The origins of cliff dancing actually date all the way back to before the Information Age. Occasional adventurers and daredevils would attempt to climb the larger multi-story structures being constructed at the time. While early instances were virtually never sanctioned by local authorities, and often ended in arrest and various penalties, the era's obsession with heights and myth-fictions built around the products of its own technology (as well as the desire of individuals for fame and acclamation) kept the practice alive. Things changed in the early Information Age itself, when advances in equipment and evolving social structures lead to some pioneering artists and their supporters transforming what had been limited feats of climbing skill into a true art-form, incorporating dance, acrobatics, and multiple participants into the climbing event. The goal became not just to climb to a great height, but to perform there. Over time, the would-be adventures and artists graduated from climbing city towers to climbing entire arcology cities but the basics remained the same.
One of the most famous instances of cliff-dancing took place in 2132c.e. (164 AT) at the dedication of the third Terran space elevator. As part of the dedication ceremony, the Republique du Tchad presented a series of performances by troupes of acrobats, climbers, and parachutists who used a combination of geckotech pads, buckyfiber cables, gliders, and spectacular lighting effects to entertain the dedication crowds while suspended as much as a kilometer above the ground on the side of the elevators central boosting tower. The effect on the crowds (usually watching via a combination of magnifying lenses and remote mounted holocams) was overwhelming and from this point forward cliff dancing was to have its place assured among the pantheon of performance art.
Over the following millennia, cliff dancing evolved from avant garde spectacle, to classical performance school, to dismissed conventional exercise, and back again. During this period it split into a number of different styles and schools, from "traditional" groups who entertained on the outside of buildings and space elevators, to those who worked in vacuum on the underside of large rotating habitats, to those who performed only on actual natural cliffs, and so on. In addition, each of the various sub-groups within the art form could be guaranteed to encompass sub-groups of its own, based on factors such as the preferred gravity (e.g., greater than or less than Earth standard), local season, day or night time performances, etc.
The advance of technology continued the development (some would say fragmentation) of the art form, with some groups adding such things as wingpacks, or fancloth, or cybernetic balance augmentations to their repertoire of tools, while others condemned these additions as a corruption or dilution of the true spirit of the art. Perhaps the starkest example of this differentiation was the split over the use of Backup technology when such became generally available. While most groups adopted Backup devices along with other safety systems, the Purist school rejected (and continues to reject to this day) such "anesthetizing fripperies" and has spent literally thousands of years performing without the benefit of technological restoration (admittedly the rate of turnover in the school is rather higher than in any of the others).
In the Current Era, cliff dancing continues to be one of the great examples of classical art, enjoyed in all of its forms by billions of sophonts across the Civilized Galaxy.