This article first appeared in the Christian Research Journal, volume 41, number 1 (2018). For more information about the Christian Research Journal, click here.
I must have been only six or seven years old when my parents first subscribed to the local cable service and I discovered the phenomenon known as the Disney Channel. In the early 1980s, the programming consisted of everything we now know as classic Disney, including a rotating assortment of animated shorts and films featuring the iconic animal characters. One that was shown periodically was the 1959 production entitled Donald in Mathmagic Land, which introduced me to the idea that nature and mathematics are somehow intertwined. I was mesmerized by the visual demonstrations of the fact that the natural world exhibits shapes, symmetries, patterns, and proportions that are thoroughly mathematical.
While watching Donald in Mathmagic Land again not long ago, I was delighted to realize that the film draws subtle philosophical connections between the mathematical qualities of nature, the usefulness of mathematics in the sciences, and the mind of a transcendent Maker. After showing fascinating examples of how mathematics pervades the world in nature as well as in human creativity, the narrator says, “Mathematical thinking has opened the doors to the exciting adventures of science,” and then the film ends with Galileo’s famous statement about mathematics being the language in which God has written the universe. The film’s inference, deliberate or not, is that the mathematical qualities of the physical world allow mankind to carry out scientific activity, and this arrangement is evidence of a rational Creator in whose image we are made.
The notion that there is a mysterious resonance between the structure of the material world, the abstract world of mathematics, and the human mind — what I call Cosmic Resonance — not only has major implications for the contemporary debate between materialism and theism but also is rooted in some of the earliest thought of the Western tradition. A few historical snapshots will be helpful in demonstrating the rich intellectual pedigree of Cosmic Resonance and how well this great idea endured, and indeed flourished, through periods of major scientific advancement. As we shall see, this effectively dispels the myth that progress in the sciences has been driven by materialism and has undercut the case for design.
SNAPSHOT #1: PYTHAGOREAN–PLATONIC THOUGHT
Followers of the ancient Greek philosopher and mathematician Pythagoras of Samos (c. 570–495 BC), the very thinker traditionally credited with coining the term “philosophy” (philo = love, sophia = wisdom), believed that the world of numbers is a sort of divinity that underlies all of physical reality, a pervasive “world soul” of which human souls are fragments.1 In other words, nature was regarded as the manifestation of number. The Pythagoreans saw the orderliness of the world as something deep and all encompassing, with mystical interconnections between number, mind, and the material world.
Pythagoreanism influenced later Greek philosophy, particularly through the work of Plato (c. 429–347 BC). Plato agreed that number is related to the organization of the visible cosmos, but, for him, this was not the result of number being the essence of material existence. Rather, he taught that the physical world is composed of imperfect copies of immaterial, transcendent “Forms.” This idea is artfully illustrated in Plato’s Timaeus dialogue, which includes an elaborate, poetic account of the creation of the cosmos.
Timaeus, a Pythagorean character, maintains that the beauty, regularities, and intelligibility of nature are explained by a benevolent Craftsman who brought order out of formlessness and purposively framed the universe according to the eternal, mathematical Forms. Thus, the world was “crafted in reference to that which is grasped by reason,” meaning the abstract perfections the human mind can attain when reasoning from what is actually visible to us.2 For example, when we encounter a spherical object, we can reason to the idea of a perfect sphere, which only exists in the abstract realm of Forms.
Timaeus goes on to explain that “God invented and gave us sight to the end that we might behold the courses of intelligence in the heaven, and apply them to the courses of our own intelligence which are akin to them.”3 Notice the connection he sees between the rationality of the world and the human mind — a resonance that allows us to perceive and comprehend the patterns of nature. Plato believed that there are characteristics of the natural world that draw the human mind upward to a higher reality, that the divine creative intelligence is reflected in both the material world and the human intellect.
