Turing machine is mathematical model for computation. Deterministic Turing machine (DTM) is computationally equivalent to Non-Deterministic Turing machine (NTM) but the time complexity may not be the same.
>What I'm ultimately interested in is if we, as humans, are operating in a realm that logic cannot operate in. If that makes any sense?
Any mix of logic and randomness is still a machine. You must assume something spiritual if you think there exist rational action without computation behind it. Randomness does not help there.
> You must assume something spiritual if you think there exist rational action without computation behind it.
I'm still uncertain i.e. spiritual. I'm finding, as I grow older, logic and reason fail to answer for my experiences. Whether that's a shortcoming in my own ability to comprehend logic and reason, or because logic and reason simply do not have all the answers, I do not know.
> Randomness does not help there.
The human condition, one might argue, emerged as a way to handle randomness. I suppose, at some level, if we were to remove all randomness from the universe, life would be pretty pointless (insomuch as life is not already pointless.)
Well, the future as a mystery, something to be discovered, not known in advance, depends on randomness. I would argue if life weren't random and we could see past, present, and future with perfect clarity, it would be a little pointless. Every action you took, you'd know the outcome before taking the action. It's boring.
There is no purpose of life, in my opinion. But with randomness it's a lot more intresting.
>What I'm ultimately interested in is if we, as humans, are operating in a realm that logic cannot operate in. If that makes any sense?
Any mix of logic and randomness is still a machine. You must assume something spiritual if you think there exist rational action without computation behind it. Randomness does not help there.