Just saw some discussion on the difference between non-deterministic algorithm and random algorithm. And I found a very interesting metaphor saying

''Deterministic: I choose.

Non-deterministic: Someone choose for me.

Random: No one choose.''

where choice seems to be a synonym of decision, which suddenly reminds me of the famous Axiom of Choice. Regardless of its fancy name, it seems that le truc is introduced by the mathematicians to overcome their decidophobia.

No it's not a joke of OCD. On the contrary, it involves our basic acknowledgements. What means a decision? What means freedom? What means fate? What means randomness? This constructs a main part of western philosophy. In this metaphor, what is the difference between Someone and I? If no one choose then how? Here, someone cannot mean the others I don't and I can't know, it means something beyond me and my species, yes like the western god. Another formulation of non-deterministic Turing Machine is an ordinary Turing Machine equipped by an extra hint occuring somehow. The machine simply checks if the hint is right or wrong. This formulation obviously made a reservation for the God. A famous saying goes: only children make choices, the adult wants them all. But maybe the fact is: only humans are concerned about choice, the God does not even care. The saying, actually reflects the dream that human wants to transcend its pitiful finiteness and to imitate the God. The Axiom of choice, together with the mysterious non-deterministic Turing machine and others, are all such things. However, any such effort will push the God from the heaven into the void in the end.