A few centuries later, aspects of Platonism became integrated with Jewish and Christian thinking about God, the order and regularities of nature, and man’s ability to detect it. However, rather than embracing the idea of an abstract realm of Forms, theologians believed that mathematical truths existed in the mind of God, who created the cosmos according to a preconceived plan, much like a building that is constructed based upon an architect’s blueprints. The ancient Greek idea of logos — the rationality of the world — was seen as a foreshadowing of the Logos in the apostle John’s writings — Jesus Christ, the eternal Word through whom all things were made (John 1:1–3).4 Thus, pagan philosophical thought bequeathed a useful tool to Christianity — a way to communicate certain aspects of the doctrine of creation effectively.
SNAPSHOT #2: JOHANNES KEPLER AND THE SCIENTIFIC REVOLUTION
In the sixteenth and seventeenth centuries, the intellectual advancements made by the giants of the Scientific Revolution offered a whole new level of validation to the idea of a mathematically structured cosmos that is accessible to the human mind. One excellent example is Johannes Kepler (1571–1630), a German mathematician and astronomer whose laws of planetary motion (published in his 1609 New Astronomy and his 1618 Harmonies of the World) helped to transform the field of astronomy into a sophisticated theoretical science. Using sophisticated mathematics, Kepler discovered that by representing the planetary orbits as ellipses rather than perfect circles, the reams of observational data recorded by astronomers could mathematically be represented more simply and with greatly improved predictive accuracy.
Both a brilliant natural philosopher and a devout Christian of the Lutheran tradition, Kepler was thoroughly convinced that God had intentionally ordered the universe in a way that could be comprehended by the human intellect. This is particularly evident in his private correspondence with fellow scholars and other associates. In a letter to the Baron von Herberstein dated May 15, 1596, Kepler declared that “God, like a human architect, approached the founding of the world according to order and rule and measured everything in such a manner, that one might think not art took nature for an example but God Himself, in the course of His creation took the art of man as an example.”5 There are two particularly notable things about this statement; first, the conviction that God created the cosmos according to a mathematical plan and second, that the mind of God and the mind of man must be somehow analogous. He states this idea more plainly in what are perhaps his most famous words: “To God there are, in the whole material world, material laws, figures and relations of special excellency and of the most appropriate order….Those laws are within the grasp of the human mind; God wanted us to recognize them by creating us after his own image so that we could share in his own thoughts.”6
Kepler’s unapologetically Christian philosophy of nature — that it is rationally structured in a manner compatible with the mind of man, a creature made in God’s image — harmonized exceptionally well with both early Christian teaching on God’s natural revelation (the idea that God is clearly seen through what He has made) and with some aspects of Pythagorean–Platonic thought. Kepler actually considered his life’s work — unlocking the mysteries of planetary motion — as an act of Christian worship. He said, “I had the intention of becoming a theologian…but now see how God is, by my endeavors, also glorified in astronomy.”7 By investigating God’s natural revelation, the natural philosopher (what we now call the scientist), who is made in God’s image, illuminates some of the divine wisdom made manifest in creation. Kepler said, “The chief aim of all investigations of the external world should be to discover the rational order which has been imposed on it by God, and which he revealed to us in the language of mathematics.”8
SNAPSHOT #3: EINSTEIN AND THE TWENTIETH-CENTURY PHYSICS EXPLOSION
Arguably the most important theoretical physicist of the twentieth century, Albert Einstein (1879–1955) is best known for his theories of special and general relativity, which transformed the scientific understanding of space, time, and gravity. His name has become practically synonymous with “genius,” and most everyone recognizes his famous equation, E=mc2. In 1905, he proposed his theory of special relativity, which revealed the very weird fact that time slows down at a rate relative to an object’s acceleration through space, and would (theoretically) stop altogether if the object reached light speed.9 Then, after another decade of painstaking and frustrating labor over the mathematical equations, he published another groundbreaking paper, “The Foundation of the General Theory of Relativity.” These equations (once empirically confirmed) overthrew the Newtonian conception of gravity by showing that the curvature of space-time around objects — rather than a pulling force exerted by massive objects — is responsible for gravitation. Some of Einstein’s work served as a foundation for the emerging field of quantum mechanics (QM), but, the theory of QM conflicted with the theory of general relativity. Einstein was convinced that nature is a coherent whole, and his ultimate goal was to discover a theory that unified the equations of both theories (a goal that remains the Holy Grail of theoretical physics).
