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78-501: The problem was originally formulated in unpublished work in the mid-1980s by Arnold Zuboff (the work was later published as "One Self: The Logic of Experience") followed by a paper by Adam Elga. A formal analysis of the problem of belief formation in decision problems with imperfect recall was provided first by Michele Piccione and Ariel Rubinstein in their paper: "On the Interpretation of Decision Problems with Imperfect Recall" where

156-442: A "weak" and "strong" anthropic principle in a way very different from Carter's, as discussed in the next section. Carter was not the first to invoke some form of the anthropic principle. In fact, the evolutionary biologist Alfred Russel Wallace anticipated the anthropic principle as long ago as 1904: "Such a vast and complex universe as that which we know exists around us, may have been absolutely required [...] in order to produce

234-594: A 1973 Kraków symposium honouring Copernicus's 500th birthday. Carter, a theoretical astrophysicist, articulated the Anthropic Principle in reaction to the Copernican Principle , which states that humans do not occupy a privileged position in the Universe . Carter said: "Although our situation is not necessarily central , it is inevitably privileged to some extent." Specifically, Carter disagreed with using

312-406: A brute fact is less astonishing than the idea of an intelligent creator. Furthermore, even accepting fine tuning, Sober (2005) and Ikeda and Jefferys , argue that the anthropic principle as conventionally stated actually undermines intelligent design. Paul Davies 's book The Goldilocks Enigma (2006) reviews the current state of the fine-tuning debate in detail, and concludes by enumerating

390-518: A form of the strong anthropic principle in his 2006 book The Human Touch , which explores what he characterises as "the central oddity of the Universe": It's this simple paradox. The Universe is very old and very large. Humankind, by comparison, is only a tiny disturbance in one small corner of it – and a very recent one. Yet the Universe is only very large and very old because we are here to say it is... And yet, of course, we all know perfectly well that it

468-422: A framework for maximizing our confidence in any theory, given a limited sequence of physical observations, and some prior distribution on the set of possible explanations of the universe. Zhi-Wei Wang and Samuel L. Braunstein proved that life's existence in the universe depends on various fundamental constants. It suggests that without a complete understanding of these constants, one might incorrectly perceive

546-500: A large number of possible universes, called the "backgrounds" or "vacua". The set of these vacua is often called the " multiverse " or " anthropic landscape " or "string landscape". Leonard Susskind has argued that the existence of a large number of vacua puts anthropic reasoning on firm ground: only universes whose properties are such as to allow observers to exist are observed, while a possibly much larger set of universes lacking such properties go unnoticed. Steven Weinberg believes

624-418: A remarkably low value, some 120 orders of magnitude smaller than the value particle physics predicts (this has been described as the " worst prediction in physics "). However, if the cosmological constant were only several orders of magnitude larger than its observed value, the universe would suffer catastrophic inflation , which would preclude the formation of stars, and hence life. The observed values of

702-468: A result. He writes: Many 'anthropic principles' are simply confused. Some, especially those drawing inspiration from Brandon Carter's seminal papers, are sound, but... they are too weak to do any real scientific work. In particular, I argue that existing methodology does not permit any observational consequences to be derived from contemporary cosmological theories, though these theories quite plainly can be and are being tested empirically by astronomers. What

780-466: A universe not to support life. Probabilistic predictions of parameter values can be made given: The probability of observing value X is then proportional to N ( X ) P ( X ) . A generic feature of an analysis of this nature is that the expected values of the fundamental physical constants should not be "over-tuned", i.e. if there is some perfectly tuned predicted value (e.g. zero), the observed value need be no closer to that predicted value than what

858-502: A universe in which an observer cannot exist. Philosopher John Leslie states that the Carter SAP (with multiverse ) predicts the following: Hogan has emphasised that it would be very strange if all fundamental constants were strictly determined, since this would leave us with no ready explanation for apparent fine tuning. In fact, humans might have to resort to something akin to Barrow and Tipler's SAP: there would be no option for such

