The notion of scales
Elementary / Math / Ratios and Proportions
In this video I discuss the notion of scales. It is a way of thinking which involves grouping elements into larger sets, which are grouped into even larger sets, and so on. One particular application of scales is known as hierarchy, and another is order both of which rely on the notion of nesting. Nesting is one of the two interpretations of such basic concepts as numbers, duration, distance, area and volume, and their variants such as time, extent, space, height, depth, width, mass, weight, energy, continuity, infinity, or infinitesimals, etc. Alternative interpretation, which involves concatenation, was discussed in Video 1 about duality of mathematical concepts and in Video 2 about dimensions. This video, just like all other videos in this series, is about cognitive patterns underlying mathematical thinking. The ideas in this video come from a book published in 2014 under a title CONCEPTUAL UNDERSTRUCTURE OF HUMAN EXPERIENCE which could be purchased from AMAZON.