Understanding the Different World Views of Christians & Atheists
Perhaps the best way to understand why Christians and atheists see and interpret “miracles” differently is by understanding the difference between how two physicists looked at reality itself and saw two very different things. Those two physicists were Albert Einstein and Niels Bohr, and while one studied the motion of planets, the other studied the motion of subatomic particles.
Looking through the lens of classical physics, Einstein saw how planets operated in the universe in an orderly manner, obeying definite deterministic laws of Newtonian mechanics. For the Christian, those laws were written and set in motion by the hand of God. Bohr, on the other hand, saw something different. He saw the world through the prism of quantum physics, where reality itself was indefinite, animated by the unruly hand of a nature that, like the Christian God murdering the whole world with a flood, seemed free to ignore the laws of nature whenever it wanted. As a result of the indeterminate nature of quantum physics, Bohr famously said “those who are not shocked when they first come across quantum theory cannot possibly have understood it.”
So who was right: Einstein or Bohr? The answer to that question came in 1972, when John Clauser performed what are today known as the Bell experiments. Based on the theoretical work of John Bell, those experiments finally demonstrated that Einstein's deterministic view of reality was, in fact, only half of the picture of the whole of reality. Those findings have not altered the way that Christians think about miracles, of course, but they should have. But that's the thing about "beliefs": their greatest virtue is also their greatest vice. And both boiled down to a simple fact: beliefs never die.
Like Einstein's belief in Newtonian mechanics, organized religion tends to deify mechanical laws of order and tradition much in the same way it glorifies a well ordered social system (but only ones in which it enjoys an elevated position of power, which it then uses to defend the system as more good than bad overall). It also demonizes ideas of chaos and change (especially if such change demotes the role of the organized religion having a say in how to order the society, as happened in Rome under the emperor Julian, which is why Christians called him an "apostate"). Like quantum mechanics, however, nature itself tends to honor such laws more in the breach than in the observance. One runs like a clock - hence the idea that God is a watchmaker who "does not play with dice"- which requires divine intervention to create something new, while the other operates through a feedback loop that can perpetually evolve into something different; with life and death acting as the revolving door between these two sides of reality. The former is as limited in its habits as a well oiled machine, while the latter has "free will" to produce anomalies.
The discovery that Einstein's mathematical worldview was inaccurate turned out to be both a blessing and a curse for the Christian concept of miracles. The blessing was that it demonstrated how the material world was not as entirely deterministic as so many Calvinists and atheists often argued it was. The curse, at least with regard to miracles, was that it demonstrated how "miracles" did not need to come from a deity operating outside of a clock-like universe, but could bubble up from within the system itself, out of the cauldron of chaos and uncertainty that underwrote reality on the quantum level. In 1952, the English mathematician who cracked the German enigma code during World War II, Alan Turing, demonstrated how this happens in an article, "The Chemical Basis of Morphogenesis." In it, Turing described how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. And he demonstrated how such patterns could form using the language of mathematics. What he proved, in short, was that there was no need for a God to give the zebra its stripes and the leopard its spots, but mother-nature. And rather than building every level of reality with the exacting precision of a German watchmaker, mother nature painted reality from atoms to the Andromeda galaxy with brush strokes that could be as arbitrary as the hand of Jackson Pollock.
From Einstein's point of view, a miracle only happens when a supernatural agent intervenes in the mechanically deterministic operations of the system it created in order to produce a different outcome from that which the system itself was designed to produce. This would be like Henry Ford altering the assembly line in one of his auto factories so that it would assemble an airplane instead of a car. In such a system, a child being spontaneously cured of cancer would be no different than that same child suddenly becoming immune to the force of gravity, since both would equally require as much supernatural intervention to override the laws governing reality as Henry Ford altering the production of one of his factories from building cars to building an airplane. From Bohr's point of view, on the other hand, as Turing helped to illustrate, a miracle is simply the result of a system that operates with infinite possibilities producing an outcome that only seems "miraculous," not because it is the opposite of how the system actually works, but because, like Einstein, we are only looking at half of the picture of reality and assuming it is the whole thing. But despite beliefs to the contrary, reality does not operate like an auto factory, nor is the human body simply an automobile for the soul. Instead, as it turns out, mother nature does indeed like playing with dice.
