>>14363725Tensors and multivectors are two different paths you can follow to generalize vectors. I'm not sure if it's possible to unify them, since multivectors allow for the summation of scalars, vectors, bivectors etc, while these kinds of inhomogeneous sums are usually not allowed with tensors. Scalars, vectors, bivectors etc in isolation can each be represented as tensors though, so it might be possible to emulate the inhomogeneous sum somehow.
>>14363988>>14364499Abstraction is like a <= trade-off between depth and breadth. Usually you sacrifice depth for breadth:
>A persian and a dobermann>A cat and a dog>A mammal and a mammal (this point is special, since the beyond here the things are no longer distinguishable)>An animal and an animal>A thing and a thingIf I go to the vet and tell them my thing is limping, that's not going to be anywhere near as useful to them as telling them my dobermann is limping. Abstraction in and of itself isn't the holy grail, the holy grail is zero-cost abstractions, where we don't need to sacrifice depth in exchange for the gains in breadth. There might be additional trade-offs in other contexts too, such as in programming where abstraction also tends to come at the cost of performance. Again, the holy grail here is zero-cost abstractions, not necessarily abstractions in and of themselves.
