The nature of reason itself

While studying the Dijkstra algorithm for networks to compute the shortest path I developed a method that has "Big O" constant time. I studied this very thoroughly including interviews with the originator and many different variations on the theme. I am absolutely certain that this is true because I can physically test it with a network. The relationship of this and TSP would suggest that it influences the possible running times of TSP, though I have not yet considered it.

The real problem is not that it is provable, but that it is assumed that it is impossible and general accounts say that it is perhaps provable to be at least some larger factor complex. The method to trisect ,or for that matter n-sect, any angle with compass and straight edge was said to be provable impossible. Similar to this. It suggests that my methods are in conflict with generally accepted practice. I must assume that the practice is at fault since it has a physical proof. Experimental observable and operational results always trump any theory. Thus it is a source of great confusion. If the methods of analysis can't always be trusted, then there is a critical flaw in how the methods are defined or applied.

At this moment I have no idea what that might be, but I suspect it revolves around the basic assumption that there is singularity and that reasoning proceeds from unity to infinity and fails because of this. My method is to assume infinity in all things and work backward to a limiting scenario.

I am confounded by two incidents where it is assumed that a certain logic is impeccable and yet fails. I have also been studying the nature of secure communications and if I discover that the security methods as applied to the Internet are crackable by some tractable process then the consequence is dire. I suspect that it is so, but have no real answer as yet.

On another topic, the Spartans were some kind of f'd up society IMHO. They rejected intellect and trained themselves to die in physical conflict that an ape could mimic. They were eventually deselected , of course , but I do not understand the admiration of the ethic which included killing the weak and disposing of new born children if they were not physically fit. The concept that physical strength and viciousness is the prime biological selector in a species with such a long generational scale is absurd.