Shalizi on Altemeyer

Altogether, the fact that a non-trivial fraction of the North American population is willing to say, in so many words, that it’d be happy to collaborate in persecution and oppression is one of the most unsettling things I’ve read in a long time.

So says Cosma Shalizi about Bob Altemeyer’s The Authoritarians (2007). Unsurprisingly, I agree.

If you haven’t done so already, kick back for an afternoon and read through Altemeyer’s book. It’s very much worth the investment. After that, we can join together in debating the details — every day, I become more convinced that a significant chunk of my species just likes to argue.
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Rosenhouse on Amanda Shaw

Following up on his previous post, “Is Math a Gift From God?” — calculus students say, “No!” — Jason Rosenhouse has a new essay for your delectation, “Is God Like an Imaginary Number?” Again, the short answer is, “Nope.” The longer answer will take us into the history of mathematics, the role of mysticism in theology and the relationship between science and verbal description.

Rosenhouse sets himself the task of fisking an essay in the religious periodical First Things, by a “Junior Fellow” of that publication named Amanda Shaw. Shaw’s thesis is that the notion of God is akin to that of an imaginary number, and moreover that the same closed-minded orthodoxy which rejected the latter from mathematics for oh so many years is unjustly keeping the former out of science. I find this stance to be, in a word, ironical: if you’re looking for dogmatism and condemnations of the heterodox, your search will be much more rewarding if you look among the people who reject scientific discoveries because they are inconsistent with a Bronze Age folk tale than if you search through science itself!

Still, it’s a fun chance to talk about history and mathematics.


As I described earlier, “imaginary” and “complex” numbers arise naturally when you think about the ordinary, humdrum “real numbers” — you know, fractions, decimals and all those guys — as lengths on a number line. In this picture, adding two numbers corresponds to sticking line segments end-to-end, multiplication means stretching or squishing (in general, scaling) line segments, and negation means flipping a segment over to lie on the opposite side of zero. Complex numbers appear when you ask the question, “What operation, when performed twice in succession upon a line segment, is equivalent to a negation?” Answer: rotating by a quarter-turn!

Historically, mathematicians started getting into complex numbers when they tried to find better and better ways to solve real-number equations. Girolamo Cardano (1501–1576), also known as Jerome Cardan, posed the following problem:

If some one says to you, divide 10 into two parts, one of which multiplied into the other shall produce […] 40, it is evident that this case or question is impossible. Nevertheless, we shall solve it in this fashion.

Writing this in more modern algebraic notation, this is like saying [tex] x + y = 10 [/tex] and [tex] xy = 40 [/tex], which we can combine into one equation by solving for [tex] y [/tex], thusly:

[tex] xy = x(10 – x) = 40.[/tex]

In turn, shuffling the symbols around gives

[tex] x^2 – 10x + 40 = 0,[/tex]

which plugging into ye old quadratic formula yields

[tex] x = \frac{10 \pm \sqrt{100 – 160}}{2}, [/tex]

or, boiling it down,

[tex] x = 5 \pm \sqrt{-15}. [/tex]

Totally loony! Taking the square root of a negative number? Forsooth, thy brains are bubbled! Oh, wait, didn’t we just realize that we could maybe handle the square root of a negative number by moving into a two-dimensional plane of numbers? Yes, we did: that’s the prize our talk of flips and rotations won us!
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Irony, Noun

James Boyle writes in today’s Financial Times:

The world wide web was designed in a scientific laboratory to facilitate access to scientific knowledge. In every other area of life — commerce, social networking, pornography — it has been a smashing success. But in the world of science itself? With the virtues of an open web all around us, we have proceeded to build an endless set of walled gardens, something that looks a lot like Compuserv[e] or Minitel and very little like a world wide web for science.

Discuss: should science publishing be more like pornography?

(Via Open Access News.)

Neurophilosophy on Synaesthesia

Over at Neurophilosophy, Mo — who has just added Sunclipse to his blogroll! — gives us a nice summary of the neuropsychology of synaesthesia. What makes some people see letters in color, either indelibly in their visual field or vividly in their “mind’s eye”? What causes an association between colors and musical sounds, and why do people experience the “mirror touch” effect, in which a person feels a tactile sensation when they observe another individual being touched? Moreover, if — as it now appears — these phenomena are more common than previously expected, might they in fact be the extremes of a spectrum of variation?

