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You could say that at DNA level a mutation can contain the exact same amount of information as a non-mutation if you use Shannon's measure e.g.:

GTTACA to GAATCA

would be the same. But of course there is a vast difference in terms of the phenotype that would happen from this mutation (if the mutation happens in the relevant area).

Of course strictly speaking you can also add a mutation, the most trivial example is:

AAAAAA to ACAAAA

Obviously entropy is higher in second string.

All those examples show, however, that laws of information entropy (as well as thermodynamic entropy) don't really have much to do with evolution.

There isn't going to be a logical or semantic trick to "disprove" evolution either, as it's not a suggested mathematical theorem: it's not in the a-priori space. It's an enumeration that flows from evidence. No one is claiming that evolution is a logical necessity: it's merely a theory (just like gravity is merely a theory) that is the best one supported by evidence.

How would one disprove evolution? To quote an evolutionary biologist, find something along the lines of rabbits in the Pleistocene. Until that is found, evolution through natural selection is what best fits the evidence.



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