Understanding: a way of seeing
Know is see. Understand is grasp. These are rather common metaphors. Such metaphors help us comprehend.
Empathy is a technique for understanding. We can try to understand another person by creating a means whereby we can ‘walk a mile in her shoes’. We can create analogies of what the other person experiences as a means for us to ‘put on their shoes’.
An artist may paint in the manner of Picasso, or perhaps in the manner of a Rembrandt, or perhaps in the manner of a Monet. These different forms of painting represent different ways of seeing. They represent a personal understanding which provides us with a prism for seeing.
Mathematics is a way of seeing. Mathematics is the science of pattern. Imagine a very elaborate Persian rug. Imagine that you have only a small fragment of that rug. Mathematics offers a means whereby you might be able to construct the rest of that rug to look exactly like the original. Math can perhaps create a formula for the pattern in the rug such that you can, by following that math formula, exactly duplicate the pattern from which that rug was created.
Understanding is a stage of comprehension whereby a person can interject them self into the pattern through imagination. ‘Understanding is math’ because it helps the individual to ‘walk in the shoes’ of some other entity.
Understanding might correctly, in my opinion, be considered to be a personal paradigm. Knowledge is about truth but understanding is about meaning. Understanding is a means for placing the individual within the picture including the entity about which the individual wishes to become very familiar.
Understanding is a creative process that extends knowing. Understanding may or may not enhance the truth quality of comprehension. Picasso and Monet may paint the same object but have they captured the truth of that object.?
Is truth anything beyond what is normally considered to be truth?
Is truth anything beyond what humans have normalized (standardized)?
Does understanding aid or deter normalization?
Are you normal? Would you rather be normal than right?
Dare to be abnormal, but not foolish!