The interest of research workers has frequently been focused on the phenomenon of regularly shaped crystals suddenly forming from a liquid, e.g. a supersaturated salt solution. According to the atomic theory the forming force in this process is to a certain extent the symmetry characteristic of the solution to Schrodinger's wave equation, and to that extent crystallization is explained by the atomic theory. Nevertheless this process retains a statistical and - one might almost say - historical element which cannot be further reduced: even when the state of the liquid is completely known before crystallization, the shape of the crystal is not determined by the laws of quantum mechanics. The formation of regular shapes is just far more probable than that of a shapeless lump. But the ultimate shape owes its genesis partly to an element of chance which in principle cannot be analysed further.
About this quote
- What does it mean?
- Crystal formation shows statistical, historical elements and chance beyond quantum law; shape is probabilistic not deterministic.
- In plain terms
- Crystallization involves chance that can't be fully predicted.
- What can you take from it?
- Accept probabilistic outcomes in complex processes.
Where it applies
Putting it to work
Questions to consider
- How much randomness can you tolerate?
- When is a statistical approach insufficient?
Another view
Deterministic models still useful for many predictions.
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