Einstein recognized that the materialist view of nature is inadequate for explaining why we live in a universe that is fundamentally mathematical and comprehensible to the human scientist. Though he was not a theist in the traditional sense, leaning more toward some sort of pantheism, the fact remains that he saw marks of intelligence in the natural order and sensed that there was something more to the world than matter in motion. Einstein perceived a kind of inscrutable divinity in the mathematical organization of the universe and found it remarkable that human beings have the capacity to comprehend even a small part of it; he said, “We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws. Our limited minds grasp the mysterious force that moves the constellations.”10 Einstein admitted to having “a humble admiration of the infinitely superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble minds.”11 In several of his writings, he spoke of his “rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all systematic thinking and acting of human beings is an utterly insignificant reflection.”12
Einstein more explicitly mentions the themes of a rationally structured universe and its correspondence with the human mind in a series a letters to Romanian philosopher and mathematician Maurice Solovine, in which he says, “I have never found a better expression than ‘religious’ for this trust in the rational nature of reality and of its peculiar accessibility to the human mind.”13 He was careful to distinguish between the idea of the human mind imposing order on the cosmos and discovering order within it:
Well, a priori one should expect a chaotic world which cannot be grasped by the mind in any way. One could (yes one should) expect the world to be subjected to law only to the extent that we order it through our intelligence. Ordering of this kind would be like the alphabetical ordering of the words of a language. By contrast, the kind of order created by Newton’s theory of gravitation, for instance, is wholly different. Even if the axioms of the theory are proposed by man, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the “miracle” which is being constantly reinforced as our knowledge expands.14
Einstein rightly emphasizes that there is no reason to expect the universe to be arranged in a way that the human mind can grasp. Moreover, he insists that even if human scientists devised the mathematical starting point from which to investigate, an amazing degree of orderliness must be inherent to the universe for this type of mathematical research even to be possible.
THE CONTEMPORARY RESPONSE TO COSMIC RESONANCE
If mathematics did not map onto the material world with such incredible precision and the human intellect was not so well suited for highly complex mathematical reasoning, the scientific advancements of the past several centuries would have been impossible. A rationally ordered universe and intelligent life that can comprehend it well enough to unlock its deeper mysteries are two necessary preconditions of science, yet it seems quite strange to expect this state of affairs if, at the fundamental level, reality is nothing more than matter in motion. Significantly, nonreligious scientists and philosophers acknowledge this and have postulated alternative explanations that attempt to circumvent the need for a mindful Creator.
Cosmologist Max Tegmark of MIT is convinced that some version of Platonism — a real domain of abstract mathematical objects — is somehow “out there” and informing the structure of the material world. Tegmark’s explanation is quite radical; he claims that the reason mathematics applies so well to the natural world and why we can discern and make sense of these patterns is that the cosmos (human minds included) is the colossal material manifestation of a mathematical entity. He says we are “self-aware parts of a giant mathematical object.”15 In his view, mathematics is the essence of all reality, much like the ancient Pythagoreans taught. According to Tegmark, we are parts of the physical actualization of an elaborate scheme that has only mathematical properties. He believes that this is precisely why the natural world exhibits rationality and why it is intellectually transparent to human beings.
