The Doomsday argument (DA) is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far. Simply put, it says that supposing the humans alive today are in a random place in the whole human history timeline, chances are we are about halfway through it. In some contexts, probabilistic argument means any argument involving probability theory. ... Prediction of future events is an ancient human wish. ... For other uses, see Future (disambiguation). ... The Human Race could be: The Human race. ...

It was first proposed in an explicit way by the astrophysicist Brandon Carter in 1983,^[1] from which it is sometimes called the Carter catastrophe; the argument was subsequently championed by the philosopher John A. Leslie and has since been independently discovered by J. Richard Gott^[2] and Holger Bech Nielsen.^[3] Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others. Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ... Year 1983 (MCMLXXXIII) was a common year starting on Saturday (link displays the 1983 Gregorian calendar). ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... Prof. ... For the eschatological beliefs of various religions, see End Times. ... He is a twat He was born in Vienna and died in Pescadero, California. ...

World population from 10,000BC to AD 2000

The Copernican principle suggests that we are equally likely (along with the other N-1 humans) to find ourselves at any position n, so assume our fractional position f is uniformly distributed on the interval (0,1] prior to learning our absolute position. Image File history File links Population_curve. ... Image File history File links Population_curve. ... Prehistory (Greek words προ = before and ιστορία = history) is the period of human history prior to the advent of writing (which marks the beginning of recorded history). ... Year 2000 (MM) was a leap year starting on Saturday (link will display full 2000 Gregorian calendar). ... In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ... In mathematics, the uniform distributions are simple probability distributions. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...

Let us further assume that our fractional position f is uniformly distributed on (0,1] even after we learn of our absolute position n. This is equivalent to the assumption that we have no prior information about the total number of humans, N.

Now, we can take an arbitrary number, say 95% confidence, that f = n/N is within the interval (0.05,1]. In other words we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. Given our absolute position n, this implies an upper bound for N obtained by rearranging

n / N > 0.05

to give.

N < 20n.

If we take that 60 billion humans have been born so far (Leslie's figure) then we can say with 95% confidence that the total number of humans, N, will be less than 20·60 billion = 1.2 trillion.

Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, one can calculate how long it will take for the remaining 1140 billion humans to be born. The argument predicts, with 95% "confidence", that humanity will disappear within 9120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that the human species may become extinct. Map of countries by population — China and India, the only two countries to have a population greater than one billion, together possess more than a third of the worlds population. ... Map of countries by population — China and India, the only two countries to have a population greater than one billion, together possess more than a third of the worlds population. ... This article is about the measure of remaining life. ... Longevity is a term that generally refers to long life or great duration of life.[1] Reflections on longevity have usually gone beyond acknowledging the basic shortness of human life and have included thinking about methods to extend life. ... The Human Race could be: The Human race. ...

Remarks

• The step that converts N into an extinction time depends upon a finite human lifespan. If immortality becomes common, and the birth rate drops to zero, N will never be reached.^[4]
• The total number of humans born so far may depend on one's definition of "human".
• A precise formulation of the DA requires the Bayesian interpretation of probability, which is widely, if not universally, accepted.
• Even among Bayesians some of the assumptions of the argument's logic would not be acceptable; for instance, the fact that it is applied to a temporal phenomenon (how long something lasts) means that N's distribution simultaneously represents an "aleatory probability" (as a future event), and an "epistemic probability" (as a decided value about which we are uncertain).
• The U(0,1] f distribution is derived from two choices, which whilst being the default are also arbitrary:
  • The principle of indifference, so that it is as likely for any other randomly selected person to be born after you as before you.
  • The assumption of no 'prior' knowledge on the distribution of N.

The Fountain of Eternal Life in Cleveland, Ohio Immortality (or eternal life) is the concept of living in physical or spiritual form for an infinite length of time, or in a state of timelessness. ... This article is about modern humans. ... Bayesian probability is an interpretation of probability suggested by Bayesian theory, which holds that the concept of probability can be defined as the degree to which a person believes a proposition. ... Statistical regularity has motivated the development of the relative frequency concept of probability. ... Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of statements, or to the degree of belief of rational agents in the truth of statements; when used with Bayes theorem, it then becomes Bayesian inference. ... The principle of indifference is a rule for assigning epistemic probabilities. ...

Simplification: two possible total number of humans

Assume for simplicity that the total number of humans who will ever be born is 60 billion (N₁), or 6,000 billion (N₂).^[5] If there is no prior knowledge of the position that a currently living individual, X, has in the history of humanity, we may instead compute how many humans were born before X, and arrive at (say) 59,854,795,447, which would roughly place X amongst the first 60 billion humans who have ever lived.

Now, if we assume that the number of humans who will ever be born equals N₁, the probability that X is amongst the first 60 billion humans who have ever lived is of course 100%. However, if the number of humans who will ever be born equals N₂, then the probability that X is amongst the first 60 billion humans who have ever lived is only 1%, such that the total number of humans who will ever be born is more likely to be much closer to 60 billion than to 6,000 billion. In essence the DA therefore suggests that human extinction is more likely to occur sooner rather than later. Human extinction is the as-yet hypothetical extinction of the human species, Homo sapiens. ...

