Mathematical Rubbish
Most recent answer: 06/16/2014
- Anonymous
You're right that it's rubbish, sophisticated rubbish. I'll answer from a math point of view, because that seems more appropriate for a math problem.
1. As you say the series 1-1+1-1....simply does not converge to any value. There are ways of regularizing such sums that can lead to conversion, but that's a different process, not simple summation. Here, for example, one could multiply the Nth term by exp(-aN), sum, then let the parameter a→0. That sort of recovers the initial sequence, and gives 1/2 for an answer. It's bogus to say the answer is 1/2, however, without including some account of the procedure used to get that.
2. Again, the new series is one that does not converge. If you try to make it converge by using some procedure like the one above, you run into problems because the shift means you're multiplying each part by a different exp(-aN). It's a reminder that you have to define what you're doing, otherwise you can just make up any answer.
3. I believe this is all based on some calculations in which, for some parameter values, the desired function (Riemann zeta) looks just like an infinite sum. If you look at the function for other parameters, you get other values (e.g. -1/12) that are correct for the initial physics problem. Then if you pretend that the function is still an infinite sum for those parameters and write down what the infinite sum would be, as if you could still use the same recipe for translation, you get the nonsense sums of the video.
4. I don't know why Larry Krauss decided to ham it up by peddling the bogus claim. Usually he makes a lot of sense.
Mike W.
(published on 06/16/2014)