Why does Euler love studying infinite series? Because studying infinite series is essentially exploring the boundaries of human cognition. Convergence to invariants is the pathway from finite cognition to understanding the infinite world. But as times evolve, the boundaries between convergence and divergence become increasingly profound. Convergence invariants shift from static to dynamic, from rational numbers to transcendental numbers, to linear functions. Bitcoin is a form of linear convergence. It converges into a linear time mechanism formed by Nash's non-cooperative game, dual Turing ordinal logic system.