Physical prime factorization ⛅
Prime factorization is a well known and interesting math problem. Primes — “the atoms of math” — form the basis for most cryptographic algorithms to date; Internet security is based on the premise that factorization is hard for large (1024 bits in case of RSA-2048) primes.
I once came up with a physical method for calculating primes, as illustrated above: Fill a square container with a fluid volume representing half the number to factor (35 in the above case). Gradually turn the device such that the thin conductive layer tests subsequent combinations of factors; when the tilt reaches a valid pair of prime factors, the light will turn on.
Unfortunately, it is estimated that there are only between 10⁷⁸ to 10⁸² atoms in the known universe — so primes of order 2¹⁰²⁴ are a bit hard to represent accurately, today in 2021. Perhaps one day we will be able to split matter into sub-atomic particles to such a degree — CERN has reported 59 new particles over the past 10 years — though one could wonder if the sun would still be shining by the time they are done creating collisions. How could we accelerate the LHC discovery process?
Any problem can be solved given enough resources (including time), but I have discovered that the real problem I would like to solve in my lifetime, is connecting with interesting people — like yourself — who would not be appalled by a somewhat “silly” or “geeky” article about hard math problems, but instead would see the positive intent behind it: The stars behind the clouds ⛅.