Question

This questions started with a question I had about gravity. If two objects of different weights fall to the earth at the same rate of acceleration, then it seems to me that gravity is in some ways 'calculating' the weight of each item and applying the appropriate force to each item so as to have it fall at the same rate of acceleration. Is this true (or at least close to the truth)?

This got me think that perhaps this is what all of the mathematical equations of physics are really saying - namely that there are mathematical equations that are getting applied to the real world in one way or another.

Is this right? If not, why not?

Answer 1

A mathematical description of an observation does not say how the observed was created.

Draw a perfect circle of radius a. Do the ink points "know" that a compass and your hand was used to make this mathematical description: r=a , into a perfect circle?

There are many referential levels, meta levels, in any mathematical description. Sometimes known by construction as in the circle example, sometimes as in your gravity question still a point of research. The referential level of two objects dropping are different from the level of the gravitational equations of general relativity which are the ultimate at the moment mathematical model for gravity. The earth is not calculating anything, in the same sense that the points on the circle were not calculating the r=a. The equations of motion of bodies is a mathematical model of observations.

Edit: When one says "Nature does this or that" a level of anthropomorphism enders. It certainly belongs to metaphysics questions and not to physics. My almost metaphysical view is that mathematical forms exist , the way 2+2 exists, and matter as we know it, given the appropriate conditions "crystallizes" out following the energy levels etc. of the mathematical equations. Our mathematical models are successive levels of approximations to these ideal equations. No calculations by nature or anybody are involved, imo.