One of the most important aspects of Bohr's discovery with regards to what each person may define as a "miracle," is the fact that quantum physics demonstrated that nothing observed is unaffected by the observer. The enormity and power of this statement is arguably even more miraculous than anything we have labeled a miracle before, because it means that everyone sees a different truth because everyone is creating what they see. Neuroscientists have described this idea as through each of us is looking at the world through our own reality tunnel, or through a lens that is wholly unique to ourselves in the particulars of what we are able to see. And how we interpret what we see is even more unique still.
In Chinese philosophy, the two perspectives of reality offered by Einstein and Bohr, of astro and quantum physics, are reflected in the dualistic concept of the yin and the yang. Yin and yang represent how seemingly opposite or contrary forces may actually be complementary, interconnected, and interdependent in the natural world. Summing up the relationship between Einstein’s astrological yin and Bohr’s quantum yang, physicist Jim Al-Khalili explained that “the paradoxical truth of reality itself is that everything that we regard as real (which Einstein spent his life studying) is made of things that cannot themselves be regarded as real” (which Bohr discovered lurking underneath everything Einstein was studying). And for the atheist, it is in the manger that sits in the intersection between these two points where all miracles are born.
That the yin of an orderly universe emerges out of the yang of quantum mechanics not only demonstrates that the order we rely on to give us some certainty of reality is mostly a perceptual illusion, one which our senses cling to anxiously to make sense of the world we live in, but it is also what leads the atheist to conclude that anything a person defines as a "miracle" is simply the result of our inability to understand exactly how one produces the other, and why. Because we do not understand the specifics of how and why the order of our reality grows out of the soil of such quantum chaos, it is impossible to ever clearly understand the difference between "miracles" that are said to come from an "intentional agent" like a God, who is said to exist outside of the system, and which miracles come from out of the chaos that underwrites the fabric of reality itself, which our "neurological agency detector" leads us to "believe" comes from an intentional agent like a God, even if didn't. What it does do, however, is demonstrate that the chaos Christians attribute to their devil, and the order which they attribute to their God, are actually two sides of the same reality; a reality which reveals "miracles" and "anomalies" to be simply subjective qualifications that reflect only our own culturally inclined biases for approving of one, and our indifference or disapproval of other. In other words, they are distinctions that are determined not by how things are, but by how we are, and how we think, and what we “believe” to be true, even if it ain't.
When the atheist sees the world from this perspective, they see the chaos that underwrites reality, and understand that only because of that chaos is anything possible, including what we may call “miracles.” As Mel Schwartz explores using quantum physics in his book, “The Possibility Principle,” only with uncertainty is anything possible, including anything that looks like a miracle or even "free will." Yet when the Christian sees the world, they see a system of laws and order, and conclude that nothing is possible - not even free will - without the "God" who designed the system to be as orderly as a clock (even though a clock is a man-made device designed to regiment people's lives in the same way that religion was designed to regiment and thus domesticate the human mind). One claims that a much greater reality of law and order exists that is far greater than our own, a reality filled with God, angels, and divine immutable moral laws, while the other recognizes that the only "greater reality" we know for sure to exist is one built entirely upon the cornerstone of a chaos pregnant with infinite possibilities. But the real difference between how the Christian and the atheist see miracles comes from the fact that the former sees the world through a veil of sacred words, the limitations of which end up obscuring a deeper complexity, while the latter reveals that complexity through a use of numbers, which extend our ability to see the ultraviolet light of patterns that exist beyond the ken of words alone.
