The anthropic principle: science, philosophy or guesswork?
Autor: Mariano Artigas
Publicado en: Unpublished text
Fecha de publicación: Lecture in "The Impact of the Humanities on the Development of European Science", Summer School, 10-15 June 2004, Venice (Italy), Istituto Veneto di Scienze, Lettere ed Arti, and The Galileo Chair of History of Science of the University of Padua
- 1. Constants of nature and natural units
- 2. The dimensionless constants of nature
- 3. Dimensionless constants and large numbers
- 4. The formulation of the anthropic principle
- 5. The anthropic principle comes of age
- 6. Fine-tuning, teleology, and other worlds
- 7. Science, philosophy, or gueswork?
"A total of over thirty anthropic principles have been formulated and many of them have been defined several times over — in nonequivalent ways — by different authors, and sometimes even by the same authors on different occasions. Not surprisingly, the result has been some pretty wild confusion concerning what the whole thing is about".
Nick Bostrom *(3) (4)
One of the main characteristics of our age is the dichotomy between the objective world of empirical science, possessing an intersubjective character, and the subjective world of the knowing being, i.e. ourselves, which would remain forever alienated from the rational level of objective scientific discussion. The anthropic principle can be considered as a bridge between science, philosophy and theology. Apparently it enables us to introduce the human being, under the label of «the observer», in the otherwise impersonal scientific world, and to find a meaning to the world. This explains the interest this principle has raised.
Nevertheless, it is not easy to define the status of the anthropic principle. Some philosophically or theologically minded people like it, while many people think that its weaker form is a tautology, and its stronger form is untenable. In any case, it is linked with a host of interesting scientific and humanistic problems, and can serve to illustrate the interaction between the sciences and wider human problems.
The anthropic principle says, roughly, that the existence of life (specifically, human or «anthropic» life) in the Universe can set constraints on the way the Universe is now, and how it got to be the way it is now. An example. In order for us to exist, there has to be one star (the Sun), orbited at the appropriate distance by one planet (the Earth), made of the right mixture of chemical elements (particularly including carbon, nitrogen, oxygen and hydrogen: four elements that play a key role in life processes). At first sight, the existence of the vast Universe containing millions of galaxies would be irrelevant for us. But the elements of which we and the Earth are made have been manufactured within the stars. The Big Bang only produced hydrogen, helium and traces of a few light elements. Carbon and other heavier elements are made as a consequence of the nuclear processes within the stars. Stars have their life cycle, and eventually explode and liberate those elements, which congregate in planets like the Earth. A very long time has been necessary for galaxies and stars having been formed, for stars to have completed their life cycle and have exploded, for a planet like the Earth to be formed containing the elements necessary for the evolution of life. Thus, we are led to think that perhaps, for us to be here, the Universe must have existed for billions of years. Our existence may help to "explain" why so much years have elapsed since the Big Bang until now. At the same time, our existence imposes constraints upon many features of the natural world: as we are here, the natural world must possess the characteristics necessary to make possible our existence, which include a striking number of coincidences between distant branches of physics. For instance, if the gravitational constant (G) were slightly larger, stars would have burned too hot and much too quickly to support the needs of life; if it were slightly smaller, the intrastellar process of nuclear fusion would have never initiated, and life would have been incapable of arising on the Earth. Something similar happens with the expansion rate of the nascent universe, and other quantities of the physical world.
One first interesting thing is that, contrary to what we could expect, the anthropic principle was not proposed in a humanist context. We can trace back its origin and development to some speculations by physicists of a good reputation in the scientific ambit. We are going to examine the prehistory of the principle, how it was formulated for the first time, the variety of formulations that came afterwards, and their main interpretations.
The speculations that would lead to the anthropic principle begun with some reflections on the so-called «constants of nature».
Physicist use to describe the world using mathematical equations where we find two kinds of magnitude: the «variables» that take different values depending on the particular phenomena under consideration, and the «constants», whose value is the same for some kinds of bodies or phenomena. Some constants have always the same value, and serve to define the basic characteristics of our world. These are called «universal constants» or «constants of nature».
Also called «fundamental» or «universal» constants, they are those quantities that appear in the equations and do not change throughout the universe. In some way they define the basic physical characteristic of the world, they define how our world is. If they were different, the world would also be different: there would be no trees, or even atoms, because even though their components were assembled, they would not be stable. Five of these constants are the following:
The charge of an electron (e), is the natural unit of electric charge. It is equal but opposite in effect to the positive charge of the proton = 1.602 x 10-19 coulombs
The speed of light in a vacuum (c), is the speed at which electromagnetic radiation travels = 2.99792458 x 108 m s-1(roughly 300,000 kilometers per second)
The Planck constant (h). Equal to the ratio of the energy E of a quantum of energy to its frequency ν (E = h ν) = 6.626 176 x 10-34 Js. In quantum-mechanical calculations the Dirac constant is frequently used: ħ = h / 2π = 1.054589 x 10-34 Js
The gravitational constant (G). The constant that appears in Newton's law of gravitation = 6.67259 x 10-11 N m2 kg-2 (m3 kg-1 s-2)
Fine structure constant (α). The coupling constant of the electromagnetic interaction in quantum field theory. It is a dimensionless quantity and has a value of approximately 1 /137. In terms of fundamental constants, α = e2/2ε0 hc
(Fine structure: closely spaced optical spectral lines arising from transitions between energy levels; are visible only at high resolution)
Some 19 universal constants are known. Besides the 5 listed above, others are: the Boltzmann constant, the mass of an electron, the mass of a proton, Avogadro's number, the gas constant, the Rydberg constant.
Physicists know quite well the values of these universal constants, and refine them with ever increasing accuracy. But at present there is no theory that explains why they have the values they really have. Physicists find this inconvenient, and would like to deduce their value from a theory that would explain them. Instead, they are sheer facts, they can only be measured. John Barrow, one of the physicists that have worked more on the anthropic principle, expresses the situation this way:
This is the Holy Grail of fundamental physics and it means the numerical calculation of one of the constants of Nature. This has never been done. So far, the only way we can know their values is by measuring them. This seems unsatisfactory. It allows the constants that appear in our theories to have a huge range of different possible values without overthrowing the theory *(4). (8)
In this line, some attempts were made in the last decades of the 19th century to reduce the degree of arbitrariness in the universal constants, defining some «natural units» based on basic phenomena of the natural world.
In 1874 an Irish physicist, George Johnstone Stoney (1826-1911), was searching a way to avoid the conventional units used in measurements, and to find "natural" units given by Nature itself. For this purpose he turned to the constants of Nature known at the time, specifically three of them: the speed of light c, the unity of electric charge e, and the constant of gravity G. Using the values known at the time, he derived from these constants new values for "natural units" of mass, length and time:
M = (e2 / G)1/2 = 10-7 gram
L = (Ge2 / c4)1/2 = 10-37 meters
T = (Ge2 / c6)1/2 = 3 x10-46 seconds
These units are useless in practice. If we call them Stoneys, instead of asking for 100 grams of peanuts, we should ask for one billion Stoney-mass, and instead of speaking of 45 minutes, we should speak of 9 x10-44 Stoney-time! Nevertheless, they paved the way for further speculation that has proved extremely fruitful in our time.
Max Plack (1858-1947) rediscovered Stoney's idea in a slightly different form in 1899. He was a central figure in physics of his time,. He discovered the quantum nature of energy, won the Nobel prize for physics in 1918, and died in 1947 aged 89. He was deeply religious and greatly admired by his younger contemporaries like Einstein and Bohr.
Planck's conception of Nature placed great emphasis upon its intrinsic rationality and independence of human thought: he was a realist. Unlike Einstein, he did not believe in any attainable all-encompassing theory of physics which would explain all the constants of Nature, for if this theory arrived then physics would cease to be an inductive science. Here we perceive how philosophical ideas can influence the scientific agenda of the most prominent physicists.
Planck was suspicious of attributing fundamental significance to quantities that had been created as a result of the "accident" of our situation. He wanted to see the establishment of
units of length, mass, time and temperature which are independent of special bodies or substances, which necessarily retain their significance for all times and for all environments, terrestrial and human or otherwise *(5).
Using G, c, his new constant of action h (Planck's constant), and also Boltzman's constant k (converts units of energy into units of temperature), Planck obtained the only combinations of them which can be formed with the dimensions of mass, length, time and temperature. Their values are not very different from Stoney's:
m = (hc / G)1/2 = 5,56 x 10-5 gram
l = (Gh / c3)1/2 = 4,13 x 10-33 centimeters
t = (Gh / c5)1/2 = 1,38 x10-43 seconds
T = k-1(hc5 / G)1/2 = 3,5 x1032 Kelvin
There is something strange about the extremely big or small values of these units (especially of length, time and temperature). Again, in Planck's time nobody found them useful, but they acquired new meaning many years later, at the end of the 20thcentury, when physicist were searching for theories that unify gravitation with quantum physics, a very difficult task. Quantum theory and gravitation govern different kingdoms that have little cause to talk to one another. No one knows how to join the theories together. When the Universe is smaller than the Planck length in size (10-33 cm), less than the Planck time in age (10-43secs), and hotter than the Planck temperature (1032 degrees), the known laws of physics cease to work. John Barrow says:
Planck's units mark the boundary of applicability of our current theories. The constants of Nature mark out the frontiers of our existing knowledge and show us where our theories start to overreach themselves *(6). (12)
Stoney and Planck were searching for "natural" units, based on fundamental phenomena of the physical world. But even those natural units had to be expressed in terms of some units which involve human conventions. The speed of light, for instance, must be expressed in terms of a unit of longitude per unit of time, say 300,000 kilometers per second. This is an inconvenient in some practical affairs, and theoretical physicists also feel the attraction of pure numbers, and want to find out the characteristics of the world expressed in pure numbers. Thus the real characteristics of the world would be better appraised. Albert Einstein's dream was to find out a final theory that would encompass the whole world and leave no room for conventions: the constants should be derived from the final theory, and there could exist only one such final theory.
