Mathematicians love zeroes in the first place, and relish on infinities. Much more so when they are brewing exam exercises for unlucky high school students. Infinities come handy to place bounds on formulae, to handle otherwise untreatable concepts and equations. The big boost to science in general, came after the routine management of infinities with the emergence of Calculus, and with it the tools to model the physical world in a way undreamed of before.
But infinities in Nature are accepted mostly as a qualifier for unbounded magnitudes, for something we cannot embrace in a sweeping view like the whole Universe, or some large enough physical magnitude that for its inclusion in a theoretical derivation it comes handy to represent with a simple symbol rather than with a pages long number with mostly academic loss of generality or precision. Infinities in the backyard are another thing altogether, and we do not know of such things. Except for black holes.
Problem with black holes in the first place, is they should - according to prevailing theory - home a singularity at its center. A place where in a zero size region, a point, a nonzero amount of matter is squeezed leading to an infinite in density (density = mass/volume, something divided by zero is anathema or infinite, as you like). This is hard to swallow, but then there comes a further offense this time to those who swear by Thermodynamics.
According to the Second Principle of Thermodynamics, a consequence of its validity implies among other things that information cannot be destroyed. Information in a more general sense that is, than newspapers or late afternoon TV. Wherever matter is arranged in a particular fashion, it carries information. Synapses in our brains, electrons trapped in electric field wells inside computer chips, orderly branches in trees and layered or crystallized rock to name a few, are examples of ordered matter where information is implicitly stored. When matter crosses the event horizon in a black hole, it was customarily thought to converge to the center where it compresses and sinks to oblivion. And Stephen Hawking, the black hole guru of all times, proposed black holes themselves are destined to evaporate by a quirky mechanism of quantum fluctuation, leaving in the end an empty weightless naked singularity in space time.
This implies information as carried by the formerly structured matter unfortunate enough to be swallowed, should vanish in violation of the Second Principle.
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