The Copernican Principle

I saw a recent article in the New York Times, â€œA Survival Imperative for Space Colonizationâ€ that grabbed my attention. I know it isnâ€™t necessarily related to DNA, but I loved the article and the essence behind it, The Copernican Principle.

The Copernican Principle, is named after Nicolaus Copernicus, who stated that the Earth is not in a central, specially favored position. Although it might look like our galaxy is the center of the Universe, observers in all other galaxies would observe the same thing. This idea has been applied to the field of statistics. For example, if you are observing something and your location is not special, then you are observing the thing at a random point during its existence. That is, there is a 95% chance that you are seeing it in the middle 95% of its existence, and not during the beginning 2.5%, or the last 2.5%. That idea can be expressed using the following formula:

(1/39) tp < tf < 39 tp (P = 95% )

tp = past longevity (how long something has already existed)

tf = future longevity

Okay, now for an example letâ€™s use my lifespan. If Iâ€™ve been alive for 377 months, then there is a 95% chance that I will continue to live between 9.67 months and 1225 years. Hopefully, 9.67 months is on the low side! If Iâ€™ve been married for 57 months, then there is a 95% chance that I will continue to be married between 1.46 months and 185 years. Note the Copernican Formula does not work well for the very young and the very old, people who are already in the beginning 2.5% or final 2.5% of their longevity.

Now when I first saw results like these, my thought was â€œso what, itâ€™s such a large range how can it be useful?â€ But then I read about some of the applications of the formula by J. Richard Gott III, the subject of the New York Times article. In 1993, Mr. (Dr.?) Gott used the formula to predict the longevity of all 44 musicals currently on and off Broadway. To date, 40 of the 44 musicals have closed, and all 40 were within the timeframe predicted by the Copernican Formula. A few examples:

Kiss of the Spider Woman (tpast = 24 days, tfuture = 765days)

Miss Saigon (tpast = 777days, tfuture = 2803 days)

The Copernican Formula was also used to predict the longevity of the 313 world leaders in power in 1993. As of 2003, all but one of the cases has been decided, and the Formula was right in 295 cases and wrong in 17 cases. That is a success rate of 94.55%.

Here you can see a story from the New Scientist about the Copernican Formula, and here you can even use a calculator to predict longevity.

In the New York Times story, Mr. Gott discusses the vast importance of future spaceflight to the human race and then opines that there is a 50% chance that we are in the second half of the duration of spaceflight (which has been 46 years). I donâ€™t agree with his reasoning here, as he seems to abandon the true usefulness of the Copernican Formula. So, I thought it would be more fun (and better math) to apply the Copernican Formula to predict the longevity of human spaceflight. Given that we have been in space for 46 years, there is a 95% chance that space exploration will endure between 1.18 years and 1,794 years. I wonder, though, if weâ€™re still in the beginning 2.5% of spaceflight, suggesting that the Principle isnâ€™t very useful for analysis in this situation. I guess weâ€™ll know the answer to that in a few thousand years.

I also found an interesting post about the Copernican Principle at TierneyLab at the New York Times. Comment #80 to the post, written by PSD, contained a few interesting additions.

First, the Copernican Principle requires 3 assumptions:

â€œOne, the given process has a definite beginning in time. Two, the given process will have a definite end. And three, the only information to be used concerning the given process is its known time of duration, regardless of what other information may exist about the process itself or similar processes. In essence, we treat the total (start to finish) duration as if it is completely random: not only could the end occur at any time, but it has an equal chance of ending at any given time. We do not assume to know what those chances are, only that they are constant with time for a given process. All of the examples (thus far) of supposed problems with Dr. Gottâ€™s method are assuming non-randomness and a knowledge of how the chances (of the process ending) vary with time.â€

Second, the Copernican Principle can be used in reverse:

â€œAs an aside, Dr. Gottâ€™s statistical method can be applied in reverse to find the statistical certainty associated with a process having begun within a given time span. The data point required to work backwards is the time span between when it became known that the process was occurring and the time at which the process ended.â€

Can you come up with any useful predictions using the Copernican Formula?