I was going to say something's wrong here. In normal math you don't just average your set of possible values to reach a scalar. That 1 - 1 + 1 - 1 + ... summation is the basis of the entire video...
I was going to say something's wrong here. In normal math you don't just average your set of possible values to reach a scalar. That 1 - 1 + 1 - 1 + ... summation is the basis of the entire video but it defies traditional mathematical rules.
It can be shown that the sum of all natural numbers (1 + 2 + 3 + 4 + ...) equals -1/12. Weird, huh? The math problem can be approached in a number of different ways and the result is still -1/12....
It can be shown that the sum of all natural numbers (1 + 2 + 3 + 4 + ...) equals -1/12. Weird, huh? The math problem can be approached in a number of different ways and the result is still -1/12. Professor Edward Frenkel provides a great follow up video explaining the philosophy behind the math, and some of the logical consequences of it. This weird result is even backed up by observations in quantum physics, including the calculation of the Casimir force and in calculating the lowest possible energy level of a string in Bosonic String Theory.
I was going to say something's wrong here. In normal math you don't just average your set of possible values to reach a scalar. That
1 - 1 + 1 - 1 + ...summation is the basis of the entire video but it defies traditional mathematical rules.It can be shown that the sum of all natural numbers (1 + 2 + 3 + 4 + ...) equals -1/12. Weird, huh? The math problem can be approached in a number of different ways and the result is still -1/12. Professor Edward Frenkel provides a great follow up video explaining the philosophy behind the math, and some of the logical consequences of it. This weird result is even backed up by observations in quantum physics, including the calculation of the Casimir force and in calculating the lowest possible energy level of a string in Bosonic String Theory.
Equality is not the term here. It's just the value of the analytic continuation of the Dirichlet series to the zeta function evaluated at -1.