It's not that we can process a lot of data but it seems like there is a fundamental rule within us that we use unconsciously that applies to everything else that is logically consistent in the abstract or physical world.

An example I can think of is that you can give a computer 1 billion simulations complete a task but it will take human an order of magnitude less time than that to figure out the same result. You can give an AI or Machine Learning the rules of reality and they will come up with huge complex solutions to make predictable outcomes but some exceptional humans are able to write it out in one line of paper.

Does it not seem like humans have something beyond the physical world that separates us from all other objects and information systems (doesn't necessarily mean supernatural)? I can't see it any other way.

I could that imagine if you gave a human mind the processing power and latency of computers we would be like gods almost. Maybe something about the structure that we haven't figured out yet is what makes it so special.