Apologies if this is a dumb question, but aren't all computations inherently serial? In that a Turing machine performs operations serially?
No. "inherently serial" refers to problems that are specified serially and can't be spend up by parallel processing. The sum of a set of N numbers is an example of a problem that is not inherently serial. You can use parallel reduction to perform the computation in O(log(N)) time on an idealized parallel computer but it takes O(N) time on an idealized serial computer.
And, it turns, exactly which problems are really are inherently serial is somewhat challenging problem.
But addition with floats (not reals) is non associative.
In lambda calculus, disjoint redexes can be reduced in parallel.
And in interaction nets, all active pairs can be reduced in parallel [1].
But I'm not aware of what "inherently serial" means. The right idea likely involves talking about complexity classes. E.g. how efficiently does a single Turing machine simulate a product of Turing machines? An inherently serial computation would then be something like a problem where the simulation is significantly slower than running the machines in parallel.