It is possible to sum the probabilities for each value of N and therefore to compute a statistical 'confidence limit' on N. For example, taking the numbers above, it is 99% certain that N is smaller than 6,000 billion.

What the argument is not

The Doomsday argument (DA) does not say that humanity cannot or will not exist indefinitely. It does not put any upper limit on the number of humans that will ever exist, nor provide a date for when humanity will become extinct. In biology and ecology, extinction is the ceasing of existence of a species or group of species. ...

An abbreviated form of the argument does make these claims, by confusing probability with certainty. However, the actual DA's conclusion is:

There is a 95% chance of extinction within 9120 years.

The DA gives a 5% chance that humans will still be thriving circa 11125 AD. (These dates are based on the assumptions above; the precise numbers vary among specific Doomsday arguments.)

Variations

This argument has generated a lively philosophical debate, and no consensus has yet emerged on its solution. The variants described below produce the DA by separate derivations.

Gott's formulation: 'vague prior' total population

Gott specifically proposes the functional form for the prior distribution of the number of people who will ever be born (N). Gott's DA used the vague prior distribution: A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...

.

where

• P(N) is the probability prior to discovering n, the total number of humans who have yet been born.
• The constant, k, is chosen to normalize the sum of P(N). The value chosen isn't important here, just the functional form (this is an improper prior, so no value of k gives a valid distribution, but Bayesian inference is still possible using it.)

Since Gott specifies the prior distribution of total humans, P(N), Bayes's theorem and the principle of indifference alone give us P(N|n), the probability of N humans being born if n is a random draw from N: Prior is a title, derived from the Latin adjective for earlier, first, with several notable uses. ... The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... Bayes theorem is a result in probability theory, which gives the conditional probability distribution of a random variable A given B in terms of the conditional probability distribution of variable B given A and the marginal probability distribution of A alone. ... The principle of indifference is a rule for assigning epistemic probabilities. ...

This is Bayes's theorem for the posterior probability of total population exactly N, conditioned on current population exactly n. Now, using the indifference principle: The posterior probability can be calculated by Bayes theorem from the prior probability and the likelihood function. ... Conditioning is a psychological term for what Ivan Pavlov described as the learning of conditional behavior. ...

.

The unconditioned n distribution of the current population is identical to the vague prior N probability density function,^[6] so:

,

giving P (N | n) for each specific N (through a substitution into the posterior probability equation):

.

The easiest way to produce the doomsday estimate with a given confidence (say 95%) is to pretend that N is a continuous variable (since it is very large) and integrate over the probability density from N = n to N = Z. (This will give a function for the probability that N ≤ Z): By one convention, a random variable X is called continuous if its cumulative distribution function is continuous. ... This article is about the concept of integrals in calculus. ...

Defining Z = 20n gives:

.

This is the simplest Bayesian derivation of the DA: Bayesian refers to probability and statistics -- either methods associated with the Reverend Thomas Bayes (ca. ...

The chance that the total number of humans that will ever be born (N) is greater than twenty times the total that have been is below 5%

The use of a vague prior distribution seems well-motivated as it assumes as little knowledge as possible about N, given that any particular function must be chosen. It is equivalent to the assumption that the probability density of one's fractional position remains uniformly distributed even after learning of one's absolute position (n). A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...

Gott's 'reference class' in his original 1993 paper was not the number of births, but the number of years 'humans' had existed as a species, which he put at 200,000. Also, Gott tried to give a 95% confidence interval between a minimum survival time and a maximum. Because of the 2.5% chance that he gives to underestimating the minimum he has only a 2.5% chance of overestimating the maximum. This equates to 97.5% confidence that extinction occurs before the upper boundary of his confidence interval. For the history of humans on Earth, see History of the world. ...

97.5% is one chance in forty, which can be used in the integral above with Z = 40n, and n = 200,000 years:

This is how Gott produces a 97.5% confidence of extinction within N ≤ 8,000,000 years. The number he quoted was the likely time remaining, N − n = 7.8 million years. This was much higher than the temporal confidence bound produced by counting births, because, it applied the principle of indifference to time. (Producing different estimates by sampling different parameters in the same hypothesis is Bertrand's paradox.) Bertrands paradox is a problem in probability theory. ...

His choice of 95% confidence bounds (rather than 80% or 99.9%, say) matched the scientifically accepted limit of statistical significance for hypothesis rejection. Therefore, he argued that the hypothesis: “humanity will cease to exist before 5,100 years or thrive beyond 7.8 million years” can be rejected. In statistics, a result is significant if it is unlikely to have occurred by chance, given that a presumed null hypothesis is true. ... Look up Hypothesis in Wiktionary, the free dictionary. ...

Leslie's argument differs from Gott's version in that he does not assume a vague prior probability distribution for N. Instead he argues that the force of the DA resides purely in the increased probability of an early Doomsday once you take into account your birth position, regardless of your prior probability distribution for N. He calls this the probability shift.

