There is a connection to turbulent Euler solutions as counterexample to P=NP in Eschers's descending-ascending Monks, who walk around either descending or ascending all the time, yet coming back to where they started again and again. If you believe this is an illusion, then you have a good chance in understanding the counterexample.
Recall that turbulent dissipation forward/backward always means loosing energy and thus descending all the time. And then you cannot get back to where you started, unless you believe in the illusion of Escher's monks...Thus you cannot recover the initial state from a later state.
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