Igon Value Problems Over Dilettante Matrices

Friday the 13th is, apparently, a day of must read articles. This time it's Steven Pinker's review of Malcolm Gladwell's What the Dog Saw: And Other Adventures. Readers who have taken linear algebra will be amused:

He provides misleading definitions of "homology," "saggital plane" and "power law" and quotes an expert speaking about an "igon value" (that's eigenvalue, a basic concept in linear algebra). In the spirit of Gladwell, who likes to give portentous names to his aperçus, I will call this the Igon Value Problem: when a writer's education on a topic consists in interviewing an expert, he is apt to offer generalizations that are banal, obtuse or flat wrong.

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That's awesome.

What would an igonvalue actually be?

Maybe it could be used for unitary matrices: if e^{i \theta} are the eigenvalues, then 0 \leq \theta < 2 \pi are the igonvalues.

You could generalize it for an arbitrary matrix, using the unitary factor in the polar decomposition to define the igonvalues.

I like it, Michael. Since quantum computing folk need to talk about eigen, I mean, igonvalues of unitary matrices all the time, I think we need to adopt it. If only we could get this into your book :)

This reminds me of the time I help induce a collaborator to say the term "Rabi flopping" as if there was a Jewish teacher flopping. (What did I know, I'm from the sticks.)

My banalitation: I'm always trying to induce people to end their verbs with '-ate'.

The definition is obvious, isn't it?

Igonvalue: the exponent i\theta of an eigenvalue e^{i\theta} of a unitary matrix, where \theta is measured in units of gon (1 gon=2pi/400). Thus, every eigenvalue of a unitary matrix is uniquely determined by exponating its igonvalue e^{i*gon} = e^{i\theta}.

It's even simpler than that: an igonvalue is simply the real element of a complex eigenvalue - i-gone.


By Clare Horsman (not verified) on 14 Nov 2009 #permalink

What I find really impressive about this is that the "igon value" mistake was published in a 2002 New Yorker article (don't they have fact checkers?), it's been available, uncorrected, for years on his web-site


and it's now published again uncorrected in the new book. Does anyone who knows anything about math read Gladwell? If so wouldn't at least one of them have told him or the New Yorker about the problem? Accuracy doesn't seem to be one of his strong points...

It looks plausible. The results seem sensible, and, as G and T say, people think they understand it. It depends on each layer receiving and absorbing radiation from above and below, and re-radiating half up and half down as heat energy, capable of raising temperature.

Former friends of mine kept telling me why I needed to read Malcolm Gladwell books. I'd ask why. They'd tell me, excited, something that I knew decade ago and published or blogged about. I'd look in Gladwell. He'd have a glib anecdote, and a nice soundbite, but always draw the wrong conclusion. Yet he's a rich best-selling author. I guess I'll continue aiming high. I refuse to make a profit by assuming that my audience is clueless. I'd rather assume that my audience, as with my classroom students, bring culture and wisdom to the interaction.

JVP: Sarah Palin is also a best selling author. I wonder if Gladwell in his next book will zero in on this particular useless statistic, book sales.

Glad to find your comments on igon value. I'm a statistician, so what do I know, but I wondered if it was an error for eigenvalue. Interestingly, I read the original article in the New Yorker, and missed it.

I once owned a wheaten terrier (called a Wheaton terrier by Gladwell on p.130--but Google knows better). Most stubborn dog I ever met. Had I read Gladwell's piece on the dog whisperer 30 years ago--I think it might have helped.

BTW: Excellent recent article (in the New Yorker) by John McPhee on fact checking.

Further on the Wheaten/on terrier. See http://www.gladwell.com/pdf/dog_whisperer.pdf

This appears to be a .pdf of the pages from the New Yorker. The error is included on page 50. Does this mean that the New Yorker's crack fact checkers missed that one?

McPhee's excellent article, 'Checkpoints' was published in this year's February 9 issue of the New Yorker. Only a summary is available online. A public library might still have a dog-eared copy.

By Barrie Humphrey (not verified) on 05 Dec 2009 #permalink

From RealClimate - 2009 temperatures by Jim Hansen:

"..the information conduit is a process. Scientists do their job and produce technically correct statements, and hopefully some context, and then the various levels of popularisers take that information and make pithier and more palatable (though less informative statements) that are nonetheless consistent with the scientific statements. So here, soundbites like 'it's weather not climate', or 'look globally, not locally', can follow knowing that there is some factual basis for that. Scientists can of course be popularisers as well, but we can't neglect the technical stuff that stands behind it. - gavin"

I was unable to identify "gavin" (I assume he is involved in the website, perhaps as a moderator), but his opinion is spot on.

Gladwell's writing is part of the process of popularisation, condensation and explanation, and he writes in an engaging and easily read style that whets one's appetite to learn more about the subject; encouraging the reader to consider it with critical and reflective thinking rather than simply accept what Gladwell has written as being all one needs to know. This discussion is surely proof of that.

"igon value" appears to be a phonetic transcription of "eigenvalue"; shouldn't have been transcribed incorrectly, should have been caught in proofreading. Mea Cupa due from someone, and let's get on with it. The broad strokes are unchanged. (I've had my battles with so called technical editors, who have completely changed meaning and intent because of editorial changes they've made without knowledge of the subject)

Let's not throw out the baby with the bathwater!