When this sum hit the mainstream interwebz a while back, we had some discussion about it in the physics department where I work. The consensus was that it was misrepresented as a spooky non-intuitive fact about adding numbers, when really it’s closer to a particular notation for assigning a finite value to a diverging sum that happens to be useful in physics*. Some of us were annoyed, because it feels like it’s reinforcing this idea that math is impossibly opaque, a notion that we have to deal with on a regular basis when trying to teach physics to undergraduates.
Also, FWIW, I don’t recall seeing this presented in my QFT class, but then again, I only took one semester.
*I think you’re actually characterizing a it a little differently and a little more precisely, as a way of actually evaluating the sum, while subtracting off a term of order infinity, in a way that allows for certain kinds of manipulations that happen to be useful in physics.
Yeah, that’s the exact same conclusion I’m pushing here. That and “you should feel equipped to come to this conclusion even if you’re not an expert.” I know.. several people, and have seen more online (including in this comment section) who seem okay with “yeah, it’s negative one twelfth, isn’t that crazy?” and I think that’s really not ok.
My friend who’s in a physics grad program promised me that it does eventually show up in QFT, and apparently also in nonlinear dynamics. Good enough for me, for now.
When this sum hit the mainstream interwebz a while back, we had some discussion about it in the physics department where I work. The consensus was that it was misrepresented as a spooky non-intuitive fact about adding numbers, when really it’s closer to a particular notation for assigning a finite value to a diverging sum that happens to be useful in physics*. Some of us were annoyed, because it feels like it’s reinforcing this idea that math is impossibly opaque, a notion that we have to deal with on a regular basis when trying to teach physics to undergraduates.
Also, FWIW, I don’t recall seeing this presented in my QFT class, but then again, I only took one semester.
*I think you’re actually characterizing a it a little differently and a little more precisely, as a way of actually evaluating the sum, while subtracting off a term of order infinity, in a way that allows for certain kinds of manipulations that happen to be useful in physics.
Yeah, that’s the exact same conclusion I’m pushing here. That and “you should feel equipped to come to this conclusion even if you’re not an expert.” I know.. several people, and have seen more online (including in this comment section) who seem okay with “yeah, it’s negative one twelfth, isn’t that crazy?” and I think that’s really not ok.
My friend who’s in a physics grad program promised me that it does eventually show up in QFT, and apparently also in nonlinear dynamics. Good enough for me, for now.