“If It Gets in the Way, Go Around It”

Normally, when I’m reading about international politics or hearing about it on the radio, I can’t help but giggle a little. It’s often just so damned funny: countires acting like squabbling kids on some playground. But when I was listening to NPR this morning, I heard a report about some international policies that fairly well blew me away.

You see, we Americans have a bit of a problem: our government doesn’t listen to us. In fact, sometimes, the current administration seems to be deliberately toying with us. When the voters say we don’t want to spend any more resources in our endless war on Iraq, the good old executive branch decides to send more resources. By now, fans of Orwell’s 1984 will be noticing a striking pattern. But recently, there arose a rare condition: somebody actually did something about the apparent deafness of our current administration.

The issue at hand is this: human beings have developed a surprising knack for destroying the planet. The American variety of human beings are especially good at it, with their ten-thousand-watt security lights hung on their houses like Christmas tree ornaments, and with their eight-ton Hummers that get about thirty miles to the tank. There are, of course some American-type human beings who are not particularly satisfied with this state of affairs, and wanted the government to perhaps consider doing something about it. But the dialogue went something like this:

Eco-Minded Americans: Mister Government, please do something about the people who are destroying all the good bits of the planet.

Mister Government: I am the decider, and I decide no!

Non-Eco-Minded Americans: Yeah! Continue tax breaks on expensive, lousy, polluting vehicles!

But, thank goodness, somebody realized that there was a problem here, and merry old England (or is it supposed to be called Britain? I never did figure that out) stepped in to help out its former colony. The result: British (English?) officials actually went around the government, and went directly to a handful of American states, in order to try to help get some reasonable “decider”-free environmental policies enacted. And I have just one thing to say about that: Finally!

Ultrafunctions Revisited

I was contemplating the properties of the ultrafuncton (see the previous post), and I was wondering if there might be some higher-level version of the ultrafunction, and I realized that the ultrafunction itself is that function. For example:

u(f(a), n) = f(f(f(f(…a…))) (f applied n times)

But then, it follows naturally that

u(u(f(a), m), n) = u(u(u(…f(a)…), m), m) (ultrafunction applied n times)

So therefore, even though in many nested-function-type situations, there is an infinite hierarchy of such functions (consider Knuth’s up-arrow system), in this case, this single function fills in the hierarchy all by itself.