Explore the fascinating world of chaos theory and geometry in this comprehensive lecture by Tim Palmer at The Royal Institution. Delve into how fractal geometry bridges Newtonian and 20th-century mathematics, understand the concept of state space, and discover the predictability of chaotic systems. Learn about applying chaos theory to hurricane prediction, examine the Bell experiment's implications for quantum physics, and investigate the application of fractals to Bell's theorem. Gain insights into how the geometry of chaos can explain our uncertain world, from weather and pandemics to quantum physics and free will, ultimately challenging the notion of spatial reductionism.