Gauss´Less Constraint Principle and Covariation

Dr. Carlson has developed ideas around mental processes associated to function graphing in mathematics. She stresses the ability of the person doing the graph, to coordinate two variables as they vary. On the other hand Gauss, many years ago developed the idea that objects move minimizing force constraints, as if free.

Is there a connection?

The actual process of doing the graph can be with straight lines between the points considered for one interval. The more points, the more faithful the graph is. In Gauss´method the particle moves as if free, between points also.

One basic difference between the two sets of ideas is that Gauss does get exactly Newton´s force law, and Carlson gets a graph without physical motivation.

It may be interesting to ask if Gauss was considering the best way to do a graph with mental processeses similar to those Carlson has drawn our attention to.