Back    All discussions

2010-06-19
Digging into the n-body problem
The n-body problem arose in the context of calculating the trajectory of planets in Newtonian terms. However, by introducing their mutual gravitational effect it was found that there ceased to be mathematical solutions (Poincaré).

This is to put the issue in epistemological terms, which is that the resulting equations are beyond our ability to solve. However, to capture the broader implications of the n-body problem, I have questions regarding its ontological implications.

Am I correct to infer that the problem arises because the force of gravity is a function of relative mass and position, but future position is a function of the force of gravity? So to put the problem very simply, is it that variables are interactive? In systemic terms, does this simply refer to a feedback loop? Is this feedback "non-linear" because the values of variables are interactive rather than unilinear?

Now a more esoteric question. If my suppositions above are true, then does it mean the gravitational force constrains the possible trajectories of the bodies? If so, then does this imply a modal realism in that possible trajectories become a factor and calculations based on observables therefore cannot be solved?

Haines Brown