Monthly Archive for September, 2012

Stopped Clocks

Paul Krugman gets this one exactly right; among the 47% of Americans who pay no federal income tax in a given year, most do pay federal income tax at some point in their lives — and thus have at least some stake in the tax system.

But even putting that aside, what’s particularly distressing about Mitt Romney’s “47%” speech is the failure to recognize at least one of the following two propositions:

a) Even people who never pay federal income tax have a substantial personal stake in a healthy, thriving economy, and therefore have a stake in federal tax policy. In particular, wages are determined by productivity, and productivity depends to a substantial extent on the accumulation of capital, which can be directly influenced by tax policy.

b) It is possible for a skilled candidate to explain the above, and to sell pro-growth tax policies as pro-wage-earner tax policies.

Yes, the candidate who tries to make such a reasoned case will be the victim of a certain amount of demagoguery about “trickle-down economics”, but the candidate who allows himself to be paralyzed by such threats should not be running for president.

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WWCT? (What Would Copernicus Think?)

In The Big Questions, I argued that math is all there is: The Universe we live in is a mathematical object and is no more or less “real” than any other mathematical object. Thus, for example, the Godel universe, where time moves in circles, so that everything eventually returns to the time and place where it started, is as real as our own — though far, far, less complicated, because it contains, for example, no sentient beings). (Though on the other hand, it’s entirely plausible that there exists a Godel-like Universe that does contain sentient beings, and the existence of such a Universe can, in principle, be settled by purely mathematical inquiry.)

Obviously, I can’t prove this, but I’ve tried to explain why it strikes me as far more plausible than any of the alternatives. It all comes down to Ockham’s Razor. I know these mathematical Universes exist (pick up any issue of any theoretical physics journal and chances are you’ll find a couple described in detail), and it seems ontologically extravagant to suggest that some enjoy a different kind of existence than others. In other words, the notion of “physical reality” is exactly the sort of unnecessary baggage that Ockham’s razor wants to cut away.

People do seem to want to believe that the Universe we inhabit is somehow “special”, which is why I believe they’ve invented the unnecessary concept of “physical reality” to distinguish it from all the others. But the history of science has not been kind to viewpoints that cast human habitats as special. People used to think that the earth occupied a special place in the Universe; Copernicus (crying “Give up your Ptolemy! Rise up and follow me!”) rejected that notion in what can be seen as a slick application of Ockham’s Razor. Nowadays, people are tempted to think that the Universe we occupy has a special status in the zoo of mathematical Universes; but as good Ockhamized Copernicans, we should resist that temptation.

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The Other Dunce

I tried listening to Mitt Romney on the radio Sunday morning, but after a few minutes it just got too depressing.

Here’s what I heard in that few minutes:

1) We need to maintain defense spending because (among other reasons) it “creates jobs”. If Mitt Romney does not understand that the creation of jobs — i.e. the consumption of resources that could be valuably employed elsewhere — is the downside of defense spending, then he has no better chance of “fixing the economy” than a blue-bottomed monkey.

2) It is “immoral” for us to “pass on debt” to future generations — future generations who will almost surely be richer than we are. Note that in this context, “pass on debt” means exactly the same thing as “leave a smaller inheritance”. So Romney’s view is that there’s a moral imperative for the relatively poor — namely us — to transfer income to the relatively rich — namely our grandchildren. What’s interesting about that is that Romney is already on record in favor of a more progressive tax code, the sole purpose of which is to transfer income in the opposite direction — from the relatively rich to the relatively poor. (More precisely: Romney would tax capital income at a lower rate for the “middle class” than for the “rich”. Since there is no conceivable efficiency-based justification for such a policy, his position can only indicate a pure preference for rich-to-poor redistribution.) Either Romney has just declared himself immoral, or he’s just spouting random words. (Or, just possibly, he has a good argument for why we have a moral obligation to redistribute from the rich to the poor in some situations but not others. I would like to hear him articulate that argument.)

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Simple as ABC

The (really really) big news in the math world today is that Shin Mochizuki has (plausibly) claimed to have solved the ABC problem, which in turn suffices to settle many of the most vexing outstanding problems in arithmetic. Mochizuki’s work rests on so many radically new ideas that it will take the experts a long time to digest. I, who am not an expert, will surely die with only a vague sense of the argument. But based on my extremely limited (and possibly mistaken) understanding, it appears that Mochizuki’s breakthrough depends at least partly on his willingness to abandon the usual axioms for the foundations of mathematics and replace them with new axioms. (See, for example, the first page of these notes from one of Mochizuki’s lectures. You can find other related notes here.)

That’s interesting for a lot of reasons, but the one that’s most topical for The Big Questions is this: No mathematician would consider rejecting Mochizuki’s proof just because it relies on new axiomatic foundations. That’s because mathematicians (or at least the sort of mathematicians who study arithmetic) don’t particularly care about axioms; they care about truth.

There’s a widespread misconception that arithmetic is about “what can be derived from the axioms”, which is a lot like saying that astronomy is about “what can be discovered through telescopes”. Axiomatic systems, like telescopes, are investigative tools, which we are free to jettison when better tools come along. The blather of thoughtless imbeciles notwithstanding, what really matters is the fundamental object of study, whether it’s the system of natural numbers or the planet Jupiter.

Mathematicians care about what’s true, not about what’s provable; if a truth isn’t provable, we’re fine with changing the rules of the game to make it provable.

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Playing the Dunce

This morning I heard President Obama call for universities to lower their tuition rates so that “everybody in America can go to college”.

I am virtually certain that the President is not stupid enough to think that if tuition rates fell to zero, there would magically be enough room in the colleges for everybody in America. So I’ve got to believe that he’s purposely saying stupid things in order to appeal to stupid voters — the sort of voters, in other words, who probably don’t belong in college.

To believe what the President wants you to believe, you’d have to be not just stupid but badly misinformed. At the University where I teach, we do not lack for applicants. The reason we don’t have more students is not that they can’t afford us; it’s that we don’t have room for them.

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