The study of jammed systems began as a culinary curiosity in 1727, when the Reverend Stephen Hales studied how peas pack when compressed in an iron pot. Fill a pot with peas and you can run your hand through them, because they can flow out of the way much like a liquid would. But as pressure, and thus the density, is increased, you will find that there is a critical point, above which the peas “jam” into a stable amorphous solid. Unlike standard phase transitions the jamming transition is a non-equilibrium phenomenon that happens deep inside the glass phase. Although entirely unphysical, a generalized understanding of the random packing of spheres (a convenient model system for jamming) in high dimensions can shed light on the low dimensional case. By separating the general effects from the idiosyncratic at each dimension it may be possible to uncover simple principles which are masked in dimensions two and three. We find evidence of a newly discovered "geometric" phase transition accompanying and underlying the jamming transition with upper critical dimension of 3 and lower critical dimension of 2.