https://en.wikipedia.org/wiki/Mathematical_coincidence
See also this blog: https://martouf.ch/tag/coudee-royale-egyptienne/
One french royal cubit ≈ one egyptian cubit ≈ about π/6 meters. One royal span ≈ 1/5 meter = 20cm.
I'm wondering whether some of these coincidences could be explained by the anthropic principle, which deals with these quasi-equalities, for instance:
>An excited state of the 12C nucleus exists a little (0.3193 MeV) above the energy level of 8Be + 4He. This is necessary because the ground state of 12C is 7.3367 MeV below the energy of 8Be + 4He; a 8Be nucleus and a 4He nucleus cannot reasonably fuse directly into a ground-state 12C nucleus. However, 8Be and 4He use the kinetic energy of their collision to fuse into the excited 12C (kinetic energy supplies the additional 0.3193 MeV necessary to reach the excited state), which can then transition to its stable ground state. According to one calculation, the energy level of this excited state must be between about 7.3 MeV and 7.9 MeV to produce sufficient carbon for life to exist, and must be further "fine-tuned" to between 7.596 MeV and 7.716 MeV in order to produce the abundant level of 12C observed in nature.
Source: https://en.wikipedia.org/wiki/Triple-alpha_process#Improbabi...
The idea goes like this:
1. A more fundamental aspect under the anthropic principle which underpins the existence of complex life and intelligent observers is the quasi-alignment of values such as the fundamental constants in physics within a short margin.
2. If you consider the universe to be the product of a random sampling process over these constants (either real or virtual, it occurred many times or just once), and given the fact we exist, which implies an abundance of coincidences, the maths seem to tell us that we should expect to observe superfluous coincidences that are non-functional for the appearance of complex life, rather than the strictly minimal set of functional coincidences necessary for its emergence.
3. This implies that coincidences and pattern seeking are not just features (or bugs) of our complex minds but are present in the universe latently since it is not just fine-tuned for the emergence of complex life but for the presence of coincidences such as these https://medium.com/@sahil50/a-large-numbers-coincidence-299c....
4. It may be even testable by running computer experiments relying on genetic programming/symbolic regression to see whether there is something special about the value of physical constants in our universe when compared to the value they would have in other universes. I think such experiments should factor the fact that not all equations with the same mathematical complexity (number of operands and operators) have the same cognitive complexity. Indeed, if you look at the big equation in the link above, you'll remark that it can be further compressed into a/b = c/d (where a is the photon redshift radius for instance). So I guess you'd also have to throw into the mix Kolmogorov algorithmic complexity to assess this aspect (which is in fact used in some cognitive theories of relevance to tackle this kind of stuff to the tune of "simpler to describe than to generate")
Thoughts ?