Tiny differences in starting conditions can produce wildly divergent outcomes

Gleick recounts meteorologist Edward Lorenz's accidental discovery, made while running a simplified weather simulation on an early computer, that rounding a input value by a seemingly negligible amount produced a completely different forecast outcome than the unrounded version, despite the underlying equations being entirely deterministic. This sensitivity to minuscule differences in starting conditions, later popularized as the butterfly effect, meant that even a system governed by precise, knowable mathematical rules could become practically unpredictable over time, because no measurement of real-world initial conditions could ever be precise enough to avoid this divergence. Lorenz's finding upended assumptions common in classical physics that more precise measurement and more powerful computation would eventually make complex systems like weather fully predictable, showing instead that some systems carry an inherent, mathematically guaranteed limit on long-range predictability regardless of computational power. Gleick treats this discovery as the founding insight of chaos theory, since it revealed that determinism and predictability, long assumed to go together, could actually be decoupled in certain kinds of systems. Takeaway: perfect rules don't guarantee perfect predictions when small errors compound.