Modern physics is all about conserved quantities. Every physical law can be described through an associated conserved quantity. Noether’s theorem establishes a connection between the two.
It makes sense to try to copy that approach to biology, or at least it’s worth a try. The conserved quantity in a living being is the genetics, i think. Because while the body has cell turnover rate, the information that says how the body is built, is constant. That’s why it can be used as a marker and to identify an individual, i.e. when we try to establish whether a person is still the same as they were last year (ship of theseus), we look at whether they have the same blueprint; Similar to how we don’t identify a river by the water molecules in it, but by its trajectory on the landscape. And if that shape is still the same, then we call it the same river, independent of whether the water molecules changed. So the abstract shape or blueprint of something is the conserved quantity that we use to define identity, and therefore it’s the conserved quantity that is relevant in the system. And that’s why it should be considered an important concept, i think.
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That sounds like a reaction norm—all the various phenotypes a single genome might potentially develop into under different environmental conditions. Which doesn’t seem quite analogous to Noetherian properties like momentum and energy, which are conserved in the sense that they can change inside a system as long as there are balancing actions that preserve the property for the system as a whole.