The Square Root of God: Mathematical Metaphors and Spiritual Tangents

The Square Root of God:

Mathematical Metaphors and Spiritual Tangents

by

Timothy Carson

Copyright 2013 Timothy Carson

Smashwords Edition

Acknowledgements

This book would have been impossible were it not for the insights of mathematicians which mostly elude me and the perspectives of theologians and philosophers that routinely dwarf my own. I have found it gratifying to stand in that rare and muddy trench between the two. Any false assumptions that might have led to erroneous conclusions are mine alone.

I could not have proceeded with this project without the wise council of two friends who love mathematics almost as much as they love Jesus, Rick McGuire and Joe Jimerson. And what I lack in composition and grammar skills was compensated for by two exacting copy editors, Nancy Miller and Leslie Clay. They always made me look like a better writer than I am.

Of course, there were all those soft spoken words of encouragement from friends, family and peers who said to keep writing. Though we might believe we have something to say, something to share, graceful souls encourage us in the face of our own deepest doubts.

My greatest hope is that these words will spark in someone, somewhere a new glimmer of understanding, awareness and insight. If they do I will feel as though the effort was worth it. And I leave the rest up to the One who is the square of itself.

Contents

Introduction

Part I The Number 1

Part 2 Circle Up

Part 3 A Piece of Pi

Part 4 The Shape beneath the Shape

Part 5 Infinity and Beyond

Conclusion

Introduction

We have seen the highest circle of spiraling powers.

We have named this circle God.

We might have given it any other name we wished:

Abyss, Mystery, Absolute Darkness, Absolute Light,

Matter, Spirit, Ultimate Hope, Ultimate Despair, Silence.

Nikos Kazantzakis, The Rock Garden

Knowledge is like an island in a sea of mystery, wrote Chet Raymo.¹ Since the sea of mystery is infinite, the growth of the island of knowledge never depletes it. To the contrary, the more the island’s area grows, the more the shoreline’s perimeter grows. And as the shoreline perimeter grows, so grows the interface with mystery. The more we know, the larger the mystery becomes.

The same thing was said differently by the 18th century English scientist Joseph Priestley, who drew on images of light and darkness.² He said that the greater the circle of light, the greater the boundary of darkness which is created by it.

These particular metaphors depend on categories of geometry. They rely on concepts such as shape, circumference and area, as well as the contrasts implicit in them. They describe boundaries, edges and thresholds. But more importantly, as a leap of a different order, they relate mathematical perspectives to a transcendent domain. What is the result? We stumble across a rarified intersection where the sacred and mathematical converge. And what we may discover is just how much light they shed on one another.

Of course, it wouldn’t be the first time people insisted that these two worlds belong together. Thinkers from every world civilization throughout history have somehow connected mystical spirituality and mathematics in order to seek truth, to express some comprehensive notion of the universe. Mathematical and spiritual truth have found common expression in cultural sources as disparate as classical Greek philosophy, Egyptian cosmology, the architectural logic of Islamic mosques, the complexity and simplicity of Buddhist temples, metric patterns embedded in Indian ragas, the proportionality of Christian gothic cathedrals, and numerology in the Jewish Kabbalah.

Why has this relationship between mathematics and spirituality been so ubiquitous? A good case can be made that these threads have been woven into the same seamless fabric from the beginning.

How do we understand the dimensions of a black hole, the distance between stars, the behavior of subatomic particles, the finely tuned symmetry of the double helix of DNA, or the veins of a leaf in relation to every other thing? How can we comprehend the relationship between shape, surface, knots, patterns, and braids? What do we make of fractals that replicate their simplicity and complexity in the deep design of every living thing?

All of these complexities hold unities; elegant design appears out of seeming chaos and multiple dimensions. But by what means can we possibly know this multi-facetted reality? What are the limits to our particular modes of knowing? Can we attribute meaning to the data? Does this reality defy logic and reason as understood in ordinary ways? And if we lift the veil, revealing the dynamics that are operative at the micro or macro levels, then what? What stands beyond those?

These questions have been deeply pondered by mathematicians, astronomers, physicists, biologists, philosophers and theologians through the centuries. In many ways their conclusions have varied as wildly as their beginning points and aims. But more often than many would like to admit, they have ended up pointing in similar directions, finding what the other has already found through different means. And when they provided room for a shared possibility, it often appeared.

As philosopher and physicist Bernard d’Espagnat reminds us, there are veiled aspects beneath what appears to be ordinary reality.³ What does that mean, veiled?

There is, on the one hand, the surface or appearance of reality, and many scientists of the past have preoccupied themselves with that plane. They fall into what might be described as the realist or empiricist camp. They base what is known on that which is measurable according to ordinary observation. This is the province of everyday physics, the Newtonian universe.

Over and against that position stand the so-called idealists who recognize that there is more than that.

The first conviction of idealists is that there is something not meeting the eye that shapes what does meet the eye. Plato is a good example. There are universal essences behind the curtain that shape everything you see in front of the curtain.

The second conviction has to do with the thoroughgoing subjectivity of the one doing the seeing, a subjectivity that participates in shaping the reality of the world. If you swing to the far side of that continuum, you hang by your fingernails with the likes of Jean Paul Sartre and the other existentialists. You are the center of an absurd world that contains no more or less meaning than you provide for it.

How do we know what we know? To begin with, we could go out and play with one of the favorite arguments of physics, intersubjectivity. If five people stand on the shore and observe a clipper ship approaching and describe it in exactly the same way, how the sails are rigged and the way it sits in the water, you would say that the ship has an objective reality. There it is, a thing existing in time and space, attested by multiple sources, several sets of eyes, several brains. This is the kind of argument that helps a positivist sleep like a baby on restless nights.

But using that same clipper ship, let us compare all that supposed objectivity with an apocryphal story often used by Postmoderns. The story has been told that during the colonial period, when clipper ships from Europe first arrived in Mesoamerica, the indigenous