DDoomsday: A Response to Simpson’s Second Question
Mike LamptonSpace Sciences Lab, UC Berkeley [email protected]
Abstract
The Doomsday Argument (DA) has sparked a variety of opinions. Here I address a key question posed byF. Simpson (2016) that confronts the views of DA proponents and those who, like me, oppose the DA. Iagree that typical locations within a complete spatial distribution are calculable using ordinary frequentistprobability. But I argue that the temporal probability distribution is unknown: we have records of ourpast yet are ignorant of our future. It is this asymmetry that upsets the idea of Copernicanism in time.Although frequentist methods do not apply to this asymmetric situation, Bayesian methods do apply.They show that the various Quick Doom and Distant Doom scenarios are equally likely. I conclude thatthe DA has no predictive power whatsoever.
Keywords—
Doomsday, Copernicanism, Bayes theorem
How long into our future will mankind last? The “Doomsday Argument” (Carter 1983,Gott 1993, Leslie 1996, Leslie 2010) is an effort to answer this question quantitatively. Theargument is based on the fact that samples from a known distribution are rarely found atits extreme ends. In only 1% of random draws would a sample be found in the distribution’sfirst percentile zone. So, the argument goes, there is only a 1% chance of finding our presenthuman rank number less than × if mankind’s total span is × individuals. Largerspans make this probability even smaller. Since we are all reluctant to accept unlikelysituations, we should be reluctant to accept the notion that the total span of humanity willexceed × individuals.I will not attempt to summarize the many discussion points on this topic except to direct thereader to five related discussions (Oliver and Korb 1998, Monton and Roush 2001, Northcott2016, McCutcheon 2018, Lampton 2019). Here I want to focus on question 2 raised by FergusSimpson (2016) that concisely captures the issue: can probabilistic arguments constrain ourfuture?“Q2. Why would your spatial location relative to other humans appear represen-tative of the parent population, but not your temporal one?” a r X i v : . [ phy s i c s . pop - ph ] F e b Spatial Distributions
In Figure 1, I show the distribution of the world population with respect to latitude. Livingin California, I find myself at latitude +37 deg and so I am at about the 60th percentileof latitudes, typically situated among the people of the world: not an extreme outlier.The entire distribution is known: each individual can be located in the chart, according tolatitude, with the span −
90 deg to +90 deg encompassing the entire human race. Becausethe distribution is known, frequentist probability applies. I must find myself in one of theseone-degree bins, so the sum of my bin probabilities is 1. Figure 1: World population vs latitude. Green: differential. Blue: cumulative percent.
In Figure 2, I show the cumulative growth of world population versus time. There is a keydifference from the cumulative distribution seen in Figure 1: here it is plotted as the numberof individuals, not as a percentage. It is merely the beginning of an integral, and unlikeFigure 1, it cannot be normalized to because we do not have the future data requiredto normalize it. l o g C u m u l a t i v e W o r l d P o p u l a t i o n Kandea,T., U.N. Pop.Ref.Bureau 2017 population3.py
Cumulative World Population
Figure 2: Cumulative number of persons versus time, worldwide
Returning to Simpson’s question 2, how do these cases differ? My reply is that the spatialdistribution is known, and my rank within this distribution is in principle measurable. Incontrast, the eventual extent of mankind’s growth is unknown: we can gather populationdata from our past but not from our future. Given some evidence, Bayesian logic provides away to quantitatively compare two alternative hypotheses. In an earlier treatment (Lampton2019), I evaluated the relative likelihoods of various Quick Doom and Distant Doom scenariosgiven the evidence that mankind has, so far, numbered about × individuals. The resultis exactly what you would expect: given only past data, those scenarios are equally likely.Given only what we know now, we have no way to decide between them. References
Carter, B. "The anthropic principle and its implications for biological evolution," Phil. Trans.Royal Soc. London A310, pp.347-363 (1983).Gott, J.R., "Implications of the Copernican Principle for our future prospects," Nature v.363,27 (1993).Lampton, M., "Doomsday: Two Flaws," arXiv 1909.11031 (2019).Leslie, J., "The End of the World," London and New York: Routledge, (1996).Leslie, J., "Risk that Humans will soon be extinct," Philosophy v85 No.4 (2010).McCutcheon, R., "What, Precisely, is Carter’s Doomsday Argument?" https://philpapers.org,(2018) cCutcheon, R., "In Favor of Logarithmic Scoring," Phil. Sci. v86 No.32 286-303 (2019)Monton B. and Roush S., "Gott’s Doomsday Argument," https://philpapers.org (2001).Northcott, R., "A Dilemma for the Doomsday Argument," https://philpapers.org (2016).Oliver, J. J., and Korb, "A Bayesian Analysis of the Doomsday Argument," Monash U.(1998).Simpson, F., "Apocalypse Now? Reviving the Doomsday Argument," arXiv 1611.03072(2016).cCutcheon, R., "In Favor of Logarithmic Scoring," Phil. Sci. v86 No.32 286-303 (2019)Monton B. and Roush S., "Gott’s Doomsday Argument," https://philpapers.org (2001).Northcott, R., "A Dilemma for the Doomsday Argument," https://philpapers.org (2016).Oliver, J. J., and Korb, "A Bayesian Analysis of the Doomsday Argument," Monash U.(1998).Simpson, F., "Apocalypse Now? Reviving the Doomsday Argument," arXiv 1611.03072(2016).