There is no algorithm that makes an algorithm

Note that this proof is not verified academically. It's just my opinion.

We know every computational algorithms can be made by Turing Machine. I assume that I have Turing Machine M that verifies the Turing Machine N correctly implements the description w, on input <N,w>. In other words, M accepts <N,w> if Turing Machine N correctly implements the algorithm based on description w. I shall try to run M on input <M,w> that w would be the description "M is the Turing Machine that implements the description w correctly". The proof is to reduce Acceptance Problem of Turing Machine to this. 

1. On input <A,w>, create a new string input w' = "A is the Turing Machine that correctly accepts string w".

2. Run Turing Machine M on input, <A,w'>

3. Accept if M accepts, reject otherwise.

Since Acceptance Problem of Turing Machine is not recursive, so is this.

Therefore, there is no algorithmic procedure to make an algorithm.


 Consider the question in the movie "Ex Machina". Is it possible to make a Artificial Intelligence(AI) program have consciousness. Before consideration in detailed, here is a specific example of "consciousness". Suppose you are having a lunch. You know the procedure how to pick up a pizza, and put it into your month. And, you also know you can stop having lunch, and leave the restaurant. However, if you make an AI program being able to have lunch, the program would not be able to leave the restaurant. Thus, what I mean by "an AI having consciousness" is that the AI program is aware of what she's doing, and she have an option not to do what she is doing. Now we know there is no algorithmic procedure to figure out a given algorithm is right or wrong on input description w. Therefore, no algorithm can create an algorithm on input description w. Furthermore, no algorithm can describe what a given algorithm does on input algorithm M.


It is proved that we can't make an AI that has consciousness. I have two questions at this point: so is not possible to create an AI people imagine? even human being has consciousness?

My opinion to the first question is that at least is not possible for Turing Machine. Imagine the future. Is human civilization still going to use Turing Machine as their main computational theory? if not, what will it be?

Second, we don't know why we are living. We don't know what we are doing? This proposition has been a long question to many philosophers. What I think is that only the amount of brain accepts is allowed to have consciousness.