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Bose-Einstein statistics
By condensation of bosons, space can get a lower energy. It is the transition of a system of bosons to its ground state.
Explanation
It has been found that around absolute zero (0 °K) so called Bose-Einstein condensation emerges that causes permanent magnetism. In this situation atomic bindings occur with a probability of
HH = 1/3
TT = 1/3
HT = 1/3
Is this an example where mathematics lets us down?
No. You cannot apply the probability definition of Laplace on all natural phenomena. It is an empirical theory, because in order to know things exactly you need an infinite number of measurements, and these all under exactly the same conditions. That is just impossible.
Probability theory is a kind of forecast. And you cannot predict the future, not even with mathematics.