One of our favorite BBC Radio4 programs is called In Our Time (available as downloadable podcast or to play on line). Every week, host Melvyn Bragg and 3 academic guests discuss some topic of interest, be it from science, philosophy, history, the arts or whatever, for about 40 minutes, explaining the topic and making it understandable and very interesting. This program is like a college education, except that it is free, eclectic, digestible.....and without grades or exams!
The May 28 episode is about glass. What is glass? How is it made? What is its molecular structure? A key point of this discussion is that glass is a complex molecular structure, composed variously of sand or polymers with other added elements heated, shaped, and then cooled. The key fact is that the molecules are irregularly arranged: what gives glass its properties is that it is not a crystal, despite what it may seem. For a given chemical composition and heating/cooling process, the properties of a piece of glass are predictable and repeatable, but not in the sense of a crystal. Glass goes through a 'phase transition' from liquid to solid when it cools, but it's not an orderly transition such as is seen in water and many other substances, and in crystal formation.
In a crystal, all the molecules are precisely arranged in spatial order relative to each other. The arrangement is generally predictable (understandable theoretically) and repeatable. It has specifiable mathematical relationships. But what makes glass glass is that it is not arranged in that way. Instead, a piece of glass's molecules are uniquely or randomly arranged; this means that the structure of any piece of glass can't be predicted, although it can be determined post hoc. What that disorderly transition means is that no two vases or windows are identical at the molecular level, even if they have the same macro-properties. The 'impurities' that are added affect the arrangement of the molecules in ways that provide different strength, melting or cooling temperatures, color, or refraction of light passing through.
There are unlimited ways to make glass; adding different materials in different relative amounts, heated according to their properties and the desired result. The molecules in each of a set of dinner glasses are basically the same in relative proportions, but entirely unrelated in their arrangement. But how then can a factory turn out countless drinking glasses, jelly jars, or optical lenses that seem identical?
The reproducible randomness of glass
The answer essentially has to do with large numbers. It is much like, say, the ideal gas law which says that the pressure or temperature of a gas in a container depends on the size of the container, and the amount of molecules of (any) gas that is inside it. Each molecule is careering around banging into other molecules of the gas or of the wall, and caroming off like billiard balls. It isn't possible to measure each encounter as there are typically gazzilions of them. But statistically, the number of collisions is roughly the same for a given set of conditions, so the net result is statistically highly predictable, without having to examine any individual molecule.
Similar properties apply to gas, according to this BBC discussion. Each piece of glass has uncountable numbers of molecules, more or less randomly arranged. But there are so many of them that their net macro-scale properties are highly predictable, without having to examine any individual molecule. But that's no longer true at the molecular level.
Thinking about the nature of glass provides an illustrative way to think about another kind of assemblage, but one that has very different properties.
The irreproducible randomness of genomes
Genomes are molecules that interact with other molecules. This interaction has been designed by evolutionary history to lead to development of fertilized seed or egg into an adult, and to respond to environmental conditions of various sorts. So the action or 'use' of genomes leads to changes in the organism. Some are gradual and 'normal', others are sudden and 'abnormal', that is, we call the change 'disease' or 'puberty' and so on. Whether these could usefully be viewed as phase transitions I don't know. The changes are, in terms of genes, only partly defined, often even if we know there are risk alleles that alter the timing of such transitions.
Like glass, the complex of any genotype's relationship to the organism's traits is empirical rather than wholly predictable from the 'molecules' (genotypic elements). Similarly, enumerating the causal elements is not that different from the situation in glass. Some properties of glass, like strength and color, can be predicted by knowing its constituents, but these are collective properties and not predictable from enumerations of the individual atoms. Genomics may be a bit more predictive, but not all that different in most cases.
Overall, the analogy seems at best imperfect in specifics, but very useful as a way of thinking about the power, or limits of power, of enumerative prediction, and an indicator of collective, if individually unique, prediction.