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Anonymous Monk
<blockquote><i>Constant speedups are one thing, but if you have a bad algorithm (like blindly searching a list to implement an associative array), the problem will scale poorly no matter how fast your computer is. The only way a futuristic computer running a linear-time algorithm could keep up with another computer running a constant-time algorithm would be if it could somehow compress time.</blockquote></i>
The good thing about these types of mental exercises is that it helps expose our shared set of (mostly hidden) assumptions. For example, we like to think that we can do array lookup (and by extension, hash lookup) in O(1) time. Geometrically though, RAM is really a tree structure, and we have wait for signals to propogate through O(log n) row and column decoders. But even this is optimistic, because if bits take up a finite volume (and the speed of light is constant), then we're really looking at O(n**(1/3)) time for a lookup.
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