- #1

PeterJ

- 27

- 0

I'm fascinated by the problem of deciding the Riemann Hypothesis. The trouble is, I'm not clever enough to understand it. The zeta function may as well be martian hieroglyphics and I have no idea what a diagonal lemma is.

I do have a good heuristic understanding the primes, however, and wondered whether there might be a way to understand the RH problem in more heuristic terms. This would require a massive simplification and maybe it can't be done, but at the moment I can't see why not. Complex (for me) mathematics often represents simple mechanical processes.

By 'heuristic understanding' here I mean that I know how the primes work. For a musician their behaviour is not hard to understand once the mechanism that generates them is understood. A correct (albeit not rigorous) heuristic proof of the TP conjecture is possible armed only with an understanding of multiplication. It is not the primes that are the problem for me it's the mathematics, it's translating the mechanics of the number line into equations, virtual landscapes and so forth.

I wondered whether it would be possible for me to approach the problem by reducing the zeta function to a black box. When we input a pair of numbers they are transduced into a new pair by some (for me) forever incomprehensible process. This would be a strictly deterministic process such that in principle it would be possible to backwards engineer the zeta function from a study of the behaviour of the inputs and outputs. Am I okay to think of the process in this way?

If this does actually represent the situation then the first thing I'd like to ask is what the inputs to the black box that produce the relevant zeros actually are, and which numbers have to be inputted in order to produce R's landscape. A very naive question, I know. Even asking sensible questions about the RH is difficult for a layman.

Also, would I be right to say that the zeta function acts like a resonator? Marcus du Sautoy's remarks about tuning forks and quantum resonators got me thinking. As an ex sound engineer I'm struck by the similarity between the way primes are produced and the way a plate reverb works. I even wonder whether a plate reverb might be a simple model of a quantum drum, but that's another story.

Anything that anyone can tell me about this problem that I can understand will be gratefully received. If I were younger I'd get some maths lessons but it's too late. Thanks.