Yes, another way to give you extra brain power. It will receive sensory input from say, your eyes, ears, touch, taste, smell, and then it will output signals to surrounding neurons.

Great way to keep up with Strong AI. Depending on how powerful the chips are you could potentially have the equivalent of hundreds or thousands of brains in your head. It will give us answers to problems the same way we already receive answers to problems, the answers will just pop into our consciousness. In fact, it could be made so that it replaces most of your neural cortex. This way you will be able to upload those chips into a computer and voila! Instant immortality.

The era of the uploadable human brain is here (OK, probably not for one, two, or three hundred years). The chip essentially takes over your human brain recording all experiences. It is implanted at birth. When you die the chip can just be implanted into a humanoid robot or a clone or you can live in virtual reality. Of course, there will be a 1000 and 1 problems to solve but sounds like one way to create uploadable humans. And to prevent death you are constantly backed up a la cylon stile (Battle Star Galactica).

Wow, this could definitely work!

A nice twist would be if a virtual heaven were created. And you could only get in if you were "good" (whatever definition they decide to use). This heaven would be necessary because there are not enough resources to keep running all the servers necessary for this virtual heaven. So at some point in history somebody decided that to control virtual population only those that were "good" would be able to get in. Those that were bad would receive eternal death.

After several thousand years a two layer system evolves. Virtual Reality and Virtual Heaven. The ones in virtual heaven hold all the strings and choose new members from Virtual Reality to join them if they have been "good". The ones in virtual reality have forgotten about their initial history and don't realize they are in a virtual reality. Hence many don't believe in this "heaven" and consequently very few actually make it through. Entire religions are created to worship this heaven and to try to get in.

Well, you get the idea. Sort of got side tracked there. Sounds like an idea for a book.

You don't even have to take it that far; imagine suddenly being able to do square roots in your head with ease!

This is a common misconception. Advances in neuronal simulation do not at all map to traditional computing. The mere fact of running on a computer does not mean the simulated brain gains features intuitively expected of a computer (like rapid maths, or being able to copy knowledge).

Sure, but I like to dream about developments that I might actually get to see. Full human level AI? Making your brain smarter? 6th senses? I don't see these happening ANY time soon. But a little coprocessor with dedicated functionality seems like an almost-realistic enough possibility to enjoy thinking about.

Yes, baby steps. Reminds of the stories of people attempting to fly with bird-like wings. Eventually somebody came along and figured out the right way to fly and it was not with flapping wings. Same here, making a lot of attempts that may seem stupid or laughable or even impossible but eventually somebody will figure it out.