Throw more workers at a job and it finishes faster — but only the part that can be split. Whatever must be done in sequence becomes a hard floor on the time, and a ceiling on the speed-up. Ten thousand workers can’t beat a 10% serial job by more than ten times. Slide the workforce and hit the wall of the unshareable.
Amdahl’s Law: if a fraction p of the work can be parallelised and (1−p) must stay serial, then N workers give a speed-up of 1 / ((1−p) + p/N). As N grows the parallel term vanishes but the serial term (1−p) remains, so the speed-up is capped at 1/(1−p) no matter how many workers you add. With p=0.9 the ceiling is 10× — forever. A fail-loud self-check throws unless the speed-up rises with N yet never reaches the 1/(1−p) ceiling — the hard limit of throwing bodies at a problem.
Amdahl fixes the PROBLEM size; Gustafson’s law notes that bigger machines usually solve bigger problems, softening the ceiling; and coordination overhead can make added workers HURT. The 1/((1−p)+p/N) formula and its ceiling are exact.