Fractals & the Mathematics of Miracles
If there is a flaw in being human it is that we were born to be natural believers rather than natural mathematicians. A large part of why we tend to “believe” so easily is the result of three aspects of human nature. The first is that we come with a brain that has an insatiable need for meaning, which means it is always seeking a deeper understanding of anything and everything. It is that desire that led the Adams and Eves of our species to invent myths. The second is that we have an incredible knack for recognizing patterns, which happens to be an innate ability of the most evolved part of our brains. In contrast to this, however, the third aspect of human nature is that we have a horrible ability for doing math with really large numbers, which is a learned skill that allows us to greatly extend our innate ability for pattern recognition. And because our brain is always looking for meaning, but is far more suited to art than arithmetic, we have a far greater craving for answers that are simple rather than complex. Like learning to use our critical thinking skills from the more evolved parts of our brains to overcome the irrationality of our emotions of the lesser evolved parts of our brains, so learning how to calculate and understand mathematical probabilities and statistics are skills which must be learned and exercised regularly. Doing so helps us to see how often simpler explanations may only be hiding from us the deeper meanings we crave to give us some degree of the certainty we seek. Such mental calisthenics is how the adult part of our brain learns to defend the child part of our brain against those who try to sell us snake oil by preying upon our fears and emotions.
So poor are we at these mathematical skills that we often fail to fully appreciate the statistical power of geometric progressions. Called "innumeracy," this failure leads to a number of probability-based cognitive biases, all of which make it increasingly difficult, if not impossible, for us to clearly distinguish between what is a "miracle" sent to us from a God and what is simply a statistical outlier that, given enough chances, happens far more often than we realize. Our talent for spotting patterns coupled with our desire for simple answers, and our difficulty computing large numbers, leads us to trust those who can offer us simple explanations to inexplicable events that provide us with some comfort and security in a scary world. And it is this “trust of the innocent,” as Stephen King pointed out, that serves as “the liar’s most useful tool.” And such trust is often the result of being either unable or simply too afraid to doubt the answers.
While words can be used to prey upon our emotions - like the play "The King in Yellow" by Richard Chambers in which a book (and here an atheist might suggest the Bible) could drive you insane just by reading it - numbers don’t lie. Between the two, words may make us swoon but it is numbers that allow us to see behind the veil of language that often serves as the prison house of our understanding. Between the classical and the quantum view of physics, physicist Werner Heisenberg explained how words can get in the way of actually understanding what is really going on with reality itself. Rather than dropping the anchor of a “belief” in the middle of a storm of ideas, and repeating a devotion to those "beliefs" like a prayer that the combative ideas all around us will not tear the boat in which we are hiding all to pieces, the only true comfort or security we can find in such a storm is to learn how to sail the boat of our own brain through the stormy seas that are only changing faster and faster all around us. And we can only do that by pulling up our anchor and learning how to seek true understanding, however scary it might be for us to do so. Part of doing that requires us to loosen our grip on the apron strings of words alone and, like Neo looking at his computer screen, learning to read the matrix of numbers all around us. And this is because, as Heisenberg explain:
“The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them for elementary particles. But it is important to realize that while the behavior of the smallest participles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate to a clear-cut account of what is going on.”
In much the same way quantum physics revealed classical physics to be only half the story of reality, so too, to understand how numbers can see what language alone cannot, and thus understand how numbers can reveal a deeper understating of both nature itself and the nature of miracles more specifically, we have to first consider something all around us that we only began to fully understand by looking through the lens provided by numbers: fractals. Although noticed centuries ago by Africans, Native Americans, and even Leonardo da Vinci, without realizing what they were, the discovery of the world’s first fractal in 1861 sent shockwaves through the mathematical community. So what the hell is a fractal anyway, and what does it have to do with understanding the difference between how Christians and atheists interpret miracles?
The term fractal was created by the unconventional 20th century mathematician Benoit Mandelbrot in 1975. It comes from the Latin word fractus meaning "irregular or fragmented." These irregular and fragmented shapes are all around us. They are a paradox; amazingly simple, yet infinitely complex. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple but grow in progressively more complexity. Mandelbrot himself defined a fractal as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.”
All fractals show a degree of what's called self-similarity. This means that as you look closer and closer into the details of a fractal, you can see a replica of the whole. A fern is a classic example. Look at the entire frond. See the branches coming out from the main stem? Each of those branches looks similar to the entire frond. They are self-similar to the original, just at a smaller scale. These self-similar patterns are the result of a simple equation, or mathematical statement. Fractals are created by repeating this equation through a feedback loop in a process called iteration, where the results of one iteration form the input value for the next.