Heinz von Foerster argued that humanity's abilities to construct societies, civilizations and technologies do not result in self inhibition. Rather, societies' success varies directly with population size. Von Foerster found that this model fit some 25 data points from the birth of Jesus to 1958, with only 7% of the variance left unexplained. Several follow-up letters (1961, 1962, …) were published in Science showing that von Foerster's equation was still on track. The data continued to fit up until 1973. The most remarkable thing about von Foerster's model was it predicted that the human population would reach infinity or a mathematical singularity, on Friday, November 13, 2026. In fact, von Foerster did not imply that the world population on that day could actually become infinite. The real implication was that the world population growth pattern followed for many centuries prior to 1960 was about to come to an end and be transformed into a radically different pattern. Note that this prediction began to be fulfilled just in a few years after the "Doomsday" was published.^[7] He is a twat He was born in Vienna and died in Pescadero, California. ... This article is about Jesus of Nazareth. ... This article is about mathematics. ... is the 317th day of the year (318th in leap years) in the Gregorian calendar. ... 2026 (MMXXVI) will be a common year starting on Thursday of the Gregorian calendar. ...

Reference classes

One of the major areas of DA debate is the reference class from which n is drawn, and of which N is the ultimate size. The 'standard' DA hypothesis doesn't spend very much time on this point, and simply says that the reference class is the number of 'humans'. Given that you are human, the Copernican principle could be applied to ask if you were born unusually early, but the grouping of 'human' has been widely challenged on practical and philosophical grounds. Nick Bostrom has argued that consciousness is (part of) the discriminator between what it is in and out of the reference class, and that extraterrestrial intelligences might affect the calculation dramatically. Look up Hypothesis in Wiktionary, the free dictionary. ... This is about the social science. ... For other uses, see Philosophy (disambiguation). ... Nick Bostrom (Boström in the original Swedish) is a philosopher at the University of Oxford, and known for his work on the anthropic principle. ... Consciousness is a quality of the mind generally regarded to comprise qualities such as subjectivity, self-awareness, sentience, sapience, and the ability to perceive the relationship between oneself and ones environment. ... Extraterrestrial life refers to forms of life that may exist and originate outside of the planet Earth. ...

The following sub-sections relate to different suggested reference classes, each of which has had the standard DA applied to it.

Sampling only WMD-era humans

The Doomsday clock shows the expected time to nuclear Armageddon by the judgment of an expert board, rather than a Bayesian model. If the twelve hours of the clock symbolize the lifespan of the human race, its current time of 11:55 implies that we are among the last 1% of people who will ever be born (i.e. that n > 0.99N). J. Richard Gott's temporal version of the Doomsday argument (DA) would require very strong prior evidence to overcome the improbability of being born in such a special time. For the Xzibit album, see Weapons of Mass Destruction (album). ... Minutes to Midnight redirects here, along with other titles incorporating that term. ... Look up Apocalypse in Wiktionary, the free dictionary. ... Cover of the Bulletin of the Atomic Scientists with the famous Doomsday Clock set at seven minutes to midnight. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ...

If the clock's doomsday estimate is correct, there is less than 1 chance in 100 of seeing it show such a late time in human history, if observed at a random time within that history.

The scientists' warning can be reconciled with the DA, however: The Doomsday clock specifically estimates the proximity of atomic self-destruction - which has only been possible for sixty years.^[8] If doomsday requires nuclear weaponry then the DA 'reference class' is: people contemporaneous with nuclear weapons. In this model, the number of people living through, or born after Hiroshima is n, and the number of people who ever will is N. Applying Gott's DA to these variable definitions gives a 50% chance of apocalypse within 50 years. Cover of the Bulletin of the Atomic Scientists with the famous Doomsday Clock set at seven minutes to midnight. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 kilometers (11 mi) above the hypocenter A nuclear weapon derives its destructive force from nuclear reactions of fusion or fission. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 km (11 mi) above the hypocenter. ... The mushroom cloud over Hiroshima after the dropping of Little Boy. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... Look up Apocalypse in Wiktionary, the free dictionary. ...

In this model, the clock's hands are so close to midnight because a condition of doomsday is living post-1945, a condition which applies now but not to the earlier 11 hours and 53 minutes of the clock's metaphorical human 'day'.

If your life is randomly selected from all lives lived under the shadow of the bomb, this simple model gives a 95% chance of Armageddon within 1000 years. This article defines some terms which characterize probability distributions of two or more variables. ... Year 1945 (MCMXLV) was a common year starting on Monday (link will display the full calendar). ... For other uses, see Armageddon (disambiguation). ...

The scientists' recent use of moving the clock forward to warn of the dangers posed by global warming muddles this reasoning, however. Global warming refers to the increase in the average temperature of the Earths near-surface air and oceans in recent decades and its projected continuation. ...

SSSA: Sampling from observer-moments

Nick Bostrom, considering observation selection effects, has produced a Self-Sampling Assumption (SSA): "that you should think of yourself as if you were a random observer from a suitable reference class". If the 'reference class' is the set of humans to ever be born, this gives N < 20n with 95% confidence (the standard Doomsday argument). However, he has refined this idea to apply to observer-moments rather than just observers. He has formalized this ([2] as: Nick Bostrom (Boström in the original Swedish) is a philosopher at the University of Oxford, and known for his work on the anthropic principle. ... In physics and cosmology, the anthropic principle states that we should take into account the constraints that our existence as observers imposes on the sort of universe that we could observe. ... Anthropic bias is the bias arising when your evidence is biased by observation selection effects, according to philosopher Nick Bostrom. ...

