LECTURE 9: THE ANTHROPIC PRINCIPLE
In physics and cosmology, the anthropic principle states that humans should take into account the constraints that human existence as observers imposes on the sort of universe that could be observed. In other words, the only universe we can see is one that supports life. If it were a different type of universe, we would not exist to see it.
Originally proposed as a rule of reasoning, the term has since been extended to cover supposed "superlaws" that in various ways require the universe to support intelligent life, usually assumed to be carbon-based, and occasionally to be specifically human beings. Anthropic reasoning involves assessing these constraints by analyzing the properties of universes with different fundamental parameters or laws of physics from the current one, and has frequently concluded that essential structures, from atomic nuclei to the whole universe, depend, for stability, on delicate balances between different fundamental forces; balances which occur only in a small minority of possible universes — so that ours seems to be fine-tuned for life. Anthropic reasoning also attempts to explain and quantify this fine tuning. Within the scientific community the usual approach is to invoke selection effects from a real ensemble of alternate universes, which cause an anthropic bias in what can be observed.
The anthropic principle has led to more than a little confusion and controversy, partly because several distinct ideas carry this label. All versions of the principle have been accused of providing simplistic explanations which undermine the search for a deeper physical understanding of the universe. The invocation of either multiple universes or an intelligent designer are highly controversial, and both ideas have received criticism for being untestable and therefore outside the purview of contemporary science..
Robert Dicke[1] noted that the age of the universe as seen by living observers is not random, but is constrained by biological factors that require it to be roughly a "golden age".[2] Ten times younger, and there would not have been time for sufficient interstellar levels of carbon to build up by nucleosynthesis; but ten times older, and the golden age of main sequence stars and stable planetary systems would have already come to an end. This explained away a rough coincidence between large dimensionless numbers constructed from the constants of physics and the age of the universe, which had inspired Dirac's varying-G theory.
Later, Dicke reasoned that the density of matter in the universe must be almost exactly the critical density needed to stop the universe from recollapsing (the "Dicke coincidences" argument, see article on Robert Dicke). It seems he was wrong: latest estimates are that matter has about 30% of the critical density, with the rest contributed by a cosmological constant. Steven Weinberg[3] gave an anthropic explanation: he noted that the cosmological constant has a remarkably low value, some 120 orders of magnitude smaller than expected from particle physics (often described as the worst prediction in physics). However, if the cosmological constant was more than about 10 times the observed value, the universe would suffer catastrophic inflation, preventing the formation of stars, and, presumably, life.
The observed values of the dimensionless parameters (such as the fine-structure constant) that govern the four forces of nature are finely balanced. A slight increase in the strong nuclear force would bind the dineutron and the diproton and all the hydrogen in the early universe would have been converted to helium. There would be no water or the long-lived stable stars that are essential for the development of life. Similar relationships are evident in each of the four force strengths. If they are modified sufficiently the universe's structure and capacity for life is greatly affected. A list of cosmological, chemical and physical "anthropic coincidences" is given by Hugh Ross[4].
One of the best known examples of anthropic reasoning used in the prediction of cosmological phenomena was by Fred Hoyle. He calculated and then reasoned that there must be an excited state at an energy of 7.6 million electron volts in the nucleus of carbon-12 since he, Fred Hoyle, a life form based upon carbon molecules, existed, then the resonance must also exist to create the carbon. [5] [6]
The phrase "anthropic principle" was coined by the theoretical astrophysicist Brandon Carter, in his contribution to a 1973 Kraków symposium honouring Copernicus's 500th birthday. Carter articulated the Anthropic Principle as a reaction to overuse of the Copernican Principle, which states that we are not at a special position in the Universe. As Carter says, "Although our situation is not necessarily central, it is inevitably privileged to some extent".[7] Carter was particularly reacting against the use of the Copernican principle to justify the Perfect Cosmological Principle, that all large regions and times in the universe must be statistically identical. This principle underlay the steady-state theory which had recently been proved wrong by unequivocal evidence for radical changes in the Universe with time (starting with the Big Bang).
Carter defined two forms of the Anthropic principle, a "weak" one which referred only to anthropic selection of privileged space-time locations in the universe, and a more controversial "strong" form which referred to the fundamental parameters of physics.
Roger Penrose explains the weak form:
The argument can be used to explain why the conditions happen to be just right for 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 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 the lifetime of what are called main-sequence stars, such as the sun. At any other epoch, so the argument ran, there would be no intelligent life around in order 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!