The influence of extra-scientific ideas was evident in Einstein's case. He was deeply religious, but his religion was a kind of pantheism where there was no place for accidental coincidences or chance, as expressed by his famous phrase, "God does not play dice".
In the second half of his life Albert Einstein (1879-1955) tried to find an "ultimate theory" of physics. The more we approach to it, the less "free constants" would contain, i. e. constants which can only be found by experiment. At present in our theories there are a number of constants of Nature which we just have to measure. According to Einstein:
There are two kinds of constants: apparent and real ones. The apparent ones are simply the outcome of the introduction of arbitrary units, but are eliminable. The real [true] ones are genuine numbers which God had to choose arbitrarily, as it were, when He deigned to create this world *(7). (15)
Einstein's dream was that there could only be one choice of them, so that the universe could only be as it is.
One of Einstein's clues was to build up dimensionless numbers which result as a combination of ordinary constants of Nature. Those dimensionless numbers would be established through the logical foundation of the final theory:
"Or one could put it like this: In a reasonable theory there are no dimensionless numbers whose values are only empirically determinable.
Of course, I cannot prove this. But I cannot imagine a unified and reasonable theory which explicitly contains a number which the whim of the Creator might just as well have chosen differently, whereby a qualitatively different lawfulness of the world would have resulted.
Or one could put it like this: A theory which in its fundamental equations explicitly contains a non-basic constant would have to be somehow constructed from bits and pieces which are logically independent of each other; but I am confident that this world is not such that so ugly a construction is needed for its theoretical comprehension" *(8). (16)
Even though we have advanced a lot towards the unification of the fundamental theories of physics, Einstein's dream continues to be a dream. It is difficult to establish that a unique world could exist. If one believes in a personal creator God, obviously God can create so many different words as He chooses. The opposite idea was condemned by the archbishop of Paris in 1277 as posing limits to God's omnipotence. The French physicist Pierre Duhem saw this condemnation as the founding date of modern empirical science, always in need of experiments to contact with the real physical world.
An approach quite different from Einstein's is possible. Instead of considering one unique possible world, we could consider many different possible worlds, each one of then defined by a set of dimensionless constants. Talk of many worlds has become one of the favorite topics today.
Let us consider, for instance, the fine structure constant α, and another similar constant referred to gravity called αG:
α = 2π e2 / hc ≈ 1 / 137 (fine structure constant)
αG = Gmpr2 / hc ≈ 10-38
In this context, John Barrow has written:
"The identification of dimensionless constants of Nature like α and αG , along with the numbers that play the same defining role for the weak and strong forces of Nature encourages us to think for a moment about worlds others than our own. These other worlds may be defined by laws of Nature which are the same as those which govern the Universe as we know it but they will be characterised by different values of dimensionless constants. These numerical shifts will alter the whole fabric of our imaginary worlds. The balances between their forces will be different from those in our world. Atoms may have different properties. Gravity may play a role in the small-scale world. The quantum nature of reality may enter in unexpected places" *(9). (17)
"The last important lesson we learn from the way that pure numbers like α define the world is what it really means for world to be different. The pure number that we call the fine structure constant and denote by á is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h and ewere changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world could be observationallyindistinguishable from our world. The only thing that counts in the definition of the world are the vales of the dimensionless constants of Nature. If all masses are doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged" *(10). (18)
We have seen that, searching for natural units, Planck found out very large or small numbers. Other numbers of this kind appear when dealing in other ways with the constants of nature. The appearance of such large numbers had been a source of amazement ever since they were first noticed by Hermann Weyl in 1919. Further speculation was carried out in this line by Sir Arthur Eddington and by the Nobel prize winner Paul Dirac.
Arthur Stanley Eddington (1882-1944) was one of the most prominent astrophysicists of his time. He always kept to his Quaker religion, was a pacifist, and never took part in active conflicts (such as the upcoming First World War: as a conscientious objector, he avoided active war service and was able to continue his research at Cambridge during the war years of 1914-1918). Since 1913 he held a position as an astronomy professor at Cambridge. In 1914, he became director of the Cambridge Observatory and a full member of the Royal Society.
He made several significant contributions to the area concerning general relativity and astrophysics. Eddington can be called the "Father of Modern Theoretical Astrophysics". He studied the properties of a solar eclipse on various expeditions around the world. This research eventually confirmed Albert Einstein's general theory of relativity (that as light passes a very massive star, its path is bent due to gravity: eclipse expedition to Principe Island in West Africa in 1919). Eddington spent a great amount of time researching the internal makeup of stars. In spite of some of his mistakes, Arthur Eddington made a great deal of valuable additions to the scientific community.
Eddington wrote several philosophical works such as The Nature of the Physical World (1928), New Pathways of Science (1935), andThe Philosophy of Physical Science (1939). He considered that epistemology is at the basis of physics, that physical laws and physical constants are the consequences of the condition of observation. He believed that pure though could succeed in arriving at a complete description of the physical world: laws of nature and constants of nature could be deduced from epistemological considerations. Eddington had a fascination with the fundamental constants of nature and produced some surprising numerical coincidences most of which were published after his death in his posthumous book Fundamental Theory (Cambridge University Press, 1946). The Fundamental Theory would explain the numerical values of the constants of Nature. He did not finish his plan.
He published parts of his results many years before. When he did this work in the 1920s, there was no good understanding of the nuclear forces, so he limited to the constants defining the gravitational and electromagnetic forces. He arranged them into three pure dimensionless numbers, and added his cosmological number NEdd.
Ratio of the masses of the proton and electron: mpr / me ≈ 1840
The inverse of the fine structure constant: 2πh / e2 ≈ 137
Ratio of the gravitational force to the electromagnetic force between and electron and a proton: e2 / Gmprme ≈ 1040
Number of protons in the visible universe: NEdd ≈ 1080
These he called "the ultimate constants". In 1935 he posed a question that continues to be posed today:
Are these four constants irreducible, or will a further unification of physics show that some or all of them can be dispensed with? Could they have been different from what they actually are?... the question arises whether the above ratios can be assigned arbitrarily or whether they are inevitable. In the former case we can only learn their values by measurement; in the latter case it is possible to find them by theory... I think the opinion now widely prevails that the [above four] constants... are not arbitrary but will ultimately be found to have a theoretical explanation; though I have also heard the contrary view expressed *(11). (21)
We have those dimensionless numbers which result from combinations of the fundamental constants. Some of them have an "strange" appearance as related with 1040, its squares and cubes (22):
total number of protons in the observable universe: 1080
ratio of the strengths of electromagnetic and gravitational forces between two protons: 1040
"action" of the observable universe in units of the fundamental Planck units of action: 10120
cosmological constant in units of the square of the Planck length: 10-120
John Barrow notes:
Eddington had tried to build a theory that made their [large numbers] appearance understandable. But he failed to convince a significant body of cosmologists that he was on the right track. Yet Eddington succeeded in persuading people that there was something that needed explaining. Completely unexpectedly, it was one of his famous neighbours in Cambridge who wrote the short letter to the journal Nature which succeeded in fanning interest in the problem with an idea that remains a viable possibility even to this day [Paul Dirac] *(12). (23)
Paul Dirac (1902-1984) was the Lucasian Professor of Mathematics at the University of Cambridge, and one of the greatest physicists in the 20th century. In Cambridge he coincided for some time with Eddington. He received the 1933 Nobel prize in physics jointly with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". His main contribution was the formulation of a theory that combined quantum mechanics with relativity.
Dirac can hardly be considered as promoting loose speculation. In a biographical note we read, "There is a standard folklore of Dirac stories, mostly revolving around Dirac saying exactly what he meant and no more. Once when someone, making polite conversation at dinner, commented that it was windy, Dirac left the table and went to the door, looked out, returned to the table and replied that indeed it was windy. It has been said in jest that his spoken vocabulary consisted of 'Yes', 'No', and 'I don't know.' *(13)
In 1937, Dirac published his first paper on large numbers and cosmological matters *(14). Years later, in an interview, he was asked, Could you summarize your thinking on the large numbers hypothesis? In his answer he referred to the coincidences between several large number of the same order of magnitude, about 1040, and he added:
Now, you might say, this is a remarkable coincidence. But it is rather hard to believe that. One feels that there must be some connection between these very large numbers, a connection which we cannot explain at present but which we shall be able to explain in the future when we have a better knowledge both of atomic theory and of cosmology.
Let us assume that these two numbers are connected. Now one of these numbers is not a constant. The age of the universe, of course, gets bigger and bigger as the universe gets older. So the other one must be increasing also in the same proportion. *(15)
Dirac relied on the work on large numbers done by Eddington, specifically three large numbers:
N1 = (size of the observable universe) / (electron radius) = ct / (e2 / me c2) ≈ 1040
N2 = electromagnetic-to-gravitational force between proton and electron = e2 / Gmempr) ≈ 1040
N3 = number of protons in the observable universe = c3t / Gmpr ≈ 1080
Dirac's Large Numbers Hypothesis was that
Any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity *(16). (25)
This is the final Summary of Dirac's paper:
It is proposed that all the very large dimensionless numbers which can be constructed from the important natural constants of cosmology and atomic theory are connected by simple mathematical relations involving coefficients of the order of magnitude unity. The main consequences of this assumption are investigated and it is found that a satisfactory theory of cosmology can be built up from it *(17)
Eddington and others had written down such hypothesis, but Eddington did not distinguish between the entire universe and the observable universe (a sphere with radius equal to the speed of light times the present age of the universe). This has as a consequence that some constants of Nature must be changing as the universe ages. Dirac chose to abandon the constancy of Newton's gravitational constant. This provoked much discussion: pages in the journal Nature with arguments for and against.