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936-432: A universe with a Big Bang origin, must include the assumption that at the initial singularity, the entropy of the universe was low and therefore extremely improbable. Paul Davies rebutted this criticism by invoking an inflationary version of the anthropic principle. While Davies accepted the premise that the initial state of the visible universe (which filled a microscopic amount of space before inflating) had to possess

1014-484: A very low entropy value—due to random quantum fluctuations—to account for the observed thermodynamic arrow of time, he deemed this fact an advantage for the theory. That the tiny patch of space from which our observable universe grew had to be extremely orderly, to allow the post-inflation universe to have an arrow of time, makes it unnecessary to adopt any "ad hoc" hypotheses about the initial entropy state, hypotheses other Big Bang theories require. String theory predicts

1092-403: A world that should be precisely adapted in every detail for the orderly development of life culminating in man." In 1957, Robert Dicke wrote: "The age of the Universe 'now' is not random but conditioned by biological factors [...] [changes in the values of the fundamental constants of physics] would preclude the existence of man to consider the problem." Ludwig Boltzmann may have been one of

1170-492: Is Monday" are in general problematic for conditionalization and proposes the use of an imaging rule instead, which supports the double halfer position. Another approach to the Sleeping Beauty problem is to assert that the problem, as stated, is ambiguous. This view asserts that the thirder and halfer positions are both correct answers, but to different questions. The key idea is that the question asked of Sleeping Beauty, "what

1248-485: Is a woman who wants to have a child with him, across the sea there is another woman who also wants to have a child with him. The sailor cannot decide if he will have one or two children, so he will leave it up to a coin toss. If Heads, he will have one child, and if Tails, two children (one with each woman; presumably the children will never meet). But if the coin lands on Heads, which woman would have his child? He would decide this by looking at The Sailor's Guide to Ports and

1326-475: Is considered a variant of 4, as in Tipler 1994). The anthropic principle, at least as Carter conceived it, can be applied on scales much smaller than the whole universe. For example, Carter (1983) inverted the usual line of reasoning and pointed out that when interpreting the evolutionary record, one must take into account cosmological and astrophysical considerations. With this in mind, Carter concluded that given

1404-411: Is even more obvious when one considers the complementary questions: "what is the probability that two red balls were placed in the box" and "what is the probability that a red ball was drawn from the box".) This view evidently violates the principle that, if event A happens if and only if event B happens, then we should have equal credence for event A and event B. This principle is not applicable because

1482-404: Is granted, the anthropic principle provides a plausible explanation for the fine tuning of our universe: the "typical" universe is not fine-tuned, but given enough universes, a small fraction will be capable of supporting intelligent life. Ours must be one of these, and so the observed fine tuning should be no cause for wonder. Although philosophers have discussed related concepts for centuries, in

1560-463: Is involved. The anthropic principle has given rise to some confusion and controversy, partly because the phrase has been applied to several distinct ideas. All versions of the principle have been accused of discouraging the search for a deeper physical understanding of the universe. Critics of the weak anthropic principle point out that its lack of falsifiability entails that it is non-scientific and therefore inherently not useful. Stronger variants of

1638-442: Is needed to bridge this methodological gap is a more adequate formulation of how observation selection effects are to be taken into account. Strong self-sampling assumption (SSSA) ( Bostrom ): "Each observer-moment should reason as if it were randomly selected from the class of all observer-moments in its reference class." Analysing an observer's experience into a sequence of "observer-moments" helps avoid certain paradoxes; but

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1716-460: Is not predictive. Max Tegmark , Mario Livio , and Martin Rees argue that only some aspects of a physical theory need be observable and/or testable for the theory to be accepted, and that many well-accepted theories are far from completely testable at present. Jürgen Schmidhuber (2000–2002) points out that Ray Solomonoff 's theory of universal inductive inference and its extensions already provide