– The Emperor's New Mind, Chapter 10
One reason this is plausible is that there are plenty of other places and other times in which we can imagine finding ourselves. But when applying the strong principle, we only have one Universe, with one set of fundamental parameters, so what exactly is the point being made? Carter offers two possibilities: first, we can use our own existence to make "predictions" about the parameters. But second, "as a last resort", we can convert these predictions into explanations by assuming that there is more than one Universe, in fact a large or infinite collection of universes; what is now called a multiverse ("world ensemble" is Carter's term), in which the parameters (and perhaps the laws of physics) do vary from universe to universe. 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 as a pay-off it offers at least a partial answer to a question which seems to be out of the reach of normal science: "why do the fundamental laws take that particular form and not another?"
Since Carter's original paper, the term "Anthropic Principle" has been extended to cover a number of ideas which are different in important ways from the ones he espoused. Particular confusion was caused by the influential book The Anthropic Cosmological Principle by John D. Barrow and Frank Tipler,[8] which makes a very different distinction between "weak" and "strong" anthropic principle, as discussed in the next section.
Brandon Carter was not the first to invoke some form of the anthropic principle. For instance, Dicke wrote in 1957 that: "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."[9] Alfred Russel Wallace anticipated the anthropic principle as long ago as 1903: "Such a vast and complex universe as that which we know exists around us, may have been absolutely required ... in order to produce a world that should be precisely adapted in every detail for the orderly development of life culminating in man."[10]
- Carter's Weak anthropic principle (WAP): "we must be prepared to take account of the fact that our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers." Note that for Carter, "location" is a space-time position.
- Carter's Strong anthropic principle (SAP): "the Universe (and hence 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.
Quite different definitions of these terms were offered by Barrow[11], and variants of these were used in his book with Tipler[12]:
- Barrow and Tipler's Weak anthropic principle: "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."[13] Unlike Carter they restrict 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 dimensions in the universe, and the cosmological constant — just the topics that Carter reserves for the SAP.
- Barrow and Tipler's Strong anthropic principle: "The Universe must
have those properties which allow life to develop within it at some stage in its
history."[14] This looks very similar to Carter's SAP, but
for Barrow and Tipler, unlike Carter, the "must" is an imperative, as shown by
their three possible elaborations of the SAP:[15]
- "There exists one possible Universe 'designed' with the goal of generating and sustaining 'observers.' " This can be seen as simply the classic design argument dressed in the garb of contemporary cosmology. It implies that the purpose of the universe is to give rise to intelligent life, with the laws of nature and their fundamental constants set to ensure that life as we know it will emerge and evolve.
- "Observers are necessary to bring the Universe into being." Barrow and Tipler believe that this can be validly inferred from quantum mechanics, as has long been suggested by John Archibald Wheeler in his "participatory universe" and Participatory Anthropic Principle (PAP).
- "An ensemble of other different universes is necessary for the existence of our Universe." Contrast this with Carter, who merely says that an ensemble of universes is necessary for the SAP to count as an explanation.
The first of these has of course been welcomed by proponents of intelligent design. Carter has protested that such teleological readings "are quite different from, and even contradictory with, what I intended".[16] The Barrow and Tipler SAP has also been rejected as a fundamental misreading of Carter by the philosophers John Leslie[17] and Nick Bostrom.[18] For Bostrom, Carter's anthropic principle just warns us to make allowance for anthropic bias, that is, the bias created by anthropic selection effects (called "observation" selection effects by Bostrom) — the necessity for observers to exist in order to get 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 is needed to bridge this methodological gap is a more adequate formulation of how observation selection effects are to be taken into account.
– Anthropic Bias, Introduction. [19]
- Bostrom's 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. Analysing an observer's experience into a sequence of "observer-moments" helps avoid certain paradoxes; but 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 a perfect choice.
- According to Jürgen Schmidhuber, the anthropic principle essentially just says that the conditional probability of finding yourself in a universe compatible with your existence will always remain 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[20] [21].
- Playwright and Novelist Michael Frayn describes a position which expresses one 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 is what it is whether we are here or not.[22]
Much confusion has been caused by Carter's decision to focus on a rather tautological component of his ideas. In fact anthropic reasoning is of interest to scientists mainly for what is only implicit in the formal definitions, namely that we should consider seriously universes with different values of the "fundamental parameters" — that is, the dimensionless physical constants and the dimensionless initial conditions at the Big Bang. Carter (and others) argue that life as we know it would not be possible in most of these; in other words, that the universe is fine tuned. Collins & Hawking (1973) characterise 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".[23] If this is granted, the anthropic principle provides a plausible explanation for the fine tuning of our universe: typical universes are not fine-tuned, but, if there are enough universes, a small proportion 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. In this sense it is in direct opposition to design arguments.
