Astronomy Wiz Falls Down a Wormhole.

I enjoy Phil Plait’s Bad Astronomy posts that I read on Slate. I’m sure his Bad Astronomy blog is well worth visiting, but I hadn’t until tonight. And I have to say, I love the handmade feel of the site. And I love his enthusiasm for the deep space photos and the climate change fight, and even mathematics.

Which is where this story comes from. Yesterday Phil wrote a story about a mathematical equation that defied description. It’s kind of like the idea, If God can do anything, can he make a rock he can’t pick up? In this case the question was, what is the sum of 1+2+3+4+5….

Those ellipses mean that the sequence goes on forever. It’s a headpounder. If the sequence of numbers is infinite, it seems like the sum of this infinite sequence must be infinite, but Phil told a story in which the sum was -1/12th.

And he posted a video. In which some giggly physicists, highly respected apparently, demonstrate by a series of algebraic transpositions (I’m certainly not using the right math lingo here) that the infinite (which Phil identifies as divergent) series has that value of -1/12th.

I watched the video in the original post and I liked the kookiness, and I loved the way math was a form of play (not something I have any familiarity with), but I didn’t understand how you could just add and subtract these infinite series and make any sense. It all seemed somewhat arbitrary. Despite Phil’s hype of this explanation as mindblowing, my mind was unblown. Good for me, it turns out.

According to Phil’s mea culpa today, you really can’t add and subtract infinite series. Phil got gulled into a bit of pop-math hocus pocus, I guess. He doesn’t call out the guys in the video. But his elaboration on the original post is good-writer magic, and explains why his blog is popular.

I think the bigger issue here is our need to question what we see and hear. Phil Plait is a thoughtful and honest writer with a lot of expertise. He notes that that expertise is not mathematical, but he does love the numbers, so he writes about them. That doesn’t mean he or his source is always right. We need to be skeptical about all claims, especially the mindblowing ones.

And welcome when someone who made a mistake admits it. As Phil did.

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