Understanding Miracles: An Athiest Perspective Part III - Merging Worldviews with Math

 

A new scientific truth does not triumph by convincing its opponents and making them see the light. but rather because its opponents eventually die and a new generation grows up that is familiar with it. 

Max Planck

 

 

 A large part of why we tend to “believe” so easily in things that we later stop believing in 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. In a sense, rather than our brain being a glorified calculator, it is more of a meaning generating machine. And that desire for ever more meaning that led the Adams and Eves of our species to seek knowledge and, in the process, explain the mysteries they encountered with stories and 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 fact, the reason all myths tend to follow the same trajectory of the "hero's journey" - what Joseph Campbell called "the monomyth"- is because those stories reflect the circular nature of the seasons of life overall. And that repeating cycle, as we will see, is reflected in the nature of crystals and fractals and virtually everything else. Indeed, even humans see themselves as merely miniature less perfect replicas of an infinite God.

 In contrast to this, however, the third aspect of human nature is that we are not mere computers or AI machines, who think in binary codes of 1s and 0s. As a result of being human and not a machine, we have a horrible ability for doing math with really large numbers. Instead, rather than being something innate to us, doing math is a learned skill that allows us to greatly extend our innate ability for pattern recognition. And thanks to computers, that skill has shed new light on understanding what miracles really are. Ironically, if we'd been born with brains that operated more like quantum computers, no one would believe miracles were anything but the most natural property of the universe we inhabit. 

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 that can only be glimpsed through the lens of mathematics.

So poor are we at these mathematical skills, however, 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" from God and what is a miracle of chance; between the intercession of a supernatural agent and simply a statistical outlier that, given enough chances, happens far more often than we realize or imagine.

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. The problem is that those who can make you believe absurdities, as Voltaire explained, can make you commit atrocities. And thus the question is simply this: is a "belief" that miracles come from our own brand of God, and from nowhere else, rational or absurd?

While words can be used to prey upon our emotions and convince us of absurdities - 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 can help us better see the difference between what is true and what merely feels like it is true. Between the two, words may make us swoon but it is numbers that allow us to see behind the veil of language that often masks a deeper more objective truth. 

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. Like Neo looking at his computer screen, to understand miracles we must first understand what our brains our really good at, like pattern recognition, and what our brains are really bad at, like dealing with super large numbers.   Holy scriptures may tell us a story about reality, but it is mathematics, from physics to economics to rocket science, that tells us what we really do and don’t know.  As Heisenberg explained:

 

“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 glosses over, 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 shock waves 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. This repeating pattern was named a Mandelbrot Set, and has been called "God's thumbprint." The thumbprint is a good point of comparison, for while every thumbprint looks different, every thumbprint also looks like a thumbprint. While such fractals never repeat themselves, nor do they ever (in any meaningful sense of the word) change.

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 labeled 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. Like mathematical models of an earth centered universe in which all the planets moved in circles (because circles were considered to reflect mathematical perfection and therefore the nature of God), the zig-zag fractal shape conflicted with how most mathematicians thought the world operated. It remained just a tantalizing glimpse of a completely new way of looking at geometric shapes until modern computing power gave mathematicians the ability to show what non-mathematicians could not see.

And this is where we begin to pull back the curtain on why some people see miracles as being the result of God and others see them being the result of chance. The former see the universe as being only capable of producing a single outcome, like a machine that makes either fish or humans, but could never end up making the latter if it had been designed by a intelligent designer to make the former. The universe itself, from this perspective, is a machine that has no free will.

 But as Turing, Bohr, and Weierstrass have shown again and again, this is not how reality actually works, it's just how some people like to believe it works, the same way it was thought that everything moved in perfect circles around the earth. Instead, what numbers revealed was that while these fractal patterns had self similarity, they were not identical copies. Like the butterfly effect, the tiniest of differences in those patterns could, given enough iterations, eventually produce something different, and new, from what a well oiled machined would be expected to produce. Because of these small variations, the machine we call the universe only looked like it was designed to make either fish or humans, but was capable of making both, and anything else, all from the very same atomic building blocks.

This resulted in "the improbability principle," which explained why miracles actually happen all the time, we just couldn't see them anymore than we could see fractals or elliptical orbits, until we developed tools to extend our ability to crunch super large numbers. Doing so allowed us to find the patterns that chance alone can produce, but which we so seldom notice that whenever we do, we think - since we assume the universe is a machine that operates with the rigidity of a watch - they must come from a watchmaker we call God, that has decided to make something different happen. 

In part IV, we will see how this principle unmasks miracles to be as common as the common cold, thanks to the every dice-rolling hand of chance.