Essays, Analyses and Meditations

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Finite States and Conscious States

  • The turtle starts a few seconds before Achilles. Achilles is the fastest runner in the world. The turtle is the slowest animal in the world. Achilles starts running. By the time Achilles reaches the point where the turtle is the turtle has moved to a new point ahead of Achilles. By the time Achilles reaches this new point the turtle has moved to a new point ahead of that point. And so forth. Achilles gets closer and closer, but logically there is no way that he can pass the turtle because the turtle is always a tiny step ahead of where it was, which is where Achilles is now.
  • Zeno's paradox is about how a discrete set of steps yields a continuum, how a finite space can have an infinite number of events. We never really solved that paradox. The mathematical proofs that we take for granted are not truly proofs: they just provide a definition for the paradox.
  • I wonder if the mystery of how consciousness arises from brain states is related to Zeno's paradox: how do a number of finite brain states give rise to the continuum of consciousness? A set of (neuro)physical states always remains a set of (neuro)physical states and logically cannot become a conscious state just like Achilles can never pass the turtle.
Proof-edited by Alexander Altaras