[toxik]

You can reduce in parallel. That was the whole point of MapReduce. For example, the sum abcdefgh can be found by first ab, cd, ef, gh; then those results (ab)(cd), (ef)(gh); then the final result by (abcd)(efgh). That's just three steps to compute seven sums.

[bjourne]

No, you can not. Your example is correct only if addition is associative. And it is not always associative. Hence the need for higher abstractions, where you model commutativity and associativity of certain operations.