When Can We Expect the Final Curtain?

Exploring the Doomsday Argument

A version of this article appears in my book, Twisted Logic: Puzzles, Paradoxes, and Big Questions (Chapman and Hall/CRC Press, 2024).

CONTEMPLATING OUR EXISTENTIAL PREDICAMENT

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The Doomsday Argument is a statistical and philosophical approach predicting humanity’s potential end. It uses principles of probability to suggest that humanity might be closer to its demise than we commonly believe.

PROBABILITY AND ITS IMPLICATIONS

Imagine attempting to estimate your enemy’s tank count. The tanks are sequentially manufactured, starting from one. You uncover serial numbers on five random tanks, all being under 10. In such a scenario, an intuitive grasp of probability would lead you to believe that your enemy doesn’t possess a large number of tanks. However, if you stumble upon serial numbers stretching into the thousands, your estimate would justifiably swing towards a much larger count.

In another scenario, consider a box filled with numbered balls, which can either contain ten balls (numbered 1–10) or ten thousand balls (numbered 1–10,000). If a ball drawn from the box reveals a single-digit number, such as seven, it is reasonable to assume that the box is much more likely to contain ten balls than ten thousand.

INVOKING THE MEDIOCRITY PRINCIPLE AND COPERNICAN PRINCIPLE

The tank and numbered balls examples tie closely to the concept of mediocrity, as captured in the ‘mediocrity principle’. This principle suggests that initial assumptions should lean towards mediocrity rather than the exceptional. In other words, we are more likely to encounter ordinary circumstances rather than extraordinary ones.

The Copernican principle dovetails with the mediocrity principle. It argues that we are not privileged or exceptional observers of the universe. This principle is rooted in Nicolaus Copernicus’s 16th-century finding that Earth does not occupy a central, special position in the universe.

GOTT’S WALL PREDICTION

Astrophysicist John Richard Gott took the Copernican principle to heart during his visit to the Berlin Wall in 1969. Lacking specific knowledge about the Wall’s expected lifespan, Gott took the position that his encounter with the Wall did not occur at any special time in its existence.

This assumption allowed him to estimate the future lifespan of the Wall. If, for instance, his visit was precisely halfway through its life, the Wall would stand for another eight years. If he visited one-quarter into its life, the Wall would stand for another 24 years. If visiting it three-quarters along its timeline, the future would be one-third of its past. Because half of its existence is between these two points (75% minus 25% is 50%), there was a 50% chance that it would last a further period between one-third and three times its current existence. Based on its age when he observed it in 1969 (eight years), Gott argued that there was a 50% chance that it would fall in between 8/3 years (2 years, 8 months) and 8 × 3 (24) years from then.

The Berlin Wall fell in 1989, 20 years after Gott’s visit and roughly 28 years after it was built. This bolstered Gott’s confidence in the Copernican-based method of making predictions, which he termed ‘Copernican time horizons’.

The implications of Gott’s Wall are far-reaching. They suggest that we could potentially apply the Copernican principle to make predictions about other systems where we have little information about their total lifespan. For example, it could be applied to predict the lifespan of a company, the duration of a war, or the longevity of a species, among many other things.

However, it’s essential to acknowledge the limitations of this method. It is predicated on the assumption that there is nothing special about the moment of observation, an assumption that may not hold true in many scenarios. Despite these limitations, Gott’s approach represents a fascinating application of the Copernican principle to real-world events, demonstrating how our position in time, just as in space, can be used to gain insights about the world around us.

THE LINDY EFFECT AND ITS LIMITATIONS

Gott’s method finds resonance with the ‘Lindy effect’, the name of which is derived from a New York delicatessen, famous for its cheesecakes, which was frequented by actors playing in Broadway shows. It suggests that a show that had been running for three years could be expected on average to last for about another three years.

However, the Lindy effect has limitations. It breaks down when applied to processes like biological ageing. For instance, a human who has lived for 100 years is very unlikely indeed to live another 100 years. The factors influencing human lifespan are far from random, rendering the Lindy effect ineffective for such predictions.

FROM COPERNICAN PRINCIPLE TO DOOMSDAY ARGUMENT

The Doomsday Argument employs Gott’s idea to estimate the Doomsday date for the human race. Applied to humanity, the argument contends that if we consider humanity’s entire history, we should statistically find ourselves somewhere around the middle of that history in terms of the human population. If our population continues to grow exponentially, this suggests that humanity has a relatively short lifespan left, potentially within this millennium.

ESTIMATES AND PROJECTIONS

This projection takes into account the fact that there have been approximately 110 billion humans on earth to date, 7% of whom are alive today. Following demographic trends forward and estimating how long it will be for a further 110 billion humans to be born, the Doomsday Argument anticipates humanity’s timeline is likely to end well within this millennium.

DEBATE AND CRITICISMS

The Doomsday Argument is not without its critics. Some argue that humanity will never go extinct, while others highlight that the argument’s assumptions might not hold true, such as the assumption that humans are at the midpoint of our existence timeline. Others claim that the argument fails to account for future scientific and technological developments that might significantly extend, or perhaps foreshorten, humanity’s lifespan.

CONCLUSION: THE FATE OF HUMANITY?

The Doomsday Argument provides a thought-provoking perspective on humanity’s potential fate. It integrates probability, statistics, and philosophical principles, offering a statistical guess at our collective demise. While it is far from conclusive, it is certainly important in serving as a reminder of our finite earthly existence and the urgency to address the global threats that could precipitate our doom. Whatever else, the debate around the argument and our ultimate fate as humans will persist, sparking further exploration into this fascinating intersection of probability, philosophy, and existential prediction.