How does a brain split operation work exactly? Do they put a barrier between the two halves? Otherwise, I would expect that signals could still propagate: cut two nerves, then push them together, and I can imagine that a signal can still pass through; if not always, then in a percentage of cases.
> cut two nerves, then push them together, and I can imagine that a signal can still pass through
If only....
Getting neurons to regrow or fuse, particularly in the central nervous system, is one of the biggest open challenges in neuroscience. If it were actually that easy, spinal cord injuries would be a thing of the past.
There are 250 million neurons in the corpus callosum, each with a diameter on the order of microns. Individually, each one transmits a very primitive signal (think biological bit) that doesn't mean much without the other millions of neurons. It's extremely complex and thus extremely frail. If the cut halves on both sides don't line up exactly, you have the equivalent of static. You wouldn't mash two cut ends of normal data cables together, and there are only on the order of 100 "neurons" there.
What you say is theoretically possible if the neurons weren't living cells and humans had the technology to reconstruct the brain's wirings. Your body isn't going to figure out which "wire" connects to which on its own.
This is an interesting question. I'm not a neuroscientist or anything, but I'd wonder how this question relates with brain waves, as well. I guess there's research into how these signals cause integration within the brain http://www.nature.com/nrn/journal/v2/n4/full/nrn0401_229a.ht... - I guess I'll check back here in a couple hours and hope somebody's chimed in.
Since I didn't quite answer your question before, the two hemispheres of the cortex are surprisingly independent. However, there's a big "interconnect" in the middle called the corpus callosum, which is a bundle of axons that cross from one hemisphere to another. It's fairly easy to find on an MRI--it's the elongated u-shaped object with the labels on it here: https://en.wikipedia.org/wiki/Corpus_callosum#/media/File:Co... (The labels indicate different parts of it).
For patients with really severe epilepsy (where the seizueres are causing slips and falls), one possible treatment is to cut this bundle to prevent the epileptic activity from spreading across both hemispheres. You basically just slice through them with a knife. Since neurons are very small and delicate, it's extremely unlikely that the membranes (essentially drops of oil) would reform in a way that would permit them to carry information.
Since the corpus callosum contains most of the inter-hemispheric connections, cutting it is often sufficient to prevent the siezure from spreading (and also to produce weird split-brain phenomena). However, there are a few other locations where there are cross-hemispheric connections. The anterior and posterior commissure are two other "interconnects." There may also some much more indirect interactions through subcortical structures.
