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RomanDavis comments on Dragon Ball's Hyperbolic Time Chamber - Less Wrong
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Think of any real-world problem that takes one day on modern hardware. When computers were 365 times slower (that is, 12 - 13 years ago), it would have taken one year to solve such problems.
Don't you think there is any real-world problem that would benefit from 365x faster hardware, even if you can interact with it only once a day?
(Even if individual tasks take less than one year to complete, you can pool several of them and run them serially on the 365x computer)
The first thing that comes to mind is evolutionary algorithms, which eat up tons of ram and keeping running at a decent pace while keeping track of dozens variables is an enormous engineering challenge.