The Mathematics of the Cosmos: Exploring Order and Chaos
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Chapter 1: The Cosmic Dance
If you were to gaze at the night sky regularly for a year, you would begin to observe some peculiar patterns.
In the stillness of the early morning, when sleep evades us and the night’s sounds spark our imaginations, numbers can feel enchanting. This isn't about formal mathematics just yet; rather, it’s about the tangible experience of counting. We counted sheep, fingers, and toes in preparation for the limitless, countless stars that shimmered above in the dark expanse. I recall feeling small, yet with the grass beneath me and the warm earth supporting me, I never felt lost. My understanding of the world felt solid, a belief shared by many throughout history. Aristotle asserted in 355 B.C.E. that "in the whole range of time past, as far as our records go, no change appears to have taken place in the cosmos." His view was that the universe existed eternally, not created, but always present—a persistent "I HAVE BEEN" rather than the transcendent "I AM." However, during the Medieval and Renaissance periods, Christian astronomers would adapt Aristotelian thought to construct intricate mathematical frameworks to comprehend the universe, which they viewed as a divinely orchestrated machine. This clockwork universe suggested that an intelligent creator was at work, and they became unlikely proponents of a "new philosophy," seeking harmony in numbers and a divine presence within the mechanism.
Paul Virilio, the French theorist known for his analyses of technological failures, reminds us that every advancement in technology also brings about its own destruction. He provocatively questions, "What did they invent with the railroad? An object enabling rapid movement, promoting progress—an idea reminiscent of Jules Verne—yet simultaneously, it birthed the railway disaster." Taking this perspective as a foundation, I penned a book titled Clockwork Futures, which balances our urge for control with our capacity for chaos. The book unfolds in paired chapters:
Part One: CHAOS | order
1 | The God of Mathematics
2 | Clockwork Boy and the Mother Machine
Part Two: DARKNESS | light
3 | Catching Lightning in a Bottle
4 | Into Dark Country
Part Three: PRIVATION | Industry
5 | The Scientist and the Engineer
6 | He Who Powers the Future
Part Four: ANARCHY | Control
7 | A Wrench in the Age of Machinery
8 | Of Acid and Accident
The concluding section delves into themes of mortality and immortality, and throughout the writing process, I sensed deeper undercurrents. It was akin to a basilisk’s egg; within it lie both desire and dread. Human beings often share fears and yearnings, which can lead to scientific breakthroughs as well as crises, miraculous medical advancements alongside horrific genocides. Below is an excerpt from the opening chapter of my book, which attempts to articulate the complex relationship between technology and humanity.
In the introduction, I proposed that the earth is ancient, while technology is relatively new. Historian David Wootton provides perspective by noting that humans have been crafting tools for approximately 2 million years, with our species, Homo sapiens, emerging around 200,000 years ago, pottery appearing 25,000 years ago, and agriculture developing between 12,000 and 7,000 years ago. George Shattuck Morison, in his 1896 lecture, described these "ages" of humanity as progressing from savagery to barbarism, with the mastery of fire marking the transition—fire initiated the first stage, weapons led to the second, and eventually, we reached the written word and the notion of "civilization." Despite our extensive history, written documentation has existed for only about 6,500 years, and the technological and scientific innovations we discuss today have emerged in the last 400 years. This timeline is strikingly brief, especially when considering the age of the United States Declaration of Independence, which is less than twice that span, occurring a mere 125 years after Columbus's arrival in North America. Wootton aptly describes our contemporary world as "box fresh." The essence of modern science began to take shape between the discovery of a new star in 1572 and the publication of Newton's Opticks in 1704. Morison referred to this "new epoch" as the pinnacle of a movement that had been evolving for forty generations, signaling the decline of "old structures, boundaries, and traditions, as well as outdated customs and ideas." Ironically, in 1664, Henry Power expressed similar sentiments, stating, "I see how all old rubbish must be discarded, and the decaying structures swept away by a powerful flood. These are days that must lay a new foundation for a more magnificent philosophy." An English physician and one of the early elected Fellows of the Royal Society, Power felt he was on the brink of a transformative era. The momentum of change is relentless, and both men were correct in their assertions, yet the narrative does not start with the gleaming future but rather in the decay and chaos of the early seventeenth century, where humanity was convinced that no new knowledge could emerge.
