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Photography by Ed Pastor, photo illustration by Pat Linse.

Photography by Ed Pastor, photo illustration by Pat Linse.

Fine-Tuning and the Multiverse

In this essay, as a follow-up to his book, The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us (in which he showed that, based on our knowledge of this universe alone, divine fine-tuning claims are without merit), Victor J. Stenger brings the arguments up-to-date with a discussion of the eternal multiverse hypothesis. This article was published in Skeptic magazine issue 19.3 in 2014. Order the back issue.

For years theologians and Christian apologists have convinced themselves and their followers that they have a knock-out scientific argument for the existence of God. They claim that the parameters of physics are so finely tuned that if any one of these parameters were just slightly different in value, then life would not be possible anywhere in the universe.

Assuming—on no basis whatsoever—that those parameters are independent and could have taken on any value over a wide range, they conclude that the probability of a universe with our particular set of parameters is infinitesimally small. Further assuming—also on no basis whatsoever—that the probability of a divine creator is not equally infinitesimally small, they conclude that a creator fine-tuned the universe for life. Note that there is also no basis whatsoever to assume … that this creator was the personal God worshipped by Christians, Muslims, and Jews or the God of any other religion. An impersonal, deist creator works equally well.

Arguments from design are essentially God-of-the-gaps arguments. They can’t succeed because the proponents would have to prove that science will never find an explanation to fill the gap, which they can never do. But they keep trying. In a book published in 2011 titled The Fallacy of Fine-Tuning, I showed that, based on our knowledge of this universe alone, divine fine-tuning claims are without merit.1 Of course this did not put an end to the notion, so in this essay I will bring the arguments up-to-date.

Fallacy mentioned (but did not rely on) the no-brainer solution to the fine-tuning problem that is regarded as the most plausible by most physicists and cosmologists: Our universe is just one of an unlimited number of individual, uncreated universes collectively called the multiverse that extend for an unlimited distance in all directions and for an unlimited time in the past and future. We just happen to live in the particular universe that is suited for our kind of life. Our universe is not fine-tuned for us; we are fine-tuned to our universe.

As we will see, recent observations have rendered the multiverse even more credible now than it was in 2011 when I first published the book.

The Multiverse

The eternal multiverse hypothesis was first put forward in 1983 by cosmologist Alexander Vilenkin.2 It was based on the model that had been proposed a few years earlier by physicist Alan Guth (and independently by several others), called inflation that solved a number of existing problems in cosmology.3 In the inflationary model, during the first tiny fraction of a second after our universe appeared it underwent a rapid, exponential expansion and increased in size by many orders of magnitude.

Vilenkin discovered from the mathematics of the model that once inflation starts it never ends, with new universes being created all the time. He called this eternal inflation. In 1986, Andrei Linde elaborated on the idea showing how it was possible that the universe reproduces itself indefinitely and “may have no beginning or end.”4

Eternal inflation, as conceived by Vilenkin and Linde, results in the continual production of bubble universes inside of other universes in a fractal-like structure.5 Basically, while a bubble universe is exponentially inflating to a much larger size, other bubbles can nucleate in an ever-growing empty “de Sitter” space.6

Note that the multiverse does not need to be proven to exist to invalidate the fine-tuning argument for a creator. It just needs to be a possible alternative. Nevertheless, theologians have vehemently objected to the multiverse. Virtually all world religions teach the divine creation of a single universe at a finite time in the past with a central place for humanity. The multiverse severely challenges that teaching.

Theological Objections

On July 7, 2005, Christoph Schönborn, Cardinal Archbishop of Vienna wrote in the New York Times, “The multiverse hypothesis in cosmology [was] invented to avoid the overwhelming evidence for purpose and design found in modern science.”7

Of course the Church also objected when early astronomers said Earth was round and later when Copernicus moved the earth from the center of the solar system. And when Giordano Bruno said that ours was just one of many planets orbiting many suns, they burned him at the stake. Theists talk about humility, but they don’t like it when science gives them a reason to be humble.

Leading Christian apologist William Lane Craig has expressed sentiments similar to Schönborn’s. In a debate at Purdue University in 2013 Craig said, “The proponents of chance have been forced to postulate the existence of a World Ensemble of other universes, preferably infinite in number and randomly ordered, so that life-permitting universes will appear by chance somewhere in the Ensemble.”8

These statements are not only wrong; they are insults to serious scholars who are committed to reason and evidence and not some ideological agenda. The “World Ensemble” or multiverse was motivated by established science—with no thought whatsoever to theology. It is the conclusion of our best current models of cosmology based on the extremely precise observations of modern astronomy and our best knowledge of fundamental physics.

