It's probably just the lowest energy state. The same way marbles at the top of a pile "know" to form a peak, and those at the bottom "know" to form a wide flat base.
In that case the direction of gravity breaks the symmetry between the peak and the base. The grandparent's question is what breaks the symmetry between the big and small end of the pear.
Any direction is as good as any other, but one will be chosen.
In this case, the ones at the big end of the pear act differently than the ones at the small end because their neighbors are different then the ones at the small end. And the mid ones behave as they do because of who their neighbors are.
The reply of colanderman seems correct, though perhaps not terribly enlightening.
I suppose, if the interactions with particles external to the nucleus are weak enough, that the nucleus could be in a quantum superposition of all/most/many orientations anyway? (Not sure whether I'm off-base here.)
Symmetry can be broken spontaneously (see the first sentence in the paper, https://arxiv.org/abs/1602.01485), if the symmetric state is not a global energy minimum. (E.g. a needle standing on its tip on a table is in a state with rotational symmetry --- however, after it has fallen on its side on the table, the symmetry is broken.) The explanation in wikipedia seems be OK: https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
