- Registrado
- 24 de Ene, 2020
Of course they're divergent, we're dealing with infinite sums which, by definition, do not fit on the number line. Complaining about it like this is like complaining about the existence of i because the square root of negative 1, similarly, does not exist on a one-dimensional plane.“if you want to fill in the singularities of the summation in an analytic way, the new function you get happens to have a value of -1/12 when s=-1; and of course the formula for this filled in function is not the summation given when s=-1, otherwise there’d be no singularity to begin with, but it makes people confused when we pretend it is, and makes us feel clever, so we’ll keep doing it”
What makes -1/12 interesting is not just that it can be reasoned algebraically but that it also applies as a constant in quantum mathematics (specifically when seemingly divergent sums do appear) that's mathematically consistent with the functions in macro physics.