A river network remembers a rainstorm not by the map of its channels, but by the volume of water. Powerful currents along winding paths carry the memory far downstream. Jumble the flows randomly, and the water quickly forgets where it came from. It's the same in any complex network: the strength of connections matters more than the layout.

An analysis of 34 real networks showed that nature and technology have specifically organized flows to slow down forgetting. Strong interactions align along major pathways, carrying echoes of the past. This slows the growth of entropy — a measure of disorder discovered by Boltzmann. The slower the entropy grows, the longer the network holds onto memory.

Computer simulations and machine learning revealed four types of memory — from blurry to instantaneous. The directionality of connections, akin to quantum information scrambling, sets the rate of forgetting. This aligns with quantum thermodynamics, where heat and information are fused together. Andrey Markov claimed that the future depends only on the present, but here the past exerts influence for longer. Even the humble E. coli bacterium is wired to learn from the past. The Photosystem I of plants and the U.S. airline network store the past with the same sharpness — a microscopic machine and a giant hub obey a single law.