Dirac's hypothesis about the variable character of the gravitational constant did not survive for long, as it was shown that it was incompatible with the past conditions necessary for life to emerge (oceans boiling in the pre-Cambrian era, 200-300 million years ago, and life had existed on Earth for at least 500 million years).
But the general idea survived that the coincidences of the large numbers were seen as consequences of a deeper set of relationships. Very large dimensionless numbers amongst the constants of Nature, taking values as 1040 and 1080, are not independent accidents: there must be consequences rather than coincidences.
By 1950 a lot of work had been done about the constants of nature and the relations existing among them, specially when very large numbers were involved. In the 1950s, this begun to be related to the conditions necessary for the existence of human beings. This was the beginning of anthropic reasoning that, some years later, would lead to the formulation of the anthropic principle.
Gerald Whitrow (1912-2000), a cosmologist and philosopher of science who served as vice-president of the Royal Astronomical Society in England, published in 1955 an article where he introduced a characteristic anthropic reasoning. The title was, "Why physical space has three dimensions" *(18). Whitrow's article begins quoting the beginning of Galileo's Dialogue, where Salviati introduces a discussion of Aristotle's arguments on this topic. After a historical sketch of different aspects of the problem, Whitrow writes:
I suggest that a possible clue to the elucidation of this problem is provided by the fact that physical conditions on the Earth have been such that the evolution of Man has been possible. *(19)
In his argument, Whitrow does not use the term «anthropic», but his reasoning has the characteristic flavor of what would later on be placed under that label, as he concludes:
A new attempt to throw light on the question indicates that this fundamental topological property of the world may possibly be regarded as partly contingent and partly necessary, since it could be inferred as the unique natural concomitant of certain other contingent characteristics associated with the evolution of the higher forms of terrestrial life, in particular of Man, the formulator of the problem *(20).
Robert Henry Dicke (1916-1997) was a physicist from Princeton. He was elected to the National Academy of Sciences in 1967. Among his many prizes and awards were the National Medal of Science (1971), the Comstock Prize of the National Academy of Sciences (1973), and the NASA Medal for Exceptional Scientific Achievement (1973). He was a member of the National Science Board from 1970 to 1976. He was appointed to the Princeton University Department of Physics in 1946.
It was Dicke who explained in 1964 to the astronomers, Arno Penzias and Robert Wilson, that they had discovered the cosmic microwave background radiation that was predicted by an important cosmological model, the big bang model. Both groups submitted papers on the subject to The Astrophysical Journal. Dicke's group presented the theoretical explanation of the radiation; Wilson and Penzias described its observation. Thirteen years later, the Nobel Prize in physics was awarded to Penzias and Wilson for their discovery. The discovery of cosmic microwave background radiation provided decisive support for the big bang model of cosmic origins, which has become the dominant paradigm in cosmology today.
In 1961 Dicke related the large numbers coincidence to biological factors *(21). The age of the universe must be large enough for the production of the chemical factors that are necessary for the existence of observers like us. This can be given a quantitative estimate. Even though he did not use the name "anthropic," the core of what would be called later on "anthropic principle" was already there.
In his very short 1961 paper, Dicke refers first of all to Eddington's and Dirac's attempts at relating the dimensionless constants, and then to Dirac's suggestion that "all the large numbers vary with time". Dicke refers to three dimensionless constants that are related to values of the order of 1040 :
(1) Gmp2 / ħ ≈ 10-39 (gravitational coupling constant)
(2) T mpc / ħ ≈ 1042 (T = Hubble age of the universe)
(3) M / mp ≈ 1080 (mass of the universe to its visible limits)
After some reflections, Dicke writes:
It will be shown that, with the assumption of an evolutionary universe, T [the Hubble age of the universe] is not permitted to take one of an enormous range of values, but is somewhat limited by the biological requirements to be met during the epoch of man.
The first of these requirements is that the universe, hence galaxy, shall have aged sufficiently for there to exist elements other than hydrogen. It is well known that carbon is required to make physicists.
It is known that the galaxy was formed initially from hydrogen only. Hence, the minimum time for the start of the epoch of man is set by the age of the shortest-lived stars, for elements, other than hydrogen, are formed in the interior, and distributed at the death, of the star.
An upper limit for the epoch of man is set by the requirement that he has an hospitable home in the form of a planet circling a luminous star. This time is set by the maximum age of a star capable of producing energy by nuclear reactions...
... Thus, contrary to our original supposition, T is not a "random choice" from a wide range of possible choices, but is limited by the criteria for the existence of physicists *(22).
After some more reflections, Dicke's final paragraph concludes:
The statistical support for Dirac's cosmology is found to be missing. However, the existence of physicists now and the assumption of the validity of Mach's Principle are sufficient to demand that the order-of magnitude relations between the three numbers, given by equations (1), (2) and (3), be satisfied *(23).
The anthropic reasoning is explicit in Dicke's article, and is used to draw consequences about the age of the universe, and also to relate large dimensionless physical numbers, rejecting Dirac's assumption that large numbers vary with time. This is why Barrow and Tipler consider Dicke as the formulator of the weak anthropic principle.
Dicke published his anthropic ideas in 1961. Other anthropic ideas were proposed by Brandon Carter, and circulated in proofs in Cambridge around 1967, and were presented at Princeton in 1970. These ideas were echoed by an article published by two other physicists from Cambridge, C. B. Collins and Stephen W. Hawking in 1973 *(24). They explained the isotropy of the universe using an anthropic reasoning: only a certain kind of models of the universe are compatible with our own existence as observers. The universe is isotropic because we are here: it is a consequence of our own existence.
Here we have an anthropic reasoning, expressed in a provocative form that would make of it the center of so much discussion in the following years.
In 1973 a meeting was celebrated at Cracow on the occasion of the 500th anniversary of Copernicus' birth. Brandon Carter, then lecturer at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, contributed with the paper «Large Number Coincidences and the Anthropic Principle in Cosmology» *(25). There he used from the first time, in the very title, the expression «anthropic principle», and also the distinction, which soon became a standard practice, between two versions of the principle, a «weak» version and a «strong» one.
Carter begins his paper saying:
Prof. Wheeler has asked me to say something for the record about some ideas that I once suggested (at the Clifford Memorial meeting in Princeton in 1970) and to which Hawking and Collins have referred (The Astrophys.J., 180, 317, 1973). This concerns a line of thought which I believe to be potentially fertile, but which I did not write up at the time because I felt (as I still feel) that it needs further development. However, it is not inappropriate that this matter should have cropped up again on the present occasion, since it consists basically of a reaction against exaggerated subservience to the "Copernican principle" *(26).
This (1974) is the first official presentation of the "anthropic principle", and a quite modest presentation: Carter feels uncertain, and he says that the thing needs further development. He feels justified because they are celebrating a Copernicus meeting, and there has been an exaggeration in interpreting the Copernican principle. It is true, Carter reminds us, that "we must not assume gratuitously that we occupy a privileged central position in the Universe", but:
Unfortunately there has been a strong (not always subconscious) tendency to extend this to a most questionable dogma to the effect that our situation cannot be privileged in any sense. This dogma (which in its most extreme form led to the "perfect cosmological principle" on which the steady state theory was based) is clearly untenable, as was pointed out by Dicke (Nature 192, 440, 1961), if one accepts (a) that specially favourable conditions (of temperature, chemical environment, etc.) are prerequisite for our existence, and (b) that the Universe evolves and is by no means spatially homogeneous on a local site *(27).
It is worth noticing that here there is a natural explanation of the use of the term «principle» to refer to the «anthropic principle». This is important because one of the main objections refers to the allegedly improper use of the term, as in this case we do not deal with a physical principle in the usual sense of the term (as in the «principle of conservation of energy», or the «principles of conservation», or the «principle of least action», which refer to well formulated physical laws of a very general character). Carter speaks of «anthropic principle» in opposition of the so-called «Copernican principle»: even «perfect cosmological principle», which Carter considers a false dogma).
Carter goes on by saying that his interest in that matter arose from reading Bondi's book Cosmology (1959), where certain "large numbers coincidences" are listed as evidence justifying the introduction of exotic theories that depart from accepted physical laws. He is convinced that the opposite is true: conventional physics and cosmology could in principle been used to predict those coincidences in advance of their observation. so that:
However these predictions do require the use of what may be termed the anthropic principle to the effect that what we can expect to observe must be restricted by the conditions necessary for our presence as observers. (Although our situation is not necessarily central, it is inevitably privileged to some extent.) *(28). (30)
With this paragraph, the anthropic principle was born. Notice also that Carter introduces it speaking of «predictions» that we can make using it. One of the main criticisms is that this principle does not lead to any prediction. So much so that in the following three sections of his article Carter examines orderly three classes of theoretical prediction of Bondi's coincidences that can be made by using: (a) «Prediction of the Traditional Kind»; (b) «Prediction Based on the Weak Anthropic Principle»; and (c) «Prediction Based on the Strong Anthropic Principle».
Prediction of the first kind (Prediction of the Traditional Kind) refers to the order of magnitude of the mass of stars.