But how seriously can we take the multiverse? And which specific multiverse should we assume? — this question must be answered before any quantitative anthropic predictions can be made. Although philosophers have discussed related concepts for centuries, in the early 1970s the only genuine physical theory giving a multiverse of sorts was the many worlds interpretation of quantum mechanics. This would allow variation in initial conditions, but not in truly fundamental constants. Since that time a number of mechanisms for producing a multiverse have been suggested: see the review by Max Tegmark[24], and the multiverse (science) article. An important development in the 1980s was the combination of inflation theory with the idea 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, eroding the distinction between Carter's weak and strong principles. At the beginning of the 21st century, the concept of the string landscape gave a mechanism for varying essentially all the constants, including the number of spatial dimensions.[25]
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 with no free parameters: as Einstein said, "What really interests me is whether God had any choice in the creation of the world". Quite recently, proponents of the leading candidate "theory of everything", String theory, proclaimed "the end of the anthropic principle"[26] since there would be no free parameters to select. Ironically, string theory now seems to offer no hope of predicting fundamental parameters, and some of its exponents have resorted to invoking the anthropic principle (see below).
Opponents of intelligent design are not limited to hypothesizing the existence of alternate universes: they may argue anti-anthropically that the universe is less fine-tuned than often claimed, or that accepting fine tuning as a brute fact is less astonishing than the idea of an intelligent creator. Furthermore, even accepting fine tuning, Sober (2005)[27] and Ikeda and Jefferys[28] argue that the Anthropic Principle as conventionally stated actually undermines intelligent design. This is discussed in more detail in fine-tuned universe.
Paul Davies has discussed fine-tuning at length, and in his book The Goldilocks Enigma (2006) he summarises the current state of the debate in detail. He concludes by enumerating the alternative responses:
- A - The absurd universe - It just happens to be that way.
- B - The unique universe - There is a deep underlying unity in physics which necessitates the universe being this way. Some 'Theory of Everything' will explain why the various features of the Universe must have exactly the values that we see.
- C - The multiverse - Multiple Universes exist which have all possible combinations of characteristics, and we naturally find ourselves within the one that supports our existence.
- D - Intelligent Design - An intelligent Creator designed the Universe specifically to support complexity and the emergence of Intelligence.
- E - The life principle - There is an underlying principle that constrains the universe to evolve towards life and mind.
- F - The self-explaining universe - A closed explanatory or causal loop: 'perhaps only universes with a capacity for consciousness can exist'.
- G - The fake universe - We are living in a virtual reality simulation.
Omitted here is Lee Smolin's model of cosmological natural selection, also known as fecund universes, which proposes that universes have "offspring" which are more plentiful if they happen to have features common to our universe. Also see Gardner (2005).[29]
Clearly all of these resolve some aspects of the puzzle, and leave other questions unanswered. Followers of Carter would allow only option C as an anthropic explanation, whereas C through F are covered by different versions of Barrow and Tipler's SAP (and also G if considered a variant on D).
The anthropic principle, at least as conceived by Carter, can be applied on scales much smaller than the whole universe. For instance Carter (1983)[30] inverted the usual line of reasoning and pointed out that in interpreting the evolutionary record, one must take into account cosmological and astrophysical considerations. With this in mind, Carter concluded that, given the best estimates of the age of the universe, the evolutionary chain probably can allow only one or two low probability links. This conclusion has been disputed.[31]
Can observational evidence be obtained for the anthropic principle, or rather for any particular version? Certainly not for Carter's WAP, which is merely good advice to the scientist and makes no debatable assertions. The obvious way to test Barrow's SAP, which says that the Universe is required to support life, is to check a number of different universes to see if they all supported life; but such a test is currently impossible.
John Leslie[32] makes a number of predictions from the point of view of the Carter SAP (with multiverse):
- Developments in physics will strengthen the idea that early phase transitions occur probabilistically rather than deterministically [so there will not be a deep physical reason for the values of fundamental constants].
- Various methods for generating multiple universes will survive theoretical investigation.
- Claims of fine tuning will be borne out.
