handed exercise of German power.
Nobody familiar with Europe's history can look at this resurgence of hostility without feeling a shiver. Yet there may be worse things happening.
Right-wing populists are on the rise from Austria, where the Freedom Party (whose leader used to have neo-Nazi connections) runs neck-and-neck in the polls with established parties, to Finland, where the anti-immigrant True Finns party had a strong electoral showing last April. ...
Last month the European Bank for Reconstruction and Development documented a sharp drop in public support for democracy in the ... nations that joined the European Union after the fall of the Berlin Wall. Not surprisingly, the loss of faith in democracy has been greatest in the countries that suffered the deepest economic slumps.
And in at least one nation, Hungary, democratic institutions are being undermined as we speak. One of Hungary's major parties, Jobbik, is a nightmare out of the 1930s: it's anti-Roma (Gypsy), it's anti-Semitic, and it even had a paramilitary arm. But the immediate threat comes from Fidesz, the governing center-right party.
Fidesz won an overwhelming Parliamentary majority last year, at least partly for economic reasons... Now Fidesz ... seems bent on establishing a permanent hold on power. ...
Taken together, all this amounts to the re-establishment of authoritarian rule, under a paper-thin veneer of democracy, in the heart of Europe. And it's a sample of what may happen much more widely if this depression continues. ...
The European Union missed the chance to head off the power grab at the start... It will be much harder to reverse the slide now. Yet Europe's leaders had better try, or risk losing everything they stand for.
And they also need to rethink their failing economic policies. If they don't, there will be more backsliding on democracy — and the breakup of the euro may be the least of their worries.

Comparing Infinities

Posted: 12 Dec 2011 12:24 AM PST

This has been bugging me all day:

Comparisons involving infinitely large numbers are notoriously tricky. ... To grasp the mathematical challenge, imagine that you're a contestant on Let's Make a Deal and you've won an unusual prize: an infinite collection of envelopes, the first containing $1, the second $2, the third $3, and so on. As the crowd cheers, Monty chimes in to make you an offer. Either keep your prize as is, or elect to have him double the contents of each envelope. At first it seems obvious that you should take the deal. "Each envelope will contain more money than it previously did," you think, "so this has to be the right move." And if you had only a finite number of envelopes, it would be the right move. To exchange five envelopes containing $1, $2, $3, $4, and $5 for envelopes with $2, $4, $6, $8, and $10 makes unassailable sense. But after another moment's thought, you start to waver, because you realize that the infinite case is less clear-cut. "If I take the deal," you think, "I'll wind up with envelopes containing $2, $4, $6, and so on, running through all the even numbers. But as things currently stand, my envelopes run through all whole numbers, the evens as well as the odds. So it seems that by taking the deal I'll be removing the odd dollar amounts from my total tally. That doesn't sound like a smart thing to do." Your head starts to spin. Compared envelope by envelope, the deal looks good. Compared collection to collection, the deal looks bad.
Your dilemma illustrates the kind of mathematical pitfall that makes it so hard to compare infinite collections. The crowd is growing antsy, you have to make a decision, but your assessment of the deal depends on the way you compare the two outcomes.
A similar ambiguity afflicts comparisons of a yet more basic characteristic of such collections: the number of members each contains. ... Which are more plentiful, whole numbers or even numbers? Most people would say whole numbers, since only half of the whole numbers are even. But your experience with Monty gives you sharper insight. Imagine that you take Monty's deal and wind up with all even dollar amounts. In doing so, you wouldn't return any envelopes nor would you require any new ones... You conclude, therefore, that the number of envelopes required to accommodate all whole numbers is the same as the number of envelopes required to accommodate all even numbers—which suggests that the populations of each category are equal (Table 7.1). And that's weird. By one method of comparison—considering the even numbers as a subset of the whole numbers—you conclude that there are more whole numbers. By a different method of comparison—considering how many envelopes are needed to contain the members of each group—you conclude that the set of whole numbers and the set of even numbers have equal populations.

Greene1Table 7.1 Every whole number is paired with an even number, and vice versa, suggesting that the quantity of each is the same.

You can even convince yourself that there are more even numbers than there are whole numbers. Imagine that Monty offered to quadruple the money in each of the envelopes you initially had, so there would be $4 in the first, $8 in the second, $12 in the third, and so on. Since, again, the number of envelopes involved in the deal stays the same, this suggests that the quantity of whole numbers, where the deal began, is equal to that of numbers divisible by four (Table 7.2), where the deal wound up. But such a pairing, marrying off each whole number to a number that's divisible by 4, leaves an infinite set of even bachelors—the numbers 2, 6, 10, and so on—and thus seems to imply that the evens are more plentiful than the wholes.

Greene2Table 7.2 Every whole number is paired with every other even number, leaving an infinite set of even bachelors, suggesting that there are more evens than wholes.

From one perspective, the population of even numbers is less than that of whole numbers. From another, the populations are equal. From another still, the population of even numbers is greater than that of the whole numbers. And it's not that one conclusion is right and the others wrong. There simply is no absolute answer to the question of which of these kinds of infinite collections are larger. The result you find depends on the manner in which you do the comparison. ...
Physicists call this the measure problem, a mathematical term whose meaning is well suggested by its name. ... Solving the measure problem is imperative.
[From Greene, Brian (2011). The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos (Kindle Locations 3609-3624). Random House, Inc.. Kindle Edition.]

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Posted: 12 Dec 2011 12:06 AM PST

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