Fractals are patterns that are the same scaled up as scaled down—broccoli, coastlines, and biological systems exhibit this property. Our bodies use fractals to gain the 1/4 power scaling laws by using the body's three dimensions plus fractals as a fourth dimension to gain advantages. This self-similarity across scales reveals deep mathematical structures underlying natural and social systems.

Scaling is often non-linear. The bigger the animal, the fewer calories it needs in proportion. The larger the city, the higher GDP per capita we expect—not perfect linear scaling. Understanding these non-linearities is crucial for predicting how systems behave as they grow. Economies of scale mean the larger you are, the less you need; increasing returns to scale mean networks grow more valuable with size.

Boundaries only exist within models but you must draw them—they're completely arbitrary yet key to differentiating the system. Most arguments come over boundaries: rich and poor, border disputes, in-group versus out-group. We must understand boundaries aren't real in ultimate sense, but they're key chokepoints and interfaces that determine system behavior.