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April 8 - April 13, 2021
But Vilenkin’s reflective question suggests two basic options, neither of which support Krauss’s atheistic or materialistic viewpoint. Either the laws that he and Vilenkin invoke to explain the origin of space (and energy) are mathematical descriptions that exist only in the minds of physicists—in which case they have no power to generate anything in the natural world external to our minds, let alone the whole universe. Or the mathematical ideas and expressions, including those describing possible universes, exist independently of the human mind. In other words, quantum cosmology suggests
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Matter out of math? Mathematical concepts, expressions, and equations exist in minds. That raises a profound question for quantum cosmologists. How do the mathematical expressions that they use to describe possible universes (or the early universe) cause an actual material universe to come into existence?
The Greek philosopher Plato argued that material objects such as chairs or houses or horses exemplify immaterial “forms” or ideas in a transcendent, changeless, abstract (immaterial) realm outside our universe. Similarly, mathematical Platonism asserts that mathematical concepts or ideas exist independently of the human mind. But this view in turn suggests two possibilities: mathematical ideas exist in an abstract transcendent realm of pure ideas, as Platonic philosophy suggests about the forms, or mathematical ideas reside in and issue from a transcendent intelligent mind.
That then gives us a total of three distinct ways of thinking about the relationship between the mathematics of quantum cosmology and the material universe: (1) these mathematical expressions exist solely in the human mind and somehow produce a material universe; or (2) these equations represent pure mathematical ideas that exist independently of the human mind in a transcendent, immateria...
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Math can help us describe the universe, yet we have no experience of mathematical equations creating material reality. Material stuff can’t be conjured out of mathematical equations. In our experience math has no causal powers by itself apart from intelligent agents who use it to understand and act upon nature.
Similarly, we also have no experience of ideas, mathematical or otherwise, existing apart from minds. Indeed, even Plato, in his dialogue Timaeus, postulated an intelligent creator of sorts—a mind that gives reality to the forms and ideas that otherwise exist in a purely abstract realm.
But what about the process of quantum tunneling to which quantum cosmologists refer? Does that provide a physical mechanism, rather than just a mathematical equation, for explaining the origin of the universe? In fact, it doesn’t. Recall that quantum cosmology is based upon an analogy with ordinary quantum mechanics. The idea of quantum tunneling extends this analogy. Quantum tunneling in ordinary quantum mechanics refers to a process by which a physically bounded subatomic particle can overcome a potential energy barrier even though the particle in question,
according to classical mechanics, lacks sufficient kinetic energy to do so. In the subatomic realm of quantum mechanics, however, the wave function that allows physicists to determine the probability of finding a given subatomic particle in various places also admits the possibility of finding that particle on the other side of a potential energy barrier—a barrier that the subatomic particle could not overcome based solely on its kinetic energy (if only classical mechanics applied).
Yet, in both cases, quantum cosmologists must presuppose the existence of a universe. But that presupposes the very thing, the origin of which, they are attempting to explain. As philosopher of physics Willem Drees notes: “Hawking and Hartle interpreted their wave function of the universe as giving the probability for the universe to appear from nothing. However, this is not a correct interpretation, since the normalization presupposes a universe, not nothing.”22
To see why, consider this. In ordinary quantum mechanics, an experimental apparatus has to exist before physicists can determine the wave function that describes the probable behavior of the photon within that apparatus. It follows, from the same analogy that justifies quantum cosmology in the first place, that a universe must first exist with possible properties before quantum cosmologists can construct the universal wave function that describes those properties in superposition. Indeed, the mathematics of quantum cosmology begins by describing a universe (or universes) already presupposed to
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There is another crucial problem with the quantum cosmological models of Vilenkin and Hawking-Hartle. It is the problem I referred to at the end of the previous chapter. Their models not only presuppose a universe in the act of explaining its origin; they also smuggle information into the mathematical calculations they make as they seek to explain it. For this reason, if quantum cosmology provides a correct description of the world, it again inadvertently models the need for a transcendent intelligence.
