Math on the Brain

Many people know that before I succumbed to the unremunerative way of all things literary, I was a young mathematician. I like to say that I have an affinity for math, literature, and philosophy because they're all nonempirical, pure works of the collective (and sometimes private) human imagination. Here are a couple of math-and-brain-related entries worth noting:

Jim Holt, "The Numbers Guy":

By “pure luck,” Dehaene recalls, Mehler happened to be doing research on how numbers are understood. This led to Dehaene’s first encounter with what he came to characterize as “the number sense.” Dehaene’s work centered on an apparently simple question: How do we know whether numbers are bigger or smaller than one another? If you are asked to choose which of a pair of Arabic numerals—4 and 7, say—stands for the bigger number, you respond “seven” in a split second, and one might think that any two digits could be compared in the same very brief period of time. Yet in Dehaene’s experiments, while subjects answered quickly and accurately when the digits were far apart, like 2 and 9, they slowed down when the digits were closer together, like 5 and 6. Performance also got worse as the digits grew larger: 2 and 3 were much easier to compare than 7 and 8. When Dehaene tested some of the best mathematics students at the École Normale, the students were amazed to find themselves slowing down and making errors when asked whether 8 or 9 was the larger number.

Dehaene conjectured that, when we see numerals or hear number words, our brains automatically map them onto a number line that grows increasingly fuzzy above 3 or 4. He found that no amount of training can change this. “It is a basic structural property of how our brains represent number, not just a lack of facility,” he told me.

The Reactionary Epicurean, "There are numbers and then there are Numbers...", on the stages of mathematical development:

At some point, every visually-inclined student of mathematics hits a wall. It happened to me at the end of my freshman year in college (I had to integrate a function over a 5-dimensional hypertorus in my Vector Analysis final, and nearly passed out from the visual strain), and it's almost an impossible feeling to describe if you haven't experienced it yourself.

The bottom of your stomach drops out as you realize that mathematics is deeper and more sublime than the constrained, geometric mockery of mathematics you have been doing up to this point. There is a moment of existential horror; an understanding that the "gift" of visualization you possessed was actually a curse, that it kept your understanding of conceptual structures chained down and crippled for so long. At this point there is a choice...

The only way to develop abstract intuition that encompasses and goes beyond what you have is to tear down the geometric intuition that you worked so hard for throughout your educational life. The devoted student must return to the formalistic methods of Stage 1 and apply them over and over until true conceptual insight breaks through and floods the brain like dawn breaking over the arctic after 6 months of darkness. The process is something akin to meditation, and beyond the first epiphany there are countless higher epiphanies. Each layer of abstraction and conceptual depth must be absorbed by the brain in its entirety, and the absorption requires a return to Stage 1 and an abandonment of the hard-won inuition that has served the student to this point.

A Failure of Imagination

Chris Anderson has an excerpt of his next book, titled "Free! Why $0.00 Is the Future of Business" over at Wired. He begins by recounting the two great inventions of disposable razor magnate King Gillette: the disposable razor and a new business model, where you give the durable product away for cheap or free and make your profit from the disposable or serial product. Cellular phones and their calling plans, video games and their consoles, cable boxes and cable all partake of this now-ubiquitous model.

It's a great analogy. But Anderson stumbles in his transition.

Over the past decade, however, a different sort of free has emerged. The new model is based not on cross-subsidies — the shifting of costs from one product to another — but on the fact that the cost of products themselves is falling fast. It's as if the price of steel had dropped so close to zero that King Gillette could give away both razor and blade, and make his money on something else entirely. (Shaving cream?)

No! For one thing, Gilette does sell shaving cream. They also sell deodorant and nose-hair trimmers and all manner of other grooming accoutrements. But more to the point, making money from shaving cream is a cross-subsidy. It's not a fundamentally different model from the razor and blades, just a weaker one, since presumably different lathers can be used with different blades.

No. The answer is that under the new model, and presumably at some point in my lifetime, when every durable surface is an information-aware screen, Gilette will give the razor and the blades and the shaving cream and deodorant all away for free. Instead, they will make their profit from the time you spend looking in the mirror. That is how the web works.

Omar Little, A Requiem

I don't know whether anyone looked at my earlier spoiler, but yes -- The Wire's Omar Little, one of the most fascinating characters in television of history, dies in Episode 8 of Season 5.

David Simon has said earlier that The Wire is modeled on Greek tragedy: "Fated and doomed protagonists are confronted by a system that is indifferent to their heroism, to their individuality, to their morality. But instead of Olympian gods, Capitalism is the ultimate god. Capitalism is Zeus."

If Capitalism is Zeus, then Omar was certainly Achilles -- the superhuman-but-mortal agent of revenge, weeping over his lover's broken body. And Achilles, however immortal he seems, is doomed.

That said, if No-Heart Anthony -- Omar's equally legendary older brother, who we hear about in Season 1 and first see in a brief prequel that aired online before season 5 -- were to escape from prison to either avenge his brother's death or take up his mantle in the final episode, I would have no problem with that. After all, Achilles may die, but Troy still will fall.

Why Don't We Just Add A Poll Tax?

