To really 'get' bike gearing, you have to come to a Zen awareness of the various ratios that are on YOUR bike. After many hours of deep meditation you will come to; Shift up when the pedaling gets too hard and shift down when it gets too easy. Then you will have it. Intellectual, engineering or mathematical understanding is an illusion born of overeducation and ego worship. Once you have the zen aspect down, all you have to do is ask your legs. They will 'know'. bk