Is it actually possible to express the entire universe as a single time-independent equation?
Yes.
If your original question, “what determines how much the universe changes from state to state?”, is meant to refer to spacelike “states”, then the answer (which requires only general relativity) is the geometry of spacetime. But the “states” in the Wheeler—DeWitt equation are spacetimes, so in that context “the universe” differs “from state to state”, but it doesn’t “change.”
According to this article, a traumatic brain injury turned a furniture salesman into a mathematician. (Not without side effects, but still.)
There is a bit of conventional wisdom in evolutionary biology that drastic improvements in efficacy are not available through trivial modifications (and that nontrivial modifications which are random are not improvements). This is an example of the principle that evolution is supposed to have already ‘harvested’ any ‘low-hanging fruit’. Although I don’t think much of this type of website (note the lack of external links), the story seems to be based in reality; it is thus one of the most surprising things I have ever heard. And, oddly, heartening as well—insofar as it suggests both a potential shortening of the timescale for human intelligence augmentation and the possibility that such augmentation may be relatively more accessible (than I previously thought) by comparison to computer-based artificial intelligence developments.