A common objection to the notion of multiple universes is that it introduces additional entities when only a single entity, a lone universe, is needed. In 1986 astronomer Edward Harrison wrote: “Take your choice: blind chance that requires multitudes of universes, or design that requires only one.”9

To help us decide on the best choice, we can apply the test of Ockham’s razor, which favors the simplest hypothesis when there are several to choose from. At first glance, it might seem that a single universe is more parsimonious than multiple universes. However, Ockham’s razor does not apply to the number of objects in a theory but rather to the number of hypotheses. The atomic theory of matter multiplied the number of objects physicists had to deal with by trillions of times. Yet it was simpler and more powerful than macroscopic thermodynamics, which preceded it and which can be completely derived from atomic theory.

Similarly, since current science based on observations implies multiple universes, to postulate that only a single universe exists requires an additional hypothesis not required by the data. That is, it’s the single universe hypothesis that violates Ockham’s razor.

Is the Multiverse Scientific?

In another objection, many nonbelieving scientists have joined theists in arguing that the multiverse is “non-scientific” because we have no way of observing a universe outside our own. This is wrong. The multiverse is a legitimate scientific hypothesis since it seems to be an unavoidable consequence of eternal inflation, which is based on our best observational data as well as our best theoretical knowledge.

Our theories often contain unobservables, such as quarks and black holes. Furthermore, empirical evidence for other universes is not beyond the realm of possibility. Early in the history of our universe another universe may have been sufficiently close for its gravity to affect the spherical symmetry of the cosmic microwave background (CMB). Or, the bubbles may have collided leaving a bruise on each. A detection of a large-scale asymmetry in the CMB could provide evidence for a universe outside our own. In fact, the Planck space telescope has confirmed several unexplained asymmetries of this nature that were hinted at in earlier observations by the Wilkinson Microwave Anisotropy Explorer (WMAP).10

Now, since the observation of another universe beside our own would be the greatest scientific discovery in history, don’t expect any cosmologists to make such a claim until they have ruled out every other possibility to the highest level of confidence and had their discovery independently verified. In the case of the Planck experiment, the investigating team has not deemed the evidence sufficiently significant to make any published claim. We’ll have to wait and see. But the fact that other universes are in principle observable suffices to keep them on the table of science.

In 2014, inflationary cosmology—and by inference the multiverse—received a major boost from the observation of what appear to be primordial gravitational waves. A unique type of polarization in the cosmic microwave background called “B-mode” had been predicted to arise from the gravitational waves induced by the quantum fluctuations that are posited to have produced our universe. The observation of this polarization was announced with great fanfare on March 17, 2014 by an experiment called BICEP2 (Background Imaging of Cosmic Extragalactic Polarization) located at the South Pole.11 The null hypothesis was ruled out at a statistical significance level of less than one part in 3.5 million. However, this result is currently being questioned and we have to await further developments.

Fine-Tuning in Our Universe

Despite the greatly improved status of the multiverse hypothesis since 2011, it remains unconfirmed. So it behooves us to continue to examine the credibility of the divine fine-tuning hypothesis for our single, lone universe.

In The Fallacy of Fine-Tuning I provided purely natural explanations for the values of the so-called fine-tuned parameters that appear most frequently in the theistic literature. Again, I did not have the burden of proving these explanations correct. I just needed to show that there are plausible alternatives. This approach is sufficient to invalidate the need for a supernatural creator. Those who dispute this argument have the burden of proving otherwise. This they have not done.

My theist critics continue to fail to understand that they are making the less parsimonious hypothesis—that an all-powerful supernatural being for which no evidence exists brought the universe into being.

Recently I contributed a chapter arguing against fine-tuning to an anthology called Debating Christian Theism.12 Christian philosopher Robin Collins of Messiah College presented the case for fine-tuning in an accompanying chapter.13 In it he criticizes a number of my previous arguments, to which I will briefly respond here. Referring to the possibility that the parameters can vary randomly, Collins asks, “Why should they give rise to precisely the right set of laws required for life?”14 He obviously thinks only one form of life is possible—ours. Well, that’s the whole point he and other divine fine-tuners miss. The parameters didn’t have to be precise to lead to some form of life somewhere in this vast universe. In Fallacy I showed that wide ranges of physical parameters could plausibly lead to conditions, such as long ages of stars, that could in principle allow for the evolution of life of one form or another.

