User blog comment:Cloudy176/Forging R numbers/@comment-27516045-20160705001818

Good point, Peng. A system of naming numbers doesn't have to cover anything in the notation. As long as the notation is well defined, then all googolisms in it are well defined too. For instance, Bowers's naming system has large gaps (it is not obvious how you would name, say, {10,10,100,1,2} or {10,100(1,1)2} in Bowers's notation). Which brings up an interesting challenge...

Challenge, create a systematic naming scheme for Bowers' or Bird's array notation, adhering as closely as possible to Bowers's original scheme. It should ideally be able to name numbers of any ordinal (at least ordinals with only numbers up to a limited size).

Is this even possible? We shall see...