British physicist Paul Davies, who seems to ascribe to a pantheistic flavor of agnosticism, is, like Tegmark, convinced that the mathematical structure of nature is discovered, not a fiction imposed upon nature by the human mind. Though most scientists take it for granted that natural laws are mathematical, the fact that mathematics applies “stunningly well” to the physical world, says Davies, “demands explanation, for it is not clear we have any absolute right to expect that the world should be well described by mathematics.”16 “Why,” he asks, “should the mathematical approach prove so fruitful if it does not uncover some real property of nature?”17
Davies refers to the secrets of the physical world as having been written in interconnected code that must be deciphered, much like a highly complex crossword puzzle. “What is remarkable,” he says, “is that human beings are actually able to carry out this code-breaking operation, that the human mind has the necessary intellectual equipment for us to ‘unlock the secrets of nature.’”18 What makes this so surprising is that the human mind is, allegedly, the product of unguided biological evolution, a process based upon survival and reproduction, not the higher cognitive abilities required to practice science. Davies says,
One of the oddities of human intelligence is that its level of advancement seems like a case of overkill. While a modicum of intelligence does have a good survival value, it is far from clear how such qualities as the ability to do advanced mathematics…ever evolved by natural selection. These higher intellectual functions are a world away from survival “in the jungle.” Many of them were manifested explicitly only recently, long after man had become the dominant mammal and had secured a stable ecological niche.19
Davies admits that “there is no logical reason why nature should have a mathematical subtext in the first place, and even if it does, there is no obvious reason why humans should be capable of comprehending it.”20 He speculates about some as-yet-to-be-discovered, or undiscoverable, principle inherent to nature that has allowed it to blindly engineer mental awareness and rationality: “Mindless, blundering atoms have conspired to make not just life, not just mind, but understanding. The evolving cosmos has spawned beings who are able not merely to watch the show, but to unravel the plot.”21 Davies considers currently available naturalistic explanations, as well as theistic ones, “either ridiculous or hopelessly inadequate.”22
In his controversial book, Mind and Cosmos: Why the Neo-Darwinian Conception of Nature Is Almost Certainly False, atheist philosopher Thomas Nagel similarly argues that the deeper truths of cosmic reality cannot be explained by mindless physical processes. “The intelligibility of the world is no accident,” he says; “Mind, in this view, is doubly related to the natural order. Nature is such as to give rise to conscious beings with minds; and it is such as to be comprehensible to such beings.”23 Human beings are the product “of the lengthy process of the universe gradually waking up and becoming aware of itself.”24 Rather than espousing a theistic explanation for what we observe, Nagel, like Davies, is convinced that there is some unknown principle at work, a predisposition of the natural order to produce creatures with higher mental faculties that enable them to access mathematical truths and effectively apply them to the material world.
According to Nagel, the currently popular Darwinian approach never will be able to explain this principle of “natural design,” and thus needs to be revamped. He insists that we need “a much more radical departure from the familiar forms of naturalistic explanation” — if such a thing is even within the reach of human rationality.25 It is worth mentioning that in his earlier philosophical work, The Last Word, where he explored some of these same ideas, Nagel admits that his rejection of theistic explanations of the world are entirely philosophical: “I don’t want there to be a God; I don’t want the universe to be like that.”26 But interestingly, he concedes that his idea of a developmental principle in nature that has led to rational minds is compatible with the idea of a divine Creator.
Tegmark, Davies, and Nagel all recognize that strict materialism is insufficient for explaining the connections that exist between mathematics, the material world, and the human mind. However, the solutions they suggest are far from convincing. In Tegmark’s view, the ultimate explanation of the universe and our aptitude for its language is because all things are, as the Pythagoreans believed, essentially mathematical. The problem with this theory is that it leaves us without an explanation for (1) the existence of the alleged realm of mathematical structures and (2) how such abstract entities could give rise to physical phenomena.
Davies and Nagel’s idea that the cosmos is somehow inherently mindful and that it operates on some sort of mysterious, impersonal teleological principle raises more questions than it answers. For instance: Why is there such a principle in the first place? How would the same principle that causes the inorganic world to have mathematical order also operate through the evolutionary process that allegedly led to human consciousness and rationality?
