Side Comments: Is there really information being conveyed within a cell?

The math is the same. I wouldn’t say the interpretation is the same, but rather it is parallel.

There is no Second Law of Information Theory preventing the creation of new Information. There Information inequalities (ex: Cramer-Rao, Kullback–Leibler) that are roughly equivalent.

For two probability distributions A and B that are not identical (do not contain all the same Information), you cannot make B more similar to A (more of the same Information) by using any deterministic function on B.

You CAN make B more similar to A by adding random Information, then discarding “waste” Information that does not reduce the difference.

Arguments claiming that “evolution cannot create new Information” are making a parallel version of the old “2LoT prevents evolution” argument.

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