- Attempts to discover exotic (non-carbon-based) life will repeatedly fail.
- Mathematical studies of galaxy formation will confirm that it does depend delicately on expansion rate.
Hogan[33] 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 we might have to resort to something like Barrow and Tipler's SAP: there would be no option for such a universe not to support life.
Probabilistic predictions of parameter values can be made given (i) a particular multiverse with a "measure", i.e. a well defined "density of universes" (so, for parameter X, one can calculate the prior probability P(X0) dX that X is in the range X0 < X < X0 + dX), and (ii) an estimate of the number of observers in each universe, N(X) (e.g. this might be taken as proportional to the number of stars). The probability of observing value X is then proportional to N(X) P(X). (A more sophisticated analysis is offered by Nick Bostrom[34]). A generic feature is that the expected values should not be "over tuned", i.e. if there is some perfectly tuned value (e.g. zero) we don't expect to be much closer to it than needed to allow life. The small but (apparently) finite value of the cosmological constant is often regarded as a successful prediction in this sense.
One thing that would not count as evidence for the Anthropic principle is anti-Copernican evidence that the Earth or the Solar System were literally in a special position in the universe (for possible hints of this see Copernican principle), unless there was some reason to think that said position was a necessary condition for our existence as observers.
The most thorough extant study of the anthropic principle is the book The Anthropic Cosmological Principle by John D. Barrow, a cosmologist, and Frank J. Tipler, a mathematical physicist. This book sets out in great detail the many known anthropic coincidences and constraints, including many found by its authors. While the book is primarily a work of theoretical astrophysics, it also touches on quantum physics, chemistry, and earth science. An entire chapter argues that homo sapiens is, with high probability, the only intelligent species in the Milky Way.
The book begins with an extensive review of many topics in the history of ideas the authors deem relevant to the anthropic principle, because the authors believe that principle has important antecedents in the notions of intelligent design, the writings of Fichte, Hegel, Bergson, and Alfred North Whitehead, and the omega point cosmology of Teilhard de Chardin. Barrow and Tipler carefully distinguish teleological reasoning from eutaxiological reasoning; the former asserts that order must have a consequent purpose; the latter asserts more modestly that order must have a planned cause. They attribute this important but nearly always overlooked distinction to Hicks (1883).[35]
Seeing little sense in a principle requiring intelligent life to emerge while remaining indifferent to the possibility of its eventual extinction, Barrow and Tipler propose the:
- Final anthropic principle (FAP): "Intelligent information-processing must come into existence in the Universe, and, once it comes into existence, it will never die out."[36]
Barrow and Tipler submit that the FAP is both a valid physical statement and "closely connected with moral values." FAP places strong constraints on the structure of the universe, constraints developed further in Tipler's The Physics of Immortality.[37] One such constraint is that the universe must end in a big crunch, which seems unlikely in view of the tentative conclusions drawn since 1998 about dark energy, based on observations of very distant supernovas.
In his review[38] of Barrow and Tipler, Martin Gardner ridiculed the FAP by quoting the last two sentences of their book as defining a Completely ridiculous anthropic principle (CRAP):
"At the instant the Omega Point is reached, life will have gained control of all matter and forces not only in a single universe, but in all universes whose existence is logically possible; life will have spread into all spatial regions in all universes which could logically exist, and will have stored an infinite amount of information, including all bits of knowledge which it is logically possible to know. And this is the end."[39]
In fairness to the authors, they state at the outset that they are not necessarily committed to the ideas they describe, and admit that the SAP and FAP are "quite speculative."
A common criticism of Carter's SAP is that it is an easy get-out which discourages searches for physical explanations. To quote Penrose again: "it tends to be invoked by theorists whenever they do not have a good enough theory to explain the observed facts."[40]
Some applications of the anthropic principle have been criticized as an argument by lack of imagination for assuming that the only possible chemistry of life is one based on carbon compounds and liquid water (sometimes called "carbon chauvinism", see also alternative biochemistry).[41] The range of fundamental physical constants allowing evolution of carbon-based life may also be much less restrictive than proposed.[42] For instance, Harnik et al.[43] propose a Weakless Universe in which the Weak nuclear force is eliminated apparently without significant effect, provided some adjustments are made in the other forces. However, some of the fine-tuned details of our universe would rule out complex structures of any kind — stars, planets, galaxies etc — if violated.
