Interesting article.
When you say "coordinate-free" do you mean "independent of any fixed frame of reference"?
Because AIUI coordinate-free actually means something else, it's really just a mathematical detail: the choice to work with vectors as first-class objects rather than arrays of coordinates. It's a question of elegance rather that meaning.
Given the date of this article, the history of the Technocracy movement may be relevant to those who find these ideas appealing.
Yes. Einstein's field equation can be derived using differential geometry, e.g. a coordinate-free approach. Prof. Smith discusses the evolution from egocentric (early Greek) to absolute fixed-frame (Newtonian) to coordinate-free (relativistic).
https://en.wikipedia.org/wiki/Manifold
The mature formulation of classical (pre-relativistic) physics circa Hamilton and Poincaré was already coordinate-free in this sense.
"The world of physics is then," as Planck says, "a deliberate hypothesis put forth by a finite mind in an attempt to reduce the facts of observation to a system based on certain physical principles such that known phenomena are necessary consequences of the system."
The basic principles are chosen on experimental grounds. Whether they are true or false in the absolute sense is not a pertinent question. Their consequences must agree with nature. They are working hypotheses which are to be discarded whenever they cease to be effective or helpful.
Progress means bringing new sets of observations with the system in a way to give a complete mathematical description of physical phenomena in terms of the fewest principles or entities, that is to find in a variety of physical phenomena essential relations from which future phenomena can be predicted.
Physics is thus a result of our quest for order and harmony among physical phenomena. It is man's best attempt to think vigorously whatever permits of vigorous thinking. It is not fixed but is subject to change and evolution. Whatever comes out must go back to enrich the soil from which it came
I think it's worth the full read, 20 pages of pretty good physics history
He basically works his way through history to demonstrate the development of the modern experimental method and extrapolates that society would be best served by extending the scientific method to many more aspects of society (social and cultural issues, etc).
