The second part of your analogy is off.

It's not billiard physics to general relativity, it's billiard physics to fluid dynamics and predicting the exact route of a stick through a set of rapids.

In economics our biggest complaints are around failure to determine that we're near a singularity and failure to predict behaviour through singularities (in a signal processing sense). It's understandable, as we all strongly care about the path of the stick, yet still unreasonable.

Macro is a decent enough tool most of the time, as are traditional fluid mechanics approaches. What we don't have are ultra precise CFD tools but in our arguments we act like we should/do. Sometimes traders think that they do have a great CFD solution and that's how we get LTCM crashes!