The Asymptote of Importance
Jun 30th, 2009 by Micah Tillman | 7 Comments |
Today I got a letter.
It told me my education is “more important today than ever.”
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That’s a theme I hear a lot. Keeping track of my finances is more important than ever before. Energy efficiency is more important now than ever. Cultural sensitivity is more important than it’s ever been. Etc.
And since I’ve been hearing such things ever since I can remember, I thought to myself:
“Why haven’t all the various importances reached infinity by now? If they’re constantly going up, and seem to have been going up forever, what sense does it make to say they’re any higher now than before? Infinity plus one equals infinity.”
(What is the unit of measure for importance, anyway?)
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Then I realized that perhaps the various importances had been increasing forever, but had all been approaching some asymptote or other.
But do curves actually reach their asymptotes in infinity? If they do, then every importance would have reached its asymptote by now (if they’d been increasing forever).
Oh, whatever. Enough of this post.
Seems to me that if the absolute importance of everything is increasing, then proportionally or relatively speaking, they’d all be staying the same… If education was once worth 10 importounits, and at this time, there was 100 importounits to be had, even if education is now worth 50 importounits, if the total is 500, then really, nothing much has changed.
This post is more important now than ever before. I give it 501 importounits.
Jeff–
Ooo. That’s something I hadn’t thought of. Interesting. I think you’re right.
Proportions rather than absolute measures.
Hmmm. . . .
Adam–
*laugh* That pleases me greatly. :-D
Continuing the proportionality thought, what we really need is at least one thing’s level of importance to remain constant, or even decrease.
Otherwise, we just have importance or value “inflation.” Perhaps we need to institute some kind of Axiological Reserve (rather than Federal Reserve) to try to keep value inflation under control.
Maybe it could keep a store of oxygen. It seems like oxygen ought to keep a pretty constant level of importance.
(Saying ‘oxygen is more important than ever before’ would imply that it used to be a little valuable in terms of cellular respiration)
Everything is increasing in importance exponentially. Since the derivative of exp(x) is exp(x), that means that the rate of increase is also increasing in just the same way, as is the rate of increase of the rate of increase of the increase, and so on. It doesn’t matter what units of scale you use. In fact, the curve y = exp(x) is the only curve besides a straight line that looks just like itself when you blow it up at any scale.
So when Socrates complained about youth, and we complain in the same way, we merely show that complaining is exponential:
And Socrates was two and a half millennia ago!
What is the world coming to?