# Design or the multiverse?

In the last couple of decades, physics journals have begun publishing articles containing "anthropic reasoning." (1) Anthropic reasoning attempts to explain why physical constants governing our universe seem to be "finetuned" to allow the existence of life. Such reasoning typically presumes the existence of a plethora of universes-collectively known as the "multiverse"--each universe governed by different values of physical constants or even different physical laws. It is then reasoned that the only properties that an "observer" in a universe could ever measure would be those that permit the observer to exist in that universe. Hence, the properties of a universe such as ours only appear to be "fine-tuned" to support intelligent life. Huge numbers of other universes with properties that are not fine-tuned also exist, but go unobserved. Arguments such as this have been advanced by Andrei Linde, (2) John Barrow and Frank Tipler, (3) and others. An example described by Garriga et al. involves the density of "dark energy" in the universe, which is governed by the so-called "cosmological constant." (4) The value of this constant appears to be more than a hundred orders of magnitude smaller than what it is expected to be based on quantum mechanics. It has been suggested that anthropic selection may help account for this deviation from what might be expected a priori.

To make anthropic reasoning quantitative (and hence more scientific), one must specify the a priori probabilities of the various constants of nature, and the conditional probability that intelligent life will emerge which is capable of "observing" a universe characterized by those constants. These probabilities then enter a Bayesian inference calculation, which, in principle, might allow one to explain why we observe the physical constants that we do, given the fact that intelligent life must exist within the universe in which the observations are made. (Bayesian inference is a statistical method for adjusting the probability that a particular hypothesis is true by using "new" information that was not used to obtain the initial "a priori" probability. For example, suppose that half the population of the USA vote Democratic and half vote Republican, and that half of the Republicans support a "flat tax," but no Democrats do. If I learn that a randomly chosen person in the population does not support a flat tax, then I can use Bayesian inference to update the probability of this person being a Democrat from 50% to 66.7%.)

It is worth noting that there are multiple foundational problems that bedevil anthropic reasoning (such as how to define an "observer" (5)) and even if these are overcome, there are good reasons to doubt that the probabilities needed to carry out the Bayesian inferences can ever be made accurate enough to be of value to science. Nevertheless, it is argued that, despite the difficulties, anthropic reasoning involves only material entities and physical laws, and so qualifies as science, (6) albeit at its speculative edge.

Anthropic Reasoning and Design

Anthropic reasoning is controversial among both theistic and atheistic scientists, and raises a host of difficult questions for both camps. (7) Here, I wish to point out the potential that such reasoning has to upset entrenched positions regarding the validity of the notion of "design," both in the laws of physics and in the biological world. Viewed optimistically, perhaps the emergence of anthropic reasoning may offer a way to move toward more constructive interactions among scientists with differing religious and metaphysical perspectives.

Most modern scientists tend to reject the validity of "design" as a principle of science, for one of two reasons. Some atheists, such as Richard Dawkins, believe that science can address the possibility of "design" in the universe, and in fact, has already shown that design is absent. Thus, Dawkins' book The Blind Watchmaker is subtitled "How the Evidence of Evolution Reveals a Universe without Design." (8) Oddly enough, in accepting design as a topic suitable for scientific inquiry, Dawkins puts himself in the same camp with his archrivals, the intelligent design theorists, who also hold that design can be addressed scientifically, but, contra Dawkins, conclude that the universe does show evidence of design. (9) Most scientists, however, seem to regard "design" as a concept that science does not, or should not, address.

Anthropic reasoning within science has the potential to upset these entrenched positions, in that anthropic reasoning accepts that some attributes of our universe appear to be highly improbable, and that science should try to explain this. However, this is a position also taken by advocates of intelligent design.