The Strong Self-Sampling Assumption (SSSA): Each observer-moment should reason as if it were randomly selected from the class of all observer-moments in its reference class.

If the minute in which you read this article is randomly selected from every minute in every human's lifespan then (with 95% confidence) this event has occurred after the first 5% of human observer-moments. If future mean lifespan is twice historic, this implies 95% confidence that N < 10n (the average future human will account for twice the observer-moments of the average historic human). Therefore, the 95th percentile extinction-time estimate in this version is 4560 years.

Rebuttals

We are in the earliest 5%, a priori

If you agree with the statistical methods, still disagreeing with the Doomsday argument (DA) implies that:

1. We are within the first 5% of humans to be born.
2. This is not purely a coincidence.

Therefore, these rebuttals try to give reasons for believing that we are some of the earliest humans.

For instance, you are member 50,000 in a collaborative project, the Doomsday argument implies a 95% chance that there will never be more than a million members of that project. This can be refuted if your other characteristics are typical of the early adopter. The mainstream of potential users will prefer to be involved when the project is nearly complete. If you enjoy the project's incompleteness, we already know that you are unusual, prior to the discovery of your early involvement. Diffusion is the process by which a new idea or new product is accepted by the market. ...

If you have measurable attributes that set you apart from the typical long run user, the project DA can be refuted based on the fact that you would expect to be within the first 5% of members, a priori. The analogy to the total-human-population form of the argument is: Confidence in a prediction of the distribution of human characteristics that places modern & historic humans outside the mainstream, implies that we already know, before examining n that it is likely to be very early in N. The terms a priori and a posteriori are used in philosophy to distinguish between two different types of propositional knowledge. ... In probability theory, every random variable may be attributed to a function defined on a state space equipped with a probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied. ...

For example, if you are certain that 99% of humans who will ever live will be cyborgs, but you are not a cyborg, you could be equally certain that at least one hundred times as many people remain to be born as have been. For other uses, see Cyborg (disambiguation). ...

Robin Hanson's paper sums up these criticisms of the DA: Robin Hanson is an associate professor of economics at George Mason University. ...

"All else is not equal; we have good reasons for thinking we are not randomly selected humans from all who will ever live."

Drawbacks of this rebuttal:

1. The question of how the confident prediction is derived. We need an uncannily prescient picture of humanity's statistical distribution through all time, before we can pronounce ourselves extreme members of that population. (In contrast, project pioneers have clearly distinct psychology from the mainstream.)
2. If the majority of humans have characteristics we do not share, some would argue that this is equivalent to the Doomsday argument, since people like us will become extinct. (Friedrich Nietzsche outlines this pseudoextinction point of view in Also sprach Zarathustra.)

Prescience is the ability to predict the future through vision. ... In probability theory, every random variable may be attributed to a function defined on a state space equipped with a probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied. ... Friedrich Wilhelm Nietzsche (October 15, 1844 – August 25, 1900) (IPA: ) was a nineteenth-century German philologist and philosopher. ... Pseudoextinction of a species occurs where there are no more living members of that species, but members of a daughter species or subspecies remain alive. ... The cover for the first part of the first edition. ...

Critique: Human extinction is distant, a posteriori

The a posteriori observation that extinction level events are rare could be offered as evidence that the DA's predictions are implausible; typically, extinctions of a dominant species happens less often than once in a million years. Therefore, it is argued that Human extinction is unlikely within the next ten millennia. (Another probabilistic argument, drawing a different conclusion from the DA.) A Posteriori is the title of the musical project Enigmas sixth studio album, released in September 2006. ... An extinction event (also extinction-level event, ELE) is a period in time when a large number of species die out. ... For other uses, see Extinction (disambiguation). ... For other uses, see Species (disambiguation). ... Human extinction is the as-yet hypothetical extinction of the human species, Homo sapiens. ... In some contexts, probabilistic argument means any argument involving probability theory. ...

In Bayesian terms, this response to the DA says that our knowledge of history (or ability to prevent disaster) produces a prior marginal for N with a minimum value in the trillions. If N is distributed uniformly from 10¹² to 10¹³, for example, then the probability of N < 1,200 billion inferred from n = 60 billion will be extremely small. This is an equally impeccable Bayesian calculation, rejecting the Copernican principle on the grounds that we must be 'special observers' since there is no likely mechanism for humanity to go extinct within the next hundred thousand years. In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ...

This response is accused of overlooking the technological threats to humanity's survival, to which earlier life was not subject, and is specifically rejected by most of the DA's academic critics (arguably excepting Robin Hanson). Human extinction is the as-yet hypothetical extinction of the human species, Homo sapiens. ... Robin Hanson is an associate professor of economics at George Mason University. ...

