Lean proofs are computational verfications full stop. There is no math philosophical utilization that is integral to the core of proofs. This is akin to saying MCMC cracked open physics. At the end of day Google gets more subs and journals get flooded with noise drowning out discovery that is washed away by screening AI. If that ain't pi.
Lean proofs are computational verfications full stop. There is no math philosophical utilization that is integral to the core of proofs. This is akin to saying MCMC cracked open physics. At the end of day Google gets more subs and journals get flooded with noise drowning out discovery that is washed away by screening AI. If that ain't pi.
@martinmbauer Unfortunately, Lean proofs are not a breakthrough in technology. And should not viewed in such light. Math has been conceptual broken for a while. These gotcha moments are just "Turing" on the lights. The brute force computational answers or negations.
@martinmbauer Unfortunately, Lean proofs are not a breakthrough in technology. And should not viewed in such light. Math has been conceptual broken for a while. These gotcha moments are just "Turing" on the lights. The brute force computational answers or negations.
First, the speed of light is not a limit in Einstein's theories. There is nothing in these theories that forbids faster than light travel. It's merely that these theories also say it takes an infinite amount of energy to accelerate from below to above the speed of light.
Adding time dilation to moment in GR seems quite ad hoc especially considering neutrinos or neutrinos plus ice (with a big push). It is interesting that GR or QFT do not derive the speed limit but adamantly state that it can not be broken in a vacuum. Oh yeah what is a vacuum again! Where is it again?!
The Drake equation is too coarse if technological civilizations are spatially clustered and temporally intermittent. It is a function the sparse fermion distribution in the universe. There is too much scatter as well. What matters is the overlap between civilization density, their EM-emitting lifetime, and our detection window; if those windows are short or misaligned, mutual detectability can be rare even when civilizations are not intrinsically rare.