Prediction of the second kind (Prediction Based on the Weak Anthropic Principle) refers to the coincidence (in order of magnitude) of Hubble's fractional expansion rate of the Universe and the gravitational coupling constant. Following Dicke, this could be predicted taking into account that the present age of the Universe is constrained by anthropic limits. In this context Carter writes:
This prediction provides a good illustration of the use of the "weak"anthropic principle to the effect that 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 *(29). (31)
With this paragraph, the «weak anthropic principle» was born. And it was born as related to a specific prediction.
It is also important to notice that Carter's original version of the «weak» principle refers to «our location in the universe». The whole thing originated in contrast with the so-called «Copernican principle», i. e. that we do not occupy any privileged location in the universe. In contrast, Carter stated that our location is privileged at least in one respect, namely that it must lead us to observe precisely what we really observe. Our own existence poses some conditions to the result of our observation and, therefore, to our theories. We cannot admit observations or theories that are incompatible with «our existence as observers».
Prediction of the third kind (Prediction Based on the Strong Anthropic Principle) refers to a relationship between constants related to the age of the Universe. Carter writes:
Condition  is a good example of a prediction based on what may be termed the "strong" anthropic principle stating that 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" *(30). (32)
The «strong anthropic principle» was born. Further reasoning shows that it makes possible to predict the third of the large numbers coincidences listed by Bondi, the one that relates the number of particles in the visible universe to the gravitational coupling constant.
The «strong» principle refers to the Universe and its fundamental characters in relation with our existence, whilst the «weak» principle refers to our location in the Universe as related to our quality of observers. Carter notices that there is no reason to abandon conventional theories, and adds that the character of the predictions is different in both cases:
whereas a prediction based only on the weak anthropic principle (as used by Dicke) can amount to a complete physical explanation, on the other hand even an entirely rigorous prediction based on the strong principle will not be completely satisfying from a physicist's point of view since the possibility will remain of finding a deeper underlying theory explaining the relationships that have been predicted *(31).
Carter entitled the last section of his article «World Ensembles and the Gravitational Constant». It begins with this words:
It is of course always philosophically possible — as a last resort, when no stronger physical argument is available - to promote a prediction based on the strong anthropic principle to the status of an explanation by thinking in terms of a "world ensemble"... The existence of any organism describable as an observer will only be possible for certain restricted combinations of the parameters, which distinguish within the world-ensemble an exceptional cognizablesubset. A prediction based on the strong anthropic principle may be regarded as a demonstration that the feature under consideration is common to all members of the cognizable subset *(32). (33)
Carter provides further details about possible predictions (of the weakness of the gravitational constant, restrictions on the fundamental parameters of nuclear physics). Clearly his paper is centered around the predictive value of the anthropic principle. Then he concludes:
The acceptability of predictions of this kind as explanations depends on one's attitude to the world ensemble concept. Although the idea that there may exist many universes, of which only one can be known to us, may at first sight seem philosophically undesirable, it does not really go very much further than the Everett doctrine (see B. S. De Witt: 1967, Phys. Rev. 160, 113) to which one is virtually forced by the internal logic of quantum theory. According to the Everett doctrine the Universe, or more precisely the state vector of the Universe, has many branches of which only one can be known to any well defined observer (although all are equally "real"). This doctrine would fit very naturally with the world ensemble philosophy that I have tried to describe.
Even though I would personally be happier with explanations of the values of the fundamental coupling constants etc. based on a deeper mathematical structure (in which they would no longer be fundamental but would be derived), I think it is worthwhile in the meanwhile to make a systematic exploration of the a priori limits that can be placed on these parameters (so long as they remain fundamental) by the strong anthropic principle. If it were to turn out that strict limits could always be obtained in this way, while attempts to derive them from more fundamental mathematical structures failed, this would be able to be construed as evidence that the world ensemble philosophy should be taken seriously — even if one did not like it *(33). (34)
Once the anthropic principle was formulated in 1974 by Brandon Carter, it developed its own life. Different authors interpreted the principle in diverse ways, and proposed new extensions. Until 1974 the discussions remained confined within the scientific ambit, even though they were sometimes in the borderline with philosophy. Since 1974 the discussion trespassed those frontiers, and other very different issues entered the scene. Three of them are specially important: the so-called fine-tuning of the Universe; its philosophical consequences for teleological arguments, including the design argument to prove the existence of God; and talks about other worlds. The three items are related. We are going to see some of the main events that contributed to the expansion of the anthropic principle.
Two other astronomers from Cambridge, Carr and Rees, echoed the interest on the anthropic principle in an article published inNature in 1979 *(34). On the one hand, apparently they endorsed the principle. In the entry of the article we read:
several aspects of our Universe — some of which seem to be prerequisites for the evolution of any form of life — depend rather delicately on apparent 'coincidences' among the physical constants *(35). (36)
In the conclusion, they highlighted the same idea:
The possibility of life as we know it evolving in the Universe depends on the values of a few basic physical constants — and is in some respects remarkably sensitive to their numerical values *(36). (37)
Later on in the conclusion, however, they showed that the anthropic principle did not reach the status of a physical theory, even though they pointed out that the principle expresses a remarkable fact:
These arguments [Wheeler's and Everett's ensembles of universes] go a little way towards giving the anthropic principle the status of a physical theory but only a little: it may never aspire to being much more than a philosophical curiosity. One day, we may have a more physical explanation for some of the relationships discussed here that now seem genuine coincidences... However, even if all apparently anthropic coincidences could be explained in this way, it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life *(37). (38)
On 25 and 26 May 1983 a Discussion Meeting of the Royal Society was held in London, with the purpose of studying the issues related with the constants of physics. Martin Rees was also involved in it. The discovery of a close relationship between progress in particle physics and the concept of the very early Universe fuelled a new study of the classical problems about the relationship between the constants, their unique character, other worlds, etc. *(38).
In the Introductory remarks by one of the editors of the Proceedings we are told that, out of the 16 topics discussed,
interest in [three of them] in recent times originally instigated the proposal to hold this Discussion. However, because of their speculative character and of their inability as yet to produce new predictions, it was considered that the main emphasis ought to be upon the study of the constants themselves rather than the role of the constants in these applications *(39). (39)
A prudent reservation is, therefore, placed on those three topics, which were the last ones: «The origin and significance of certain 'cosmological numbers': possible relation to the constants of physics» (number 13, by Rees) *(40) ; «The dependence upon the values of the constants of physics of macro-phenomena on the Earth and in the cosmos» (number 14, by Press and Lightman) *(41) ; and «The anthropic principle and the significance for physical and biological theory of the values of the constants of physics» (number 16, by Carter) *(42). Though not signaled by the editor, the missing number was obviously connected with these three: «Dependence of physics upon the basic constant of dimensionality» (number 15, by Barrow) *(43).
We continue to find out the same kind of problems treated, as ever before, within a scientific ambit, and a very illustrious one: The Royal Society of London (Carter being a fellow of it). Also, the problems were treated with some reservation, «because of their speculative character and of their inability as yet to produce new predictions» (as already seen, several predictions had been produced, but referring to previously known phenomena, and without the precision characteristic of mature physics).
It is worth noting also that, besides Carter, two other among the participants (Martin Rees and John Barrow) were playing already or would play a very important role in further developments and discussions of the anthropic principle. Rees notes that
The masses and lifetimes of stars can be expressed in term of fundamental constants. Such expressions always involve powers of the number ħ/Gmp2 [the gravitational coupling constant: ≈10-38], whose huge magnitude stems from the weakness of gravity on microphysical levels. Our physical understanding of what determines galacticdimensions is not yet, however, on the same firm footing. Observational cosmology gives us three basic numbers that characterize our Universe... We are unsure how (or, indeed, whether) these cosmological numbers can be derived from known physics *(44).
Rees ends his paper with an interesting remark:
Insofar as the aim of physics is to erode the number of independent underivable constants, it is gratifying that there is a serious chance of calculating the quantities listed above in terms of microphysical parameters *(45).
In their contribution, Press and Lightman review the manner in which the fundamental constants affect our daily lives.
Barrow examines the role played by the dimensions of space-time in determining the form of various physical laws and constants of Nature, and suggests a formulation of the anthropic principle. In fact, the title of the 8th and final section of his paper is «The anthropic principle», a prelude of the big book that he (jointly with Frank Tipler) would publish a few years later (which is quoted as «in press» in this paper). He refers to the previous publications on related subjects by Whitrow, Dicke, Carter and others, and says that it is difficult to determine if small changes in the values of some fundamental constants could not be compensated by changes in other constants *(46) : also a prelude of vast discussions that were going to grow around the anthropic principle.
Since 1975, Carter worked at the Paris-Meudon Observatory in France. In the 1983 Meeting of the Royal Society, Carter reflected on the principle he had formulated ten years before.