The second kind of fractal is the most dizzying. It is known as the "infinite intricacy" fractal. The first example of this fractal was only found in 1872, by mathematician Karl Weierstrass, when he constructed a zig-zag that was so jagged it was comprised of nothing but zigzags. No matter how many times the shape was magnified, any glimmer of a smooth line would invariably dissolve into a never-ending cascade of corners, packed ever-more tightly together. Weierstrass’ shape had irregular details at every possible scale - the first key feature of a fractal shape. Mathematicians labelled Weierstrass’ shape as “pathological” – meaning they thought it was insane - as it stood in defiance of the tried-and-tested tools of calculus that had been so painstakingly assembled over the previous few hundred years. It remained just a tantalizing glimpse of a completely new way of looking at geometric shapes until modern computing power gave mathematicians the keys to the promised land.
Like Weierstrass’s glimpse of a new kind of shape that challenged the traditional ways of thinking about calculus and geometry, and Bohr’s glimpse of quantum mechanics that revealed how chaos underwrote the order of reality, statistician David Hand also uses the lens of mathematics to reveal a deeper understanding about miracles. While Weierstrass and Bohr were able to see a deeper truth about reality by looking more deeply into the microscopic realm of shapes and particles, Hand noticed something about miracles by looking at them on a macroscopic scale. By zooming out from looking at any one “miracle” at a time, he used computers to crunch super large numbers in a way that the human brain alone is unable to process. By doing so, he was able to see collections of miracles from a God’s-eye-view. When he did, as Hand explains in his book, “The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day," he discovered that what we call “miracles,” rather than being the rare exception to the rules of reality, are actually the rule.
Through his study of patterns in massively large data sets, Hand discovered the improbability principle. Mainly comprised of five rules, which he defined as laws, Hand defines those five laws as the Laws of Inevitability; of Truly Large Numbers; of Selection; of the Probability Lever; and of Near Enough. He goes on to offer convincing evidence for how such a principle reveals miracles to be everyday events that we interpret instead as evidence that confirms our belief that miracles are extremely rare gifts of fate or God.
Of all of the examples that Hand provides to illustrate how miracles are as common as the common cold, the simplest example of all is winning the lottery. According to Lottery USA, the odds of winning the Mega Millions jackpot are 1 in 302.6 million. Because of our craving for meaning and talent for recognizing patterns, mixed with our difficulty for processing large numbers which leads us to prefer answers that are simple rather than complex, the simplest way to respond to winning with those odds leads us to feel like, if we win, it must be a miracle. Notice also that wining triggers an emotional euphoria that leads our more irrational and emotional brain to override our more evolved critical thinking brain. More than anything else, it is the euphoric feeling that we are interpreting as evidence that we are experiencing a miracle, rather than a mathematical probability. After all, no one ever felt euphoric from learning that 2 + 2 = 4. To us, winning the lottery feels like not only a once-in-a-lifetime event, but it can also potentially change our life forever. When looked at from the perspective of those picking lottery winners, however, this “miracle” happens on average to at least 13 people every year. From the perspective of the winner, it can only feel like a miracle, but from the perspective of Lottery USA, it’s just another day at the office, because someone always has to win. Otherwise, no one would bother playing at all.
However common it may be for someone to experience the “miracle” of winning the lottery, we still think it must be a genuine “miracle” when one person wins it multiple times. Take Richard Lustig, for example, who came to prominence for winning relatively large prizes in seven state-sponsored lottery games from 1993 to 2010. That must be a miracle, right? Well, according to Hand, the Law of Truly Large Numbers establishes that, “with a large enough number of opportunities, any outrageous thing is likely to happen.” To illustrate how this law applies to Lustig, consider the chances of getting struck by lightning. The average number of lightning strikes worldwide every second is 100. That’s 8.6 million strikes per day, and 3.139 billion strikes each year, 20 million of which occur in the U.S.A. Enter Roy Cleveland Sullivan, a U.S. Park Ranger in Virginia’s Shenandoah National Park. Virginia isn't even on the top-10 list of biggest lightning hot spots. But between 1942 and 1977, Sullivan was struck by lightning the same number of times Lustig won the lottery. All seven strikes occurred in the same basic geographic location. Some might say even surviving seven lightning strikes is a miracle. But the fact that people overwhelmingly avoided Lustig as a result, leading him to eventually end his own life in 1983 at the age of 71, suggests surviving such strikes was anything but a blessing.