Let’s look at some of the parameters that are supposed to be fine-tuned for life.

Trivial Parameters

Two of the parameters that appear in most lists of fine-tuned quantities are

  • The speed of light in a vacuum c
  • Planck’s constant h

As basic as these parameters are to physics, their values are arbitrary. The fundamental unit of time in physics is the second. The units for all other measurable quantities in physics, except for those that are dimensionless, are defined relative to the second. The value of c is chosen to define what units will be used to measure distance. To measure distance in meters you choose c = 3×108. To measure distance in light-years you choose c = 1.

The value of Planck’s constant h is chosen to define what units will be used to measure energy. To measure energy in joules you choose h = 6.626×10-34. To measure energy in electron volts you choose h = 4.136×10-15. Physicists like to work in what they call “natural units,” where ħ = h/2π = c = 1. Then the three defining properties of matter—mass, energy, and momentum—all have the same units.

Other arbitrary quantities that are often claimed to be fine-tuned include Boltzmann’s constant, kB, which simply converts from units of absolute temperature—degrees Kelvin—to energy, and Newton’s gravitational constant, G, which also depends on the choice of units. In what are called Planck units, ħ = c = G = 1.

In other words, dimensioned constants such as c, h, and G have no significance in physics because they are just arbitrary conversion factors. For a constant to be meaningful, it must be dimensionless.

Parameters Needed for Any Form of Life

Less trivially, let us look at five parameters that are claimed by theists to be so finely tuned that no form of life could exist in a universe in which any one of the values differed by an infinitesimal amount from its existing value in our universe.15 These are:

  • The ratio of electrons to protons in the universe
  • The ratio of electromagnetic force to gravity
  • The expansion rate of the universe
  • The mass density of the universe
  • The cosmological constant
The ratio of electrons to protons in the universe

Physicist and Christian apologist Hugh Ross asserts that if this ratio were larger, there would be insufficient chemical binding. If smaller, electromagnetism would dominate gravity preventing galaxy, star, and planet formation.

The fact that the ratio is exactly equal to one can be easily explained. The number of electrons in the universe should equal the number of protons from charge conservation, on the reasonable expectation that the total electric charge of the universe is zero. While other charged particles exist, the proton and electron are the only ones that are stable.

The ratio of electromagnetic force to gravity

Ross says that if this ratio were larger, there would be no stars less than 1.4 solar masses and hence short and uneven stellar burning. If it were smaller, there would be no stars more than 0.8 solar masses and hence no heavy element production.

The ratio of the forces between two particles depends on their charges and masses. Despite the statement often heard in most (if not all) physics classrooms—that gravity is much weaker than electromagnetism—there is no way one can state absolutely the relative strengths of gravity and any other force. Indeed, if one were to define the strength of gravity using the only natural mass that can be formed from fundamental constants, the Planck mass (2.18 × 10-8 kilograms), you find that gravity is 137 times stronger than electromagnetism.

The reason gravity is so weak in atoms is the small masses of elementary particles. Collins misunderstands this point when he writes: “Stenger’s attempt to explain away this apparent fine-tuning [the low mass of the proton and neutrons] is like someone saying protons and neutron are made up of quarks and gluons, and since the latter masses are small, this explains the smallness of the former masses.”16

This is a complete misrepresentation of my position. Nowhere have I used this argument. Collins provides no direct quotation or citation. In truth, I make the very reasonable assumption that all the elementary particles (the proton and neutron are not elementary) were massless when they were first generated in the early universe. All have low masses today compared to the Planck mass, since those masses were just small corrections provided by the Higgs mechanism and other effects.

The expansion rate and mass density of the universe

Ross claims that if the expansion rate of the universe, given by the cosmological Hubble parameter H, were larger there would be no galaxy formation; if smaller the universe would collapse prior to star formation.

As Stephen Hawking stated in his 1988 bestseller A Brief History of Time, inflation results in the mass density of the universe being very close to the critical value, which depends on H. This, in turn implies that H also has a critical value.17 Only one of these two parameters is adjustable. Let’s assume it is H.

