‘Adding manpower to a late software project makes it later.’ A new hire must be trained (stealing time from the people who know), and every extra person adds not one line of communication but many — the channels grow as the SQUARE of the team. Past a point, the coordination cost outruns the extra hands. Slide the team size and watch output peak, then sink.
Brooks’s Law (The Mythical Man-Month, 1975): people and months are not interchangeable. Two costs break the swap — ramp-up (new members are unproductive while learning and consume mentors’ time) and communication: n people have n(n−1)/2 pairwise channels, so coordination overhead grows QUADRATICALLY while productive capacity grows only linearly. Net output therefore rises, peaks, and then FALLS as added coordination outweighs added hands — and on a late project the ramp-up hits precisely when there’s no slack. A fail-loud self-check throws unless the channels grow as n(n−1)/2 and net output eventually declines with team size. ◆ real software-engineering economics, node-verified.
A toy net-output = n − (channels × cost) model (the exact quadratic channel count and the peak-then-fall shape); real projects partition work to limit channels — the coordination-overrides-hands mechanism is exact.