1794-399: Is now called the multiverse ("world ensemble" was Carter's term), in which the parameters (and perhaps the laws of physics) vary across universes. The strong principle then becomes an example of a selection effect , exactly analogous to the weak principle. Postulating a multiverse is certainly a radical step, but taking it could provide at least a partial answer to a question seemingly out of

1872-460: Is put forth by intelligent design . Proponents of intelligent design often cite the fine-tuning observations that (in part) preceded the formulation of the anthropic principle by Carter as a proof of an intelligent designer. Opponents of intelligent design are not limited to those who hypothesize that other universes exist; they may also argue, anti-anthropically, that the universe is less fine-tuned than often claimed, or that accepting fine tuning as

1950-611: Is required to make life possible. The small but finite value of the cosmological constant can be regarded as a successful prediction in this sense. One thing that would not count as evidence for the anthropic principle is evidence that the Earth or the Solar System occupied a privileged position in the universe, in violation of the Copernican principle (for possible counterevidence to this principle, see Copernican principle ), unless there

2028-664: Is the number of potential wakings; Zuboff used a large number. Elga created a schedule within which to implement his solution, and this has become the canonical form of the problem: Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: In either case, she will be awakened on Wednesday without interview and

2106-406: Is therefore to gain 0.5 but also lose 1.5 times her wager, thus she should break even if her wager is 1/3. David Lewis responded to Elga's paper with the position that Sleeping Beauty's credence that the coin landed heads should be 1/2. Sleeping Beauty receives no new non-self-locating information throughout the experiment because she is told the details of the experiment. Since her credence before

2184-421: Is told and she comes to fully believe that the coin landed tails. By even a highly restricted principle of indifference , given that the coin lands tails, her credence that it is Monday should equal her credence that it is Tuesday, since being in one situation would be subjectively indistinguishable from the other. In other words, P(Monday|Tails) = P(Tuesday|Tails), and thus Suppose now that Sleeping Beauty

2262-407: Is told upon awakening and comes to fully believe that it is Monday. Guided by the objective chance of heads landing being equal to the chance of tails landing, it should hold that P(Tails|Monday) = P(Heads|Monday), and thus Since these three outcomes are exhaustive and exclusive for one trial (and thus their probabilities must add to 1), the probability of each is then 1/3 by the previous two steps in

2340-455: Is unremarkable that humanity happens to inhabit a Boltzmann universe, as that is the only place where intelligent life could be. Weak anthropic principle (WAP) ( Carter ): "... our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers." For Carter, "location" refers to our location in time as well as space. Strong anthropic principle (SAP) (Carter): "[T]he universe (and hence

2418-415: Is what it is whether we are here or not. Carter chose to focus on a tautological aspect of his ideas, which has resulted in much confusion. In fact, anthropic reasoning interests scientists because of something that is only implicit in the above formal definitions, namely that humans should give serious consideration to there being other universes with different values of the "fundamental parameters"—that is,

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2496-439: Is your credence that the coin came up heads", is ambiguous. The question must be disambiguated based on the particular event whose probability we wish to measure. The two disambiguations are: "what is your credence that the coin landed heads in the act of tossing" and "what is your credence that the coin landed heads in the toss to set up this awakening"; to which, the correct answers are 1/2 and 1/3 respectively. Another way to see

2574-476: The Big Bang ). Carter defined two forms of the anthropic principle, a "weak" one which referred only to anthropic selection of privileged spacetime locations in the universe, and a more controversial "strong" form that addressed the values of the fundamental constants of physics. Roger Penrose explained the weak form as follows: The argument can be used to explain why the conditions happen to be just right for

2652-473: The Big Crunch (the "Dicke coincidences" argument ). The most recent measurements may suggest that the observed density of baryonic matter, and some theoretical predictions of the amount of dark matter , account for about 30% of this critical density, with the rest contributed by a cosmological constant . Steven Weinberg gave an anthropic explanation for this fact: he noted that the cosmological constant has

