Alan Dix, Lancaster University [ my comments on Gott's Grim Reckoning || synopsis of GGR || anthropic principle || related links ]
by J. Richard Gott III
New Scientist, 15 Nov. 1997, pp 36-39
This is a brief summary of Gott's New Scientist article to put my comments on his article in context.
You can read the article in the New Scientist archive but only if you have an appropriate subscription [direct link to article]
Gott describes a visit to the Berlin Wall in 1969. At the time he wondered how long it would last and started to make some calculations. His visit was not special, just a chance visit during a European holiday, and so was as likely to be near the beginning of the Wall's lifetime as its end. If his visit was a random point during the Wall's lifetime there is a 50% chance it lies somewhere between the first 1/4 and the last 3/4 of the lifetime. Given the wall had been up for 8 years this meant there was therefore a 50% chance that the remaining lifetime was between two and two-thirds years (if he happened to be at the 3/4 point of the life of the wall) and 24 years (if he happened to be at the 1/4 point).
Years later, after the collapse of the wall, he realised the same argument could be applied more widely and he wrote a paper (Nature, vol. 363, p315, 1993) describing it. Statisticians would regard a 50% chance as being a bit weak for prediction, but the argument can be repeated for any desired probability (or confidence interval in statistics parlance). In this case, there is a 95% chance that a random moment during the duration of a phenomenon will lie between the first 1/40th and the last 1/40th. I the former case, we would expect the phenomena to last 39 times linger than it has already, in the latter case 1/39th as long.
Gott relates this argument to the Copernican principle, that is that we are not at a special place in the Universe (the earth is not the centre), but just a typical place. (This same principle of relativity underlies Newtonian dynamics (relativity of speed), Einstein's special relativity (relativity of the speed of light), and Einstein's general relativity (relativity of acceleration).) Gott's reasoning could therefore be seen as a Copernican principle of events.
The 'grim reckoning' of the title comes when he applies this to the survival of humanity. With 200,000 years of existence behind us, Gott's fleeting visit is a random occurrence within the duration of homo sapiens. Using his calculations there is, with 95% certainty, between 1/39th of this time and 39 times as long to go, that is between 5100 years and 7.8 million years before the demise of our race. Applied to space travel with only a mere 32 years under its belt, the end is likely within 1248 years.
Gott's article rightly points out that the above calculations are dependent on the point in time not being special. It would be reasonable, he says, to apply this to one's current relationship as the arrival of New Scientist (or even this web page) is a random point within it. However, it would be wrong to apply it to the bride and groom at a wedding ceremony. This is not a random point in the life of the marriage, but a special point, the beginning. Therefore the analysis cannot be applied. Also, the argument can only be applied in its simple form if there is no other evidence.
In my comments I note two reasons why the analysis cannot be applied to the history of humanity. The first is due to the reflexive nature of Gott's observation. he could only make it during the stage in which humanity has developed sophisticated probabilistic reasoning. This changes ones view of which phenomenon is significant (homo sapiens or homo statistica), but not the basic structure of the argument. The second critique is more damaging, in that the event is not a random event, but a special one, namely the first.
To see why the latter is important, suppose Gott had not been making a special, once in a lifetime, post-graduation European tour, but instead was a business traveller making irregular, but frequent, approximately monthly, visits to Berlin. Applying this argument to his first visit to the Berlin Wall would clearly not be appropriate. He would predict that nothing could last more than 39 months! Knowing that an observation is indeed at a random point in the duration of a phenomenon, is clearly quite difficult.
Another word of warning is that events one is likely to apply such reasoning to are precisely those which you encounter. If the nature of events in the world change over time (i.e. the world is not stationary in the statistical sense) then one is likely to observe the older events towards their end and the newer events towards their beginning. Imagine sampling people at random. One might predict with 95% confidence that they will live to no more than 40 times their current age, or that their expected age of death would be twice their current age. In a stationary population (assuming everyone lives to exactly a Biblical three score years and ten), the average age of someone you sampled would be 35 and the prediction of twice that number would be accurate (of course your actual predictions would range from nothing to 140 years depending on the person chosen, but the average prediction would be 70). If however, you were sampling from a population in rapid growth (as in Africa today), the life expectancy of everyone would still be 70, but the average age would be well below 35 and your estimate too low. In the UK with birth rates below replacement, the estimate would be marginally too high.
Having said all this, of course the most important thing about Gott's Copernican principle of events is that, even if it is not quite valid for predicting homo sapiens' future, it is great fun.
Alan Dix
Lancaster University
alan@hiraeth.com
alan@hcibook.com