"Why are amplitudes complex?" and "why should amplitudes have been complex numbers?" are not the same question as "Why do we choose to use complex numbers in ou

"Why are amplitudes complex?" and "why should amplitudes have been complex numbers?" are not the same question as "Why do we choose to use complex numbers in our description of the universe?". Aaronson is using "amplitude" to refer to things out there in the external world. He explicitly refers to other ways the universe could have been: "quaternionic QM [i.e., QM with quaternion amplitudes] allows superluminal signaling". I don't know what to tell you except to read more carefully. It's philosophy of physics.