[Fractal Turing Machines] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Fractal Turing Machines
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Posted by: yottzumm
So what If I had a Turing machine, that instead of going left and right by one symbol, went left and right by a fractional amount, such that under the read/write head, there were two partial symbols instead of a full symbol. Let's call this a fractal turing machine. Isn't this how the real world works? Isn't a classical Turing machine something that's made up, and not based on reality? It's just that we've discovered these thing called transistors that allow us to think in digital ways.
Thinking about a Turing machine in terms of cellular automata, I might imagine a single symbol being replaced by 2 symbols, and so on (quadtrees, octrees etc). This would be another kind of fractal Turing machine.
Posted by: yottzumm
This sounds like Zeno's Paradox to me! So Zeno's paradox applies to computability!
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