2730-452: The dimensionless physical constants (such as the fine-structure constant ) governing the four fundamental interactions are balanced as if fine-tuned to permit the formation of commonly found matter and subsequently the emergence of life. A slight increase in the strong interaction (up to 50% for some authors ) would bind the dineutron and the diproton and convert all hydrogen in the early universe to helium; likewise, an increase in

2808-461: The dimensionless physical constants and initial conditions for the Big Bang . Carter and others have argued that life would not be possible in most such universes. In other words, the universe humans live in is fine tuned to permit life. Collins & Hawking (1973) characterized Carter's then-unpublished big idea as the postulate that "there is not one universe but a whole infinite ensemble of universes with all possible initial conditions". If this

2886-495: The fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage. To paraphrase Descartes , cogito ergo mundus talis est ." The Latin tag ("I think, therefore the world is such [as it is]") makes it clear that "must" indicates a deduction from the fact of our existence; the statement is thus a truism . In their 1986 book, The anthropic cosmological principle , John Barrow and Frank Tipler depart from Carter and define

2964-752: The philosophy of mind , ethics , metaphysics , epistemology , and the philosophy of probability . and a view analogous to open individualism —the position that there is one subject of experience, who is everyone—which he calls "universalism". Arnold Stuart Zuboff was born in January 1946. He was raised in West Hartford, Connecticut . Zuboff received a BA in philosophy from the University of Connecticut in 1968, and attended Princeton University Graduate School until 1972. In 2009, he successfully defended his thesis titled Time, Self, and Sleeping Beauty , under

3042-590: The triple-alpha process . He then calculated the energy of this undiscovered resonance to be 7.6 million electronvolts . Willie Fowler 's research group soon found this resonance, and its measured energy was close to Hoyle's prediction. However, in 2010 Helge Kragh argued that Hoyle did not use anthropic reasoning in making his prediction, since he made his prediction in 1953 and anthropic reasoning did not come into prominence until 1980. He called this an "anthropic myth", saying that Hoyle and others made an after-the-fact connection between carbon and life decades after

3120-506: The weak interaction also would convert all hydrogen to helium. Water, as well as sufficiently long-lived stable stars, both essential for the emergence of life as it is known, would not exist. More generally, small changes in the relative strengths of the four fundamental interactions can greatly affect the universe's age, structure, and capacity for life. The phrase "anthropic principle" first appeared in Brandon Carter 's contribution to

3198-454: The "paradox of the absent minded driver" was first introduced and the Sleeping Beauty problem discussed as Example 5. The name "Sleeping Beauty" was given to the problem by Robert Stalnaker and was first used in extensive discussion in the Usenet newsgroup rec.puzzles in 1999. As originally published by Elga, the problem was: The only significant difference from Zuboff's unpublished versions

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3276-565: The Copernican principle to justify the Perfect Cosmological Principle , which states that all large regions and times in the universe must be statistically identical. The latter principle underlies the steady-state theory , which had recently been falsified by the 1965 discovery of the cosmic microwave background radiation . This discovery was unequivocal evidence that the universe has changed radically over time (for example, via

3354-459: The WAP and SAP as follows: Weak anthropic principle (WAP) (Barrow and Tipler): "The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirements that the universe be old enough for it to have already done so." Unlike Carter they restrict

3432-491: The ages of 18 and 21, which he has made available online. Zuboff was a close friend and engaged in philosophical discussions with the Canadian philosopher G. A. Cohen . Anthropic principle The anthropic principle , also known as the observation selection effect , is the hypothesis that the range of possible observations that could be made about the universe is limited by the fact that observations are only possible in

3510-437: The anthropic principle essentially just says that the conditional probability of finding yourself in a universe compatible with your existence is always 1. It does not allow for any additional nontrivial predictions such as "gravity won't change tomorrow". To gain more predictive power, additional assumptions on the prior distribution of alternative universes are necessary. Playwright and novelist Michael Frayn describes

