I always thought of quantum space and quantum time as a solution, but then i figured out that "quantum space-time" is not actually true(yet). I've also heard of the calculus approach and limits, but i don't see how the paradox is resolved since limits tell you what happens as you approach a value not at that value itself.
What's the solution?
The question is where is anything going to go if everything is changing direction based on where everything else is.
A computational method effectively depends on an evolution of Euler's approximations which introduces error based on step size and the grouping of bodies into clusters for utilization of centers of mass. (as well as stimulated low probability particles.)
The solution is that everything does exist.
Unfortunately we could never write this entire solution down in simulation or computation as a abstraction's introduce a lessening or error in that which they simulates. That error may reduced into a quantity which provides for the possibility of an except-able solution or approximation. For instance our ability to predict the motion of the stars through the sky has been good enough for the purposes of terrestrial navigation for millennia, and recently we have even committed solar investigations and orbital excursions.
This boundary of computational "excitability" is the foremost ethical edge in academia, in my humble opinion.
I don't know if this really answered your question but I can hope.
