[KirillPanov]

Counting is very different from integrating.

Lots of stuff in biology integrates continuous signals. Discrete counting of discrete events is quite rare.

In many senses you can compute with things that count discretely: Peano Arithmetic is undecidable. Yet unbounded dense linear orders (i.e. the theory of the rationals) are decidable, so you can't embed "program X halts" into them.