Here’s his write-up’s final paragraph: There is an enduring debate about how far we should deviate from the rigorous academic approach in order to engage the wider public.
#A negative plus a positive equals license#
He also defends the license he and Copeland have taken to reach out to the public. Padilla notes that the result is “utterly counterintuitive,” but he explains it at some length and in some mathematical detail, and he offers links for further reading. Minus a twelfth is far less crazy a value when you start talking about physics. Therefore, only a very brave individual would dream of attaching the value infinity to sums like this. The trouble is that divergent sums like the one we discuss in the video do appear in calculations of physical observables, such as the Casimir energy, or in the dimensionality of the Universe in bosonic string theory. David Hilbert, one of the founding fathers of quantum mechanics, described infinity as “a mathematical abstraction that does not have a physical content.” I think most physicists would firmly agree with this sentiment. In my opinion, as a physicist, infinity has no place in physical observables, and therefore no place in Nature. He begins with this explanation: It’s by no means obvious, but this is the only sensible value one can attach to this divergent sum.
On the web, Padilla has posted a write-up for physicists. They open the textbook String Theory, by Joseph Polchinski of the University of California, Santa Barbara, and point to a page showing his use of the mathematics in question.
#A negative plus a positive equals series#
is not equal to −1/12, but both the infinite series and the negative number are associated with each other in a way that can be seen in this graph.”Īt the Times, Overbye quips, “After watching the video myself, I checked to make sure I still had my wallet and my watch.” But he also reports something that Padilla and Copeland adduce in the video. = −1/12? Absolutely Not!” It begins by pointing to a graph: “Brief Summary: 1 + 2 + 3 + 4 +. The American Physical Society’s PhysicsCentral website offers the Physics Buzz Blog posting “Correction: Does 1 + 2 + 3 + 4 +. Phil Plait, science blogger at Slate, did a posting about the video, corrected it, and then-in response to complaints-had to post a revised version. But in the aggregate, what they argue goes well beyond that simplicity.
Minute by minute, what they explain requires from the viewer no mathematical grounding beyond simple addition and a smattering of the most basic algebra.
Tony Padilla and Ed Copeland, physicists at the University of Nottingham in the UK, appear in and narrate the eight-minute video.
Well, that's clearly ridiculous, right? How can increasingly big numbers, when added together, make a small number? How can whole numbers make a fraction? How can positive numbers make a negative? Then, out of nowhere, a bunch of mathematicians try to tell you that the sum of all positive integers, that is, 1 + 2 + 3 + 4 + 5 + 6 +. So there you are living your life, content in your grasp on how the world works: up is up, down is down, the Sun rises in the east and sets in the west. = −1/12” had drawn well more than 1.5 million hits as of the morning of 4 February.Ĭolin Schultz at expresses nonmathematicians’ intrigued befuddlement: How far should scientists go in simplifying complexity to engage the public imagination? Boosted by a Dennis Overbye article in the New York Times’s Science Times section, the YouTube version of the video “ASTOUNDING: 1 + 2 + 3 + 4 + 5 + . . .
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