4,464 reputation
816
bio website motls.blogspot.com
location Czech Republic
age 40
visits member for 2 years, 11 months
seen Mar 12 at 7:48

Hi, I am a string theorist and a publicist.


May
18
answered Linear Algebra Question
May
18
revised Global conformally flat coordinates in 2d spacetimes
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May
18
revised Global conformally flat coordinates in 2d spacetimes
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May
18
answered Global conformally flat coordinates in 2d spacetimes
May
18
answered Branch cut of the logarithm
May
18
answered Energy functional in Poisson's equation: what physical interpretation?
May
18
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.
May
18
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.
May
18
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.
May
18
revised Why does $1+2+3+\dots = {-1\over 12}$?
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May
18
revised Why does $1+2+3+\dots = {-1\over 12}$?
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May
18
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.
May
18
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.
May
18
awarded  Editor
May
18
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.
May
18
revised Why does $1+2+3+\dots = {-1\over 12}$?
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May
18
awarded  Teacher
May
18
answered Why does $1+2+3+\dots = {-1\over 12}$?
May
7
awarded  Autobiographer