Amdahl said parallel speedup hits a ceiling because of the serial part — discouraging. Gustafson answered: in practice you don’t run the SAME job on more machines, you run a BIGGER job. Grow the workload with the workforce and the parallel part dominates, so speedup keeps climbing almost linearly. Both are right — they just ask different questions. Slide the worker count and watch Gustafson rise past Amdahl’s wall.
Amdahl’s Law fixes the problem size: with serial fraction s, speedup on N processors is 1/(s + (1−s)/N), which is CAPPED at 1/s no matter how many you add. Gustafson’s Law fixes the TIME instead and lets the problem grow with N (a bigger simulation, more data): scaled speedup S = N − (N−1)·s, which rises almost linearly with N and is UNBOUNDED. Neither contradicts the other — Amdahl asks ‘same work, faster?’, Gustafson asks ‘more work, same time?’ — and most real high-performance computing lives in Gustafson’s world. A fail-loud self-check throws unless Gustafson’s speedup keeps growing with N while Amdahl’s caps at 1/s. ◆ real parallel-computing theory, node-verified.
Both laws with a fixed serial fraction s=0.1 (the exact formulas); real scaling adds communication and memory limits that bend Gustafson too — the fixed-size-caps vs scaled-size-grows distinction is exact.