Deterministic Chaos
Edward Lorenz · 1963
"Fully deterministic systems — with no randomness anywhere in their equations — can still become practically unpredictable, because tiny differences in starting conditions grow exponentially over time until prediction becomes impossible."
A meteorologist rerunning a weather simulation in 1961 rounded one input from six decimal places to three, expecting a negligible difference. The forecast came out completely different — and chaos theory was born.
Lorenz's simplified model of atmospheric convection was entirely deterministic — the same starting conditions always produced the same output, with no randomness in the equations at all. Yet a minuscule rounding difference in initial conditions, smaller than any real-world measurement could ever detect, produced wildly divergent outcomes after enough iterations. This 'sensitive dependence on initial conditions' — later nicknamed the butterfly effect — meant that even a perfectly deterministic, fully-understood system could be practically unpredictable beyond a certain time horizon, because no measurement of the starting state is ever infinitely precise. This reframed a huge class of real-world systems — weather, ecosystems, some economic and biological systems — as inherently limited in long-range predictability, regardless of how good the underlying model is.
What did Lorenz's 1963 discovery reveal about deterministic systems?
Read more about the topic
The explanation above is written with AI assistance. These are the originals — go to them to check it.
- Deterministic Nonperiodic FlowJournal of the Atmospheric Sciences, 1963
Entropy and the Second Law of Thermodynamics
"Every closed system trends toward disorder, and that one-way drift is the only law of physics that distinguishes past from future."