Imagine a city circa 1600: Animals were slaughtered, and their remains were left to rot in the streets, creating a breeding ground for bacteria. Illumination came from flickering animal-fat candles, producing a foul odor and soot. Inhabiting close quarters without plumbing meant that human and animal waste mingled in the streets. Science writer Edward Dolnick paints a bleak picture of London, noting that even the palace of Louis XIV cleared its hallways of refuse only once a week. While we debate public restroom policies today, it’s important to remember that public facilities and toilets were nonexistent until relatively recently. Pests thrived everywhere—from rats to lice. Even "romantic" literature referenced the ever-present flea, as famously noted by John Donne. Skin diseases, decay, and infections plagued the urban populace, regardless of wealth. Rural dwellers had it only slightly better, their bodies ravaged by hard labor. Ongoing wars and religious strife, from the Thirty Years' War in Germany to the English Civil War, meant that national governments were in a constant state of flux and instability. The Black Plague further complicated matters, sweeping across Europe from the fourteenth century through devastating outbreaks in the 1650s and 1660s. Medicine was largely powerless against the relentless tide, often causing more harm than good. It must have been scant comfort to think that God was in His heaven, ordering the world, even as chaos reigned below. The educated individual of 1600 would likely have believed the earth was fixed in place, with everything else revolving around it, and that God was intricately involved in human affairs. In this deeply flawed but stable world, man's only refuge lay in the divine, whose ways were beyond human comprehension yet provided answers to all questions, even regarding death. The world was as it was because God willed it, and mathematics could demonstrate that order.
The Mechanics of the Universe
Nicholas Kratzer arrived in England in 1516, bringing innovative ideas in mathematics and astronomy that endeared him to the court of the notorious Henry VIII. A true Renaissance man, he believed that the "secrets of the universe could be unlocked through precise engineering." As Dr. James Fox notes in the BBC series A Very British Renaissance, Kratzer fulfilled this promise by creating intricate, remarkably accurate sundials, one of which had a nine-sided dial, effectively "capturing" the sun. This grand design was rendered into a manageable, mechanized form, demonstrating to his patrons that everything was orderly: God created the heavens to revolve around the earth. Kratzer designed his dials to align with England's specific location, ensuring that the sun rose and set directly over the king and his court—the center of their universe. Nothing in this divine clockwork suggested otherwise. Kratzer's friend and collaborator, Hans Holbein, reinforced this orderly perspective in his painting The Ambassadors. This artwork features a table adorned with celestial instruments at the top and earthly items below, symbolizing the connection between the heavens and human experience. Aristotle and his successors, including Claudius Ptolemy, were not merely philosophers pondering the cosmos; they were integral to a system that, nearly two millennia later, underpinned everything, from royal authority to the everyday lives of common people. Yet, this system was not without its flaws.
If you were to observe the night sky consistently over a year, you would note something strange. Stars and planets do not merely glide across the visible horizon in predictable patterns; they appear in varying quadrants throughout the year. To an astute observer, particularly one who believed in an earth-centered cosmos, these movements would seem erratic. The established view of a fixed universe provided comfort in a world fraught with turmoil, so these anomalies had to be reconciled. The astronomer Ptolemy confronted this challenge in the second century, accepting as a given that the sun orbited the earth. He theorized that planets must navigate in "epicycles"—small circular paths—while simultaneously following a larger "deferent" path around the earth. A diligent stargazer might also notice that planets and stars appeared to speed up and slow down. Ptolemy faced this complication by asserting that half of the epicycle moved counter to the deferent, making it seem as though celestial bodies changed speed or direction. He further advanced the concept of the "equant," positioning the observational point off-center to explain variations. This convoluted model was built on mathematical principles that can be complex to articulate, though Giovanni de' Dondi devised an intricate gear mechanism known as the astrarium in the 1380s to visually represent Ptolemy's understanding of the solar system. To meet the demand for mathematical precision, Ptolemy's framework suggested that we inhabit a universe functioning like a clock. While the mathematics was sound, the model—insisting on a constant, predictable universe—was fundamentally flawed.
In 1572, a new star emerged. Tycho Brahe, the discoverer, employed trigonometry to demonstrate that this brilliant star, visible to the naked eye, resided in the heavens, not among the corruptible lower realms. How many of us would be fortunate enough to witness such an event? New stars are exceedingly rare; an earthbound observer might glimpse one once every millennium. Yet, for it to appear in the supposedly "unchanging" cosmos at a time when demons were believed to cause misfortunes and witches were still being persecuted, this nova heralded ominous implications. Why did it exist? How did it come to be? Was the world facing an end? For the next fifteen years, Brahe dedicated himself to celestial observations and measurements, though he never fully questioned the earth's stationary position. That task fell to another: Galileo Galilei, the Italian astronomer, mathematician, and engineer. Galileo wasn't the first to see the flaws in the geocentric model; he was simply the first to clash with the Inquisition, the Catholic Church’s apparatus for combating heresy. Nicolaus Copernicus had already raised objections against Ptolemy in the 1500s, publishing De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) just before his death in 1543, marking the onset of a true "paradigm shift"—a significant transformation credited with initiating the "Scientific Revolution." However, this new perspective did not gain immediate traction, remaining largely unnoticed by the Church until sixty years later, when Galileo faced condemnation for his Copernican beliefs.