3588-445: The anthropic principle may be appropriated by cosmologists committed to nontheism , and refers to that principle as a "turning point" in modern science because applying it to the string landscape "may explain how the constants of nature that we observe can take values suitable for life without being fine-tuned by a benevolent creator". Others—most notably David Gross but also Lubos Motl , Peter Woit , and Lee Smolin —argue that this

3666-410: The anthropic principle which are not tautologies can still make claims considered controversial by some; these would be contingent upon empirical verification. In 1961, Robert Dicke noted that the age of the universe , as seen by living observers, cannot be random. Instead, biological factors constrain the universe to be more or less in a "golden age", neither too young nor too old. If the universe

3744-438: The argument. An alternative argument is as follows: Credence can be viewed as the amount a rational risk-neutral bettor would wager if the payoff for being correct is 1 unit (the wager itself being lost either way). In the heads scenario, Sleeping Beauty would spend her wager amount one time, and receive 1 money for being correct. In the tails scenario, she would spend her wager amount twice, and receive nothing. Her expected value

3822-679: The best estimates of the age of the universe , the evolutionary chain culminating in Homo sapiens probably admits only one or two low probability links. No possible observational evidence bears on Carter's WAP, as it is merely advice to the scientist and asserts nothing debatable. The obvious test of Barrow's SAP, which says that the universe is "required" to support life, is to find evidence of life in universes other than ours. Any other universe is, by most definitions, unobservable (otherwise it would be included in our portion of this universe ). Thus, in principle Barrow's SAP cannot be falsified by observing

3900-643: The case with Carter's SAP, the "must" is an imperative, as shown by the following three possible elaborations of the SAP, each proposed by Barrow and Tipler: The philosophers John Leslie and Nick Bostrom reject the Barrow and Tipler SAP as a fundamental misreading of Carter. For Bostrom, Carter's anthropic principle just warns us to make allowance for anthropic bias —that is, the bias created by anthropic selection effects (which Bostrom calls "observation" selection effects)—the necessity for observers to exist in order to get

3978-422: The dimmest red dwarfs , and stable planetary systems would have already come to an end. Thus, Dicke explained the coincidence between large dimensionless numbers constructed from the constants of physics and the age of the universe, a coincidence that inspired Dirac's varying- G theory . Dicke later reasoned that the density of matter in the universe must be almost exactly the critical density needed to prevent

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4056-423: The discovery of the resonance. An investigation of the historical circumstances of the prediction and its subsequent experimental confirmation shows that Hoyle and his contemporaries did not associate the level in the carbon nucleus with life at all. Don Page criticized the entire theory of cosmic inflation as follows. He emphasized that initial conditions that made possible a thermodynamic arrow of time in

4134-440: The early 1970s the only genuine physical theory yielding a multiverse of sorts was the many-worlds interpretation of quantum mechanics . This would allow variation in initial conditions, but not in the truly fundamental constants. Since that time a number of mechanisms for producing a multiverse have been suggested: see the review by Max Tegmark . An important development in the 1980s was the combination of inflation theory with

4212-450: The existence of (intelligent) life on the Earth at the present time. For if they were not just right, then we should not have found ourselves to be here now, but somewhere else, at some other appropriate time. This principle was used very effectively by Brandon Carter and Robert Dicke to resolve an issue that had puzzled physicists for a good many years. The issue concerned various striking numerical relations that are observed to hold between

4290-488: The experiment ends. Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?" This problem continues to produce ongoing debate. The thirder position argues that the probability of heads is 1/3. Adam Elga argued for this position originally as follows: Suppose Sleeping Beauty

4368-462: The experiment is P(Heads) = 1/2, she ought to continue to have a credence of P(Heads) = 1/2 since she gains no new relevant evidence when she wakes up during the experiment. This directly contradicts one of the thirder's premises, since it means P(Tails|Monday) = 1/3 and P(Heads|Monday) = 2/3. The double halfer position argues that both P(Heads) and P(Heads|Monday) equal 1/2. Mikaël Cozic, in particular, argues that context-sensitive propositions like "it

