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InquilineKea comments on Utility Maximization and Complex Values - Less Wrong
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What exactly do you mean by complex value? Do you mean vector values? (e.g. a complex number can be expressed as a 2-vector).
If you want to maximize utility, then yes, you need a way to compare between two different utility values, and you can only do that if your function outputs a scalar value. If it outputs a vector value, you can't do that unless you assign some function to convert that vector into a scalar. That function can be a 2-norm, p-norm, or really, any type of arbitrary function you like
He is referring to Eliezer's complexity of value thesis
It has nothing to do with complex numbers, which in turn have little to do with vectors if I understand my maths correctly.