Geraldine Ferraro gets silly in the New York Times:

In the Democratic primary in South Carolina, tens of thousands of Republicans and independents no doubt voted, many of them for Mr. Obama. The same rules prevail at the Iowa caucuses, in which Mr. Obama also triumphed.

He won his delegates fair and square, but those delegates represent the wishes not only of grassroots Democrats, but also Republicans and independents. If rank-and-file Democrats should decide who the party’s nominee is, each state should pass a rule allowing only people who have been registered in the Democratic Party for a given time — not nonmembers or day-of registrants — to vote for the party’s nominee.

The notion is that the superdelegates represent grassroots Democratic voters better than voters in a presidential primary -- where turnout often fails to crack 30 percent. This, despite the scandalous fact that each of these elected officials won in a general election in which both Republicans and independents were gratuitously allowed to participate, often after winning uncontested or even more sparsely attended primaries.

In fact, Ferraro is so concerned about these superdelegates winning their primaries that she worries about them being coerced to vote for Obama in order to stave off a primary challenge. Meanwhile, let's keep as many people who might not have their party bona fides together (especially the young people and nonvoters we keep talking about turning out in the general) from participating in the party. Now that's grass-roots democracy.

Ferraro also reminds us of her history in the long tradition of mediocre big-D Democratic politics. The superdelegate system was created after Ted Kennedy tried to introduce amendments to make the party platform more liberal after his unsuccessful primary challenge to Carter in 1980.

In 1984 I headed the party’s platform committee. We produced the longest platform in Democratic history, a document that stated the party’s principles in broad terms that neither the most liberal nor the most conservative elected officials would denounce. It generated no fights at the convention. It was a document that no one would walk away from. We lost in 1984, big time. But that loss had nothing to do with Democratic Party infighting.

Kudos to you, Ms. Ferraro. Democrats lost the Presidency again in '88, needed a third-party challenger to win in 1992 and 1996, quietly accepted a stolen election in 2000 and nominated another unobjectionable and unelectable candidate in 2004. Heaven forbid anyone see Democrats disagree with each other on TV. Let's just bleed for another quarter-century.

The Approved Platitudes

Andrew Sullivan's recent vacation introduced me to the fistful of smart conservative bloggers (e.g. Reihan Salam) who pitch-hit for him, along with some of the other bloggers they plugged. For example, here's Eunomia's Daniel Larison, talking about the election in "The Meme Lives On" :

Every mistake of analysis I have made over the past year has come from believing that policy mattered to voters and that the candidates with the policies most in line with their constituents’ priorities would prevail.  That was a pretty stupid assumption. Worse than a pundit’s fallacy, this is the error of the high-information voter, who thinks that because he wastes his time learning about the policy positions of two dozen politicians that everyone else is as, well, brain-damaged and conditioned as he is...

The candidates of bold ideas and major changes were, of course, the ones who were consistently marginalised and ridiculed as “kooks,” and in a narrow sense this label is correct in that you do have to be a bit eccentric to care deeply about foreign policy paradigms, much less monetary policy. The one candidate who routinely spoke about the declining value of the dollar, one of the more important questions of the moment, was Ron Paul. The best McCain has ever been able to do when confronted with a question about monetary policy is to recycle his lame joke about propping up Alan Greenspan’s corpse in a chair, and he stands a frighteningly good chance of becoming the next President. Paul’s rivals typically battled with each other over things that were relatively trivial by comparison–”sanctuary mansions” comes to mind–and they have been rewarded for their triviality. They are the serious ones, because while they may mouth platitudes, these are the approved platitudes. Paul’s candidacy was focused heavily on his dissenting policy views, and it was, whether or not you endorse his proposals, the most substantive campaign of them all.

This strikes me as both 1) true and 2) likely to make Angela happy, who recently and insightfully wrote this:

i am beginning to think ralph nader has an uncontrollable ego. and need for constant attention. and is jealous of what ron paul was able to do without a substantial personal fortune and rich pals backing him.

Deadblogging

● Kottke, "Liveblogging the Oscars":

10:00p: Just checked the movie times at the theater two blocks from my apartment. Juno at 10:50, There Will Be Blood at 10:20, Atonement at 10:30, and No Country for Old Men at 10:15 & 10:55. Michael Clayton is on Movies OnDemand for $4.99 at any time.

9:32p: Is this a good time to go to the movies? Lots of empty seats at There Will Be Blood maybe?

9:07p: My liveblogging outfit this evening: jeans by Banana Republic, long sleeve tshirt by American Apparel, socks by Wal-Mart, boxer shorts by Muji.

8:55p: What else is on right now: The Mummy on Encore, Buffy the Vampire Slayer on Fox Movie Channel, Miller's Crossing on Encore Action, The Departed on Cinemax, episode #8 of The Wire on HBO, the Masterpiece version of Pride and Prejudice on PBS, Bulls vs. Rockets on ESPN, Godfather II on AMC, and Born Into Brothels is just ending on IFC but Spanking the Monkey starts in 20 minutes.

Not So New But Noteworthy

I've had three tabs open all week, intending to blog about each of them. Now it's Saturday, so it's time for rapid-fire.

