linkpoint1's comments

The experiments about people with their brain hemispheres separated indicate that conciousness is an effort of many mental areas to create an integrated and coherent mental state. For example, consider subjects whose verbal area is separated from their visual area, when the subject tries to explain what he saw he tell us an imaginary story. This strongly suggests that our brain is working hard to integrate all the information that it receives. At this moment, I can't recall any concrete experiments, but they are something like this: one of your eyes see a message telling that you kid is crying, then you begin to try to phone home, when asked what are you doing, you gives some explanation like my kid was acting a little strange this morning, I need to call to see what is happening at home. More on split-brains and dual conciousness theory at https://en.wikipedia.org/wiki/Dual_consciousness

if you program in Lisp the function list-length gives nil for circular lists. Ninety-nine problems contains similar problems with lists.

I should have said that the difference between increments must be coprime with n to guarantee that the differece becomes 0 module n, that is both pointers get equal.

A proof that the algorithm detects the existence of a cycle.

If there is a cycle of length n then eventually both pointers get into the cycle. Since at each step the distance between the two pointers is increased by one module n then the distance becomes zero. Also the time to detect the loop is bounded by the time it takes both pointers to get into the loop plus the cycle length. Also this proof shows that the key ingredient is that the difference between the pointers must be coprime with n but still n steps are required to guarantee that the difference eventually becomes zero. So there is no advantage in choosing other values for the increment of the pointers except to achieve that the slowest get faster into the cycle.