Is a habit of the mind to quantify (measure, or view geometrically, or topologically) what we know about physical shapes? Is the use of geometry or topology or metrics underlying our perception shapes? Or do typically live on an intuitive rather than a quantitative level in our encounters of shapes?
A should-be-useful introductory material: Elastic Shape Matching of Parameterized Surfaces Using Square Root Normal Fields
@Ian H. Jermyn1, Sebastian Kurtek, Eric Klassen, and Anuj Srivastava
This is a good and very tricky question. I am tempted to say that humans are inherently metric in their perception of reality. Just imagine a hunter 10000 years ago estimating the distance to the pray and trying to use the right amount of strenth to throw a spear. But then, I see the work of a potter usind clay and I have to accept that he may have some (at least intuitive) topological knowledge acquired by mere practice.
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