Now, the age of the universe is approximately given by T = 1/H. It is currently 13.8 billion years. Life could just as well have evolved for T = 12.8 billion years or T = 14.8 billion years. In fact, suppose T = 1.38 billion years. Then we could not have life now, but it would come along ten billion years or so later. Or, suppose T = 138 billion years. Then life would have already appeared a hundred or so billion years earlier.

So, neither the density of the universe nor the expansion rate was fine-tuned. The density is just what it should be and the expansion rate could be almost anything.

The cosmological constant

The cosmological constant is equivalent to an energy density of the vacuum and is the favorite candidate for the dark energy, which is responsible for the acceleration of the universe’s expansion—constituting over 68 percent of the total mass/energy of the universe.

The original calculations of the energy density of the vacuum gave answers that are 50–120 orders of magnitudes larger than the maximum value allowed by observations. So fine-tuning of up to one part in 120 orders of magnitude is claimed by fine-tuners. “How could anyone do this but God?,” they ask.

The original energy density calculations made a fundamental error by summing all the states in a given volume. The entropy of a system is given by the number of accessible states of the system. Thus, the entropy calculated by summing over a volume will be greater than the entropy of a black hole of the same size, which depends on its area rather than its volume. Since we cannot see inside a black hole, the information that we have about what is inside is as small as it can be and so the entropy, which is negative information, is as large as it can be.

Therefore, it was a mistake to calculate the number of states by summing over the volume. Correcting this by summing over the area, or, equivalently, setting the number of states equal to the entropy of a black hole of the same volume, we can naturally constrain the vacuum energy density. This calculation yields the result that an empty universe will have a vacuum energy density about equal to the critical density—just the value it appears to have.

For technical reasons, cosmologists are not ready to accept this solution to the cosmological constant problem. Nevertheless, I think it is fair to conclude that the original calculation is simply wrong—as far wrong as any other calculation in the history of physics—and should be ignored. Apologists have no right to take an obviously wrong calculation of a parameter and then claim that since the parameter does not have that value, it must have been set by God.

This takes care of the five parameters that are supposedly fine-tuned to such precision that even a tiny deviation would make life of any kind impossible. None are fine-tuned. Next let us move to another parameter that theists claim had to be fine-tuned for life based on carbon chemistry.

The Hoyle Prediction

In 1951, astronomer Fred Hoyle predicted that the carbon nucleus would need an excited state at about 7.7 MeV (million electron-volts) above its ground state in order for enough carbon to be produced in stars to make life in the universe possible. This story is of great historical interest because it is the only case where anthropic reasoning has led to an empirically verified prediction. Shortly thereafter the excited state was found at 7.656 MeV.18

However, calculations since have demonstrated that the same amount of carbon would have been produced if the excited state were any place between 7.596 MeV and 7.716 MeV. Furthermore, sufficient carbon for life would have occurred for an excited state anywhere from just above the ground state to 7.933 MeV.19 A state somewhere in such a large range is expected from standard nuclear theory. Furthermore, carbon is not the only element upon which life might be based.

Other Physics Parameters

Some of the other parameters that are claimed to be fine-tuned for life are:

  1. The relative masses of elementary particles.
  2. The relative strengths of the forces and other physics parameters.
  3. The decay rate of protons.
  4. The baryon excess in the early universe.

In Fallacy I showed that all have a wide range of possible values that allows some kind of life to form.

Cosmic Parameters

We have already disposed of the cosmic parameters that were deemed so crucial in making any livable universe possible: the mass density of the universe, the expansion rate, and the ratio of the number of protons and electrons are not only not fine-tuned, they are fixed by conventional physics and cosmology or, in the case of the expansion rate, practically any value would allow for life. Here are two other cosmic parameters that are said to be fine-tuned:

  1. The deuterium abundance.
  2. The lumpiness of matter.

Cosmologists now have a model referred to as ΛCDM (Lambda Cold Dark Matter) that gives a precise fit to the anisotropies of the cosmic microwave background and is consistent with observations on galactic structure. That model contains only six adjustable parameters. Neither the deuterium abundance nor the lumpiness of matter is one of these parameters. They come out of the model. The density of matter is not a parameter but assumed to equal the critical value. The expansion rate (Hubble parameter) is not an adjustable parameter but calculated in the model. In this model the cosmological constant is assumed to be the source of dark energy and its energy density is one of the six adjustable parameters.