In fact, many futurologists believe the empirical situation is worse than Gott's DA estimate. For instance, Sir Martin Rees believes that the technological dangers give an estimated human survival duration of ninety-five years (with 50% confidence.) Earlier prophets made similar predictions and were 'proven' wrong (e.g. on surviving the nuclear arms race). It is possible that their estimates were accurate, and that their common image as alarmists is a survivorship bias. Futurology or futures studies (called futurism in the United States) is the study of the medium to long-term future, by extrapolating present technological, economic or social trends, or by attempting to predict future trends. ... The Right Honourable Martin John Rees, Baron Rees of Ludlow, FRS (born 23 June 1942) is a professor of astronomy. ... Our Final Hour is a 2003 book by the British Astronomer Royal Sir Martin Rees. ... The Doomsday argument (DA) is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far. ... Survivorship bias is the tendency for failed companies to be excluded from performance studies due to the fact that they no longer exist. ...

The prior N distribution may make n very uninformative

Robin Hanson argues that N's prior may be exponentially distributed: Robin Hanson is an associate professor of economics at George Mason University. ... In probability theory and statistics, the exponential distributions are a class of continuous probability distribution. ...

Here, c and q are constants. If q is large, then our 95% confidence upper bound is on the uniform draw, not the exponential value of N.

The best way to compare this with Gott's Bayesian argument is to flatten the distribution from the vague prior by having the probability fall off more slowly with N (that inverse proportionally). This corresponds to the idea that humanity's growth may be exponential in time with doomsday having a vague prior pdf in time. This would mean than N, the last birth, would have a distribution looking like the following: In mathematics, a probability density function (pdf) is a function that represents a probability distribution in terms of integrals. ...

This prior N distribution is all that is required (with the principle of indifference) to produce the inference of N from n, and this is done in an identical way to the standard case, as described by Gott (equivalent to α = 1 in this distribution):

Substituting into the posterior probability equation):

Integrating the probability of any N above xn:

For example, if x = 20, and α = 0.5, this becomes:

Therefore, with this prior, the chance of a trillion births is well over 20%, rather than the 5% chance given by the standard DA. If α is reduced further by assuming a flatter prior N distribution, then the limits on N given by n become weaker. An α of one reproduces Gott's calculation with a birth reference class, and α around 0.5 could approximate his temporal confidence interval calculation (if the population were expanding exponentially). As (gets smaller) n becomes less and less informative about N. In the limit this distribution approaches an (unbounded) uniform distribution, where all values of N are equally likely. This is Page et al.'s "Assumption 3", which they find few reasons to reject, a priori. (Although all distributions with are improper priors, this applies to Gott's vague-prior distribution also, and they can all be converted to produce proper integrals by postulating a finite upper population limit.) Since the probability of reaching a population of size 2N is usually thought of as the chance of reaching N multiplied by the survival probability from N to 2N it seems that Pr(N) must be a monotonically decreasing function of N, but this doesn't necessarily require an inverse proportionality. A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... In mathematics, the uniform distributions are simple probability distributions. ... It is recommended that the reader be familiar with antiderivatives, integrals, and limits. ... A monotonically increasing function (it is strictly increasing on the left and just non-decreasing on the right). ...

A prior distribution with a very low α parameter makes the DA's ability to constrain the ultimate size of humanity very weak. The factual accuracy of this article is disputed. ...

Infinite Expectation

Another objection to the Doomsday Argument is that the expected total human population is actually infinite. The calculation is as follows: In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...

The total human population N = n/f, where n is the human population to date and f is our fractional position in the total.

We assume that f is uniformly distributed on (0,1].

The expectation of N is

This infinite expectation shows that, under the framework of the DA, humanity still has some chance of surviving an arbitrarily long time.

For a similar example of counterintuitive infinite expectations, see the St. Petersburg paradox. In probability theory and decision theory the St. ...

SIA: The possibility of not existing at all

One objection is that the possibility of you existing at all depends on how many humans will ever exist (N). If this is a high number, then the possibility of you existing is higher than if only a few humans will ever exist. Since you do indeed exist, this is evidence that the number of humans that will ever exist is high.

This objection, originally by Dennis Dieks (1992), is now known by Nick Bostrom's name for it: the "Self-Indication Assumption objection". It can be shown that some SIAs prevent any inference of N from n (the current population); for details of this argument from the Bayesian inference perspective see: Self-Indication Assumption Doomsday argument rebuttal. Year 1992 (MCMXCII) was a leap year starting on Wednesday (link will display full 1992 Gregorian calendar). ... Nick Bostrom (Boström in the original Swedish) is a philosopher at the University of Oxford, and known for his work on the anthropic principle. ... Self-Indication Assumption (SIA) is the philosophical principle defined by Nick Bostrom (who opposes it) in 2000 as: SIA: Given the fact that you exist, you should (other things equal) favor hypotheses according to which many observers exist over hypotheses on which few observers exist. ... Self-Indication Assumption (SIA) is the philosophical principle defined by Nick Bostrom (who opposes it) in 2000 as: SIA: Given the fact that you exist, you should (other things equal) favor hypotheses according to which many observers exist over hypotheses on which few observers exist. ... The Self-Indication Assumption Doomsday argument rebuttal is an objection to the Doomsday argument (that there is only a 5% chance of more than twenty times the historic number of humans ever being born) by arguing that the chance of being born is not one, but is an increasing function...

