Avogadro's Number and the Stars – An Anthropic Near Miss
Avogadro's number (10^23) is close to the cube of the Planck-to-proton-mass ratio (~10^61), which also approximates the number of protons in the Sun. This coincidence relates to stars being just massive enough to sustain fusion, linking fundamental constants to stellar physics.
Background
For the Sun to start burning hydrogen, protons must first fuse into deuterium via the weak nuclear force — an extremely rare process. The reaction rate depends on a fundamental constant (the Fermi coupling constant), and if it were just a few percent weaker, the Sun would never ignite, making life as we know it impossible. Yet the rate is not vastly larger than needed; it's only about 10¹⁶ times the minimum. That may sound huge, but in physics numbers often span 10¹⁰⁰ or more. The fact that this number is "only" 10¹⁶ — a so-called "anthropic near miss" — has been cited as evidence against the idea that our universe is fine-tuned for life. The post (by physicist Anders Sandberg) re-examines the calculation and argues the near miss is likely not a coincidence but a necessary consequence of stellar dynamics: stars that fuse hydrogen too easily would burn out too fast for planets and life to form, setting a natural upper bound on the reaction rate. This shifts the puzzle from "why is the rate so close to the minimum?" to "why is stellar structure what it is?" — a question with plausible astrophysical answers, not requiring fine-tuning.