Here’s why. Vilenkin notes that the Wheeler-DeWitt equation, like all differential equations, allows for an infinite number of solutions. To determine a unique solution—a unique universal wave function—theoretical physicists must carefully choose boundary conditions and impose them on the equation at the outset. Yet unlike the boundary conditions imposed on a vibrating string (recall the discussion in Chapter 13), no physical system yet exists that can determine the appropriate constraints on the Wheeler-DeWitt equation.
a revealing passage in his technical work, Vilenkin describes the need for boundary conditions to restrict degrees of mathematical freedom on possible solutions to the Wheeler-DeWitt equation. He remarks: “In ordinary quantum mechanics, the boundary conditions for the wave function are determined by the physical setup external to the system under consideration. In quantum cosmology, there is nothing external to the universe, and a boundary condition should be added to eq. (9) [the Wheeler-DeWitt equation].”28
This passage is revealing because it shows that physicists themselves must arbitrarily restrict the infinite degrees of mathematical freedom inherent in the Wheeler-DeWitt equation in order to solve it. Vilenkin did so by choosing specific boundary conditions to restrict the values of superspace (creating what theorists call a “mini-superspace”). He also made arbitrary assumptions about the nature of the universes that could emerge out of the singularity. In particular, his mathematical apparatus presupposed that such universes would be homogeneous, isotropic, and closed.29 Only such
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Vilenkin has explained his procedure in detail.30 His method of restricting superspace by imposing carefully chosen boundary conditions on the Wheeler-DeWitt equation does result in a more or less unique solution to the equation. The resulting universal wave function ψ does include a universe like ours as a probable observation. Consequently, quantum cosmologists regard such an outcome as an explanation of the origin of the universe, indeed, as an explanation of the universe “from nothing,” as Krauss puts it. Nevertheless, the specific universal wave function ψ that “explains” the origin of
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Solving the Wheeler-DeWitt equation allows quantum cosmologists to construct a universal wave function (ψ) that describes possible universes with different possible gravitational fields. If our universe is included in the ensemble described by a universal wave function (ψ), quantum cosmologists will regard (ψ) as a description or explanation of the origin of the physical universe. This figure shows a mathematical expression called a “path integral” that is used to solve the Wheeler-DeWitt equation and construct the universal wave function (ψ). The arrows point to variables, functions, and
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Leading critics of Hawking and Hartle’s and Vilenkin’s quantum cosmological models have noted the arbitrary nature of the constraints they impose.39 For example, Christopher Isham has noted that although quantum cosmologists do generate a wave function that includes universes such as ours, they only do so as the result of their use of restrictive mathematical approximations and their own decisions to impose many arbitrary constraints on the possible universes (in “superspace”) that they will consider.
Thus, the choice to exclude a nearly infinite number of possible mathematical solutions to the Wheeler-DeWitt equation, whether by (a) directly imposing boundary conditions on the equation, (b) limiting the possible universes under consideration when constructing the universal wave function (limiting “paths through superspace”), or (c) both, represents an enormous input of information into the mathematical equations and procedures that quantum cosmologists use to model the origin and development of the universe.
As Halliwell notes of the Hawking-Hartle model, “The wave function is therefore only fixed uniquely after one has put in some extra information fixing the contour.”42 Indeed. The source of that “extra information” is precisely what is at issue.
The Hawking-Hartle method also reminds me of Richard Dawkins’s famed computer simulation of the alleged creative power of natural selection and random mutation. The simulation, described in his book The Blind Watchmaker, allegedly generated an information-rich line from Shakespeare’s Hamlet, “Methinks it is like a weasel,” through random changes in a string of text.44 In both cases, the cosmological and the biological, the modeler had a distant goal in mind. Dawkins had a target sequence in mind; Hawking-Hartle and Vilenkin each had a target wave function in mind.
These physicists knew that getting to the target would require making selections among a vast ensemble of possibilities according to certain criteria. Dawkins provided the target sequence to his computer and programmed it with selection criteria that would ensure that it converged on the sequence he wanted.
Hawking and Hartle understood the kind of wave function that would have physical and cosmological relevance and then chose possible universes for inclusion in their summing procedure in accord with selection criteria that would ensure that kind of wave function. Similarly, Vilenkin knew the boundary conditions he would need to choose, and the assumptions about allowable universes he would need to make, to ensure the construction of a relevant wave function. Both the selection criteria in Dawkins’s biological simulation and the physical selection criteria ...
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A Cosmic Observer? The traditional Copenhagen interpretation of the collapse of the wave function—when applied to the universal wave function in quantum cosmology—would seem to require a transcendent “Cosmic Observer” to cause the collapse and, thus, the emergence of a specific universe among the various possible universes described by the universal wave function.
As Tegmark explains: Physics is all about predicting the future from the past, but inflation [one of many infinite-universe cosmologies] seems to sabotage this. When we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts there will be infinitely many copies of you, far away in our infinite space, obtaining each physically possible outcome; and despite years of teeth-grinding in the cosmology community, no consensus has emerged on
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Thus, infinite-universe cosmologies, including Tegmark’s, have an unexpected liability: once they are permitted as a possible explanation for anything, they undermine confidence in practical and scientific reasoning about everything.