As it turns out, miracles are less of an exception than something almost to be expected. As Hand convincingly illustrates from what we know about statistics and probability, events that seem rare or extraordinary are seen that way not because they are in fact rare, but because they so rarely happen to any one person. The fallacy of such thinking is that it can lead us to feel special and “approved of” by a father figure if ever it happens to us. Yet we can only be chosen by such a figure when that same figure rejects everyone else. A perfect example of this is what happened to Frank Martin.
Frank Martin was the assistant basketball coach at Kansas State University. In 2006, Martin was admitted to the hospital in a deteriorating condition and eventually diagnosed with pancreatic cancer. Dubbed “The Miracle in Manhattan” by ESPN, Martin reports that, after being told he would likely die, a mysterious Asian woman (why Asian? Is she like the Bagger Vance of the far East?) entered his room and prayed with him. This, according to Martin, led to him being miraculously cured. God must be one hell of a fan of Kansas State basketball, because that same woman never bothered to visit the child wing of that same hospital to help facilitate miracles for children dying of cancer. The bigger miracle, as a result, is how many Christians choose to interpret Martin’s “cure,” which was required perhaps to override the consequences of Martin’s “free will” to live a less healthy life than he could have, as a miracle that proved the existence of the very same God that choose to ignore all of the innocent children who He choose not to protect from pedophile priests, let alone cure from cancer who were in that same hospital. The list of other people God chose also not to cure with this very same miracle includes Aretha Franklin, Steve Jobs, Luciano Pavarotti, Jack Benny, Margaret Mead, Joan Crawford, "Dizzy" Gillespie, Patrick Swayze, and countless others around the world. Nor did God choose to “cure” anyone else in the hospital that night of a terminal condition, or any other hospital for that matter, including mothers, children, infants, and even the unborn. And He didn’t because, as we all know too well, “God works in mysterious ways.” Using mathematics, however, David Hand helps to pull back the curtain on that “mystery.”
So is it really true that God is more of a miser with His miracle cures than Ebenezer Scrooge was with his money? And if so, wouldn’t worshiping such a miser be like Bob Cratchit worshiping Ebenezer Scrooge, before getting a raise in his salary? Fortunately, thanks to Hand removing the cross shaped beam from our eyes by providing us with a larger context of perception, we can see that what we define as “miracles” are actually the result of recurring patterns. And just like both the chaos of quantum mechanics could only be understood, and fractals were only discovered to exist on the microscopic level, by using mathematics as our looking glass, so Hand demonstrates how that same looking glass allows us to zoom out and see miracles from a God’s-eye-view and discover they are comprised of a trinity of human components: a penchant for pattern recognition, a craving for meaning, and a lousy aptitude for complex mathematics that disposes us to crave simple answers to life’s most complex questions. And to top it all off, engaging in all three of these components triggers an endorphin release in those areas of our brain that make us feel an agent somewhere must be looking out for us, “saving” us from a cold cruel and wholly indifferent universe.
What all of this boils down to for the atheist is that it is certainly not a belief in "miracles" that is the problem between Christians and atheists, but the different meanings that each derives from them. The Christian accepts miracles to be “signs” sent from a God who, rather than ever showing himself, prefers instead to offer only hints of his existence by selectively showing to those who “believe” He exists already “miracles” that are ambiguous enough to be highly debatable to anyone who thinks they have the moral responsibility to use their God-given powers of skepticism to question whether a miracle is truly evidence of a God that wants us to subscribe to one religion or another (even though such a God never clarifies which religion He wants us to start subscribing to), or if some people only want us to believe they are miracles from the God they happen to be selling, much to their own financial benefit. In short, the Christian thinks a miracle informs us about the existence of a higher intelligence, while the atheist knows a miracle is simply evidence of our own ignorance. And while one sees them as a license to act like God, the other sees them as a reminder that we are only human.
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