I am nearly sure this piece refers to the work of J. Richard Gott.
I've personally found the principle, as stated, to be relevant to my life ever since I first read about it in 1993, so, if my experience is to be believed, you may not have to be in such a hurry to make use of it anymore.
Date: Sat, 5 Jun 93 14:59:26 EDT
Subject: Self-destructing stats
This is from the APS What's New Digest:
3. HURRY! MAKE USE OF THE "COPERNICAN PRINCIPLE" WHILE IT LASTS. An article in Nature can be ignored, but when it gets into the Science Times section of the New York Times, it has to be taken seriously. Right? Well, this week we learn that things have a 95% likelihood of being in the middle 95% of their lifetime. You aren't impressed, but stay with me. A Princeton astrophysicist points out that this simple fact allows you to derive limits for the longevity of just about anything--at the 95% confidence level. It's all because we are likely to be in a "nonspecial place." That's the Copernican principle. The author applies his powerful statistical concept to our specie--he's 95% sure we have 0.2 to 8 million years left. He can even derive the probability that humans will get around to building a "Dyson sphere"--it doesn't look good. (If you don't know what a Dyson sphere is, you aren't ready for this stuff.) Nature published the paper on 27 May 93, just 8 days ago; at the 95% confidence level, we predict that this theory will die between 8pm tonight and 20 April 1994.
Edited and converted to HTML by Dan Bornstein, email@example.com.