4446-474: The first in modern science to use anthropic reasoning. Prior to knowledge of the Big Bang Boltzmann's thermodynamic concepts painted a picture of a universe that had inexplicably low entropy . Boltzmann suggested several explanations, one of which relied on fluctuations that could produce pockets of low entropy or Boltzmann universes. While most of the universe is featureless in this model, to Boltzmann, it

4524-573: The following responses to that debate: Omitted here is Lee Smolin 's model of cosmological natural selection , also known as fecund universes , which proposes that universes have "offspring" that are more plentiful if they resemble our universe. Also see Gardner (2005). Clearly each of these hypotheses resolve some aspects of the puzzle, while leaving others unanswered. Followers of Carter would admit only option 3 as an anthropic explanation, whereas 3 through 6 are covered by different versions of Barrow and Tipler's SAP (which would also include 7 if it

4602-415: The hypothesis that some parameters are determined by symmetry breaking in the early universe, which allows parameters previously thought of as "fundamental constants" to vary over very large distances, thus eroding the distinction between Carter's weak and strong principles. At the beginning of the 21st century, the string landscape emerged as a mechanism for varying essentially all the constants, including

4680-449: The laws and constants of any such universe must accommodate that possibility. The term anthropic in "anthropic principle" has been argued to be a misnomer . While singling out the currently observable kind of carbon-based life, none of the finely tuned phenomena require human life or some kind of carbon chauvinism . Any form of life or any form of heavy atom, stone, star, or galaxy would do; nothing specifically human or anthropic

4758-407: The leading candidate for a "theory of everything", string theory , proclaimed "the end of the anthropic principle" since there would be no free parameters to select. In 2003, however, Leonard Susskind stated: "... it seems plausible that the landscape is unimaginably large and diverse. This is the behavior that gives credence to the anthropic principle." The modern form of a design argument

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4836-520: The lifetime of what are called main-sequence stars, such as the Sun. At any other epoch, the argument ran, there would be no intelligent life around to measure the physical constants in question—so the coincidence had to hold, simply because there would be intelligent life around only at the particular time that the coincidence did hold! One reason this is plausible is that there are many other places and times in which humans could have evolved. But when applying

4914-436: The main ambiguity is the selection of the appropriate "reference class": for Carter's WAP this might correspond to all real or potential observer-moments in our universe; for the SAP, to all in the multiverse. Bostrom's mathematical development shows that choosing either too broad or too narrow a reference class leads to counter-intuitive results, but he is not able to prescribe an ideal choice. According to Jürgen Schmidhuber ,

4992-428: The number of spatial dimensions. The anthropic idea that fundamental parameters are selected from a multitude of different possibilities (each actual in some universe or other) contrasts with the traditional hope of physicists for a theory of everything having no free parameters. As Albert Einstein said: "What really interests me is whether God had any choice in the creation of the world." In 2002, some proponents of

5070-418: The physical constants (the gravitational constant , the mass of the proton , the age of the universe , etc.). A puzzling aspect of this was that some of the relations hold only at the present epoch in the Earth's history, so we appear, coincidentally, to be living at a very special time (give or take a few million years!). This was later explained, by Carter and Dicke, by the fact that this epoch coincided with

5148-528: The principle to carbon-based life, rather than just "observers". A more important difference is that they apply the WAP to the fundamental physical constants, such as the fine-structure constant , the number of spacetime dimensions , and the cosmological constant —topics that fall under Carter's SAP. Strong anthropic principle (SAP) (Barrow and Tipler): "The Universe must have those properties which allow life to develop within it at some stage in its history." This looks very similar to Carter's SAP, but unlike

5226-406: The question from the original problem resolves to one of two different questions: "what is the probability that a green ball was placed in the box" and "what is the probability a green ball was drawn from the box". These questions ask for the probability of two different events, and thus can have different answers, even though both events are causally dependent on the coin landing heads. (This fact