Charles McGrath, "Is PBS Still Necessary?":

Argument: PBS's ratings are declining, cable is ascendant, and the public network doesn't compete in prime-time.
My counter-argument: Not everyone has cable, jack, and lots of channels don't do so well in prime-time, especially arts, culture, and science channels on cable. We need PBS to have strong programming all day long, when networks take a bath and where it does pretty well.
Big idea: Public radio, both NPR and PRI, have been more innovative than PBS and have actually gained audience because of it. So PBS needs to try more innovation.

Scott Horton, "Jonah's Fascism": Everyone's taken a crack at Jonah Goldberg's Liberal Fascism, but few people are in the position to be as systematic as Scott Horton, aka the most culturally and historically informed political blogger on the web.

Mark Bernstein, "NeoVictorian Computing": Bernstein calls for a revival of "personal computing," taking the 19th-century Arts and Crafts movement as a model. Exposed joints, handicrafts, and an emphasis on objects and software designed to get things done. It's more a chain of insightful critiques than a full-fledged program, but as someone who spends a lot of time thinking about historical analogues to our digital moment, this is a very useful and potentially fruitful strand to follow.

A New GI Bill

Melissa Harris-Lacewell, Princeton prof, blogger, and writer for Slate, at BigThink. Stick around to the end, when she promotes the notion of a new GI Bill for African-Americans (and, presumably other minorities), i.e., investments in education, housing, schools, and transportation to benefit the people largely cut out of the postwar middle-class boom because of race.

Smart stuff -- and a surprisingly persuasive frame for thinking about both the history of the civil rights movement and current political issues.

The Problem of the Problem of Evil

Everyone seems to know the rules. God is all-powerful, all-knowing, and both loving and good. Yet evil or suffering exists. This appears to be a contradiction. Goodness and suffering are compatible only when the power to combat suffering is lacking. And power and suffering suggest a God who either wishes us to suffer or somehow requires suffering for the fulfillment of a moral order that he himself created and is presumably at liberty to change. Free will is only an apparent solution to the problem, since only a subset of suffering can be attributed to human will, and begs both the question of God's ultimate responsibility for suffering (natural and manmade) and the question of whether free will is in itself a good, and if so, why.

The problem of evil cuts to the heart of any apologia for monotheism since it calls into question the existence of an organizing principle to the universe, the moral intentions and/or competence of the deity, and His fitness for worship.

But the trouble isn't with the logic of the problem of evil, but its psychology. That suffering exists is undeniable -- the existence of pain may be the closest thing to a religious fact. But the other premises are rarely if ever denied. Why couldn't God be well-meaning but incompetent? Why couldn't God be all-powerful but not fully good? Neither of these seem to be live possibilities for us -- either God is possessed of all perfections, as St. Anselm thought, or God cannot exist. Yet the notion that our souls are at the mercy of a God who may neither be totally powerful nor totally beneficent is far from contradictory, and was a meaningful and live proposition for millennia. Just not for us moderns.

Those who follow the logic of the problem of evil reveal something about themselves in the course of their syllogism. Even those who disbelieve in the existence of God believe that were God to exist, He should be -- must be -- both totally powerful to eradicate suffering and totally willing to do so out of love for mankind and His lesser creations. In other words, there may not be a moral order to the universe, but the absence of one is keenly felt as a detriment, a betrayal to the sense of individual fate and cosmic destiny.

At its psychological root, the problem of evil poses a much more melancholic dilemma. Looking outward, we see a universe of suffering and ask why the universe is indifferent to it -- and in particular, we ask why the universe is indifferent to our suffering. And looking inwards, we find a person full of shallow and selfish and hostile intentions, and we ask -- why couldn't I have been made good?

"Conservatives Just Aren't Into Academe"

From the Chronicle of Higher Ed: Two researchers (a husband and wife) have crunched data to explain academics are so liberal and why conservatives aren't interested in the academy. Turns out, it isn't political bias, class considerations, or the trauma of disagreement.

Instead the Woessners looked at differences in interests and personality. They found that in a variety of ways, conservative students were less interested than liberals in subject matter that often leads to doctoral degrees, and less interested in doing the kinds of things that professors spend their time doing.

For example, liberal students reported valuing intellectual freedom, creativity, and the chance to write original work and make a theoretical contribution to science. They outnumbered conservative students two to one in the humanities and social sciences — which are among the fields most likely to produce interest in doctoral study. Conservative students, however, put more value on personal achievement and orderliness, and on practical professions, like accounting and computer science, that could earn them lots of money.

The Woessners also found that conservative students put a higher priority than liberal ones on raising a family. That does not always fit well with a career in academe, where people often delay childbearing until after they earn tenure.

The research led the Woessners to conclude that if higher education wants to attract more conservatives to the professoriate, it should smooth the way financially, offering subsidized health insurance and housing for graduate students, and adopting family-friendly policies for professors.

Yes! Hear, hear! Let's raise salaries and graduate stipends, too! Anything, ANYTHING, to make the profession more appealing to conservatives. That is a sacrifice I am eminently willing to make.