Many worlds

John Eastmond's "Many-Worlds Resolution of the Doomsday Argument" claims that when the Doomsday Argument is extended from a form that deals with a single historic timeline into one dealing with the many bifurcating simultaneous histories suggested by the many-worlds interpretation of quantum mechanics then one finds that the generalized argument no longer makes any prediction about the future total size of the human race. More specifically, if each finite value of total population size is realized in a different future, then learning of our present position from the beginning of the human race does not change our prior belief about which particular total population size we will find ourselves experiencing in one of humanity's many futures (assuming that versions of us live long enough to see versions of Doomsday). The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to every event to... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ...

Caves' rebuttal

Caves' Bayesian argument says that the uniform distribution assumption is incompatible with the Copernican principle, not a consequence of it. Bayesian refers to probability and statistics -- either methods associated with the Reverend Thomas Bayes (ca. ... In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ...

He gives a number of examples to argue that Gott's rule is implausible. For instance, he says, imagine stumbling into a birthday party, about which you know nothing:

Your friendly enquiry about the age of the celebrant elicits the reply that she is celebrating her (t_p = ) 50th birthday. According to Gott, you can predict with 95% confidence that the woman will survive between [50]/39 = 1.28 years and 39[×50] = 1,950 years into the future. Since the wide range encompasses reasonable expectations regarding the woman's survival, it might not seem so bad, till one realizes that [Gott's rule] predicts that with probability 1/2 the woman will survive beyond 100 years old and with probability 1/3 beyond 150. Few of us would want to bet on the woman's survival using Gott's rule. (See Caves' online paper below.)

Although this example exposes a weakness in J. Richard Gott's "Copernicus method" DA (that he does not specify when the "Copernicus method" can be applied) it is not precisely analogous with the modern DA; epistemological refinements of Gott's argument by philosophers such as Nick Bostrom specify that: The Doomsday argument (DA) is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... The Doomsday argument (DA) is a probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far. ... Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Nick Bostrom (Boström in the original Swedish) is a philosopher at the University of Oxford, and known for his work on the anthropic principle. ...

Knowing the absolute birth rank (n) must give no information on the total population (N).

Careful DA variants specified with this rule aren't shown implausible by Caves' "Old Lady" example above, because, the woman's age is given prior to the estimate of her lifespan. Since human age gives an estimate of survival time (via actuarial tables) Caves' Birthday party age-estimate could not fall into the class of DA problems defined with this proviso. Prior is a title, derived from the Latin adjective for earlier, first, with several notable uses. ... Damage from Hurricane Katrina. ...

To produce a comparable "Birthday party example" of the carefully specified Bayesian DA we would need to completely exclude all prior knowledge of likely human life spans; in principle this could be done (e.g.: hypothetical Amnesia chamber). However, this would remove the modified example from everyday experience. To keep it in the everyday realm the lady's age must be hidden prior to the survival estimate being made. (Although this is no longer exactly the DA, it is much more comparable to it.)

Without knowing the lady’s age, the DA reasoning produces a rule to convert the birthday (n) into a maximum lifespan with 50% confidence (N). Gott's Copernicus method rule is simply: Prob (N < 2n) = 50%. How accurate would this estimate turn out to be? Western demographics are now fairly uniform across ages, so a random birthday (n) could be (very roughly) approximated by a U(0,M] draw where M is the maximum lifespan in the census. In this 'flat' model, everyone shares the same lifespan so N = M. If n happens to be less than (M)/2 then Gott's 2n estimate of N will be under M, its true figure. The other half of the time 2n underestimates M, and in this case (the one Caves highlights in his example) the subject will die before the 2n estimate is reached. In this 'flat demographics' model Gott's 50% confidence figure is proven right 50% of the time. Demographics refers to selected population characteristics as used in government, marketing or opinion research, or the demographic profiles used in such research. ... For other uses, see Uniform (disambiguation). ...

Self-referencing doomsday argument rebuttal

Main article: Self-referencing doomsday argument rebuttal

Some philosophers have been bold enough to suggest that only people who have contemplated the Doomsday argument (DA) belong in the reference class 'human'. If that is the appropriate reference class, Carter defied his own prediction when he first described the argument (to the Royal Society). A member present could have argued thus: Self-referencing doomsday argument rebuttals attempt to refute the Doomsday argument (that there is a credible link between the brevity of the human races existence and its expected extinction) by applying the same reasoning to the life time of the Doomsday argument (DA) itself. ... This article is about modern humans. ... Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ... For other uses, see Royal Society (disambiguation). ...

"Presently, only one person in the world understands the Doomsday argument, so by its own logic there is a 95% chance that it is a minor problem which will only ever interest twenty people, and I should ignore it."

Jeff Dewynne and Professor Peter Landsberg suggested that this line of reasoning will create a paradox for the Doomsday argument: Look up paradox in Wiktionary, the free dictionary. ...

If a member did pass such a comment, it would indicate that they understood the DA sufficiently well that in fact 2 people could be considered to understand it, and thus there would a 95% chance that 40 people would actually be interested. Also, of course, ignoring something because you only expect a small number of people to be interested in it is extremely short sighted - if this approach were to be taken, nothing new would ever be explored, if we assume no a priori knowledge of the nature of interest and attentional mechanisms.