Thus, I argue here that whoever takes anthropic reasoning to be scientific will have difficulty maintaining the claim that design, or at least apparent design, is nonscientific. For example, in a recent book The Cosmic Landscape, (10) renowned string theorist Leonard Susskind argues that anthropic reasoning is in the vanguard of physics and cosmology, and he gives his book the provocative subtitle, "The Illusion of Intelligent Design." Note that, if it were somehow possible to demonstrate that there is only one universe, then the "apparent design" (or "illusion of design") addressed by anthropic reasoning would become evidence of real design. This could, of course, be avoided by asserting that the existence of the multiverse must be accepted as a scientific certitude that no evidence could ever refute. However, in that case, the multiverse would become an untestable concept (not "falsifiable"), and therefore would fail to satisfy an important criterion for a scientific hypothesis. Thus, anthropic reasoning "opens the back door" to design, and there does not seem to be a principled way to boot it back out.

Anthropic reasoning brings the design argument not only back into physics and cosmology, but even back into biology. To see why, we note that the Bayesian calculus used in anthropic reasoning contains both the a priori probabilities of various physical constants (putatively derivable from some ultimate physical theory), and the conditional probabilities for the emergence of intelligent life, given those a priori probabilities. Let us initially simplify matters greatly by assuming that we have only one physical constant to explain--call it [lambda]--which we shall assume takes on an improbable value in our universe. To be more concrete, let us assume that the a priori probability distribution for [lambda] is given by a Gaussian:

[P.sub.[lambda]]([lambda]) = 1/[square root of 2[pi][[sigma].sub.[lambda]] exp(-([lambda] - [[lambda].sub.0]).sup.2]/[2[[sigma].sub.[lambda]].sup.2]) (1)

and that the value of [lambda] that we observe, [[lambda].sub.obs], might be far from the a priori most probable value [[lambda].sub.0].

Now let us define the conditional probability density [P.sub.e] (IL|[lambda]) for the evolution of intelligent life that is able to make physical measurements in the cosmos (i.e., an "observer"), given a particular value of [lambda]. IL = 1 for the presence of an intelligent observer in that universe, and IL = 0 for the absence of one. Here, I will ignore the many obstacles to formulating this probability, such as how to decide what constitutes an "observer," how to weight this probability for the number of such "observers" in a given universe, etc. The goal is not to defend such reasoning but only to see its consequences. Let us assume that this function is also a Gaussian in [lambda], for IL = 1; that is,

[P.sub.e] (IL = 1|[lambda]) [varies] exp(-[([lambda] - [[lambda].sub.e]).sup.2]/[2[[sigma].sub.e].sup.2]) (2)

(We use a proportionality since [P.sub.e] (IL|[lambda]) need not integrate to unity, and its pre-factor is irrelevant in what follows.) Now we ask, what value of [lambda] is most likely to be observed? Conceptually, this can be determined by first generating a large number of universes randomly according to the distribution [P.sub.[lambda]]([lambda]), and then weighting them by the conditional probability density function [P.sub.e] (IL=1|[lambda]). The probability that an intelligent observer will measure a given value of [lambda] is then the product of these two probabilities:

[P.sub.obs]([lambda]) = [P.sub.e] (IL = 1|[lambda])[P.sub.[lambda]]([lambda]).

The value of [lambda] most likely to be observed is obtained by maximizing the above product of probabilities by differentiating the product with respect to [lambda] and setting this differential to zero. This yields the most likely observed value [[lambda].sub.obs]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Thus, [[lambda].sub.obs] is a weighted mean of the individual optimal values [[lambda].sub.0] and [[lambda].sub.e] of the two functions [P.sub.e] (IL = 1|[lambda]) and [P.sub.[lambda]]([lambda]). The relative weighting given to the values of [[lambda].sub.0] and [[lambda].sub.e] is controlled by the inverses of the variances of their respective distributions. The narrower distribution dominates the value of [[lambda].sub.obs] chosen. If life can evolve almost equally well under a very wide range of values of [lambda], and the value of [lambda] has a preferred a priori value, then [[sigma].sub.[lambda].sup.2] << [[sigma].sub.e.sup.2] and [[lambda].sub.obs] will be close to the a priori most likely value; i.e., it will not be affected much by anthropic considerations. However, if the emergence of intelligent life requires a very precisely tuned value of the physical constant, which would otherwise be free to range over a very wide range of values with nearly equal probability, then [[sigma].sub.e.sup.2] << [[sigma].sub.[lambda].sup.2] and [[lambda].sub.obs] will be close to the value [[lambda].sub.e], implying that anthropic considerations will dominate the value of [lambda] that is selected.

