Imaginary numbers are the proof that even in mathematics you can discover stuff even though you don’t understand what you have found. Complex numbers encode rotation.
Yup. When you have a circuit that is not purely resistive the inductive or capacitive load causes the voltage and current to not be in phase. It looks like ohms law is being violated. However the missing part of the energy is in the imaginary component to be returned latter.
Ever since I went down a particularly nasty rabbit hole and came out with a tenuous grasp on quaternions, imaginary numbers started feeling very simple, familiar and logical.
Yeah. The thing that made me “get” quaternions was thinking about clocks. The hands move around in a 2d plane. You can represent the tips position with just x,y. However the axis that they rotate around is the z axis.
To do a n dimensional rotation you need a n+1 dimensional axis. So to do a 3D rotation you need a 4D axis. This is bassicly a quat.
You can use trig to get there in parts but it requires you to be careful to keep your planes distinct. If your planes get parallel you get gimbal lock. This never happens when working with quats.
I still maintain that quats are the closest you can get to an actual lovecraftian horror in real life. I mean, they were carved into a stone bridge by a crazy mathematician in a fit of madness. How more lovecraftian can you get?
Imaginary numbers are the proof that even in mathematics you can discover stuff even though you don’t understand what you have found. Complex numbers encode rotation.
Yup. When you have a circuit that is not purely resistive the inductive or capacitive load causes the voltage and current to not be in phase. It looks like ohms law is being violated. However the missing part of the energy is in the imaginary component to be returned latter.
Ever since I went down a particularly nasty rabbit hole and came out with a tenuous grasp on quaternions, imaginary numbers started feeling very simple, familiar and logical.
Yeah. The thing that made me “get” quaternions was thinking about clocks. The hands move around in a 2d plane. You can represent the tips position with just x,y. However the axis that they rotate around is the z axis.
To do a n dimensional rotation you need a n+1 dimensional axis. So to do a 3D rotation you need a 4D axis. This is bassicly a quat.
You can use trig to get there in parts but it requires you to be careful to keep your planes distinct. If your planes get parallel you get gimbal lock. This never happens when working with quats.
I still maintain that quats are the closest you can get to an actual lovecraftian horror in real life. I mean, they were carved into a stone bridge by a crazy mathematician in a fit of madness. How more lovecraftian can you get?