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I'm sorry that my understanding of set and computation theory is lacking. Please excuse my ignorance while I study up on the topic further. But, I do believe t

by kefka 11y ago

I'm sorry that my understanding of set and computation theory is lacking. Please excuse my ignorance while I study up on the topic further. But, I do believe the original commenter misunderstood my question. Why is it that we humans, when armed with how a computer works, can identify halting problems? Why do we not get stuck in a loop when studying a potential halting problem? What allows us to make the intuitive leap past that? And to follow up, what are the implications about "brains are 10^10 200Hz computers in parallel" hypothesis?

eli_gottlieb 11y ago
>But, I do believe the original commenter misunderstood my question. Why is it that we humans, when armed with how a computer works, can identify halting problems? Why do we not get stuck in a loop when studying a potential halting problem? Well, given my current understanding, I'd say it's because human beings reason inductively. We pick up new axioms by observing our environment, which includes things like equations and programs. Since we reason inductively, we're only bound by incompleteness theorems for phenomena too random/complex for our current understanding. We "catch up" eventually to be able to solve computability problems, at least to some degree.