2013! what's the difference between running a program (interpreting it), and compiling it? where's (and what's) the line that distinguishes the program from t

2013! what's the difference between running a program (interpreting it), and compiling it? where's (and what's) the line that distinguishes the program from the output of the program where both parts are just software? -- the most interesting thing about turning machines is the universal turing machine because it actually invents/defines/showcases software as we understand it nowadays; this makes me reflect on how the busy beaber problem just misses out on this realization