Nitpick: A change of basis might also be combined with a projection into a subspace. In the example, if one doesn’t care about animals, or about the long term future at all, then instead of the volume of the cuboid they’d just consider the area of one of its faces.
Another nitpick: The ratio of humans to animals would depend on the specific animals. However, I sort of feel that the high level disagreements of the sort jackmalde is pointing to are probably in the ratio of the value between a happy human life and a happy cow life, not about the ratio of the life of a happy cow to a happy pig, chicken, insect, etc.
Nitpick: A change of basis might also be combined with a projection into a subspace. In the example, if one doesn’t care about animals, or about the long term future at all, then instead of the volume of the cuboid they’d just consider the area of one of its faces.
Another nitpick: The ratio of humans to animals would depend on the specific animals. However, I sort of feel that the high level disagreements of the sort jackmalde is pointing to are probably in the ratio of the value between a happy human life and a happy cow life, not about the ratio of the life of a happy cow to a happy pig, chicken, insect, etc.