Oracle-bone 以 showed a person carrying or wielding an object — using it. The meaning stayed abstract and load-bearing: by, with, according to, in order to. It's grammar's quiet workhorse.
可以 'can, may' is the everyday yes. 以前 'before now' and 以后 'after now' split all of time in two. 以为 means 'thought (wrongly)' — the word for realizing you were mistaken. Few characters do more invisible lifting.
A person putting a tool to use — BY MEANS OF; it makes 可以 'CAN'.
以前/以后 'before/after' literally read 'taking the front / taking the back' — Chinese time faces the past: what came before is in front of you, because you can see it.