5304-426: The reach of normal science: "Why do the fundamental laws of physics take the particular form we observe and not another?" Since Carter's 1973 paper, the term anthropic principle has been extended to cover a number of ideas that differ in important ways from his. Particular confusion was caused by the 1986 book The Anthropic Cosmological Principle by John D. Barrow and Frank Tipler , which distinguished between

5382-432: The sample spaces are different. Credence about what precedes awakenings is a core question in connection with the anthropic principle . This differs from the original in that there are one million and one wakings if tails comes up. It was formulated by Nick Bostrom . The Sailor's Child problem, introduced by Radford M. Neal , is somewhat similar. It involves a sailor who regularly sails between ports. In one port there

5460-468: The strong principle, there is only one universe, with one set of fundamental parameters, so what exactly is the point being made? Carter offers two possibilities: First, humans can use their own existence to make "predictions" about the parameters. But second, "as a last resort", humans can convert these predictions into explanations by assuming that there is more than one universe, in fact a large and possibly infinite collection of universes, something that

5538-475: The supervision of his doctoral advisor, Thomas Nagel . His examiners were Gilbert Harman , Adam Elga, John P. Burgess , Alexander Nehamas , and Nagel. Zuboff lectured at the University College London 's Department of Philosophy from 1974 till his retirement in 2011. He is now an Honorary Senior Research Associate. Zuboff created a series of paintings and poems inspired by his dreams between

5616-400: The two different questions is to simplify the Sleeping Beauty problem as follows. Imagine tossing a coin, if the coin comes up heads, a green ball is placed into a box; if, instead, the coin comes up tails, two red balls are placed into a box. We repeat this procedure a large number of times until the box is full of balls of both colours. A single ball is then drawn from the box. In this setting,

5694-445: The type of universe that is capable of developing intelligent life. Proponents of the anthropic principle argue that it explains why the universe has the age and the fundamental physical constants necessary to accommodate intelligent life. If either had been significantly different, no one would have been around to make observations. Anthropic reasoning has been used to address the question as to why certain measured physical constants take

5772-431: The values that they do, rather than some other arbitrary values, and to explain a perception that the universe appears to be finely tuned for the existence of life . There are many different formulations of the anthropic principle. Philosopher Nick Bostrom counts thirty, but the underlying principles can be divided into "weak" and "strong" forms, depending on the types of cosmological claims they entail. The principle

5850-536: The woman in the port that appears first would be the woman that he has a child with. You are his child. You do not have a copy of The Sailor's Guide to Ports. What is the probability that you are his only child, thus the coin landed on Heads (assume a fair coin)? Arnold Zuboff Arnold Stuart Zuboff (born January 1946) is an American philosopher who is the original formulator of the Sleeping Beauty problem . He has worked on topics such as personal identity ,

5928-510: Was formulated as a response to a series of observations that the laws of nature and parameters of the universe have values that are consistent with conditions for life as it is known rather than values that would not be consistent with life on Earth . The anthropic principle states that this is an a posteriori necessity , because if life were impossible, no living entity would be there to observe it, and thus it would not be known. That is, it must be possible to observe some universe, and hence,

6006-437: Was one tenth as old as its present age, there would not have been sufficient time to build up appreciable levels of metallicity (levels of elements besides hydrogen and helium ) especially carbon , by nucleosynthesis . Small rocky planets did not yet exist. If the universe were 10 times older than it actually is, most stars would be too old to remain on the main sequence and would have turned into white dwarfs , aside from

6084-440: Was some reason to think that that position was a necessary condition for our existence as observers. Fred Hoyle may have invoked anthropic reasoning to predict an astrophysical phenomenon. He is said to have reasoned, from the prevalence on Earth of life forms whose chemistry was based on carbon-12 nuclei, that there must be an undiscovered resonance in the carbon-12 nucleus facilitating its synthesis in stellar interiors via

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