And I suppose once you've reached zero you can't subtract any more because there aren't any numbers less than zero?
Nope, but once you get to the North Pole, can you keep going North beyond the North Pole?
Clearly this just means that "north" is a poorly defined direction. Try the same thought experiment with the East Pole and you'll find that you can easily keep going east.
No, what this means is that "North" is well-defined, and "East" is poorly-defined. The point of poles is that they allow opposites. If you admit an "East pole," then that means that a "West pole" is naturally defined to be directly on the other side of the globe.
Essentially, if we say that some location is "East," rather than just some direction being "East," then we'll get the situation Neruz has outlined. The question is whether or not humanity is a direction or a state of being (i.e., is humanity a "location" on our map). I'd say that people are defined with a direction, to be sure, because there is such a thing as "more or less human." However, it seems apparent that we
do have a Human Pole, because people exist as well-defined entities with various characteristics.
This brings me to my next point:
Perhaps a better way to explain what I'm trying to say is that F(human) would take all the things that make us human (perceptively, not biologically) and make them more so.
The truth is that we're already doing this, though, by considering "human" as a generalized category. We're working with the human archetype, which is to say the very essence of humanness. It's the difference between holotypes and paratypes, if you want. The concept in our mind of what constitutes "human" is already more human than any one human, or really than the group as a whole (if we take a good hard look at ourselves).
This is especially important if you think about it this way: what is f
42(human), under your definition? We'll end up with something that is more and more "human," but will really have gross exaggeration of human characteristics until it reaches the point of monstrosity. Just like "east" and "west" ultimately don't mean much without referencing poles, the function won't mean much, either.
That's even more true on a sphere with no other poles defined. If we don't have any reference points whatsoever, we're going to be totally screwed. We need some sense of direction and markers to go exploring, and in this case we've got no sun or stars.
What this really means is that if we don't define a "human pole," so to speak, so that f(human) == human, our function will be extremely poorly defined. It looks like it's best to go with the previous idea of f as a closure operation, so that f is idempotent on the space of anthropomorphizable stuff. That way it will have all kinds of nice properties for free.
The next question is what kind of output we'll get for a subset, like the chimeric function other people have been talking about.