Additionally, it should be considered that because Carter did present and describe his argument, in which case the people to whom he explained it did contemplate the DA, as it was inevitable, the conclusion could then be drawn that in the moment of explanation Carter created the basis for his own prediction. Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ... Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ...

Math-free explanation by analogy

Think of the human race like a car driver. We've had some bumps, but no catastrophes, and our car (Earth) is still road-worthy, but we want insurance. We ask the cosmic insurer how much a millennium’s cover will be, but they haven't dealt with humanity before. How should they work out the premium? The Doomsday Argument says that all they have to ask is how long we've been on the road (at least 40,000 years without an accident), they should calculate our insurance based on us having a 50% chance of having a fatal accident inside another 40,000 years. This article is about Earth as a planet. ...

Insurance companies try to attract drivers with long accident-free histories not because they necessarily drive more safely than newly qualified drivers, but for statistical reasons: They calculate that each driver looks for insurance quotes every year, so that the time since the last accident is a random sample between accidents. The chance of being more than halfway through a random sample is half, and if they are more than half way between accidents then they are heading for an accident in less time than the time since their last. A driver who hasn't had a scratch in 40 years will be quoted a very low premium for this reason, but you shouldn't expect cheap insurance if you've only passed your test two hours ago (equivalent to the accident-free record of the human race in relation to 40 years of geological time.) A railing accidentally collapses at a college football game, spilling fans onto the sidelines An accident is something going wrong unexpectedly. ... The table and timeline of geologic periods presented here is in accordance with the dates and nomenclature proposed by the International Commission on Stratigraphy. ...

Analogy to the estimated final score of a cricket batsman

A random in-progress cricket test match is sampled for a single piece of information: the current batsman's run tally so far. If the batsman is dismissed (rather than declaring), what is the chance that he will end up with a score more than double his current total? This article is about the sport. ... For the womens version of the game, see Womens Test cricket. ... Warwickshire batsman Mike Powell A batsman in the sport of cricket is, depending on context: Any player in the act of batting. ...

A rough empirical result is that the chance is half (on average).

The Doomsday argument (DA) is that even if we were completely ignorant of the game we could make the same prediction, or profit by offering a bet paying odds of 2-to-3 on the batsmen doubling his current score. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. ... In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. ...

Importantly, we can only offer the bet before the current score is given (this is necessary because the absolute value of the current score would give a cricket expert a lot of information about the chance of that tally doubling). It is necessary to be ignorant of the absolute run tally before making the prediction because this is linked to the likely total, but if the likely total and absolute value are not linked the survival prediction can be made after discovering the batter's current score. Analogously, the DA says that if the absolute number of humans born gives no information on the number that will be, we can predict the species’ total number of births after discovering that 60 billion people have ever been born: with 50% confidence it is 120 billion people, so that there is better-chance-than-not that the last human birth will occur before the 23rd century.

It is not true that the chance is half, whatever is the number of runs currently scored; batting records give an empirical correlation between reaching a given score (50 say) and reaching any other, higher score (say 100). On the average, the chance of doubling the current tally may be half, but the chance of reaching a century having scored fifty is much lower than reaching ten from five. Thus, the absolute value of the score gives information about the likely final total the batsman will reach, beyond the “scale invariant”.^[9] Batting has several meanings: In baseball, batting is the act of attempting to hit the ball thrown by the pitcher, in order to score runs. ... Positive linear correlations between 1000 pairs of numbers. ...

An analogous Bayesian critique of the DA is that we somehow possess prior knowledge of the all-time human population distribution (total runs scored), and that this is more significant than the finding of a low number of births until now (a low current run count). A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...

There are two alternative methods of making uniform draws from the current score (n): For other uses, see Uniform (disambiguation). ...

1. Put the runs actually scored by dismissed player in order, say 200, and randomly choose between these scoring increments by U(0, 200].
2. Select a time randomly from the beginning of the match to the final dismissal.

The second sampling-scheme will include those lengthy periods of a game where a dismissed player is replaced, during which the ‘current batsman’ is preparing to take the field and has no runs. If we sample based on time-of-day rather than running-score we will often find that a new batsman has a score of zero when the total score that day was low, but we will rarely sample a zero if one batsman stayed at the crease, piling on runs all day long. Therefore, the fact that we sample a non-zero score would tell us something about the likely final score that the current batsman will achieve. In the sport of cricket, the crease is the area demarcated by white lines painted or chalked on the field of play. ...

Choosing sampling method 2 rather than method 1 would give a different statistical link between current and final score: any non-zero score would imply that the batsman reached a high final total, especially if the time to replace batsman is very long. This is analogous to the SIA-DA-refutation that N's distribution should include N = 0 states, which leads to the DA having reduced predictive power (in the extreme, no power to predict N from n at all). Self-Indication Assumption (SIA) is the philosophical principle defined by Nick Bostrom (who opposes it) in 2000 as: SIA: Given the fact that you exist, you should (other things equal) favor hypotheses according to which many observers exist over hypotheses on which few observers exist. ... The New York Times reported on Einsteins confirmed prediction. ...

