Registered: Nov 2007
Posts: 5

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.

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Registered: Nov 2007
Posts: 5

This sounds like Zeno's Paradox to me! So Zeno's paradox applies to computability!

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