In 2016, Peter Trueb computed 22.4 trillion digits of π. Ahead of π Day on 14 March, he reflects on the nature of π and its role in mathematics, science and philosophy.
"π as we know it and love it is 3.141592. It’s only an approximation, but it’s accurate enough for most computations and more precise than any value used in Europe before 1500 AD. Only the advent of calculus boosted the knowledge of π to more than 100 decimals at the beginning of the eighteenth century. The last record was set two years ago, when my employer DECTRIS allowed me to use a fast server and ample storage to compute πe × 1012 digits of π (https://pi2e.ch/blog). The computation was performed with the y-cruncher code1, which implements the amazingly fast converging Chudnovsky formula.
Mathematical platonism...considers mathematical objects to be abstract, that is, causally impotent. So how can they affect the physical world at all? A possible answer was given by Saint Augustine of Hippo who believed that numbers pertain to the rationes aeternae, the eternal and divine reasons. By being part of God’s mind, π is 3.141… not only now, but forever. And in this view, God ordains our Universe to behave according to mathematical concepts: “You [God] have arranged all things by measure and number and weight”. The mind of God — indeed, a very exciting place for π to exist.
- Trueb, P. π ≈ 3.141, not only now, but forever. Nat. Phys.15, 302 (2019). https://doi.org/10.1038/s41567-019-0444-5
Pi and Process Theology
Once upon a time in a small town nestled amidst rolling hills, there lived a young woman named Emily. Emily was known for her inquisitive nature and her insatiable thirst for knowledge. She was always seeking answers to life's profound questions, often pondering the mysteries of the universe.
One sunny afternoon, while sitting under the shade of a towering oak tree, Emily found herself contemplating the enigmatic nature of pi. She marveled at its infinite decimal expansion, wondering if there was a hidden order within its never-ending sequence. As she delved deeper into the mathematical realm, her mind began to wander into the realms of philosophy and theology.
Lost in thought, Emily stumbled upon the concept of process theology, a belief system that suggests that God is not an all-powerful being, but rather a dynamic and evolving entity intertwined with the world's ongoing processes. This idea fascinated her, for it presented a fresh perspective on the nature of existence.
As Emily pondered the interplay of pi and process theology, a spark ignited within her. She saw pi as a representation of the never-ending journey of life, an unbroken cycle of growth and change. Each digit of pi symbolized a moment, a unique experience, and a step in the evolutionary process.
Inspired by her newfound realization, Emily decided to explore the world of process theology further. She devoured books and engaged in philosophical discussions, eagerly absorbing the ideas of theologians who believed in an interactive and evolving relationship between God and the universe.
With time, Emily's fascination transformed into a deep-seated belief. She embraced the notion that life, like pi, was an infinite series of interconnected moments, each contributing to the grand tapestry of existence. She saw beauty in the continuous becoming, the constant flux of the world around her.
As Emily's understanding of process theology grew, so did her desire to share her insights with others. She began organizing study groups, inviting like-minded individuals to join her in exploring the transformative power of this theological framework. She gave lectures, wrote articles, and even started a blog to reach a wider audience. Word of Emily's teachings spread far and wide, attracting people from various backgrounds and beliefs. Her discussions centered around the idea that we are all participants in the unfolding of the divine story, connected to the evolving cosmos in a profound and meaningful way.
Emily's journey from a young woman contemplating pi to becoming a process theologian had a ripple effect on those she encountered. Her teachings inspired individuals to view the world through a new lens, embracing the uncertainties of life with hope and curiosity. And so, under the gentle guidance of pi's infinite wisdom, Emily embarked on a life devoted to exploring the mysteries of existence and sharing the transformative power of process theology. Her influence spread far and wide, leaving an indelible mark on the hearts and minds of those who sought a deeper understanding of the intricate dance between God, the universe, and humanity.
Emily's contemplations took her on a profound journey of reflection. As she dove deeper into the realm of process theology, she pondered the intricate relationship between God, the universe, and the mysteries they encompassed.
With each passing thought, Emily began to see pi not only as a symbol of life's infinite moments but also as a manifestation of the divine potentialities contained within the mind of God. She wondered if, within the vast expanse of God's consciousness, the digits of pi were intricately woven, representing the limitless possibilities of the universe.
As Emily sat beneath the starry night sky, she found herself pondering the idea that God, being the mind of the universe, encompassed all knowledge and understanding. If this were true, she then wondered if God had counted all the digits of pi, for nothing would be beyond the grasp of the divine. But she knew that they digits go on forever, without end, and decided that perhaps God was always counting them, such that, even for God, the process would never end.
However, in her contemplation, Emily realized that the significance of pi went beyond mere calculation. It was a symbol of the mysteries that remained ever elusive, an eternal dance between the known and the unknown. Just as the digits of pi extended infinitely, so did the universe's potentialities and the depths of God's mind.
Emily recognized that the true beauty lay not in the final count of pi's digits, but rather in the ongoing exploration, the unending journey of discovery. Each digit represented a door to new revelations, inviting humanity to delve further into the intricate fabric of existence.
With this realization, Emily's faith in process theology deepened. She understood that within the divine tapestry, pi played a role—a symbol of the boundless potentialities and the perpetual unfolding of the universe. It was a reminder that God's mind encompassed both the known and the unknowable, the seen and the unseen.
Armed with her newfound insight, Emily continued her pursuit of understanding, sharing her thoughts with others and engaging in conversations that explored the intricate interplay between God, the universe, and the enigma of pi. Through her teachings, she encouraged others to embrace the mysteries of life, to marvel at the infinite possibilities that resided within the mind of God.
In her quest, Emily discovered that the true essence of pi and its connection to process theology lay not in the counting of its digits but in the journey of exploration and the recognition of the profound unity between the human mind and the mind of God. And with each passing day, she found solace and inspiration in the continuous unfolding of these divine mysteries.
ChatGPT -with help from Jay McDaniel
Melvyn Bragg and guests discuss the history of the most detailed number in nature. In the Bible's description of Solomon's temple it comes out as three, Archimedes calculated it to the equivalent of 14 decimal places and today's super computers have defined it with an extraordinary degree of accuracy to its first 1.4 trillion digits. It is the longest number in nature and we only need its first 32 figures to calculate the size of the known universe within the accuracy of one proton. We are talking about Pi, 3.14159 etc, the number which describes the ratio of a circle's diameter to its circumference. How has something so commonplace in nature been such a challenge for maths? And what does the oddly ubiquitous nature of Pi tell us about the hidden complexities of our world? With Robert Kaplan, co-founder of the Maths Circle at Harvard University, Eleanor Robson, Lecturer in the Department of History and Philosophy of Science at Cambridge University; and Ian Stewart, Professor of Mathematics at the University of Warwick.