cache vs. math
Cache's definition of inflection contradicts mathematical terminology in that it is not a transition through a smooth point, but either a smooth point or a singular point. He further contradicts mathematical definitions when he states that inflection is never the product of a reflection but rather two separate entities: concave curvature and convex curvature.
Cache's inflection is produced when any concave curve meets any convex curve at any junction. It is not a reflection because concave and convex are separate entities.
Mathematically speaking, the curves that meet at an inflection point could be the product of a reflection or a variety of other transformations.
Mathematical inflection may be the product of a reflection. Inflection here is a result of a transformation.
Cache defines inflection as "the molecule of all things visual", hence why it must include transitions at a singular point. Similarly, mathematical inflection remains a transitional point that defines the in-between, the vague etc. however, it is the the transformative, multifarious, rarer type of inflection.
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