This is known as the halting problem, and we don’t know how to build any machine that could solve it.
Humans can’t “solve” it either, in that sense. We can pattern-recognize that some programs will halt or not halt, but there exist huge spaces of programs in between where we would be just as helpless to give a yes or no answer as any computer program.
I’m not sure what this should be considered evidence of, but somehow it seems relevant. ;-)
For that matter, it’s perfectly possible to build algorithms that can accurately tell you whether or not some systems will halt—certain types of infinite loop are easily machine-detectable, to give one simple example. It’s doing it in the general case that’s impossible.
Humans can’t “solve” it either, in that sense. We can pattern-recognize that some programs will halt or not halt, but there exist huge spaces of programs in between where we would be just as helpless to give a yes or no answer as any computer program.
I’m not sure what this should be considered evidence of, but somehow it seems relevant. ;-)
For that matter, it’s perfectly possible to build algorithms that can accurately tell you whether or not some systems will halt—certain types of infinite loop are easily machine-detectable, to give one simple example. It’s doing it in the general case that’s impossible.