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My viewpoint is that mathematical models, which assert a numericalGood points all. We humans do have this irresistible drive to draw
equality between functions of the readings of defined measurement devices,
are indeed testable and can be branded "right or wrong" as an empirical,
mathematical model.
The human mind is not satisfied to stop here. It goes on to account for
these device readings and their connections by erecting a conceptual
model of the object under consideration, the measuring devices and their
interactions. The device readings then acquire conceptual meanings within
the context of that conceptual model. These concepts come from our
library of sensory-provoked ideas.
Eg; the point particle model of the "reality" behind the empirical ideal
gas equation PV=RT. Another example is the meaning of the particle
velocity in the magnetic force F=qVxB. Common wisdom was to (delightedly)
take it as an absolute velocity (or at least, relative to an ether
medium}; Einstein's weird conception was that it was the particle
velocity in whatever inertial frame the physics was being done. One man's
(or generation's) weirdness is often another's beauty.
Perhaps the best example is the plethora of conceptual models being
invented to conceptualize the reality behind the (notoriously useful)
equations of quantum mechanics.