But that doesn't take away from the fact that an intelligent human could look at a source printout and figure out if it halted or not, but no general algorithm can be deduced that would do so.
Consider the case in which the source code distributed represents a complete simulation of one of the players. That is, it contains his genetic profile, encoded representations of all of his experiences, and any other input data that may have shaped his existence up to exact point at which he makes the game's crucial decision.
Now, modify that source code so that if the simulated player chooses "doesn't halt," the program enters an infinite loop (just as one would do to demonstrate the limitations of algorithms). If "he" doesn't halt, he loses. If "he" halts, he also loses.
Obviously, this depends on the ability to algorithmically simulate human consciousness, and there are some who say that this is not possible. However, my point is that people are often too quick to turn to the halting problem as proof that human intelligence is somehow fundamentally superior to algorithmic intelligence, when in fact we don't know for certain that they're not equivalent.
Slashdot Mirror
But that doesn't take away from the fact that an intelligent human could look at a source printout and figure out if it halted or not, but no general algorithm can be deduced that would do so.
Consider the case in which the source code distributed represents a complete simulation of one of the players. That is, it contains his genetic profile, encoded representations of all of his experiences, and any other input data that may have shaped his existence up to exact point at which he makes the game's crucial decision.
Now, modify that source code so that if the simulated player chooses "doesn't halt," the program enters an infinite loop (just as one would do to demonstrate the limitations of algorithms). If "he" doesn't halt, he loses. If "he" halts, he also loses.
Obviously, this depends on the ability to algorithmically simulate human consciousness, and there are some who say that this is not possible. However, my point is that people are often too quick to turn to the halting problem as proof that human intelligence is somehow fundamentally superior to algorithmic intelligence, when in fact we don't know for certain that they're not equivalent.