I’ve seen different figures for information content of DNA but they’re all mostly misleading. What we actually inherit is much more. We are the result of an unpacking algorithm starting from a single cell over time, so our information content should at the very least include the entirety of the cell (which is probably impossible to calculate). Additionally, in a more general sense, arbitrarily complex behavior can be derived from very simple mathematics, e.g. cellular automata. With sufficient complex dynamics (which for us are given by the laws of physics), even very small information changes lead to vastly different “emergent behavior”, whatever that means. One could improperly say that part of the information is included in the laws of physics itself.
A biological example that I like: the neural structures for vision develop almost fully formed from the very beginning. The state of our network at initialization is effectively already functional. I’m not sure to which extent this is true for humans, but it is certainly true for simpler organisms like flies. The way cells achieve this is through some extremely simple growth rules as the structure is being formed for the first time. Different kinds of cells behave almost independently of each other, and it just so happens that the final structure is a perfectly functional eye. I’ve seen animations of this during a conference talk and it was one of the most fascinating things I’ve ever seen. It truly shows how the complexity of a biological organism is just billions of times any human technology. And at the same time, it’s a beautiful illustration of the lack of intelligent design. It’s like watching a Lego assemble by just shaking the pieces.
Problems like this will turn out to have simple solutions. Once we get past the idea of "inherited instinct" (obvious nonsense and easily proved to be so) the solution will be easier to see.
An example that might be useful: dragonflies lay their eggs in water. Since a dragonfly has like a 4-bit CPU you might be amazed at how it manages to get all the processing required to identify a body of water from a distance into its tiny mind, and also marvel at what sort of JPEG+++ encoding must be used to convey what water looks like from generation to generation.
But they don't do that at all: instead they have eyes that are sensitive to polarized light. The surface of water polarizes reflected light. So do things like polished gravestones. So dragonflies will lay their eggs on gravestones too.
One I like to ponder is: beavers building damns. Do they have an encoded algorithm that knows that they need to damn the river to have a place to live, by gnawing on trees, carrying them to the right place on the river bed, etc? Nope, certainly they don't have that. Perhaps they have teeth that grow so long that they hurt, motivating the animal to gnaw on something solid to wear them down. The only solid thing they have available is a tree.
