Dunbar’s framework highlights the challenge of maintaining large, stable social networks given cognitive constraints. Expanding on this, I propose that fractal social networks function as lossy compression algorithms, efficiently reducing the complexity of social storage and retrieval. Rather than tracking all relationships explicitly, individuals rely on hierarchical abstractions and transitive inference, shifting storage complexity from
$O\left( {{N^2}} \right)$ to
$O\left( {N\log N} \right)$. This insight suggests broader implications for cognitive evolution, institutional organization, and artificial intelligence.