Our regions will not be natural unless they mark out real discontinuities both of origin and affinity, and these we can only seek to explain by reference to past changes in the earths history.
Thus there appear to be discontinuities in the values of y.
Even in the uniformly hyperbolic case, systems with discontinuities do not have many of the good properties of their smooth counterparts.
The numerical method then must be able to handle discontinuities without introducing non-physical, spurious oscillations.
The importance of these has become more and more evident, and the difficulty of reconciling the apparently inevitable discontinuities of the product of energy and time which experiment indicates, with our accepted habits of mind, always had a peculiar fascination for Einstein.