In some cases, we may observe a value of some property that lies far away from the value of that property that is a priori most likely. An example of this might be the value of the cosmological constant cited earlier. In this case, an anthropic argument would hold that the observed value is pushed away from the a priori most likely value by anthropic considerations. Suppose we observe a value [lambda] = [[lambda].sub.obs] that is far out on the tail of the Gaussian distribution function [P.sub.[lambda]]([lambda]). The above equations imply that it is on the opposite side of the distribution function for [P.sub.e] (IL = 1|[lambda]). The explanation for this is straightforward. Anthropic selection explains the improbability of the observed value of [lambda] by arguing that a rare value of this physical parameter is needed for life to evolve. So [lambda] is pushed away from the value that is apriorimost likely, in order to enhance the conditional probability that intelligent life emerges. Since the a posteriori probability reflects both of these probabilities, a compromise is struck whereby a lower-than-optimal likelihood for the conditional probability for life to emerge is accepted to keep the a priori probability of a given value of [lambda] from becoming too low. One can show from the above optimization that the probability density for life to emerge in a universe with [lambda] = [[lambda].sub.obs] is a factor

exp{-1/2[([[lambda].sub.0] -[[lambda].sub.e])/[[[[sigma].sub.[lambda]]([[sigma].sub.[lambda]] / [[sigma].sub.e] + [[sigma].sub.e]/[[sigma].sub.[lambda]])]].sup.2]}

times the probability density under the most favorable conditions for life (i.e., when [lambda] = [[lambda].sub.e]). This factor is much less than unity if [[sigma].sub.e] is comparable to [[sigma].sub.[lambda]] and

[absolute value of [[lambda].sub.0] -[[lambda].sub.e]] >> [[sigma].sub.[lambda]].

We can easily extend the argument to a set of several fine-tuned constants {[[lambda].sub.i]}, where i = 1, 2, ... N. If each of these has a Gaussian a priori distribution function and if the conditional probability [P.sub.e] (IL = 1|{[[lambda].sub.i]}) is a product of Gaussian functions for each [[lambda].sub.i], then optimization with respect to each [[lambda].sub.i] yields an equation similar to Eq. 3 for each value of [[lambda].sub.i]. The conditional probability [P.sub.e] (IL = 1|{[[lambda].sub.i]}) will then be a product of Gaussians [P.sub.e](IL = 1|[[lambda].sub.i,obs]).

From the foregoing, it follows that intelligent life has a relatively low probability to evolve in the most likely observed universe if even one of the finetuned variables has a distribution [P.sub.e,i] (IL = 1|[[lambda].sub.i]) whose breadth [[sigma].sub.i,e] is similar to [[sigma].sub.[lambda],i] of the corresponding distribution function [P.sub.[lambda]]([[lambda].sub.i]), and for which the difference between [[lambda].sub.0,i] and [[lambda].sub.e,i] is much greater than either [[sigma].sub.e,i] or [[sigma].sub.[lambda],i]. The reason is that, in this case, there is no single value of [[lambda].sub.i] that has both a high a priori probability and a high conditional probability. Thus, the chosen optimal value of [[lambda].sub.i] is one that compromises between the degrees of improbability of the two functions. We then must settle for a universe whose constants make intelligent life improbable in any single universe, in order to keep the observed constants of the universe from being even more improbable than they are. This suggests that if the observed constants are improbable ones, then the evolution of intelligent life might be similarly improbable.

