We discuss the concept of extradimensional bypass as it was developed by the late theoretical biologist Michael Conrad. An evolving system that optimizes its performance by gradient ascent (hill climbing) can avoid being trapped in local maxima by increasing the effective dimensionality of its search space. Many local maxima may become saddle points in the higher dimensional space, such that gradient ascent can continue unimpeded. Extradimensional bypass as a concept has parallels in theories of open-ended learning and functional emergence, where new structural, functional, and informational primitives can increase the effective dimensionality of material systems.