In the Introduction to his paper Carter provides some explanation of his anthropic principle. He describes the extreme antithesis between the ancient anthropocentric outlook and the (dangerous) perfect cosmological principle (Bondi & Gold, 1948) that the Universe is entirely homogeneous apart from minor local fluctuations, and he comments on the formulation of the «weak anthropic principle»:
It was in an attempt to draw attention to the need for a more balanced intermediate attitude, between primitive anthropocentrism and its equally unjustifiable antithesis that I came to introduce the term anthropic principle (Carter 1974) to express the notion that 'although our situation is not necessarily central is necessarily privileged to some extent', in so much as special conditions are necessary for our very existence. The practical scientific utility of this principle arises from its almost tautological corollary to the effect that in making general inferences from what we observe in the Universe, we must allow for the fact that our observations are inevitably biased by selection effects arising from the restriction that our situation should satisfy the conditions that are necessary a priori, for our existence. The term self-selection principle would be an alternative and perhaps more appropriate description for this hardly questionable but easily overlooked precept. (If I had guessed that the term 'anthropic principle' would come to be so widely adopted I would have been more careful in my original choice of words. The imperfection of this now standard terminology is that it conveys the suggestion that the principle applies only to mankind. However, although this is indeed the case as far as we can apply it ourselves, it remains true that the same self-selection principle would be applicable by any extraterrestrial civilization that may exist.) *(47) (40) (41)
Carter comments three applications of the «weak (selection) anthropic principle», using Bayesian probabilities to discriminate between the probabilities of theories in the light of a given evidence. Afterwards he introduces a digression on the strong anthropic principle, rewriting it, and almost (as will become apparent in the following) rejecting it:
As I originally formulated it (Carter 1974) this 'strong' principle consisted in the remark that our mere existence as intelligent observers imposes restrictions not just on our situation but even on the general properties of the Universe, including the values of the fundamental parameters that are the subject of the present meeting. Although this 'principle' has aroused considerable enthusiasm in certain quarters, it is not something that I would be prepared to defend with the same degree of conviction as is deserved by its 'weak' analogue *(48). (42)
Carter's doubts arise from our ignorance about the unified theories towards which we are progressing, and our ignorance of alternative life forms and, therefore, on the restrictions we should assume. Carter finds even the name inappropriate:
Even the choice of the term 'anthropic' is less judicious in the 'strong' than in the 'weak' case: in retrospect, I regret not having used an expression, such for example as 'the cognition principle', having a more transcendent connotation *(49).
Immediately, Carter vigorously rejects the view of the philosopher Gale who has proposed to promote the principle to the status of a "reality" principle, and he includes a quite long appreciation on science, reality and realism, which has a phenomenist and instrumentalist flavour. He adds that applications of the strong anthropic principle should be judged by the standards of a humble, merely explicative rather than predictive, category. And notes that in the rest of his article he will deal only with the «weak» anthropic principle, whose genuinely predictive power should become apparent.
The rest of the article (sections 3-6) is concerned with a very specific issue, which is the new significant point Carter wants to make: the remarkable coincidence between the timescale of past biological evolution on Earth and the future life expectancy of the Sun. Carter concludes that civilizations comparable with our own are likely to be extremely rare. His conclusions seem highly disputable, and his last moral is that
one should try to steer a moderate course between the Scylla of excessive anthropocentrism and the Charybdis of unjustifiable neglect of anthropic selection effects *(50).
Shortly afterwards, in 1986, John Barrow and Frank Tipler published their influential work on the anthropic principle *(51). They provided the versions of the anthropic principle that prevailed in posterior discussion. The formulation of the weak anthropic principle is the following:
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 requirement that the Universe be old enough for it to have already done so *(52). (43)
And the formulation of the strong anthropic principle is the following:
The Universe must have those properties which allow life to develop within it at some stage in its history. *(53) (44)
Both formulations present remarkable differences with Carter's original ones. Carter's strong version is quite similar to the version usually presented as the weak principle, and Carter's weak version is even weaker. This is important, if only because many discussions usually consider the strongest version as the central one, and conclude that the anthropic principle is nonsense. We have also seen that Carter was very cautious, to the extreme of nearly repudiating it, with his strong version (to say nothing with even stronger versions).
As a representative of the usual presentation of the anthropic principle in the two versions, and also of the confusions associated with it, we can take the following text:
Carter was not, however, claiming that the Universe was our own personal playground, made specifically with humanity in mind. The version of the Anthropic Principle that he proposed that day, which is now referred to as the Weak Anthropic Principle (WAP) stated only that by our very existence as carbon-based intelligent creatures, we impose a sort of selection effect on the Universe. For example, in a Universe where just one of the fundamental constants that govern nature was changed - say, the strength of gravity - we wouldn't be here to wonder why gravity is the strength it is. The following is the official definition of the WAP: "Weak Anthropic Principle (WAP): the observed values of all physical and cosmological quantities are not equally probable but they take on the values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so." (The Anthropic Cosmological Principle by John Barrow and Frank Tipler, p. 16). Later, Carter also proposed the Strong Anthropic Principle (SAP), which states that the Universe had to bring humanity into being. This version is much more teleological, if not theological, and is of a highly speculative nature. Nonetheless, Carter had scientific reasons to propose it. The definition of the SAP is as follows: "Strong Anthropic Principle (SAP): the Universe must have those properties which allow life to develop within it at some stage in it's history." (The Anthropic Cosmological Principle, p. 21) *(54). (45)
The examples of confusion could be easily multiplied. On the other hand, we have seen that Carter himself extended his original ideas (1973) in the Meeting of the Royal Society (1983), and to some extent changed them. Also, in 2003, working as director of research in the observatory of Paris-Meudon, in a paper on the anthropic interpretation of quantum theory, Carter proposed to introduce an «entropy principle» that would supersede the weak anthropic principle *(55). In another paper also from 2003, Carter stated that «the only reality of which we have a direct knowledge is that of a subjective mental perception», concluding in a kind of «sollipsism without sollipsism» *(56) (which is not an easy idea to assimilate).
In 1986, the new book by Barrow and Tipler considered the anthropic principle as a contemporary continuation of teleological reasoning. It begins with a historical overview of design arguments, and continues with modern ideas about teleology where Bergson, Whitehead and Teilhard de Chardin find their place. Then, after more than 200 pages, we arrive to Dirac, Dicke and Carter, in a chapter entitled «The Rediscovery of the Anthropic Principle», as though this principle had always been there, changing only its formulation according to the state of science in the different times.
Barrow and Tipler provide an interesting overview of the many aspects of the anthropic principle, and examine in detail its manifestations in physics, astrophysics, cosmology, quantum mechanics, and biochemistry, carrying their analysis until the search for extraterrestrial intelligent life. One may wonder, however, whether they really clarify the issues, or rather make them even more complex than they previously were. This holds especially for the meaning of the anthropic principle, which is the central issue.
In any case, ever since 1986, discussion on the anthropic principle has extended enormously and has produced an immense amount of bibliography. We are going to consider some of the latest and more impressive discussions, which place the whole discussion on new feet.
Discussions on the anthropic principle usually centers now on three closely related issues: fine-tuning, teleology, and other worlds.
A number of relationships between the universal constants are «fine-tuned», which means that they are fine-tuned for human life. If their values were slightly different, human life could not exist. As Nick Bostrom puts it,
One aspect of anthropic reasoning that has attracted plenty of attention from both philosophers and physicists, is its use in cosmology to explain the apparent fine-tuning of our universe. "Fine-tuning" refers to the supposed fact that there is a set of cosmological parameters or fundamental physical constants that are such that had they been very slightly different, the universe would have been void of intelligent life. For example, in the classical big bang model, the early expansion speed seems fine-tuned. Had it been very slightly greater, the universe would have expanded too rapidly and no galaxies would have formed. There would only have been a very low density hydrogen gas getting more and more dispersed as time went by. In such a universe, presumably, life could not evolve. Had the early expansion speed been very slightly less, then the universe would have recollapsed very soon after the big bang, and again there would have been no life. Our universe, having just the right conditions for life, appears to be balancing on a knife's edge ( Leslie 1989). A number of other parameters seem fine-tuned in the same sense — e.g. the ratio of the electron mass to the proton mass, the magnitudes of force strengths, the smoothness of the early universe, the neutron-proton mass difference, perhaps even the metric signature of spacetime ( Tegmark 1997) *(57).(47)
It is tempting to relate this fine-tuning with teleological arguments. If one believes in the existence of a provident God who governs the world, it is easy to interpret the fine-tuning of the universe as the result of the providence of God: the universe is fine-tuned because God prepared it to make possible the appearance and the life of the humankind. Then the anthropic principle would be related to the teleological argument.
The teleological argument is usually presented in the English-speaking world as the «argument from design». It is worth noting, however, that the «argument from design» is only one of the formulations of the teleological argument. For instance, one of the most important formulations of the teleological argument is the famous «fifth way» of Thomas Aquinas. This is Aquinas' text:
The fifth way is taken from things' being directed. We see that there are things that have no knowledge, like physical bodies, but which act for the sake of an end. This is clear in that they always, or for the most part, act in the same way, and achieve what is best. This shows that they reach their end not by chance but in virtue of some tendency. But things which have no knowledge do not have a tendency to an end unless they are directed by something that does have knowledge and understanding. An example is an arrow directed by an archer. Therefore there is some being with understanding which directs all things to their end, and this, we say, is God *(58). (48)
Here there is no reference to design. The fifth way is based on the existence of finality (tendencies) in the natural world, and on the fact that the result of these natural tendencies is «what is best» (id quod est optimum). The argument assumes this «fact». The obvious objection is that there is evil in the world, and Thomas Aquinas answers theologically: God permits the existence of evil because He is able to produce good out from evil. This shows that we are not here in front of an argument that intends to prove the existence of God beginning from a zero point. This argument, as usually any argument to prove the existence of God, is a reflection that believers make to provide a rational basis for their beliefs, or to help other people to grasp the rationality of believing in God.
