DNA is not English

I know that you were just using insulin as an example but I thought I should correct some of what you said. Insulin is no longer harvested from animals but produced recombinantly in e.coli. Also this insulin is often not "human" but an engineered varient. For example I take two forms of insulin, one for rapid release "NovoRapid" and one for slow release. The slow release has the human sequence but the "rapid" contains a point mutation which inhibits dimer and hexamer formation and allows the protein to leave the circulation more rapidly.
On a more general note I notice that everyone keeps using the example of protein coding as if this is all DNA dose. In the human the vast majority of DNA dose NOT code for protein. The codon coding is the closest DNA comes to forming a linear digital code.
An example of where the DNA code can be thought of as more of an anologue rather than digital code is in transcription factor binding sites. Here the "code" is bound based on its "shape". The binding protein can recognise varients of the sequence and will bind more or less strongly and so will activate/deactivate transciption depending on the concentration of the transcription factor.

I'm not 100% sure but I don't think animal insulin is used anymore-its much cheaper and "cleaner" to make it recombinantly.I agree that the issue of nuance is extremely important. In my example of transcription factor binding the "context" in which the "word" is found can change its meaning. However there is a sense in which these sequence differ from a language. The sequence itself is what is bound. There is no "translation" from the language into the effect. The "word" is the object. I'm a bit out of my depth in linguistics so I'm not sure if I am being clear. An example of the idea I'm trying to get at is if you think of droping an apple. The apple falls to the ground. Do we say that the mass of the apple is the code or word that is translated by the laws of physics into an acceleration?