I suspect that what happens in and between those synapses that you're pretty fascinated with tortoise, has greater complexities than galaxies (yes, in topological and systemic senses). But... the jury is out as to how much of this complex occurs in the physical realm, now isn't it? Maybe that particular jury is in its own conference room and prefers to keep it that way, ordering-in pizza and Chinese as it wishes.
One might conjecture there is a clue to this special transcendent interface in that there is an in-between in between synapses.
Sister Jean, if I did believe in spontaneous evolution, I might wish to study you. As it is, I never cease to be one of many, studious.
The lovely thing is that we do have good metrics of true complexity. Every test ever done that I am aware of on the human brain gives strong evidence that it is a complex but nonetheless finite state mechanism. The structural and operational complexity is reasonably similar to many of the other more complex systems in the body. This is true even of the output of our minds as well, which show a very high level of finite state regularity in all aspects. The Kolmogorov complexity of the brain IS very high, arguably substantially more so than our current computers, but is otherwise achievable without invoking magic.
Heck, it is this which tantalizes the people who work on these things. We can definitely measure and see that we could construct such a thing in theory, making it a grand puzzle to unravel. Scientists don't waste their time on problems we know we can't solve; there is no value or glory in it. Powered flight attracted human scientists for centuries for the same reason before it was finally solved.
Very interesting observation, unspun!!!! Walker has suggested this, in his The Physics of Consciousness.