How Big Will the Intelligence Explosion Be?

A software intelligence explosion (SIE) = fully automating AI R&D, with hardware held fixed. Better AI → more effective R&D labour → faster progress → better AI, looping until the effective algorithmic ceiling binds. Davidson and Houlden’s Monte Carlo samples the four parameters above from wide distributions and reports how often the loop compresses years of AI progress into months. This lab compresses that logic into a deterministic toy: same four inputs, same directions, anchored to their headline numbers — ~57% chance ≥3 years of progress lands in ≤1 year, ~41% in ≤4 months, ~18% for ≥10 years in ≤1 year, ~12% in ≤4 months.

For scale: 3 years of AI progress ≈ 1000× effective compute — software has historically doubled effective compute roughly every 3 months.