20) Which do you think is more or less rational, as practiced today? Math or physics?
Huh, this is an easy question. Mathematics is way, way more rational. Mathematicians keep a healthy sense of curiosity and they care about ideas and conceptual understanding beyond symbols. Physicists, as you just said, are much more careless about that.
For example, a paradigmatic example of this is the infamous statement that the sum of all positive integers somehow gives minus one over twelve.
It’s mostly physicists that enjoy dazzling their audience with this (and that should ring a bell if you remember how they favor nonsensical interpretations in quantum mechanics just because they look mysterious).
Instead, a proper mathematician, and I say proper, will hack this confusion into pieces by stating the simple truth, which is the job of a proper mathematician, by the way.
What happens in this particular case, is that the function which gives that value cannot be associated with an infinite sum in that case because that infinite sum representation of the function is valid for arguments strictly greater than positive one, actually, real numbers, and the argument giving minus one over twelve is negative one.
So, this infinite series representation does not apply to that argument. But, physicists prefer not to say anything about that, they conveniently omit it because it somehow spoils the fun, I think. So then they can keep the magic alive that somehow such an apparent contradiction could hold in the real world.
Ashna: If I remember correctly, that silly equation you mentioned originally came up in the context of string theory.
Juanma: Yeah, it is true. They get these infinite matrices. And there are the positive integers on the diagonal. So, they want to characterize the matrix by its trace, which is the sum of the elements in the diagonal. So, of course, they get the sum of all the positive integers.
End of Interview
That was the last question in this interview. There was more to his answer, but unfortunately, the audio in that part is very difficult to make out, so it was cut out.
So, that brings us to the end of this episode. Thanks for your very thoughtful and interesting answers, Juanma! We cannot wait to have you back on the show in the hopefully not very distant future!
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