There is another version of the teleological argument, also in the works of Thomas Aquinas, centered on the order of the cosmos, where different parts contribute to a unitary result. This argument is more similar to the «argument from design»:
It is impossible for things contrary and discordant to fall into one harmonious order always or for the most part, except under some one guidance, assigning to each and all a tendency to a fixed end. But in the world we see things of different natures falling into harmonious order, not rarely and fortuitously, but always or for the most part. Therefore there must be some Power by whose providence the world is governed; and that we call God *(59). (49)
The «argument from design» is characteristic of the modern age, when the development of modern empirical science showed that the natural world is governed by laws, and God was seen as a supreme Architect who has designed those laws that determine the characteristics of the world, which, in turn, was seen as a marvelous machine full of intelligent contrivances. This argument received a strong blow when Darwin proposed his theory of the formation of the living beings (the beings where design is more apparent) as the result of the combination of chance mutations and natural selection. As a result, some claim that the theory of evolution has shown that there is no need of a divine designer: natural causes would be sufficient to explain the working of the natural world.
In this context, fine-tuning is sometimes seen as providing new strength to the argument from design.
An alternative explanation of the fine-tuning of the universe has been proposed, consisting on the existence of many different worlds. If many worlds exist that have different characteristics governed by different universal constants, then it is no surprise that there may exist one like ours, with those constants so fine-tuned that they appear as the result of a plan. Divine design and many worlds are seen as opposed explanations. But there are not really opposed. Nick Bostrom has written:
Some philosophers and physicists take fine-tuning to be an explanandum that cries out for an explanans. Two possible explanations are usually envisioned: the design hypothesis and the ensemble hypothesis. Although these explanations are compatible, they tend to be viewed as competing. If we knew that one of them were correct, there would be less reason to accept to the other *(60). (50)
In spite of this, Bostrom presents them as rival, disqualifies the design explanation, and adds:
In contrast to some versions of the design hypothesis, the meaningfulness of the ensemble hypothesis is not much in question. Only those subscribing to a very strict verificationist theory of meaning would deny that it is possible that the world might contain a large set of causally fairly disconnected spacetime regions with varying physical parameters *(61). (51)
But the existence of a divine plan should not be considered as an alternative explanation to the many-worlds hypotheses. The divine plan can operate through natural causes. Theconfusion between the scientific and the metaphysical or religious levels of explanation is crucial and very frequent.
John Leslie, one of the most active philosophers in this field, has listed a whole collection of many-worlds theories. He writes that
Cosmologists have suggested numerous ways in which greatly many, greatly varied universes could be generated *(62). (52)
Then he lists four types of such argument: oscillating universes where Big Bangs are succeeded by Big Collapses, each cycle counting as a new universe; a gigantic or infinite space divided into domains or regions with very different properties; many-worlds quantum mechanics; and quantum-fluctuational universes *(63). The main idea is:
In short, modern theorists find it easy to invent mechanisms for making apparent physics and overt properties differ from one universe to another even when the underlying physics and the most fundamental properties remain always the same *(64).
Quantum fluctuations are specially popular in this line. Our universe, and other universes, would be the result of quantum fluctuations in empty space. The quantum world would made possible the production of universes out of a physical state that, even though it cannot by identified with the metaphysical «nothingness», would be practically «nothing» (and is presented very often as produced «ex nihilo»). Thus, Edward P. Tryon wrote in a famous seminal paper published in Nature in 1973:
In my model, I assume that our Universe did indeed appear from nowhere about 1010 yr ago. Contrary to widespread belief, such an event need not have violated any of the conventional laws of physics. The laws of physics merely imply that a Universe which appears from nowhere must have certain specific properties. In particular, such a Universe must have a zero net value for all conserved quantities *(65). (53)
I offer the modest proposal that our Universe is simply one of those things which happen from time to time *(66).
Of course it is very difficult (to say the least) to control empirically such ideas, and Tryon himself acknowledged at the end of his article that his model was admittedly speculative. Nevertheless, there is no reason to deny, in the name of philosophy or theology, the possibility of such «mechanisms» provided we do not identify the vacuum with nothingness, even though it is surprising how easily many different of them are found, and how easily they seem to be accepted without empirical support.
Nevertheless, the main point is not this. What is relevant from the philosophical and theological point of view is to notice that those mechanisms are not a real alternative to the divine creation of the world, and that divine action should not be presented as an alternative explanation of the fine tuning of the universe. God's action as the First Cause extends to everything in the universe, in any moment of its existence, from the very beginning until the present time. Only a self-sufficient Being can be the source of limited, changeable, finite beings. Empirical science deals with secondary causes or natural mechanisms, which always depend ultimately on the action of God. As it is nonsense opposing evolution to creation, it is also nonsense opposing any physical theory about the origin of the universe to God's action. It is irrelevant for metaphysics and for theology that the universe may have originated from a fluctuation of the quantum vacuum, or that there are many universes. What is impossible is that the material world may be completely self-sufficient, not needing a metaphysical transcendent Cause.
There is now a great amount of literature, including TV films whose protagonists are well known physicists and even Nobel prize winners, to the effect that the existence of many, even infinite universes is a triviality. We could be surrounded by them here and now. Superstring theories provides us with 11 dimensions, 7 of them not manifest in our ordinary experience, and they would be real and could contain items similar and even identical with those of the visible universe. In the May 2003 issue of Scientific American an article by Max Tegmark begins with these words (54):
Not just a staple of science fiction, other universes are a direct implication of cosmological observations.
And then he goes on saying:
Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on.
The idea of such an alter ego seems strange and implausible, but it looks as if we will just have to live with it, because it is supported by astronomical observations. The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 1028 meters from here. This distance is so large that it is beyond astronomical, but that does not make your doppelgänger any less real. The estimate is derived from elementary probability and does not even assume speculative modern physics, merely that space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate. In infinite space, even the most unlikely events must take place somewhere. There are infinitely many other inhabited planets, including not just one but infinitely many that have people with the same appearance, name and memories as you, who play out every possible permutation of your life choices *(67). (55)
Tegmark proposes a kind of «postulate of reality» that runs thus:
One of the many implications of recent cosmological observations is that the concept of parallel universes is no mere metaphor. Spare appears to be infinite in size. If so, then somewhere out there, everything that is possible becomes real, no matter how improbable it is...
Tegmark follows a line of thought that begun with Alan Guth (57), who proposed in the early 1980s the idea of «inflation» (derived from this we have the «inflationary universe»). The universe, in its first moments after the Big Bang (actually, in a very tine fraction of the first second) would have experienced a tremendous «inflation»: from a very small beginning, its volume would have expanded to a much greater size. This is a respectful scientific idea that explains several features of the very early universe, and provides us with predictions that have been successfully tested by the WMAP (Wilkinson Microwave Anisotropy Probe):
One of the intriguing consequences of inflation is that quantum fluctuations in the early universe can be stretched to astronomical proportions, providing the seeds for the large scale structure of the universe. The predicted spectrum of these fluctuations was calculated by Guth and others in 1982. These fluctuations can be seen today as ripples in the cosmic background radiation, but the amplitude of these faint ripples is only about one part in 100,000. Nonetheless, these ripples were detected by the COBE satellite in 1992, and they have now been measured to much higher precision by the WMAP satellite and other experiments. The properties of the radiation are found to be in excellent agreement with the predictions of the simplest models of inflation *(69). (58)
Inflation has been re-elaborated by the Russian physicist Andrei Linde (59) (now in the USA), who has proposed a theory named «Self-Reproducing Inflationary Universe» (the title of an article published by Linde in Scientific American, November 1994, pp. 48-55):
Initially, inflation was considered as an intermediate stage of the evolution of the universe, which was necessary to solve many cosmological problems. At the end of inflation the scalar field decayed, the universe became hot, and its subsequent evolution could be described by the standard big bang theory. Thus, inflation was a part of the big bang theory. Gradually, however, the big bang theory became a part of inflationary cosmology. Recent versions of inflationary theory assert that instead of being a single, expanding ball of fire described by the big bang theory, the universe looks like a huge growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more new balls, ad infinitum. Therefore the evolution of the universe has no end and may have no beginning. After inflation the universe becomes divided into different exponentially large domains inside which properties of elementary particles and even dimension of space-time may be different *(70). (60)
Today we can find physicists who speak of creating universes in our garden, of self-reproducing eternal universes, and so on. Some of them explicitly say that these theories change our ideas about man's place in the cosmos.
But the theistic perspective is not altered by any of these theories. Inflation is a scientific respectable idea, and, as already said, natural mechanisms belong to the level of the actions of created beings that are compatible with God's action and need it to exist and operate. Once said this, we can add that Tegmark's reasoning about identical parallel universes, as well as the idea of infinitely self-reproducing universes, belong much more to mere fancy than to serious thinking, however they may be presented as linked to scientific data (even in our universe, nothing is repeated exactly in the same way: much less should we admit that our lives are repeated identically in other places). One can have the impression that these ideas try to counterbalance theological reasoning about divine action, but leaving aside that they sound quite strange from the scientific and the logical point of view, the main fact is that, as far as they belong to scientific reasoning about the natural world, they cannot oppose the metaphysical and theological reasoning about divine action, which is fully compatible with natural causes and provides the foundation for their action.
The anthropic principle was first formulated as a borderline aspect of cosmological issues. Gradually it has shifted to the ambit of teleology. Then a kind of antagonism emerged between many worlds and the theistic idea, as competitors to explain the fact that our universe is fine-tuned for human life. Now a respectable idea (inflation), proposed first in order to solve problems of the big bang model, is used to speculate about parallel universes and eternally self-reproducing universes. Whatever may be of those theories in the future, one can safely assume that the theistic perspective, and the Christian view of the human being, are quite independent from those speculations.
