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Here's a link to a video talking about infinite sums...

The way this problem is related to non-integer dimensions (maybe only in my mind) is that crazy math and crazy physics somehow support each other.

I believe that the concept of non-integer dimensions is crazy math, and if physicists claim that there was a time when there were non-integer dimensions then that is crazy physics.

Crazy math is OK because it is all hypothetical. However, crazy physics seems counterproductive. It no longer gives us insight into how things are, it just makes it easy to solve physics problems.

Thanks!

“Crazy math is OK because it is all hypothetical. However, crazy physics seems counterproductive. It no longer gives us insight into how things are, it just makes it easy to solve physics problems.”

History shows that explorations into new realms of math have revealed truths (as far as we know) about nature. It was math that led Einstein to his theories. This, to me, is miraculous.

I suppose I’m not sure what qualifies for “crazy.” Sometimes math and the world are both crazy and they happen to match. Sometimes they don’t. I’m not yet prepared to write off fractional dimensions.

Good discussion! ;)

A excellent comment at the link:

In Tony's article he persists in saying that the series is the Reimann zeta function, even for s=-1, which is plain wrong. The analytically continued function zeta* spliced onto the domain of convergence (of the series) does have the value -1/12 at s=-1, but it is no longer that sum in the new domain; the two functions differ substantially in that domain extension. If the physicist wants to use analytic continuation to change the result that the original mathematical model gave, which had already shown that the model didn't work for the situation that it attempted to describe, then there needs to be a justification for the change, instead of just saying "Oops, my prediction is outside its domain of validity, so I must change the rules to flatten the function out in a way that violates my actual model, while pretending that the model hasn't changed."

In layman's terms, there are rules that must be followed to do infinite sums, and the physicists violate those rules to make the sum "work" with their theory.