First of all, when we say that the program halts, does this mean that the program comes to a final answer, and therefore stops running? I believe that this is what it means, so I'm going to take that as a fact. I just don't get why trying to solve the halting problem is a very smart idea, or even logical. Let's say i invite a program that tells us if a program halts while running a certain value. Well, that is great, but what is the actual value? One might say, well now you know that you can get an actual value when the program is run with the specific value. This is true, but wouldn't it be better to just write your program and put in the value and let it run for a long time? If you don't do this, you have to write your program, then say to yourself, I wonder if this program halts with this value. Then you spend a really long time trying to write another program telling you whether your original problem halts or not. I am basically just thinking out loud here, and I by no means claim to be educated on this subject. In fact, I am uneducated on this subject. However, I just want to see if anyone shares these beliefs, or knows of a way to show my logic is flawed. --Aoser 17:49, 14 November 2008 (UTC)
Response:
The halting problem is important because is gives an example of a problem which can not be answered through computation (at least, Turing Machine computation). The idea behind the halting problem is to answer the question "What can't a computer (Turing Machine) do?". We use that knowledge about the limits of computers to ask questions about whether or not Artificial Intelligence can match Human Intelligence, and about the limits of the human mind itself.
--Nathan Claus 21:14, 16 November 2008 (UTC)