This is all fascinating stuff, particularly to an associative grapheme-color and tone-color synaesthete like me! Does my fusiform gyrus have defective feedback between area V4 and adjacent patches of cortex, and where can I sign up to find out? (I note with detachment that Drs. Rouw and Scholte, who published the evidence for this connection, work at the University of Amsterdam, clearly an interesting place to poke the brain, one way or another.)

Forthcoming from Paulos

PZ Myers points to an essay by John Allen Paulos, author of Innumeracy (1989, second edition 2001) among other books. The essay itself doesn’t venture into shockingly new territory — the cranky side of the Web has been spreading pseudomathematical myth-babble for a while now — but Paulos is a clear writer and a good debunker. Most interesting to me was the announcement in the blurb that Paulos has a new book in the works: Irreligion: A Mathematician Explains Why the Arguments for God Just Don’t Add Up, to be published in December. The ad copy says,

Are there any logical reasons to believe in God? Mathematician and bestselling author John Allen Paulos thinks not. In Irreligion he presents the case for his own worldview, organizing his book into twelve chapters that refute the twelve arguments most often put forward for believing in God’s existence. The latter arguments, Paulos relates in his characteristically lighthearted style, “range from what might be called golden oldies to those with a more contemporary beat. On the playlist are the firstcause argument, the argument from design, the ontological argument, arguments from faith and biblical codes, the argument from the anthropic principle, the moral universality argument, and others.” Interspersed among his twelve counterarguments are remarks on a variety of irreligious themes, ranging from the nature of miracles and creationist probability to cognitive illusions and prudential wagers. Special attention is paid to topics, arguments, and questions that spring from his incredulity “not only about religion but also about others’ credulity.” Despite the strong influence of his day job, Paulos says, there isn’t a single mathematical formula in the book.

That Paulos has chosen to write this book and push it towards the nation’s bookshelves is interesting. Back in the original Innumeracy, the book that made him famous, Paulos wrote,
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Bad Science Stories in 10 Easy Steps

TR Gregory offers advice on how to write really terrible, horrible, no good, very bad science stories for widespread distribution. By following these ten simple guidelines, you too can keep the public ignorant and hold back the Enlightenment!

Here’s a taste:

Appeal to common misconceptions, and substitute your own opinions and misunderstandings for the views of the scientific community.

It is important that readers’ misconceptions not be challenged when reading a news story. In fact, the more a report can reinforce misunderstandings of basic scientific principles, the better. This can be combined with step 6 [Use buzzwords and clichés whenever possible] to good effect. It is also helpful to insert your own views and misunderstandings as though they were those of the scientific community at large. For example, if you find something confusing, mysterious, or (un)desirable, assume that the scientific community as a whole shares your view.

It’s a great essay, and I don’t just say that because of the references he cites.

And while you’re visiting Prof. Gregory’s place, why don’t you help find out how much good one blog post can do?

Sunday Borges

It’s rush season at MIT. This is the time of year when food is free, rooms are filled with oobleck and alumni like me are roped into writing and performing spoof musicals in order to entice freshmen into choosing a living group. It’s a fun time to revisit the ol’ stomping grounds, but of course life manages to provide downsides, too. First, MIT rush is “dry,” meaning that the oobleck must be made with water and not alcohol, and that nobody can use liquid nitrogen to make a frozen tequila popsicle.

Underage drinking is endemic at the Institute, naturally, as is the case at every other university in the United States. Setting the legal drinking age at 21 makes umpteen gajilliion college students into criminals with no observable benefit, but the worst consequence may be that it means the students can’t have a rush activity where they turn beer bottles into Leyden jars to make capacitors for a Tesla coil.

The other downside of this season is that, like I said, I’m busy working on a spoof musical, which cuts into my blag-writing time. Instead of writing something shockingly original, I’ll just keep the beast at bay by feeding it a selection from Jorge Luis Borges. Today’s piece is a 1941 essay entitled “Dos libros” [Two books], originally published as “Dos libros de este tiempo” [Two Books of this Era], in La Nación (10 December 1941). This translation is by Eliot Weinberger and is found on pages 207–210 of Selected Non-Fictions. Borges is discussing H. G. Wells’ book, Guide to the New World: A Handbook of Constructive World Revolution, which had just been published.
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