I've spent some time online trying to track down the exact moment when someone noticed the vastly tangled internal structure of the brain's neurons, and said, "Hey, I bet all this giant tangle is doing complex information-processing!"

My guess is Ibn al-Haytham, early 11thC while under house arrest after realizing he couldn't, as claimed, regulate the Nile's overflows.

Wikipedia: "In the Book of Optics, Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example described how a small child with less experience may have more difficulty interpreting what he or she sees. He also gave an example of how an adult can make mistakes in vision due to experience that suggests that one is seeing one thing, when one is really seeing something else."