"Carter Catastrophe": The Math Equation That Predicts The End Of Humanity

Since we became a (semi) intelligent species and started studying the cosmos, humanity has been on a long journey to realizing we are not the center of the universe, the galaxy, or even the Solar System.

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While disappointing for an egotistical species, this realization has led us to discoveries about the real nature of our universe, or at least models closer to the truth. Though there have been challenges to the idea that the universe is homogeneous and isotropic in all directions, assuming that it is has led us to predictions about the cosmic microwave background (CMB) and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, which describe an expanding universe, later confirmed in astronomical observations.

“The Copernican principle is a cornerstone of most of astronomy, it is assumed without question, and plays an important role in many statistical tests for the viability of cosmological models,” Albert Stebbins of Fermilab explained to Phys.org in 2008. 

"It is also a necessary consequence of the stronger assumption of the Cosmological Principle: namely, that not only do we not live in a special part of the universe, but there are no special parts of the universe – everything is the same everywhere (up to statistical variation)."

"It is a very handy principle, since it implies that here and now is the same as there and now, and here and then is the same as there and then. We do not have to look back in time at our current location to see how the universe was in our past – we can just look very far away, and given the large light travel time, we are looking at a distant part of the universe in the distant past. Given the Cosmological Principle, their past is the same as our past."

As well as this, there is the anthropic principle: the idea that conscious observers like us can only exist in a universe that supports life. Perhaps there are many universes out there that do not support life, and we should not be surprised to find ourselves observing in a universe that does support life. Or perhaps the universe is not the same everywhere. According to some physicists and philosophers, there may be more useful information to be gained from applying the Copernican and anthropic principles to time. A smaller subset believe that this could be used to place constraints on how long humanity has left to survive.

The argument was first presented by Australian astrophysicist Brandon Carter, for which it briefly earned the name the "Carter catastrophe". The basic idea is that we should not assume we are in a special region in time as well as space. Over all time, there will be a finite number of humans, say 1 trillion for ease. Statistically, you should assume that you are born at a random point in humanity's history, not some special moment such as the beginning or the end, where most typical observers should be.

"Assuming that whatever we are measuring can be observed only in the interval between t_begin and t_ends, if there is nothing special about now we expect t_now to be located randomly in this interval. The estimate t_future = (t_end-t_now) = t_past = (t_now-t_begin) will overestimate t_future half the time and will underestimate it half the time," astrophysicist J. Richard Gott wrote on the topic in 1993.

"If r₁ = (t_now - t_begin)/(t_end - t_begin) is a random number uniformly distributed between 0 and 1, there is a probability P=0.95 that 0.025<r₁, <0.975, or equivalently:

1/39 t_past < t_future < 39t_past(95% confidence level)

Similarly,

1/3 t_past<t_future <3t_past(50% confidence level)."

According to Gott, the amount of time that something has been observable in the past provides a rough guide of how robust it is against potential danger and catastrophe in the past, but also how likely it is to survive into the future. For this equation to "work" (let's bear in mind this is probabilistic, and there are many variables that could alter it), all you need is to assume that your own position in time is random within that distribution of possible times.

Predicting the end of humanity is not something that is easily tested, unless we leave the conclusion to robots / the hyperintelligent group of mole people who inherit the Earth when we're gone. But Gott used this analysis on a less dramatic event, the fall of the Berlin Wall, to demonstrate how it works. In 1969, Gott visited the Berlin Wall and Stonehenge, which had been there for around eight and 3,900 years respectively.

"Assuming that I am a random observer of the Wall, I expect to be located randomly in time between t_begin and t_end (t_end occurs when the wall is destroyed or there are no longer any visitors left to observe it, whichever comes first). The Wall fell 20 years later, giving t_future = 2.5t_past, within the 95% confidence limits predicted by equation (1)."

The same equation predicts that Stonehenge should be observable, which it is.

"Equation (1) was satisfied not because my visit somehow caused the demise of the USSR but simply because in hindsight we can now see that the timing of my visit was unremarkable," Gott adds.

The idea, which has become known as the somewhat dramatic "Doomsday Argument", has been used to try and get a sense of where humanity may lie on its path to non-existence. Using a toy model, and estimates of the number of humans that have been born so far, Gott puts the expected total number of humans yet to be born at between 1.8 billion and 2.7 trillion (as of 1993), with a 95 percent confidence level.

Looking at birth and death rates, Gott suggests that we may not have all that much time left as a species. In fact, we could reach 1.8 billion new births in just over a decade. We'd still have to be on the unlucky side, but at this point, we could fit the bill of being randomly distributed observers, finding ourselves on Earth when the population has exploded, but very close to the end.

"Combining N_future <2.7 x 10¹² (equation (10)) with the current rate of 145 million births per year we find t_f<19,000 years unless the rate of births drops," Gott adds. "If we wish to stretch our survival out to the upper limit of 7.8 million years we require the average rate of births to drop by a factor of more than 400."

As outlined here, the equations are subject to factors such as birth rates, life expectancy, etc. For example, we could find a medical breakthrough that allows us to live much longer, or a physics breakthrough that significantly makes life more dangerous for everyone involved (we're looking at you, nuclear warfare). 

As well as this, there are problems with observer classes. For example, humans have evolved over a long time. Should our predecessors be included in the calculation? Or what if we were to meld with machines in the future? Should they be considered observers in this calculation?

In short, while it might be an interesting topic to look into, and could be a tool for investigating these sorts of questions, we wouldn't worry about it just yet. Extinction, most likely, will come after your own observation time is long over.