I’m interested in effective altruism and longtermism broadly. The topics I’m interested in change over time; they include existential risks, climate change, wild animal welfare, alternative proteins, and longtermist global development.
A comment I’ve written about my EA origin story
Pronouns: she/her
“It is important to draw wisdom from many different places. If we take it from only one place, it becomes rigid and stale. Understanding others, the other elements, and the other nations will help you become whole.” —Uncle Iroh
Well, if we allow complex numbers, a lottery over all negative utilities would result in a real geometric mean, but for a mixture of positive and negative utilities, we’d get imaginary numbers.
For example, consider lottery A with Pr(-5) = 0.5, Pr(-3) = 0.3, and Pr(-2) = 0.2. Then
G(A)=(−5)0.5⋅(−3)0.3⋅(−2)0.2.
The (-1)’s factor out, giving us
G(A)=(50.5⋅30.3⋅20.2)⋅(−1)0.5+0.3+0.2=(50.5⋅30.3⋅20.2)⋅−1,
which is a negative number.
Now consider lottery B where one of the utilities is positive—e.g. we have Pr(-5) = 0.5, Pr(3) = 0.3, and Pr(-2) = 0.2. Then we’d get
G(B)=(−5)0.5⋅30.3⋅(−2)0.2
=(50.5⋅30.3⋅20.2)⋅(−1)0.5+0.2
=(50.5⋅30.3⋅20.2)⋅(−1)0.7
=(50.5⋅30.3⋅20.2)(cos(0.7π)+isin(0.7π)),
which is an imaginary number. The magnitude is equal to the weighted product of the magnitudes of the individual utilities, but the argument (the angle it makes with the positive real axis on the complex plane) is π times the total probability mass of any negative utilities. This makes comparisons impossible because the complex plane is an unordered set.