"The proof-of-work is a Hashcash style SHA-256 collision finding. It's a memoryless process where you do millions of hashes a second, with a small chance of finding one each time. The 3 or 4 fastest nodes' dominance would only be proportional to their share of the total CPU power. Anyone's chance of finding a solution at any time is proportional to their CPU power."
- Satoshi Nakamoto
He also refers to the proof-of-work as a "partial pre-image of zero", which is an interesting way to think about it.
https://www.metzdowd.com/pipermail/cryptography/2008-November/014858.html
"... Political freedom is the resultant of unresolved conflicts among various sections of the élite. The existence of these conflicts is in turn correlated with the interplay of diverse social forces... "
- James Burnham, The Machiavellians
So: Bitcoin produces a species of political freedom via a cyclic (by which I mean permanent & dynamic) Burnham unresolved conflict between its miners.