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This curious and unexplained ability takes place in the "real world"
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I agree. I noticed the same thing. I liked the series, though I detested the end. It was truly a let down. Probably it does hint at layers of "reality."

However, what I'm saying is this: the computers in whatever real world exists might be vastly more complicated and vastly more powerful than the computers in THIS reality. Therefore, I think Dennett's argument is wrong - and pretty blatantly so.

I'm not sure how to turn this kind of conversation away from philosophy and into science. How could we detect that our reality is not real?