Of course, since we have little idea what these probability functions actually are, we can draw only the conclusions that (1) anthropic reasoning entails the potential that intelligent life might be extremely improbable in a typical "observable" universe such as ours, and that (2) this probability is entangled with the probability distribution for the constants of the universe. Thus, if there is "apparent design" in the values of the physical constants, anthropic reasoning leads us to suspect that there might be "apparent design" in biology as well. This result should not be surprising. Since biology already recognizes natural selection as an explanatory principle, the introduction of a second selection principle, namely anthropic selection, means that there will be a trade-off between the two. Hence, once anthropic reasoning enters science, natural selection ceases to be the default explanation for biological complexity. Steps in the evolution from molecules to humans that might have low probabilities for occurrence by natural selection are then candidates for explanation by anthropic reasoning--i.e., they occurred because without them, we would not be here to ponder that fact. These improbable steps would appear to have happened "by design" rather than by natural selection, just as the physical constants of the universe appear to have values that were chosen "by design." Bayesian calculus is required to adjudicate the relative explanatory roles of natural selection and anthropic selection in biology.

For those who wish to banish the idea of design from science, then, anthropic reasoning is a double-edged sword. While one can always assert that any indications of design are only evidence of apparent design, the acceptance of even "apparent design" as a scientific principle is a step that has unpleasant implications for some. A hint of this can be seen in a recent writing by science writer Amanda Geffer in the New Scientist:
```   Discussing the fact that the universe appears
fine-tuned for our existence, Weinberg told
Dawkins: "If you discovered a really impressive
fine-tuning ... I think you'd really be left with
only two explanations: a benevolent designer or
a multiverse."

Weinberg went on to clarify that invoking a
benevolent designer does not count as a genuine
explanation, but I was intrigued by his either/or
scenario. Is that really our only choice? Supernatural
creator or parallel worlds? .

But to suggest that if this theory [of the multiverse]
doesn't pan out our only other option is a supernatural
one is to abandon science itself. Not only
is it an unfounded leap of logic, it suggests intelligent
design offers as valid an explanation as
a cosmological theory does, and lends credence
to creationists' mistaken claim that the multiverse
was invented to serve as science's get-out-of-God-free
card. (11)
```

For Christians, the increasing popularity of anthropic reasoning within science also raises challenges. There are reasons to believe that the universe is much larger than we can observe, and there are reasons derived from cosmology and string theory to hint that different physical constants might apply in very remote portions of our universe or in other universes. Moreover, there are no definitive scriptural or doctrinal statements that would rule out God creating a vastly larger universe or even parallel universes. Thus, it does not appear to be wise to deny even the possibility of a multiverse. Yet it seems unwarranted, and likely detrimental to the Christian worldview, to assert dogmatically that evidences of design must be taken only as evidences of apparent design and cannot be real design. To do so would be to accept an unscriptural dogma that God is obliged to create an infinity of universes with random properties, rather than just one that he chooses to make with designed properties. Thus, many Christians and other theists are likely to see evidence of "apparent design" as suggestions of at least the possibility of real design, while atheists will resist this inference and find recourse in the multiverse.

Empirical science may not be able to settle this disagreement because both viewpoints--theistic design and anthropic selection--allow infinitely many potential universes. In the former viewpoint, our universe is designed by God and the others may not be real, while in the latter, it is the other universes that must be real while the "design" of our universe is only apparent. Since neither God nor the other universes can be observed, it seems doubtful that empirical science can, by itself, decide between these views.

Can't We All Just Get Along (at Least in Science)?

Perhaps a helpful analogy to see a way forward is to consider how the concept of purpose, or teleology, is dealt with by scientists. Even atheists sometimes use language that suggests purpose, as in "the heart's purpose is to pump blood." A prickly Darwinist might insist on restating this as "the heart evolved because by pumping blood it oxygenates tissue more thoroughly, allowing organisms possessing it to survive and propagate their genes more effectively." This clumsy formulation is unneeded, even by the atheist, if he simply re-interprets "purpose" as "apparent purpose." Shorthand references to "purpose" need not offend atheistic scientists who recognize that ultimate reality must be left to metaphysics, not science, to address. If "purpose" is not a scientific concept, but "apparent purpose" can still be recognized in biological organs, then perhaps "design" is also best left as a metaphysical or theological concept, while allowing that the natural world might display "apparent design." In this way, science can construct theories that cope with empirical or "apparent" realities, while leaving questions of ultimate reality to metaphysics, where the vigorous contest for ultimate truth can continue unabated. Such a pragmatic approach already seems to be followed by nondogmatic scientists when dealing with other ontologies that some materialists consider non-existent, such as objective morality, free will, or personhood.