Challenging the notion that humanity occupied the center of the universe and proposing that years of meticulous models needed reevaluation did not endear Galileo to his contemporaries. His conflicts began in 1611, a full sixty years posthumously to Kratzer, culminating in a formal interrogation in 1633 that lasted eighteen days, during which he faced threats of torture and ultimately spent his final years under house arrest until his death in 1642. The narrative is often simplified to a conflict between religion and science, but it is, in fact, a more intricate story. The cosmos, akin to the nine-sided sundial, upheld an unquestioned order, yet also served as a bastion of authority. The Inquisition sought to expand its influence partly to assert control over the Protestant Reformation initiated by Martin Luther’s "Ninety-Five Theses." Shortly thereafter, Henry VIII established his own authority by dismantling the Catholic Church in England, becoming a law unto himself. The ensuing struggle over power and governance would shape the backdrop of subsequent conflicts, including the English Civil War, which ultimately cost King Charles I his life and ushered in Puritan rule, accompanied by its own violence—some posthumous, as Oliver Cromwell was exhumed and hanged. Regardless of personal beliefs, the 1600s seemed chaotic, a time when stability was elusive.
We rightly fear chaos, as it embodies confusion and disorder. Chaos oozed from decaying bodies and rotted wood, but with Galileo's revelations came a chaotic challenge to the very fabric of the universe, the dwelling of God, and the systems built upon the belief in an unchanging cosmos. Today, with our understanding of an ever-expanding universe, along with concepts from quantum physics and string theory, our acceptance of Earth's minor significance in the vastness of space makes it difficult to grasp the seismic impact of new knowledge. Consider the moment when you first learned that Earth hurtles through space at a staggering speed of 1,080 miles per hour—or that the sun, which appears to rise and set, actually remains still while we spin around it. Envision the collapse of belief systems not just for you, but for an entire generation. The acceptance of the Copernican model over the Ptolemaic required new visions, fresh mathematical frameworks, and novel methods to recreate the original yearning for precision. In doing so, "magic numbers" gained newfound importance, and empirical evidence took on new meaning. Yet, with this transformation also emerged a dark shadow, a fear that the world lacked solid foundations, and that even faith could prove fallible and untrustworthy. Who would reorder the universe? The mysteries of the cosmos would be unraveled by three individuals—Johannes Kepler, Isaac Newton, and Gottfried Wilhelm Leibniz—who collectively imposed a new order, rendering both the heavens and the earth mathematically understandable.
Or so we hoped.
"Grandfather Clock is a creature of logic and precision [. . .] He allows neither change nor error."
— S. M. Peters, Whitechapel Gods
I suggest that sometimes fiction conveys truths most effectively. In S. M. Peters's modern steampunk novel Whitechapel Gods, the world does not operate like clockwork; instead, it is governed by clockwork—by Grandfather Clock, a stern, joyless enforcer of logic and order, alongside Mama Engine, whose creative power is both nurturing and destructive. The protagonist, Oliver, wrestles against the Whitechapel Gods, while also contending with his own physical being. This visceral, violent scene portrays wires and spikes piercing Oliver's flesh, intertwining beneath his ribs. This painful communion with the "father" leads him to submit without resistance, even as the relentless pulsations inflict wounds he never knew he could sustain. Oliver's monumental achievement is simultaneously his deepest fear—he loses awareness of himself while dismantling his god within the desolate expanse of Whitechapel.
Perhaps fiction articulates what I often strive to convey. The crises we encounter today—climatic, viral, political—are not novel; they are ancient, just like the earth. Yet our capacity for destruction has grown beyond our control. Technology can spiral beyond our grasp. It is not about machines gaining sentience to annihilate humanity; rather, it is about our own use of technology to self-destruct. The boundary between miraculous technology and lethal machinery is precariously thin, and the distinction between machines and our own bodies is equally blurred. Ultimately, fiction remains a powerful medium for these narratives.
The conclusion of Peters' story offers a glimmer of hope, albeit of a peculiar nature. The hero aims to dismantle the system through his own physicality. The scene is both visceral and striking: wires and spikes penetrate Oliver's skin, coiling beneath his ribs. This act symbolizes his connection to the "father," surrendering without struggle, yet suffering wounds he could never have anticipated. Oliver's greatest accomplishment is also his greatest terror—he loses his sense of self while simultaneously dismantling the god of his world within the desolate Whitechapel.
I wish to revisit the profound void of night that each of us has faced at various points in life. Growing up in an era where unveiling nature's secrets is integral to education can lead us to overlook the significance of the vast and wondrous unknown, the mystical realms of deities, demons, and sorcery. Enthusiasts of steampunk often resist being labeled as "fantasy" or "escapist," viewing those terms as pejorative.
For Newton and his contemporaries, "science" infused natural philosophy with wonder and left room for imaginative exploration. Kepler penned fictional works, Newton dabbled in alchemy and sought to decode apocalyptic texts, and Leibniz entertained the idea of training dogs to speak. They coexisted with contradictions, believing that God orchestrated the cosmos and communicated through mathematical proofs, all while also embracing a multitude of beliefs that modern society might categorize as fantastical or superstitious. Like them, we harbor both a desire for and fear of the unknown. Inspired by their legacy, we trust that these secrets are discoverable, and while we may not think in terms of magic numbers, it is precisely those numbers that have enabled our journey of discovery.
Hope still lingers in the world, and there remains a chance to retreat from the precipice.