Throughout this book, I have argued that the scientific evidence we have concerning biological and cosmological origins leads logically to the knowledge of God. Now we see that the attempt to deny the explanatory power of the God hypothesis eventually and necessarily requires positing infinite probabilistic resources and universes—a postulation that denies the possibility of knowledge. Indeed, these resulting cosmologies illustrate a maxim of St. Augustine: Crede ut intelligas, that is, “Believe in order to understand.” I have argued that we can reasonably believe in the reality of God because
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The absurd implications of infinite-universe cosmologies now raise the possibility that we might well need such belief to have confidence in scientific rationality—and thus our ability to know nature at all.
In the epilogue to a later edition of that book called “The General Scholium” and in other scientific works, notably the Opticks, Newton articulated a profoundly theological perspective. Not only did he extol the order and uniformity of nature as a reflection of God’s character and superintending care of creation; he argued for the existence of God based on the design evident in nature—in short, for a God hypothesis.
The God-of-the-Gaps Objection A common objection to Newton’s view of the relationship between science and theistic belief is known as the God-of-the-gaps objection (hereafter, the GOTG objection). According to those who pose this objection, the GOTG fallacy occurs whenever someone invokes the activity of a creative intelligence or God to explain phenomena or events in the natural world.
To depict proponents of the theory of intelligent design as committing the GOTG fallacy, critics must misrepresent the case for it. For example, as Michael Shermer claims, “Intelligent design . . . argues that life is too specifically complex (complex structures like DNA) . . . to have evolved by natural forces. Therefore, life must have been created by . . . an intelligent designer.”14 In short, he claims that proponents of intelligent design argue as follows: Premise: Material causes cannot produce or explain specified information. Conclusion: Therefore, an intelligent cause produced the
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In fact, the case for the intelligent design of life, presented in Chapters 9 and 10 and in my previous books, doesn’t rely on such logic. Instead, the argument takes the following significantly different form: Premise One: Despite a thorough search, no materialistic causes have been discovered with the power to produce large amounts of specified information necessary to produce the first cell. Premise Two: Intelligent causes have demonstrated the power to produce large amounts of specified information. Conclusion: Intelligent design constitutes the best, most causally adequate explanation for
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Some critics of intelligent design portray the case for intelligent design as a fallacious argument from ignorance. They claim proponents of the argument affirm intelligent design only because of the implausibility of various naturalistic processes (NP) as causal explanations for the origin of the specified information, the key effect (E) that needs to be explained in living systems. Nevertheless, the specified information of DNA implicates a prior intelligent cause, not only because various naturalistic or materialistic origin-of-life scenarios fail to explain it, but also because we know
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also showed that quantum cosmology—advanced by scientific materialists as an alternative to the God hypothesis—failed to provide a causally adequate materialistic explanation for the origin of the universe (and even that it has unintended theistic implications).
In addition, I argued that all materialistic theories of the origin of the material universe face a fundamental problem given the evidence we have of a cosmic beginning. Before matter and energy exist, they cannot cause, or be invoked to explain, the origin of the material universe.
Stephen Hawking’s claim that the “laws of science” or “the law of gravity” can explain “why there is something rather than nothing” betrayed a deep philosophical confusion about what the laws of physics can do. Laws of nature describe how nature operates and how different parts of nature interact with one another; they don’t cause the natural world to come into existence in the first place.
This suggests the futility of waiting for the discovery of some new law of nature or a “theory of everything.” No law of nature can close the causal discontinuity between nothing and the origin of nature itself.
that we routinely associate with the activity of intelligent agents. Based upon our uniform and repeated experience, we have often observed intelligent agents producing highly improbable systems or events that exemplify a set of functional requirements, such as finely tuned Swiss watches, digital computers, engines, recipes, and coded messages. Consequently, we have empirical evidence of the sufficiency of intelligent agency or design as the cause of finely tuned systems. Moreover, since that fine tuning of the universe originated at the beginning of the universe itself, this class of evidence
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First, Newton did indeed believe that God sustains the orderly concourse of nature in what we call the laws of nature. Thus, he stated in the General Scholium of the Principia: “In him [God] are all things contained and moved.”24 Second, Newton also believed that God could act, and had acted, in more discrete and special ways at specific times in the past history of the universe and of life. He argued that both living organisms and the solar system exhibited evidence of special creative acts distinct from the constant exercise of the divine power that, he thought, maintains the laws of nature.
