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Kindly comments on Pascal's Mugging for bounded utility functions - Less Wrong
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Whatever the information content is, unless you have an argument that it's actually infinite, it's going to be smaller than 3^^^^3.
Describe momentum in fixed space. It is acceptable to have an upper limit on momentum, provided that that limit can be arbitrarily high. It is not acceptable for two different vectors to be described differently.
I'm not sure what the smallest unit of angular measure is, or if it is continuous. If it is continuous, there's no way to describe momentum in finite bits.