Carter's SAP and Barrow and Tipler's WAP are truisms or tautologies, stating something not immediately obvious to everyone yet true. As such they are often criticized as an elaborate way of saying "if things were different, they would be different", which may not implicitly provide proof of alternatives, but are nonetheless valid arguments. Discussion of anthropic principles implicitly posits that our ability to ponder cosmology at all is contingent on one or more fundamental physical parameters having numerical values falling within quite a narrow range, which is not a tautology, and neither is the postulate of an actual multiverse. Moreover, working out the consequences of a change in the fundamental parameters for our existence is far from trivial, and, as we have seen, can lead to quite unexpected constraints on carbon-based life as we currently understand it, though not necessarily demonstrating that alternate forms of life are not possible under these transposed fundamental parameters.
Critics of the Barrow and Tipler SAP claim that it is neither testable nor falsifiable, and thus is not science. The same criticism has been leveled against the multiverse idea, although we have seen that proponents argue that it does make falsifiable predictions, albeit not very strong ones. A modified version of this criticism is that such calculations are in practice impossible because we understand so little about the emergence of life, especially intelligent life, that it is effectively impossible to calculate the number of observers in each universe; moreover the prior distribution of universes as a function of parameters is too easy to modify to get any desired result.[44]
Carter himself[45] has frequently regretted his own choice of the word anthropic as conveying the misleading impression that the principle involves humans specifically, rather than intelligent observers in general. Others[46] have criticised the word principle as too grandiose for a relatively straightforward application of selection effects.
Steven Jay Gould [47] [48], Michael Shermer [49] and others have observed that known causes and effects seem to have been reversed in the Anthropic Principle. Dr. Gould compared the claim that the universe is fine-tuned for the benefit of our kind of life to claiming that sausages were originally made long and narrow so that they would fit modern hotdog buns, or that ships had been invented to provide homes for barnacles. These critics cite the vast store of physical and evolutionary evidence which shows that life has been fine-tuned by the universe, through natural selection, to match the conditions in which life exists. Fossil, genetic and other biological evidence abundantly supports the observation that life adapts to physics, not the other way around.
The paleophysicist Caroline Miller has said: [50]
The Anthropic Principle is based on the underlying belief that the universe was created for our benefit. Unfortunately for its adherents, all of the reality-based evidence at our disposal contradicts this belief. In a non-anthropocentric universe, there is no need for multiple universes or supernatural entities to explain life as we know it.
However, Paul Davies (http://www.abc.net.au/science/bigquestions/) argues that the physical nature of the universe has to be fine tuned in a number of ways to permit any sort of life to exist, which can then adapt to its conditions - as one example, 'for life to exist there must be atoms'; and that if any one of several physical constants were different by small amounts atoms would not exist.
A critique of cosmic inflation, questioning the very premise of the theory, was offered by Don N. Page[51] who emphasized the point that initial conditions which made it possible that a thermodynamic arrow of time in a Big Bang type of theory must necessarily include a low entropy initial state of the Universe and therefore to be extremely improbable. The critique was rebutted by Paul Davies[52] who used an inflationary version of the anthropic principle. While accepting the premise that the initial state of the visible Universe (originally a microscopic amount of space before the inflation) had to possess a very low entropy value — due to random quantum fluctuations — to account for the observed thermodynamic arrow of time, he deemed it not a problem of the theory but an advantage. That the tiny patch of space from which our observable Universe grew had to be extremely orderly, to allow inflation resulting in a universe with an arrow of time, makes it unnecessary to adopt any ad-hoc hypotheses about the initial entropy state which are necessary in other Big Bang theories.
String theory predicts a large number of possible universes, called the backgrounds or vacua. The set of these universes or 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 the anthropic reasoning on firm ground; only universes with the remarkable properties sufficient to allow observers to exist are beheld while a possibly much larger set of universes without such properties go utterly unnoted. Steven Weinberg[53] refers to the Anthropic Principle as a "turning point" in modern science since, applied to the string landscape, it "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 is not predictive. Max Tegmark,[54] Mario Livio and Martin Rees[55] respond that various ingredients of well-accepted theories will never be testable, and that the test of a physical theory is not that every aspect of it should be observable and/or testable, but rather that enough is observable and testable to give confidence in the theory's correctness. Jürgen Schmidhuber (2000-2002) points out that Ray Solomonoffs theory of universal inductive inference and its extensions already provide the optimal framework for maximizing this confidence, given a limited physical observation sequence and some prior distribution on the set of possible alternative explanations of the universe.