In short, the divine fine-tuners have to go back to the drawing board and run the ΛCDM model over a range of the six adjustable parameters and show that life of any form would be impossible unless the parameters were exactly what they are for our universe.

Simulating Universes

The aggregate properties of the universe as we know them today are determined by just three physics parameters: the electromagnetic strength and the respective masses of the proton and the electron.20 From these we can estimate quantities such as the maximum lifetime of stars, the minimum and maximum masses of planets, the minimum length of a planetary day, and the maximum length of a year for a habitable planet. Generating 10,000 universes in which the parameters are varied randomly on a logarithmic scale over a range of 10 orders of magnitude, I find that 61 percent of the universes have stellar lifetimes over 10 billion years, sufficient for some kind of life to evolve.

Collins has previously objected to my preliminary and now 20-year old conclusion that long stellar lifetimes are not fine-tuned.21 He argues that not all these universes are livable—that I have not accounted for life-inhibiting features. He refers to John Barrow and Frank Tipler, who in their classic The Anthropic Cosmological Principle set a certain technical requirement for life to be possible.22 I have checked and found the Barrow-Tipler limit to be satisfied 91 percent of the time.

Applying rather tight limitations to all three parameters in order to produce life, 13 percent of all universes are capable of supporting some kind of life not too different from ours when I vary them by ten orders of magnitude. Varying by two orders of magnitude, which is more realistic since the parameters are not independent but related, I find that 92 percent of the universes have stellar lifetimes over 10 billion years and 37 percent are capable of supporting some kind of life not too different from ours. Life very different from ours remains possible in a large fraction of the remaining universes, judging from the large stellar lifetimes for most.

Summary of the Case Against Fine-Tuning

The following is a summary of the logical and scientific errors made by proponents of fine-tuning (not all make every error) that I have identified in my study of this subject.

  1. They claim fine-tuning for our form of life, ignoring the possibility of other life forms.
  2. They claim fine-tuning for physics constants such as c, h, and G, whose values are arbitrary.
  3. They claim fine-tuning for quantities such as the ratio of electrons to protons, the expansion rate of the universe, and the mass density of the universe, whose values are precisely set by cosmological physics or have wide allowable ranges. These are not even varied in the current standard cosmological model.
  4. They assert that the relative strength of the electromagnetic and gravitational forces is fine-tuned, when in fact this quantity cannot be universally defined.
  5. They assert that an excited state of the carbon nucleus had to be fine-tuned for stars to produce the carbon needed for life, when calculations show that a wide range of values for the energy level of that state will produce sufficient carbon.
  6. They claim fine-tuning for the masses of elementary particles when the ranges of these masses are set by well-established physics and sufficiently constrained to give some form of life.
  7. They assume the strengths of the various forces are constants that can independently change from universe to universe. In fact, they are dependent on one another and vary with energy, and their relative values and energy dependences are close to being pinned down by theory, in ranges that make some kind of life possible.
  8. Most make a serious analytical mistake in taking all the parameters in the universe to be fixed while varying only one at a time. This fails to account for the fact that a change in one parameter can be compensated by a change on another, opening up more parameter space for a viable universe.
  9. They misunderstand or misuse probability theory, ignoring the fact that events with “mindboggling” low probabilities occur billions of times a day. The only way one can use a low probability to argue that something is unlikely is to compare it with the probabilities of all the alternatives. What is the probability of God? In Fallacy I compared the calculations for the probability of God using sophisticated Bayesian statistics made by two physicists, one a believer and one a nonbeliever. The believer came up with 0.67, while the nonbeliever’s result was 10-17.23
  10. They claim many parameters of Earth and the solar system are fine-tuned for life, failing to consider that with an estimated sextillion planets in the visible universe in habitable regions of their stars, and the countless number beyond our horizon where light has not yet had time to reach us, a planet with the properties needed for life is likely to occur many times. Nevertheless, the universe is hardly lifefriendly. If God wanted to fine-tune it for life he could have made the universe a lot friendlier.
  11. The fine-tuners are also wrong to reject the multiverse solution as “unscientific.” It is not unscientific to speculate about invisible, unconfirmed phenomena that are predicted by existing models that, so far, agree with all the available data. The neutrino was predicted to exist in 1930 based on the well-established principle of energy conservation but was not detected until 1956, and even then indirectly.
  12. The current, highly successful ΛCDM cosmological model has only six parameters, none of which have been shown to be fine-tuned.
Skeptic magazine 19.3 (cover)

This article appeared in Skeptic magazine 19.3 (2014). Order this back issue.