An interpretation of the argument

The Doomsday argument has to be interpreted on the basis of its own definition. The central concept is about the human race and a probabilistic estimation of its end taking into consideration its beginning. If Homo sapiens is described as the evolution from Homo Erectus (or what it been), then the argument can be interpreted as an estimation on the evolution into Homo Futurus (or what it been). For other uses, see Concept (disambiguation). ...

See also

• Doomsday
• Fermi paradox
• Final anthropic principle
• Hypothetical disasters
• Mediocrity principle
• Nurgaliev's equation
• Quantum immortality
• Simulated reality
• Sic transit gloria mundi
• Survival analysis
• Technological singularity

Look up doomsday in Wiktionary, the free dictionary. ... A graphical representation of the Arecibo message - Humanitys first attempt to use radio waves to communicate its existence to alien civilizations The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for or contact with... The final anthropic principle (FAP) is defined by physicists John D. Barrow and Frank J. Tiplers 1986 book The Anthropic Cosmological Principle as a generalization of the anthropic principle as follows: Final anthropic principle (FAP): Intelligent information-processing must come into existence in the Universe, and, once it comes... A disaster is a natural or man-made event that negatively affects life, property, livelihood or industry, often resulting in permanent changes to human societies, ecosystems and environment. ... This article needs additional references or sources for verification. ... It has been suggested that Quantum suicide be merged into this article or section. ... Simulated reality is the idea that reality could be simulated — often computer-simulated — to a degree indistinguishable from true reality. ... Sic transit gloria mundi is a Latin phrase that means Thus passes the glory of the world. It has been interpreted as Fame is fleeting. ... Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. ... When plotted on a logarithmic graph, 15 separate lists of paradigm shifts for key events in human history show an exponential trend. ...

References

Brandon Carter is a theoretical physicist, most famous for his work on the properties of black holes and for introducing the anthropic principle. ... Cover of Cover of the first volume of , published in 1665 The Philosophical Transactions of the Royal Society, or Phil. ... Year 1993 (MCMXCIII) was a common year starting on Friday (link will display full 1993 Gregorian calendar). ... Nature is a prominent scientific journal, first published on 4 November 1869. ... Prof. ... Also see: 2002 (number). ... In mathematics the term countable set is used to describe the size of a set, e. ... In mathematics, an uncountable set is a set which is not countable. ... In mathematics, a probability density function (pdf) is a function that represents a probability distribution in terms of integrals. ... In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ... Bayes theorem (also known as Bayes rule or Bayes law) is a result in probability theory, which relates the conditional and marginal probability distributions of random variables. ... Andrey Korotayev (born in 1961) is an anthropologist, economic historian, and sociologist. ... Year 1949 (MCMXLIX) was a common year starting on Saturday (link will display the full calendar) of the Gregorian calendar. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... This article is about mathematical mean. ... The posterior probability can be calculated by Bayes theorem from the prior probability and the likelihood function. ... This is not an attempt at a comprehensive list of statistical topics; see that article. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... Regression toward the mean refers to the fact that those with extreme scores on any measure at one point in time will, for purely statistical reasons, probably have less extreme scores the next time they are tested. ... Stephen Baxter (born in Liverpool, 13 November 1957) is a British hard science fiction author. ...

External links

• A non-mathematical, unpartisan introduction to the DA
• A compelling lecture from the University of Colorado-Boulder
• Nick Bostrom's response to Korb and Oliver
• Nick Bostrom's summary version of the argument
• Nick Bostrom's annotated collection of references
• Kopf, Krtouš & Page's early (1994) refutation based on the SIA, which they called "Assumption 2".
• The Doomsday Argument, Consciousness and Many Worlds by John Eastmond
• The Doomsday argument and the number of possible observers by Ken Olum In 1993 J. Richard Gott used his "Copernicus method" to predict the lifetime of Broadway shows. One part of this paper uses the same reference class as an empirical counter-example to Gott's method.
• A Critique of the Doomsday Argument by Robin Hanson
• A third route to the doomsday argument by Paul Franceschi
• Chambers' Ussherian Corollary Objection
• Caves' Bayesian critique of Gott's argument. C. M. Caves, "Predicting future duration from present age: A critical assessment", Contemporary Physics 41, 143-153 (2000).
• Mark Greenberg, "Apocalypse Not Just Now" in London Review of Books
• Laster: A simple webpage applet giving the min & max survival times of anything with 50% and 95% confidence requiring only that you input how old it is. It is designed to use the same mathematics as J. Richard Gott's form of the DA, and was programmed by sustainable development researcher Jerrad Pierce.

SIA could refer to: Organizations: Secret Intelligence Australia Security Industry Authority, UK licensing authority for the private security industry ([1]). Semiconductor Industry Association SIA, an international home fashion brand founded by Sonja Ingegärd Andersson. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... J. Richard Gott is a professor of astrophysical sciences at Princeton University John Richard Gott III is especially well known for developing and advocating two cosmological theories with the flavour of science fiction: Time travel, and the Doomsday argument. ... Sustainable development is a socio-ecological process characterized by the fulfilment of human needs while maintaining the quality of the natural environment indefinitely. ...