I could write a program in Java or C or C++. Calculate the square root of 2 to 4 decimal places. If the computer could think- it would think 1, 4, 1, 4, 2. I don't think it would have the capacity to figure out what the heck I was really asking it to do. I don't think it could figure out that I was looking for the length of the legs of a triangle with hypontenuse of length of one unit. In this case the program would be an extension of my will, looking for a decimal approximation of a non repeating non terminating decimal.
If the computer can reverse engineer the process, I would change my mind here.