Virtually every language I know of is basically a variation on a theme: you create variables and functions, then manipulate them using conditionals and other constructs. I understand Functional Programming and the like are somewhat different from ‘traditional’ languages, but underneath they are almost the same. You are still working with variables (somewhat, even though they are immutable and such), and creating functions.
Is there any language or system that completely does away with what we tend to use now and has a completely different approach?
Not a language per se, but analog computers are in some ways quite different from the more popular digital computers.