Similitude, similarity, and scaling

An exceptionally rich and colorful literature, drawn in almost equal parts from pure mathematics, from the sciences, and from the technologies, has grown up over the years, which bear in different ways on the topics under discussion. It is the intent of the present paper to survey this far-flung literature, point out some of the commonalities and interrelationships which underlie it, and briefly indicate how it has been and can be applied. To my knowledge, this kind of review has not been attempted before.