Emergence and a heap of sand

A piece of gold metal is shiny but a single gold atom is not.

Tin is a superconductor but a single tin atom is not.

Water is wet but a single water molecule is not.

A brain thinks but a single neuron does not.

Shininess, wetness, and thinking are all emergent phenomena. The whole is greater than the sum of the parts. More is different. Although these ideas come from twentieth-century science I recently learn that there are ancient antecedents. According to Wikipedia

The sorites paradox (/soʊˈraɪtiːz/; sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

What is the minimum number of gold atoms needed to produce shininess?

How large must a grain of tin be for it to superconduct?

When spontaneous symmetry breaking is involved there are subtleties. Strictly, speaking it only occurs in the thermodynamic limit, i.e. for an infinite system. However, for a finite system, one can observe some properties associated with symmetry breaking such as rigidity. These issues can be addressed in the laboratory with ultracold atoms and with metallic grains of superconductors, both of which can be produced with controlled numbers of particles, ranging from a few hundred to billions. There also are some resonances with the problem of trying to identify the quantum-classical boundary. 

Finally, piles of sand were central to the discovery of self-organised criticality.