Such a pragmatic separation of science from metaphysics was advocated by Catholic scientist Pierre Duhem, who wrote
```   ... to make physical theories depend on metaphysics
is surely not the way to let them enjoy the
privilege of universal consent . If theoretical
physics is subordinated to metaphysics, the divisions
separating the diverse metaphysical systems
will extend into the domain of physics. A physical
theory reputed to be satisfactory by the sectarians
of one metaphysical school will be rejected by the
partisans of another school. (12)
```

The metaphysical disputes feared by Duhem are clearly on display in areas of science where evidence of "apparent design" can be found. Attempts by partisans of either camp to obtain decisive victory for their metaphysical position on design in science is likely to lead to continued warfare, not only between theistic and atheistic camps, but even within each of these camps. For all parties, then, a Duhemian approach might be a welcome avenue for maintaining unity within science, while allowing vigorous debate to continue in the arena of metaphysics.

Notes

(1) S. Weinberg, "Anthropic Bound on the Cosmological Constant," Physical Review Letters 59 (1987): 2607-10; V. Agrawal, S. M. Barr, J. F. Donoghue, and D. Seckel, "Anthropic Considerations in Multiple-Domain Theories and the Scale of Electroweak Symmetry Breaking," Physical Review Letters 80 (1998): 1822-5; R. Bousso, "Holographic Probabilities in Eternal Inflation," Physical Review Letters 97(2006): article no. 191302; A. Aguirre, S. Gratton, and M. C. Johnson, "Measures on Transitions for Cosmology from Eternal Inflation," Physical Review Letters 98 (2007): article no. 131301.

(2) A. D. Linde, "The Inflationary Universe," Reports on Progress in Physics 47 (1984): 925-86.

(3) J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986).

(4) J. Garriga, A. Linde, and A. Vilenkin, "Dark Energy Equation of State and Anthropic Selection," Physical Review D 69 (2004): article no. 063521.

(5) Ronald G. Larson, "Is Anthropic Selection Science?" Physics in Perspective 9 (2007): 58-69; J. Garriga and A. Vilenkin, "Prediction and Explanation in the Multiverse," Physical Review D 77 (2008): article no. 043526.

(6) Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, and Company, 2006).

(7) Larson, "Is Anthropic Selection Science?"; Robert B. Mann, "The Puzzle of Existence," Perspectives on Science and Christian Faith 61, no. 3 (2009): 139-50.

(8) Richard Dawkins, The Blind Watchmaker (New York: W. W. Norton and Co., 1996).

(9) William A. Dembski, The Design Inference: Eliminating Chance through Small Probabilities, Cambridge Studies in Probability, Induction and Decision Theory (Cambridge: Cambridge University Press, 1998).

(10) Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design.

(11) Amanda Gefter, "Why It's Not as Simple as God vs the Multiverse," New Scientist 2685 (04 December 2008). www.newscientist.com/article/mg20026852.500-why-itsnot-as-simple-as-god- vs-the-multiverse.html (last accessed November 11, 2010).

(12) Alvin Plantinga, "Methodological Naturalism? Part 2," Origins & Design 18, no. 2 (1997). www.arn.org/docs/odesign/ od182/methnat182.htm (last accessed November 11,2010).

Ronald Larson is G. G. Brown Professor of Chemical Engineering at the University of Michigan. He received BS, MS, and PhD degrees in chemical engineering from the University of Minnesota. After working for sixteen years at Bell Laboratories in Murray Hill, New Jersey, he moved to the University of Michigan in 1996. His research interests are in the structure and flow properties of "complex fluids," which include polymers, colloids, surfactant-containing fluids, and biological macromolecules such as DNA. He has written three books on these subjects. He is former president of the Society of Rheology, current chair of the Polymer Division of the American Physical Society (APS), Fellow of the APS, and a member of the National Academy of Engineering (NAE). He enjoys his marriage to his wife Bebe, his relationships with his four children Rachel, Emily, Andrew, and Eric, and worshiping at his church, Knox Presbyterian in Ann Arbor, MI.