Recognizing that around the anthropic principle «confusion reigns supreme» *(71), Nick Bostrom has attemped to clarify the problem, formulating a theory of anthropic reasoning. He devoted to this aim his doctoral dissertation, which has been published in book format (see footnote 57). Bostrom says that, in spite of the confusion, some interesting and useful insights can be found in anthropic reasoning, and gives as a reason to hope so that «it is used and taken seriously by a range of leading physicists and cosmologists» *(72).
Bostrom explains anthropic reasoning as a kind of «observation selection effect» or «anthropic bias», namely a situation where limitations on our ability to observe something can spuriously affect the distribution or type of the observed data. A selection effect is a bias introduced by limitations in one's data collection process. A classical example is the method of telephone polling used by the Literary Digest in the 1936 U.S. presidential election. The Literary Digest had harvested the addresses of the people they sent the survey to mainly from telephone books and motor vehicle registries. The poor of the depression era, a group where Roosevelt was especially strong, often did not have a phone or a car. The poll was biased against Roosevelt supporters. An observational selection effect is a selection effect that arises from the very preconditions of observership. Another example, taken from Sir Arthur Eddington: suppose you are trying to catch fish with a net that doesn't catch fish that are shorter than 20 cm. If you use such a net to catch a hundred fish and they all turn out to be 20 cm or longer, then obviously you are not allowed to regard this as evidence that the minimum length of fish in the lake is 20 cm. (61)
According to Bostron, the anthropic principle, especially in its strong version, is heavily based upon observational selection effects. Observational selection effect theory states that conclusions developed from selective or limited data cannot be used to generate conclusions which transcend the scope of the observations. Bostron develops a model to deal with observation selection effects, and applies it to a variety of problems in science and philosophy.
The anthropic principle originated within a scientific context, fueled by scientists with interests that were in the borderline with philosophy, and expanded rapidly, including problems about teleology and many worlds.
In spite of the usual name, the anthropic principle obviously is not a «principle» in the usual scientific sense, as the principle of conservation of energy or the principle of minimal action are. Neither is it clear that it has an explanatory or predictive power. From the very beginning Brandon Carter tried to show that it really has predictive power. The principal prediction attributed to anthropic reasoning is the existence of a long-lived excited state of the nucleus of carbon 12, the effect of which is to delay the conversion of carbon 12 into oxigen 16 (by combination with helium 4 nuclei), thus providing enough carbon in the cosmic mix to support carbon-based life. This process is fundamental for the existence of life as we know it, and was successfully predicted by Fred Hoyle in 1953, searching the conditions that would made the production of carbon, and therefore the existence of life on Earth, easily available.
It has often been said that the anthropic principle is tautological, even though sometimes it is added that, as mathematical tautologies enter into the physical sciences when applied to factual issues, also the anthropic principle, combined with factual problems, can be useful in the sciences. Probably this is true. The version of the anthropic principle that nobody would dispute is the usually called «weak principle», stating merely that, given our existence as scientists, the preconditions for human life must obtain. This refers to the necessary conditions for our life. This can be applied to specific issues. Although usually it will be difficult to arrive at precise conclusions, we can sometimes arrive at some interesting clues, because the «principle» may point out towards some limits in the possible explanations.
It must also be said that the recognition, in the light of observational data, that Einstein's infamous cosmological constant might not be zero has recently changed the attitude towards anthropic thinking among some scientists, even though it is not clear what they might think of the anthropic principle:
perhaps the most significant change in cosmological thinking involves a new willingness to discuss what used to be an idea that was not normally mentioned in polite company: the anthropic principle... The realization that an extremely small, but non-zero, cosmological constant might exist has changed physicists' interest in anthropic explanation of nature precisely because the value it seems to take is otherwise so inexplicable... In the end as with so many anthropic arguments, it is hard to know what to make of this result, especially in the absence of any fundamental theory *(73). (63)
On the other hand, as a speculative philosophical issue, the interest of the principle is evident, even though it is difficult to consider it as a real «principle». In the context of teleology, it points out towards a number of issues that are worth considering as a factual basis for further reasoning. The «fine tuning» of the universe for carbon-based life, and specifically for human life, should not be taken as a logical proof of the existence of a divine plan; nevertheless, it is most coherent with this plan, and reinforces the teleological and theological reasoning.
The anthropic principle has contributed to the development of a number of new scientific ideas on the existence of worlds other than the one we know, sometimes as a result of the opposition to the teleological interpretations that the principle apparently suggests. The interaction between science and philosophy (and theology) in this case can be summarized in the following sequence. In the first place, several philosophically minded scientists have tried to solve problems regarding the basic features of the world, in the limits of the science of their time. Then other scientists have used anthropic reasoning that eventually led to the formulation of the anthropic principle, always in a scientific context and trying to apply the principle to scientific problems. Then, also in the hands of other scientists, the issue exploded and merged with problems on telelology and theology. In its turn, this has provoked further speculation about other worlds and their origin. Also, the so-called fine-tuning of the universe has enlarged the perspectives for teleological reasoning.
- Barrow, John D. "Dimensionality", in: The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), pp. 127-136.
- Barrow, John D. and Tipler, Frank J. The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986).
- Barrow, John D. The Constants of Nature. From Alpha to Omega — the Numbers That Encode the Deepest Secrets of the Universe(New York: Vintage Books, 2002).
- Bostrom, Nick. Anthropic Bias. Observation Selection Effects in Science and Philosophy (New York & London: Routledge, 2002).
- Bostrom, Nick. Observational Selection Effects and Probability, doctoral dissertation, London School of Economics, Department of Philosophy, 3 July 2000: http://www.anthropic-principle.com/phd/phdhtml.html
- Carr, B. J. & Rees, M. J. "The anthropic principle and the structure of the physical world", Nature, vol. 278 (12 April 1979), pp. 605-612.
- Carter, Brandon. "Large Number Coincidences and the Anthropic Principle in Cosmology", in: Confrontation of Cosmological Theories with Observational Data, M. S. Longair, ed. (Dordrecht: Reidel, 1974), pp. 291-298. Reprinted in: Modern Cosmology & Philosophy, J. Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), pp. 131-139.
- Carter, Brandon. "The anthropic principle and its implications for biological evolution", in: The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), pp. 137-153.
- Carter, Brandon. Anthropic interpretation of quantum theory (News about that cat!), July 2003, pp. 11 and 16, in:http://luth2.obspm.fr/~carter/
- Carter, Brandon. Anthropic interpretation of quantum theory, July 2003: http://arxiv.org/PS_cache/hep-th/pdf/0403/0403008.pdf
- Collins, C. B. and Hawking, S. W. "Why is the universe isotropic?", The Astrophysical Journal, vol. 180 (1973), pp. 317-334.
- Dicke, R. H. "Dirac's Cosmology and Mach's Principle", Nature, vol. 192, No. 4801, 4 November 1961, pp. 440-441. Reprinted in:Modern Cosmology & Philosophy, John Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), pp. 127-130.
- Dicke, Robert H. "Dirac's Cosmology and Mach's Principle", Nature, vol. 192, No. 4801 (4 November 1961), pp. 440-441 [followed in p. 441 by a comment by P. A. M. Dirac]. Reprinted in: Modern Cosmology & Philosophy, J. Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), pp. 127-130.
- Dirac, Paul A. M. "A New Basis for Cosmology", Proceedings of the Royal Society of London. Series A, vol. 165, No. 921 (5 April 1938), pp. 199-208. [See also: Nature, 139, 323 (1937)].
- Dirac, Paul. (interview with): http://www.fdavidpeat.com/interviews/dirac.htm
- Eddington, Arthur S. New Pathways in Science (Cambridge: Cambridge University Press, 1935).
- Krauss, Lawrence M. "A just-so story", Nature, vol. 423 (15 May 2003), pp. 230-231.
- Leslie, J. "The Anthropic Principle Today", in: Modern Cosmology & Philosophy, J. Leslie ed. (Amherst, NY: Prometheus Books, 1998), pp. 289-310.
- McCrea, W. H. "Introductory remarks", in: The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), pp. 1-3.
- McMullin, Ernan. "Is Philosophy Relevant to Cosmology?", in: Modern Cosmology & Philosophy, John Leslie, ed. (Amherst, NY: Prometheus Books, 1998), pp. 35-56.
- Press, W. H. and Lightman, A. P. "Dependence of macrophysical phenomena on the values of the fundamental constants", in: The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), pp. 113-126.
- Rees, M. J. "Large numbers and ratios in astrophysics and cosmology", in: The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), pp. 101-112.
- Tegmark, M. "Parallel Universes", Scientific American, volume 288, number 5, pp. 41-51.
- The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983). Original publication: Philosophical Transactions of the Royal Society of London, series A, volume 310 (no. 1512), pages 209-363 (1983).
- Tryon, E. P. "Is the universe a Vacuum Pluctuation?", Nature, vol. 246, No. 5433 (14 December 1973), pp. 396-397. Reprinted in (and quoted by): Modern Cosmology & Philosophy, J. Leslie ed. (Amherst, NY: Prometheus Books, 1998), pp. 222-225.
- Whitrow, Gerald. "Why physical space has three dimensions", The British Journal for the Philosophy of Science, Vol. 6, No. 21. (May, 1955), pp. 13-31.
- Ernan McMullin, "Is Philosophy Relevant to Cosmology?", in: Modern Cosmology & Philosophy , John Leslie, ed. (Amherst, NY: Prometheus Books, 1998), p. 42.
- R. H. Dicke, "Dirac's Cosmology and Mach's Principle", Nature, vol. 192, No. 4801, 4 November 1961, pp. 440-441. Reprinted in: Modern Cosmology & Philosophy , J. Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), p. 128.
