The Geometry of Unitarianism.

I offer today a series of reflections and meditations based on geometry that highlight our personal journeys,   First, I must begin with a story that describes a split between Christianity and science. There’s lots of discussion and analysis around why one group might suspect the other over their developing lifetimes, but we UU’s know that principles from both science and religion inform our lives, both forms of higher knowledge that keep us connected to out universe. Religion and science are the two worlds I hope to work within this morning.

 

I am not a mathematician and I know some members of our church are, so I fall into the trap so many UU ministers find themselves in, that the members of their church are mostly smarter than they are. Nevertheless, I will venture on to say that while I may not be a mathematician, I remember reading Euclid’s Elements, the book upon which we base Euclidian geometry, known as plain geometry to most of us passing through high school. Since I slept through some of the discussions on Euclidian geometry in High school, I revisit it today, because visually it is a wonder. Rationally, it guides our thinking. And I want to put it together, the visual and the logical, and see if it offers a place to set my feet upon as a spiritual being, connected to the deep mystery that is math.

 

Around 300 BC, a man known as Euclid pieced together the known principles of measurement and perception inherited from the ancient world. I introduce some of the more basic concepts today, pulling from Euclid’s many definitions and postulates:

 

Definition 1.

A point is that which has no part.

 

We begin with the most mysterious, that which has no part. What is inside the point? Is it dense because it contains the answers of the universe, or light, because it contains nothing but itself? For some, it is Aristotle’s first mover, the one who, without moving itself, moves everything into being. Others know this point as the chemical and physical center of the Big Bang, every particle exploding and multiplying into existence from a single point in time. I believe this point, this most basic element, to be within us. As our Unitarian forefather William Ellery Channing said, it is the light within us that reaches out. It is our great mission to center ourselves on this point and, acting as our own Big Bang, creating from a single focal point, calling out from the place of power held inside us. 

 

Definition 2.

A line is breadthless length.

 

Most of us were students in schools where the utmost important learning concerned standing in a line. Lines are rather boring. But breadthless length. Even though breadthless, meaning it has no width to speak of, there is a marvel in its interior. To where does it go? Of what is it made?

This is a line that extends not just between two points but is a succession of points along some path. Not even a path, but a breadthless path, point after point, those points of ultimate density, of which there are no parts, they are strung together to highlight a way of motion. I imagine each point, in itself its own part, not a part of other points, yet all connected. Or forget points completely and think of the line, the length that knows no bounds except those you place on it. The line in your history, the line connecting your history to your religion, the line connecting you to your father, to that memory you had that made you feel sad the other day. If we could only understand all the lines that make up our length. If we could only know our length—Our possible and full length! Where does our line end? To what do we tie our line?

 

Definition 4.

A straight line is a line which lies evenly with the points on itself.

 

Ah, so lines don’t have to be straight. It took me 35 yrs to get this, to make a line that wasn’t straight. You would think those that struggled to build our uu faith were rebels, people who made a curved line where there were only straight. Actually, when the trinity was espoused as the Father, Son and Holy Ghost, it was the Unitarians who seemed to shoot straight through the text. Finding no evidence for it, they adopted a unifying God image, Unitarianism. Fast forward several hundred years, when only men had a voice and a vote, you could say it took a fresh and unfettered--an unbiased--look at a patriarchal system, and draw two points between a woman and the person who would represent her. Simple. Difficult, but simple.

 

 

It is difficult to build something that endures, and what if you are not a straight line? What if you’re not straight? Eucildean geometry exists in what my book calls a condition of straightness, where all right angles equal one another. Now we move to where we humans start to break down the sense of what seems basic and create new ideas.

 

 

Definition 15.

A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another.

 

…a straightforward definition of circle that is elegant but also not elegant at all. It hints at the power of a circle: all straight lines are equal that fall upon it. 

 

Here are more descriptions of a circle:

-a community creating physical vibrations that relax the body and massage the emotions, channeling anger to a place of peace in the center.

-a mechanism that blends personal rhythms with those of a larger community. Imagine a circle of drums, each rhythm leading the one next to it to a common pulse.

-the simplest way to have people from all walks of life, all colors, to gather. 

-the most inviting of places: you can see others, they see you, and you are equal in each other’s eyes.

 

Of course, creating a Euclidian circle does not create harmony itself. Inviting others into the circle can be complicated; to feel welcome takes more than an equal line from here to there. It was so simple with just a point. I remember studying Euclid’s point definition in philosophy class. I felt so competent and exhilarated, working myself intellectually. But getting from here to there is more complicated. So, acknowledging that life is very complicated and we want to save the world and our fields of science and technology have made great strides, let’s jump ahead to non-Euclidian space, hyberbolic space, chaos theory and postmodernism... not to conquer our universe but to know that we really know nothing.

 

When we look at fractals, the growth patterns in leaves, clouds, formations of rivers, landscapes, lightning… we come to understand the complexity of nature. 

 

It is finally our environment that teaches us, that leads our discovery. What Euclid imagined was admittedly not of the real world. Indeed, it was in the real world that we have come to know how chaos is beautiful, produces self-replicating and determined things that we can try to understand. Even trees are beyond us, as William McDonogh (co-author of Cradle to Cradle, a guide to environmentally sustainable human creation, architect who built one of the first solar houses ) asserts. Given a tree as a project, we probably couldn’t do all the things it does for us: Makes oxygen, sequesters carbon, fixes nitrogen, distills water, provides habitat for hundreds of species, accrues solar energy as fuel, makes complex sugars and food, changes colors for the seasons, creates micro-climates and self-replicates. And so we stand back in awe as we still try to understand. Our imagination and our faithful progress as beings who wish to understand are our best gifts. These make up our uu faith, and they hold religion and geometry, literally the measure of our earth, in balance. May this continue. It is our best hope.