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Newton made similar design arguments in a later book, the Opticks, based upon the qualities of light and the exquisite functional integration of the many parts of the eye.26 Thus, in his work Newton affirmed what theologians since the Middle Ages had conceived of as two complementary but distinct powers of God: (1) the potentia ordinata, God’s ordinary power, by which God sustains the order of nature, and (2) the potentia absoluta, the absolute or fiat power of God, by which God accomplishes special acts of creation or design or initiates events in human history at discrete times for special
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Further, he calculated that the solar system will remain stable for an “immense tract of time.”31 Newton’s analysis implies that the solar system does not require any singular divine “intervention” to compensate for perturbations. In other words, the often repeated story of Newton’s God-of-the-gaps blunder is completely false.32 Given the number of times that I’d heard the story about Newton periodically invoking divine intervention to fix the solar system, I was stunned upon reading and rereading these most relevant sections of the Principia.33 Yet those who are interested can read these
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Hawking affirmed that he thought science could help answer this question, and he reiterated a claim that he had made in his book The Grand Design. There he had said, “Because there is a law such as gravity, the universe can and will create itself from nothing. . . . Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist.”2
Oddly, the latter part of this statement represents what logicians call a tautology—a vacuous statement that simply states the same thing twice in two different ways. “Spontaneous creation” is not “the reason there is something rather than nothing.” The phrase “spontaneous creation” simply refers to something coming into existence from nothing. By invoking “spontaneous creation,” Hawking did not identify a cause of the universe, still less a materialistic one.3 Nevertheless, in The Grand Design he asserted that spontaneous creation made it unnecessary “to invoke God to . . . set the universe
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Unless those equations exist in the mind of God and reflect his way of actively ordering the universe, a possibility that Hawking rejected, they have no objective existence in the universe independent of our minds. Indeed, unless the laws express God’s ideas and action, they are not “things” or entities in nature that exist independently of the universe and certainly not things that can cause events in the world; still less would they cause the origin of the universe itself.
Saying they do is like saying that the longitude and latitude lines on the map explain how the Hawaiian Islands popped up in the middle of the Pacific Ocean.
Krebbs argued that though the reliability of the human mind—and the assumptions it makes about the world—could not be justified empirically, it could be justified theologically. If one presupposed the existence of a benevolent God, one had good reason to trust in the design of the mind and the reliability of its built-in assumptions about the world. Theists assume the uniformity of nature, because they believe that God is a God of order who sustains the regularities that we describe as the laws of nature.
Richard Dawkins has also acknowledged, if unintentionally, that survival value and true belief do not necessarily correlate given a naturalistic evolutionary account of our belief-forming faculties. For example, based on studies of the beneficial health effects of religion, Dawkins concedes that it’s “perfectly plausible” that religious belief “could indeed have highly beneficial effects upon health.”27 Yet he also argues that belief in God is false and delusional. Thus, he tacitly concedes that natural selection can preserve grotesquely false (from his point of view) beliefs.28 Dawkins’s
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If naturalism accurately depicts reality, then human beings have overwhelmingly failed to perceive this fact. Though theistic belief has declined in the increasingly secular West, especially among college-educated millennials, a recent Pew Research study shows that 84 percent of the world’s population identifies with religious systems of belief, most of which contradict strict naturalism and many of which affirm some form of theism. Moreover, multiple studies across many populations indicate that human beings are hardwired for religious belief.29 Acceptance of the supernatural appears to be
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The French philosopher Voltaire once said, “If God did not exist, it would be necessary to invent him.”43 If by that he meant that we need the concept of God to build a coherent, internally consistent worldview, then in my college years I reluctantly came to that same conclusion. I realized that presupposing the existence of God did indeed “solve a lot of philosophical problems.” Yet if Voltaire instead meant that we need to invent the concept of God to cope emotionally—to use religion as an opiate—then I would agree with Professor Krauss. It would be better to face that reality honestly than
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Nevertheless, this book has better news: neither of the widely offered responses to the death of God—angst or Sisyphean resistance—is in fact necessary. Not only does theism solve a lot of philosophical problems, but empirical evidence from the natural world points powerfully to the reality of a great mind behind the universe. Our beautiful, expanding, and finely tuned universe and the exquisite, integrated, and informational complexity of living organisms bear witness to the reality of a transcendent intelligence—a personal God.