In retrospect this shouldn’t surprise anyone, but it still feels like a radical departure from the more or less cute stories we are taught in intro Bio.
Biology is fractally weird and emphatically deals in probability distributions not binary classes. You can and should always expect an “except...” clause at the end of any declarative statement about a biological system. If it’s not there explicitly, it’s implicit.
Confusing the map (“individuals have unique DNA”) for the terrain (“...except for here and here and maybe over there, especially if you look really hard”) is always a risk.
Being able to know which map to use for which terrain (i.e., do we need to care about mosaics for this problem or not) is, more or less, the reason we do research.
They are definitely not random. Sequence context matters a lot - e.g. in humans CG mutates about 10x more often than other dinucleotides. Other contexts also contribute - genes that are expressed more are more mutable, and so on.
As the other comment says, most of the mutation have chemical and thermodinamical causes, that can be seen by a Laplace's demon. (There are some quantum effects here, so add "almost" somewhere in the previous sentence.)
Also, it is important that the mutations are random, but nut uniformly random. Some base replacements are mor common than other, some DNA patterns are more prone to get bad copies, ...
But if you put a radioactive source that produce x-ray or gamma rays, the emission is a truly quantum random phenom and even a Laplace's demon can't predict them. I'm not sure if the Laplace's demon can "see" the photons while they are traveling, it's difficult to discuss about the properties of fictional entities. But for not very high energy x-rays, the wavelength is bigger than the distance between atoms and the Laplace's demon can't predict in which atom it will hit, but they have less energy are less prone to cause mutations.
Biology is fractally weird and emphatically deals in probability distributions not binary classes. You can and should always expect an “except...” clause at the end of any declarative statement about a biological system. If it’s not there explicitly, it’s implicit.
Confusing the map (“individuals have unique DNA”) for the terrain (“...except for here and here and maybe over there, especially if you look really hard”) is always a risk.
Being able to know which map to use for which terrain (i.e., do we need to care about mosaics for this problem or not) is, more or less, the reason we do research.