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fundamentally different

I agree that Nakamoto Consensus is special, but only because it abstracts the process that life has been engaged in since there emerged selection mechanisms.

And I agree that all other forms of proof of work are contingent on their environment and context, where as Nakamoto Consensus not, being mathematical and computational.

It's the difference of analogue and digital, or Plato's Nous vs Soma.

But we've been aiming towards and purifying our consensus mechanisms for millennia. The Rei Stones of Yap, the megaliths, sport, democracy, the education system, these are all proof of work systems with a clear and unreliable trend towards attraction, from the physical to the digital.