Computability and Consciousness

There are a lot of problems that are hard for computers to solve but are easy for us. For example, driving in a closed course, walking, and handwriting detection all took many years for computers to handle tolerably (sometime within the last 20 years). Clearly we’re not like computers – it doesn’t take billions of operations in our mind to walk, see, or read or write.

Also computers can’t solve all problems. Computers have many light switches that can be used to signal two states (on or off). In terms of a computer, that means that a computer program can take in as input some finite number of 0s and 1s and return as a response some finite number of 0s and 1s. Any problem that fits within that realm is solvable. In more math terms, that means that computers can only solve problems that fit within the countably infinite set – any problem that lies on the number line from 0 to infinity. The set of countably infinite numbers is enumerable: if you add 1 to 0 you get 1, if you add 1 to 1, you get 2, and so on. You can keep going until you hit infinity.

But the actual number of questions that we can pose is more than that. If you ask the question of how many numbers there are between 0 and 1, and prove that a computer could solve them all, you would try to prove that the numbers between 0 and 1 are enumerable, and thus, countably infinite. But if you say there are 3 steps, 0, 0.5, 1, you can further subdivide those to 0, 0.25, 0.5, 0.75, 1. And so on and so forth infinitely. Thus we can’t actually enumerate from 0 to 1, because any smaller gap from 0 to the number proposed has a sea of infinity between it, even if the number was infinitely small. Thus we can’t even count the numbers between 0 and 1. Thus, computers cannot solve all problems that we care about, since there are an uncountably infinite number of them, and computers can only count to infinity.

Since we know that computers can’t solve all problems, the next question is to ask if computers can solve some other questions we care about, like consciousness. Thinking about evolution, if the Earth and all life on it could be modeled as some large state machine, where every organism would have some set of states it could call every tick of life and all life on earth would be a collection of these. If life really acted in this way, it would be possible to have life on earth be simulated by a computer. But there’s an assumption that we could model life with some state machine, which is something computable. But is what we do captured by a state machine? The actions that we perform could possibly be computable, but the motivations may not be. And if so, consciousness would be fundamentally different actions in a state machine.