I was listening to a lecture on computer functions and abstractions. A Turing complete computer is able to compute anything. That is, anything that is computable can be computer by a Turing complete computer.
However, what even a Turing complete computer lacks is abstraction. Namely, you have to rebuild a file every time you want to use it, and you can’t use the same variable names in other pieces of code. This, of course, can become quite annoying and very inefficient, if you always have to go back and change pieces of code so that variable names don’t overlap.
So this got me thinking: our brains are like Turing complete computers, but with the ability to abstract. We can replace, modify, add, and delete variables in our minds relatively easily, without the information becoming jumbled. We can also compute near anything, if we sit down to it, assuming at least average intelligence.
Further, the brain can augment its own capabilities. As you learn, plasticity kicks in, making your brain more efficient and better able to connect concepts. I don’t know of any computer or AI that can do that.
So it seems that one of the extraordinary elements of the human brain is not so much simply the ability to compute–any computer does that quite well, and typically, better than a person, or at least faster–but the ability to abstract and augment ability. Computers, I’m sure, will eventually get to that point, but for now, the human brain transcends AI abstraction abilities.
neuravinci.com 
You started by saying that human brains can do more than computers, and that makes them not Turing complete. At the end, you said that “will eventually get to that point”. If we will eventually get to the point where we can simulate a human brain, that means that we CAN do it now, we just haven’t figured out how.
You also said that human brains have abstractions and computers don’t. Computers definitely do. A program written in a high-level language could pass a simple instruction to a low-level function which then completes it. Without computer abstraction, we would be writing in machine code all the time.
You said that human brains can develop and improve, while computers can not. This is not true. Machine learning can be used to improve a computer program.
The only real way to prove that a human brain is not Turing complete is to find a special property that it has that is not possible on a Turing machine. If you could find an algorithm that only a human can complete, then you could say that we are more than Turing complete.
Hi Nathan, thanks for your response. I wrote this article a while ago when I didn’t know much about computers, so yes, you’re right about machine learning. I disagree, though, with your first statement: “human brains can do more than computers, and that makes them not Turing complete. At the end, you said that “will eventually get to that point”. If we will eventually get to the point where we can simulate a human brain, that means that we CAN do it now, we just haven’t figured out how.”—just because we can get to that point someday does NOT mean we can do it now. That makes no sense; something that can be done in the future is just that: able to be done in the future, not the present.