- N. Bostrom, Anthropic Bias. Observation Selection Effects in Science and Philosophy (New York & London: Routledge, 2002), p. 6.
- John D. Barrow, The Constants of Nature. From Alpha to Omega — the Numbers That Encode the Deepest Secrets of the Universe(New York: Vintage Books, 2002), p. 65.
- Quoted by: Barrow, The Constants of Nature , p. 25.
- Barrow, The Constants of Nature , pp. 42-43.
- Letter by Albert Einstein to Ilse Rosenthal-Schneider, Princeton, 11 May 1945: quoted by Barrow, The Constants of Nature , p. 35.
- Letter by Albert Einstein to Ilse Rosenthal-Schneider, Princeton, 13 October 1945: quoted by Barrow, The Constants of Nature, p. 40.
- Barrow, The Constants of Nature , cit., p. 48.
- Ibid., p. 49.
- A. S. Eddington, New Pathways in Science (Cambridge: Cambridge University Press, 1935), p. 233 and 234.
- Barrow, The Constants of Nature, cit., pp. 99.
- Article by J. J. O'Connor and E. F. Robertson: http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Dirac.html(visited 3 May 2004). On Dirac and large numbers, see: Barrow, The Constants of Nature, cit., pp. 99-103.
- P. A. M. Dirac, "A New Basis for Cosmology", Proceedings of the Royal Society of London. Series A, vol. 165, No. 921 (5 April 1938), pp. 199-208. [p] [See also: Nature, 139, 323 (1937)].
- Interview with Paul Dirac: http://www.fdavidpeat.com/interviews/dirac.htm (visited 3 May 2004).
- Dirac, "A New Basis for Cosmology", cit., p. 201.
- Ibid., p. 208.
- Gerald Whitrow, "Why physical space has three dimensions", The British Journal for the Philosophy of Science , Vol. 6, No. 21. (May, 1955), pp. 13-31.
- Ibid., p. 29.
- Ibid., p. 31.
- R. H. Dicke, "Dirac's Cosmology and Mach's Principle", Nature, vol. 192, No. 4801, 4 November 1961, pp. 440-441. Reprinted in: Modern Cosmology & Philosophy , J. Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), pp. 127-130.
- Ibid., pp. 128-129.
- Ibid., p. 130.
- C. B. Collins and S. W. Hawking, "Why is the universe isotropic?", The Astrophysical Journal, vol. 180 (1973), pp. 317-334.
- B. Carter, "Large Number Coincidences and the Anthropic Principle in Cosmology", in: Confrontation of Cosmological Theories with Observational Data, M. S. Longair, ed. (Dordrecht: Reidel, 1974), pp. 291-298. Reprinted in: Modern Cosmology & Philosophy, J. Leslie ed., 2nd ed. (Amherst, NY: Prometheus Books, 1998), pp. 131-139.
- Ibid., p. 131.
- Ibid., pp. 131-132.
- Ibid., p. 132.
- Ibid., p. 133.
- Ibid., p. 135.
- Ibid., p. 136.
- Ibid., p. 137.
- Ibid., p. 139.
- B. J. Carr & M. J. Rees, "The anthropic principle and the structure of the physical world", Nature, vol. 278 (12 April 1979), pp. 605-612.
- Ibid., p. 605.
- Ibid., p. 612.
- The Constants of Physics, W. H. McCrea and M. J. Rees, eds. (The Royal Society: London, 1983), p. v. Original publication:Philosophical Transactions of the Royal Society of London , series A, volume 310 (no. 1512), pages 209-363 (1983). We will quote by the separated volume, which has 153 pages
- W. H. McCrea, "Introductory remarks", ibid., pp. 2-3.
- M. J. Rees, "Large numbers and ratios in astrophysics and cosmology", ibid., pp. 101-112.
- W. H. Press and A. P. Lightman, "Dependence of macrophysical phenomena on the values of the fundamental constants",ibid., pp. 113-126.
- B. Carter, "The anthropic principle and its implications for biological evolution", ibid., pp. 137-153.
- J. D. Barrow, "Dimensionality", ibid., pp. 127-136.
- Rees, "Large numbers and ratios in astrophysics and cosmology", cit., p. 101.
- Ibid., p. 111.
- Barrow, "Dimensionality", ibid., p. 135.
- Carter, "The anthropic principle and its implications for biological evolution", cit., pp. 137-138.
- Ibid., p. 141.
- Ibid., p. 142.
- Ibid., p. 152.
- J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986).
- Ibid., p. 16.
- Ibid., p. 21.
- This text is found in a web page entitled «The Anthropic Principle»:http://www.physics.sfsu.edu/~lwilliam/sota/anth/anthropic_principle_index.html (visited on 4 May 2004).
- Brandon Carter, Anthropic interpretation of quantum theory, July 2003: http://arxiv.org/PS_cache/hep-th/pdf/0403/0403008.pdf (visited 3 May 2004).
- Brandon Carter, Anthropic interpretation of quantum theory (News about that cat!), July 2003, pp. 11 and 16, in:http://luth2.obspm.fr/~carter/
- Nick Bostrom, Anthropic Bias. Observation Selection Effects in Science and Philosophy (New York & London: Routledge, 2002), p. 15.
- Thomas Aquinas, Summa Theologiae , part 1, question 2, article 3, in the body of the article.
- Thomas Aquinas, Summa contra Gentes , book 1, chapter 13.
- Bostrom, Anthropic Bias , cit., p. 11.
- Ibid., p. 13.
- J. Leslie, "The Anthropic Principle Today", in: Modern Cosmology & Philosophy, J. Leslie ed. (Amherst, NY: Prometheus Books, 1998), p. 292.
- Ibid., pp. 292-295.
- Ibid., p. 293.
- E. P. Tryon, "Is the universe a Vacuum Pluctuation?", Nature, vol. 246, No. 5433 (14 December 1973), pp. 396-397. Reprinted in (and quoted by): Modern Cosmology & Philosophy, J. Leslie ed. (Amherst, NY: Prometheus Books, 1998), p. 223.
- Ibid., p.224.
- M. Tegmark, "Parallel Universes", Scientific American , volume 288, number 5, p. 41.
- Ibid., p. 42.
- This and the following data are taken from the web page of Alan Guth:http://web.mit.edu/physics/facultyandstaff/faculty/alan_guth.html#inflationaryuniverse .
- This and the following data are taken from the web page of Andrei Linde: http://www.stanford.edu/~alinde.
- Nick Bostrom, Observational Selection Effects and Probability, doctoral dissertation, London School of Economics, Department of Philosophy, 3 July 2000: http://www.anthropic-principle.com/phd/phdhtml.html, p. 8.
- Ibid., p. 12.
- Lawrence M. Krauss, "A just-so story", Nature , vol. 423 (15 May 2003), pp. 230-231.
The Anthropic Principle: Science, Philosophy or Guesswork ?
Ernan McMullin (1981)
Robert Dicke (1961)
Nick Bostrom (2002)
1 Constants of Nature and Natural Units
1.1. The Constants of Nature
John Barrow on the Constants of Nature
1.2. Natural Units: George Stoney (1874) (1)
1.2. Natural Units: George Stoney (1874) (2)
1.3. Natural Units: Max Planck (1899-1900) (1)
1.3. Natural Units: Max Planck (1899-1900) (2)
2 The dimensionless Constants of Nature
2.1. Einstein's Search for the Ultimate Theory of Physics (1)
Albert Einstein (1945) (2)
Albert Einstein (1945) (3)
2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (1)
2.2. Dimensionless Constants and Other Worlds (John D. Barrow) (2)
3 Dimensionless Constants and Large Numbers
3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (1)
3.1. Constants of Nature and Large Numbers: Sir Arthur Eddington (2)
Dimensionless numbers with an "strange" appearance: related with 1040, its squares and cubes
John D. Barrow on Eddington
3.2. Large Number's Coincidences are not accidental: Paul Dirac (1937) (1)
Paul Dirac (2)
4 The formulation of the Anthropic Principle
4.1. Introducing Anthropic Reasoning: Gerald Whitrow (1955)
4.2. More Anthropic Reasoning: Robert Dicke (1961)
4.3. The principle is Almost There: Collins and Hawking (1973)
4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (1)
4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (2)
4.4. The Birth of the Anthropic Principle: Brandon Carter (1973) (3)
Carter on Anthropic Principle, 1973 (1)
Carter on Anthropic Principle, 1973 (2)
5 The Anthropic Principle comes of Age
5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (1)
5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (2)
5.1. Life Depends on Delicate Coincidences: Carr & Rees (1979) (3)
5.2. A Meeting of the Royal Society (1983)
5.3. Carter Revisited by Carter (1983) (1)
5.3. Carter Revisited by Carter (1983) (2)
5.3. Carter Revisited by Carter (1983) (3)
5.4. Barrow and Tipler on the Anthropic Principle (1986) (1)
5.4. Barrow and Tipler on the Anthropic Principle (1986) (2)
Confusion increases: an example
6 Fine-Tuning, Teleology, and Other Worlds
6.2. The Teleological Argument (1)
6.2. The Teleological Argument (2)
6.3. Many Worlds (1)
6.3. Many Worlds (2)
6.3. Many Worlds (3)
6.3. Many Worlds (4)
6.3. Many Worlds (5) Max Tegmark
Max Tegmark (Scientific American, May 2003)
Max Tegmark (Scientific American, May 2003) The Reality Postulate
The inflationary universe
Eternal chaotic inflation
6.4. Observation Selection Effects
7 Science, Philosophy, or Gueswork?
In the end...
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