# Luboš Motl

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bio website motls.blogspot.com location Czech Republic age 40 member for 2 years, 11 months seen Mar 12 at 7:48 profile views 2,486

Hi, I am a string theorist and a publicist.

# 259 Actions

 May18 answered Linear Algebra Question May18 revised Global conformally flat coordinates in 2d spacetimes added 375 characters in body May18 revised Global conformally flat coordinates in 2d spacetimes added 300 characters in body; added 4 characters in body; added 1105 characters in body May18 answered Global conformally flat coordinates in 2d spacetimes May18 answered Branch cut of the logarithm May18 answered Energy functional in Poisson's equation: what physical interpretation? May18 comment Why does $1+2+3+\dots = {-1\over 12}$? Dear @joriki, your "other" method is completely legitimate, too. You just have to avoid simple errors. You never get $\zeta(0)$ by the operations. In reality, $S-2S-2S=-3S$ is $1-2+3-4+\dots$ which is equal to $+1/4$ as shown both in Matt's and my answer. And indeed, that's $-3$ times $-1/12$. When summing the terms, you can't randomly "clump" the terms into pairs and give them wrong interpretations because such a manipulation distorts the values of $n$ from which the individual terms came. May18 comment Why does $1+2+3+\dots = {-1\over 12}$? Dear @joriki, I don't have a combative tone. I was just answering some questions, by the OP, and partly by others. All answers in mathematics ultimately boil down to some propositions' being right, which is equivalent to their negations' being wrong. This is not about combat. This is the basic point of maths - and all sciences, too. I could easily argue that it's combative for someone to question that $1+2+3+\dots = -1/12$ or that $2+2=4$. Well, I am not sure whether it's combative but it's incorrect. May18 comment Why does $1+2+3+\dots = {-1\over 12}$? The comments about the zeta function were added to the wording of the question a moment ago. As far as I remember, the original unedited question by perplexed didn't refer to the zeta function. Independently of that, I wrote that it was incorrect to say - as some of the comments did - that the zeta function regularization is the only way to show that the answer $-1/12$ was correct. It is not the only method and I have explicitly shown two additional ones in my answer. Most importantly, it is the correct value that has to be assigned to the sum whenever a finite sum has to be assigned. May18 revised Why does $1+2+3+\dots = {-1\over 12}$? added 914 characters in body; added 292 characters in body May18 revised Why does $1+2+3+\dots = {-1\over 12}$? added 153 characters in body; added 129 characters in body May18 comment Why does $1+2+3+\dots = {-1\over 12}$? OK, replace the word "incorrect" by "shallow, missing the essential wisdom of complex calculus, and leading to incorrect conclusions in all of physics and all of maths that depends on mathematical relationships similar to those in physics", is that OK now? I surely insist that this is an accurate description. May18 comment Why does $1+2+3+\dots = {-1\over 12}$? Thanks, @Matt, for the diplomatic work and interpretations. ;-) I actually added this Euler method but your "translation" helped me to understand that this Euler method is actually quite manifestly equivalent to the exponential regulator. May18 awarded Editor May18 comment Why does $1+2+3+\dots = {-1\over 12}$? @Joriki, the right answer -1/12 is a deep mathematical result that is relevant not only in physics but also in any branch of maths that cares about the deep relationships between structures such as sums, functions of complex variables, and many other things. The convergent result is not the right result given the most naive mathematical ways to interpret the sum - as a limit of partial sums but it is surely the result of all the most mathematically profound interpretations of the sum. That's also why Euler who was not quite silly knew that the right sum was $-1/12$ long before quantum physics. May18 revised Why does $1+2+3+\dots = {-1\over 12}$? added 759 characters in body May18 awarded Teacher May18 answered Why does $1+2+3+\dots = {-1\over 12}$? May7 awarded Autobiographer