Hubble Ultra Deep Field, this is one of the most popular Universe images.
What you're talking about Bruce(the similarity between our neural network and the Universe) is predicted to happen if humanity will survive and will continue spreading in the Universe.
According to this prediction,
Planet-sized computers are being constructed throughout the Local Group of galaxies, with every available resource going towards their production. All of the "dead" worlds, comets, moons and asteroids considered uninhabitable are being converted into these machines, forming a vast network millions of light years across space. Each computer is capable of instant communications with any other, regardless of distance.
I extracted this paragraph from
this site. By the way, that's an interesting read.
If that ever happens, the Universe will practically become "aware" of itself.
Anyway, here's what struck my mind lately. At this moment in time, we possess the technology to overcome Earth's gravity and escape into space. Later it is supposed that we'll have this imagined "Alcubierre" drive, or something similar.
What if in the distant future we'll attain sufficient knowledge to build a device that actually creates space and time fabric? What if using the appropriate technology and devices we would be able to escape this massive bubble that we call "Universe" in our own, artificial space and time fabric, and watch it from the outside? The question is, what would the "outside" be?( it is useless to think of the outside as a relative position to the universe, like for example "being 100 km above the Universe").