As my discussion illustrates, the explanations for apparent fine-tuning are technical and require adequate training to understand. A proper analysis finds there is no evidence that the universe is finetuned for life; all we have is yet another God-of-the-gaps argument that is doomed to failure by its implicit assumption that some phenomena exist that science will never be able to explain without introducing God into the explanation. END

References
  1. Stenger, Victor J. 2011. The Fallacy of Fine-Tuning: Why the Universe is Not Designed for Us. Amherst, NY: Prometheus Books.
  2. Vilenkin, Alexander. 1983. “Birth of Inflationary Universes,” Physical Review D 27, no. 12: 2848–55. See also: Vilenkin, Alexander. 2006. Many Worlds in One: The Search for Other Universes. New York: Hill and Wang.
  3. Guth, Alan H. and Paul J. Steinhardt. 1984. “The Inflationary Universe.” Scientific American, 250, 116–28.
  4. Linde, Andrei. 1986. “Eternally Existing Self-Reproducing Chaotic Inflationary Universe.” Physics Letters B 175, no. 4: 395–400.
  5. Linde, Andrei. 1994. “The Self-Reproducing Inflationary Universe.” Scientific American, 271, no. 5: 48–55.
  6. Carroll, Sean M. 2010. From Eternity to Here: The Quest for the Ultimate Theory of Time. New York: Dutton, 310–11.
  7. Christoph Schönborn, “Finding Design in Nature,” New York Times, July 7, 2005.
  8. Craig, William Lane. 2014. “Opening Speech.” In Is Faith in God Reasonable?, edited by Paul Gould and Corey Miller. New York: Routledge.
  9. Harrison, Edward Robert. 1985. Masks of the Universe. New York: Macmillan, 252.
  10. Planck Collaboration, Ade, P.A. R., et al. 2013. “Planck 2013 Results. XXIII. Isotropy and Statistics of the CMB.” arXiv preprint arXiv:1303.5083.
  11. P.A.R. Ade et al., “Detection of BMode Polarization At Degree Angular Scales By Bicep2,” Physical Review Letters 112, no. 24 (2014): 241101.
  12. Stenger, Victor J. 2013. “The Universe Shows No Evidence for Design.” In Debating Christian Theism, edited by J.P. Moreland, Chad Meister, and Khaldoun A. Sweis. New York: Oxford University Press, 47–58.
  13. Collins, Robin. 2013. “The Fine- Tuning Evidence is Convincing, “ In Debating Christian Theism, edited by J.P. Moreland, Chad Meister, and Khaldoun A. Sweis. New York: Oxford University Press, 35–46.
  14. Collins, 2013, 38.
  15. Ross, Hugh. 1998. “Big Bang Model Refined By Fire.” In Mere Creation: Science, Faith and Intelligent Design, edited by William A. Dembski, 363–83. Downers Grove, IL: Intervarsity Press; Rich Deem. Evidence for the Fine Tuning of the Universe. (accessed July 12, 2013).
  16. Collins, Robin 2009. “The Teleological Argument: An Exploration of the Fine-Tuning of the Universe,” in The Blackwell Companion to Natural Theology, ed. William Lane Craig and James Porter Moreland. Malden, MA: Wiley-Blackwell, 43.
  17. Hawking, Stephen. 1988. A Brief History of Time: From the Big Bang to Black Holes. New York: Bantam Books, 128.
  18. Hoyle, F., et al. 1953. “A State in C12 Predicted From Astronomical Evidence,” Physical Review Letters 92: 1095.
  19. Livio, M., D. Hollowell, A. Weiss, and J.W. Truran. 1989. “The Anthropic Significance of the Existence of an Excited State of C12,” Nature 340: 281–84, 168–73; see also figure 9.1, in Stenger, 2011, 170.
  20. Stenger, 2011, 233–44.
  21. Collins, 2009.
  22. Barrow, John D. and Frank Tipler. 1988. The Anthropic Cosmological Principle. Oxford University Press, 326.
  23. Stenger, 2011, 247–52.
 
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