"Smoothing curves that look the most natural are often modeled after springs or friction. How is that not based on physics?"
To be clear, when I say "based on physics" I mean "a value that can be computed from first principles, based on a specific model".
For example the spectrum of a black body radiation can be said to be based on physics.
Gradient is a mathematical entity.
A "correct" gradient cannot be computed from first principles, nor does the article specify any specific model to use. There is no "correct" gradient. We can define some spec for a gradient and say "is according to spec" or "is not according to spec".
Gradient is an interpolation between two triplets using some function.
With gradient, in R3, we have two elements, a,b, and our task is to define a path g(t) from point a to point b so that g(0) = a and g(1) = b;
The trivial way to do this is by way of linear interpolation
g(t) = a * (1-t) + b * t
however this has lots of aesthetic pathologies. The work around gradients is about finding the most pleasing g(t).
If we start from the philosophical point of view that all smooth curves are based on intuition and inspiration from physics you are free to do so but this will summon an angry horde of mathematicians and computational geometry experts.
"This is the whole point of the article."
I think the point of the article was
1. Gradient rendering does not respect the spec
2. Any color computations should be done in linear color spaces
The points are valid, but the motivational paragraph about gradients was more misleading than correct (IMO) hence my critical response above.