Holy crap that comment (posted very quickly from a tablet hence the typos) produced a long comment thread.

Yes quantum tunneling goes on in a lot of biological processes because it happens in chemistry. There is nothing special about neurology there. I was mostly referring to writings I've seen where someone proposed that humans must be doing hypercomputation because we dont blow up at the godel incompleteness theorem (which made a cognitive scientist in my circle laugh due to the fact that we just don't actually deal with the logic) and another that actually was posted here that proposed that digital information was somehow being stored in the pattern of phosphorylation of subunits of microtubules (which made multiple cell biologists laugh because those structures are so often erased and replaced and phosphorylation is ridiculously dynamic and moderated by the randomness of enzymes hitting substrates via diffusion and not retained on any one molecule for long). In the end it mostly serves to just modify the electrical properties of the membranes and their ability to chemically affect and be affected by each other.

As for 'true randomness', we don't run on algorithms, we run on messy noisy networks. If we must frame the way cells work in terms of simulation of gross behavior its a whole lot more like noisy differential equations than discrete logic. I fail to see any circumstance in which you need quantum effects to make those behave as they usually do.

On top of that, every single cell is a soup of trillions of molecules bouncing off each other at dozens of meters per second like lottery balls. If that's not close enough to 'true randomness', such that you somehow need quantum effects like the decay of atoms, what is?