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Kindly comments on Boredom vs. Scope Insensitivity - Less Wrong
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It's not the overall growth rate of the function that becomes linear at high values; it's the local behavior. We can approximate: sqrt(1000000), sqrt(1001000), sqrt(1002000), sqrt(1003000) by: 1000, 1000.5, 1001, 1001.5. This is linear behavior.