Ultimately, these sorts of explanations seem to be ad hoc attempts to avoid theism. By contrast, Christianity has no difficulty explaining Cosmic Resonance: how beautifully the abstract truths of mathematics apply to physical reality and mankind’s corresponding intellectual capacities. If the cosmos is the creation of a rational Mind in whose image we are intentionally made, a Maker who desires our awareness of Him, this deep interconnection makes perfect sense. As Oxford mathematician John Lennox has said, it is “not surprising when the mathematical theories spun by human minds created in the image of God’s Mind find ready application in a universe whose architect was that same creative Mind.”27 Lennox echoes the theoretical physicist turned Anglican priest, John Polkinghorne, who said,
The widespread success of science is too significant an issue to be treated as if it were a happy accident that we are free to enjoy without enquiring more deeply into why this is the case….I believe that a full understanding of this remarkable human capacity for scientific discovery ultimately requires the insight that our power in this respect is the gift of the universe’s Creator who, in that ancient and powerful phrase, has made humanity in the image of God (Genesis 1:26–27).28
For the materialist, the exquisite three-part harmony of mathematics, the human mind, and the material world is an enigma that the sciences do not have, and will never have, the tools to illuminate. However, if all things seen and unseen have the same rational source — the mind of a Maker — the mystery of Cosmic Resonance dissolves.
Melissa Cain Travis is an assistant professor of apologetics at Houston Baptist University and a PhD candidate at Faulkner University. She is the author of Science and the Mind of the Maker: What the Conversation between Faith and Science Reveals about God (Harvest House, 2018).
- Cicero, The Nature of the Gods (New York: Oxford University Press, 2008), 13.
- Plato, Timaeus (Indianapolis: Focus, 2016), 14.
- Plato, Timaeus, Great Books of the Western World, vol. 6, 2nd ed. (Chicago: Encyclopaedia Britannica, 1990), 455.
- See William Lane Craig’s treatment of this topic in “God and the Platonic Host,” in S. Lewis at Poet’s Corner (Eugene, OR: Wipf and Stock, 2016), 204.
- Carola Baumgardt, Johannes Kepler: Life and Letters (New York: Philosophical Library, 1951), 33–34.
- Baumgardt, Johannes Kepler,
- Morris Kline, Mathematics: The Loss of Certainty (New York: Oxford University Press, 1980), 31.
- Quoted in Kline, Mathematics, 31.
- Brian Greene, The Elegant Universe (New York: W. W. Norton and Company, 2003), 50.
- Max Jammer, Einstein and Religion (Princeton: Princeton University Press, 2002), 48.
- Jammer, 93.
- Albert Einstein, The World as I See It (New York: Kensington, 2006), 31.
- Albert Einstein, Letters to Maurice Solovine (Paris: Gauthier-Vilars, 1956), 102–103.
- Albert Einstein, in a letter to Maurice Solovine dated March 30, 1952.
- Max Tegmark, Our Mathematical Universe (New York: Vintage Books, 2015), 271.
- Paul Davies, The Mind of God (New York: Touchstone, 1992), 150.
- Davies, The Mind of God, 151.
- Davies, The Mind of God, 148.
- Paul Davies, Are We Alone? (New York: Orion Productions, 1995), 85.
- Paul Davies, The Goldilocks Enigma (Boston: Houghton Mifflin, 2008), Kindle loc. 218.
- Davies, The Goldilocks Enigma, Kindle loc. 218.
- Davies, The Goldilocks Enigma, Kindle loc. 4780.
- Thomas Nagel, Mind and Cosmos (New York: Oxford University Press, 2012), 17.
- Nagel, Mind and Cosmos, 82.
- Nagel, Mind and Cosmos, 121.
- Thomas Nagel, The Last Word (New York: Oxford University Press, 1997), 130.
- John Lennox, God’s Undertaker: Has Science Buried God? (Oxford: Lion Books, 2009), 62.
- John Polkinghorne, Quantum Physics and Theology: An Unexpected Kinship (London: Creative Print and Design Group, 2007), 8.