This doesn't make any sense since all of the complex behaviors neurons do are emergent from very simple ones at smalled scales - described by morr fundamental laws of physics - such as ions crossing a membrane barrier. — Apustimelogist
This ignores the fact that organisms are organised by codes and so exist in a semiotic modelling relation with the world.
This neatly inverts things. An informational mechanics is precisely what biology and neurology impose on the physical world. Not the other way around.
The world is organised by dissipation. It has an emergent structure of entropy flow. This starts down at the quantum level with thermal decoherence. Our best causal model of this is symmetry-based. Complexity arises as symmetry-breaking phase transitions – step ups in terms of the holistic constraints of topological order.
Nature is holonomic in the physics jargon. Then life and mind arise as information systems able to impose non-holonomic constraints on the prevailing systems of entropic flow. A machinery of photosynthesis can be constructed that stands between the sun's rays and the earth crust that would otherwise just bounce it off into space as waste heat.
So life and mind embody the Newtonian ideal of a cause and effect system. A mechanical construction that regulates physical flows. Billiard balls roll smoothly and recoil with constrained linearity because we have carefully machined things to be that way on a baize surface with ivory spheres.
But the world itself is not a machinery of linear cause and effect. So its non-linearity is only a comment about the degree to which it has been constrained or not in regards to some entropic process. Reality is fundamentally "non-linear" if that is our best term. And linearity or classicality is something reality can only approach asymptotically or effectively.
For all practical purposes, we may regard a wave function as collapsed as some probe with a switch mounted on its end has been heard to flip state. Holism can be considered localised. Another bit of thermodynamic history has now definitely been added to universe's equation of state.
If neurology relied on ions crossing membranes as its deep explanation, then it would be getting us nowhere. What matters in terms of a suitable causal explanation is in what sense a switch was flipped. And what meaning did that flip have within a larger holistic informational economy.
All this only works in the first place by the "information processing" being as causally separate from the physics it means to control as is possible. An organism has to stand outside its world to regulate that world. Or at least swim along in a purposeful manner while also caught in the midst of its tremendously strong entropic flows.
Anyway, my general point is that complexity theory is often reduced to just complicated dynamics – which already begs the question in that dynamics is inherently not mechanical if you dig into its causality. Non-linearity is its default as linearity is only ever some emergent tendency towards an organising topological order.
And then compounding the confusion over causality, life and mind arise by being able to impose mechanical order on entropic flows. A logic of switches can tame a river to become a transport system, an irrigation system, a power generation system. Or down at the level of organic chemistry, a logic of switches turns a bag of reactions into an an information-regulated metabolism. A cell with the intelligence to repair and reproduce itself despite the storm of entropy flowing through it.
This is proper complexity when it comes to the possible causalities of nature. The combination of entropy flows and negentropic memories. The ability to construct sluice gates across non-linear dynamics and so regulate nature in intentional fashion.