Thinking a lot about ratchets lately. Internal and external. Ratchets are more fundamental than clocks. Things that can only grow in one direction, and reversed only via destruction.
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Would you still call it a "ratchet" if it's growth slowed from exponential to linear?
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I thought about that quite a bit actually. It's a functionalist concern: ratchets are mechanisms. If they hit diminishing returns regimes, they cease to function so you need a new one. It has to be a "clock" in some sense, an unbounded positive definite f(time) on average.
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Like... zeno's paradox is not a useful ratchet... 1, 1/2, 1/4,.... --> 2. At some 1/2^n < delta it loses "traction" for driving other processes
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That seems like a pretty narrow definition. Narrow enough at least that I can't think of anything in nature that would qualify.
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Okay restrict domain and range to “till death” and allow composition of a ratchet function series that’s piecewise continuous.
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