The Relativity of Stained Glass and Mathematics

A New Creation?

In the beginning was the Probability, and the Probability was greater than zero, and the Probability was One. All things were created through Probability, and outside this Probability, Zero has been created. Life was in that Probability, and that life was the light of homo sapiens. That light shines in the darkness, yet the darkness did not overcome it.

General Literacy

Literacy rates during the Medieval Period in Europe are, apparently, hard to gauge. We’re talking about the Middle Ages, roughly AD1000 to 1400 give or take 100 years, so there is a decent amount of change, and large swaths of peoples and cultures to account for, so the numbers are fuzzy at best. Depending on where you look and how you define literacy, the numbers could be lower than 5%, and restricted mainly to nobility and clergy. But with a more liberal definition, say, being able to make out enough Latin, French, or “English” to equate to a contemporary 3rd grader, numbers could look closer to 40%, but maybe up to 90%. (Source). For comparison, literacy in the United States of America today is between 80 to 99%. (Source)

Okay, maybe not the best sources, but the numbers line up with the general consensus of what I’ve been taught all my life. [And, if I think it’s true, and I can find at least one place online that agrees, it must be #FACTS! 👀]

So, what do all these boring, made-up statistics have to do with stained glass or math? Let’s start with the glass.

Stained Glass Liturgy

The technology of stained glass developed into a high art form in the Middle Ages.  Artists used a variety of techniques to create the beautiful windows of colored-glass that filled the facades of Gothic cathedrals. These windows were designed to depict symbolism from, and illustrations of, biblical narratives that helped relate the Christian Story to a mostly illiterate parish. Of course, if the pictures were all the parishioners had, the story would have been quite incomplete.

Notre Dame Cathedral, North Rose Window, detail of center, Chartres, France, c-1235

(photo- ©  Mossot / public domain, via Wikimedia Commons)

The textual, literary narrative that preceded the images, was needed to guide the subsequent interpretation of the images. More than simple illustrations though, when backlit by the flicker of sunlight, the images brought to life the stories and characters the churchgoers learned and heard about in the lectionary. The iconography not only sparked the imagination, but also helped inform ideology.

What church-goers learned was a story about an (in my understanding, the) ultimate truth. A truth that was reinforced by every authority they knew, reiterated from birth and passed down through the generations. Religion, as such, was the basis for all understanding – everything from man to Heaven, everything in between, and their origins. In the Middle Ages, the ultimate authority on that truth would have been the Papal hierarchy of the Catholic Church. And this hierarchy was intimately tied to a lineage of authority – and more specifically, a lineage of literate authors.

Here, I’ll take a minute to define what I mean by literacy: fluency in reading (and writing) that allows for comprehension. By comprehension, I mean the ability to read information well enough to interpret it. And by interpret, I mean the ability to “put it another way,” to create an analogy between the actual information (words) presented and others ways of understanding the same idea. I’m not necessarily positing a full-on hermeneutics, but something close.

That ‘something close’ is what I’m getting at with the words ‘fluency’ and ‘comprehension.’ Even if one is able to sound out all the words of a text, if it takes him/her so long to do so that by the time they get to the last words of a sentence or paragraph, that they forget the first words, it will be impossible to comprehend the full meaning of the sentence, verse, section, or chapter, much less a whole book. By that definition, my assumption is that the large majority of medieval lay persons were illiterate. But to be generous, we will assume a semi-literate population.

With this in mind, few 3rd graders have the ability to read the Bible with a fluency that allows for full comprehension. (Let’s be honest, few fully literate adults, including myself, actually read or comprehend the Bible on their own.😂😳😒)

Even if comprehension wasn’t an issue, having access to an actual Bible (or any book) to read was uncommon in the Middle Ages. In fact, books were a rare commodity in general, and essentially a luxury item similar to a nice piece of furniture. The sheer lack of books, including Bibles, almost guarantees that few people had enough practice reading to possess such a skill as reading well.

This is where the stained glass comes in. If the gap between the layperson and clergy was as wide as it appears to have been, a visual aid was sure to help with memory and comprehension – that’s why, nowadays, all presentations have PowerPoints, right? … RIGHT?!?!

Specific Literacy

The Friedmann Equation for the expanding of the universe.

The above equation models the Big Bang… wait maybe it’s the equation below this paragraph… Maybe both of them – one of them… Oh! I don’t know. They mean something about the expansion of the universe… … … I think… I mean, that’s what Google told me when I searched “mathematical equation for the Big Bang.”

The Friedmann Equation for the expanding of the universe.

(I know what you are thinking, “Which big bang?” – OUR Big Bang!) Anyways, you get the picture. Unless something has gone terribly right, no one who reads this blog post will have any clue what these cryptic arrangements of letters and symbols actually mean. We might be able to name some of the variables, symbols or letters. Maybe some of the more mathematically/scientifically inclined could parse a little of it. But most of us, not so much. Let’s try this one:

Many more people can understand the simpler math of Isaac Newton’s physics (which is interesting, as his equations describe the world we more readily perceive – large objects in motion.) Still, many fully functioning adults cannot read or understand any of them.

A Mathematical Model

In many ways, Science has become like a new religion. And school, academia, is the place most of us learn to study STEM. The language of science is Math, and while there are millions of people who claim to “f√©<ing love science,” as a society, we are largely illiterate in the kind of mathematics it takes to truly understand science. Ask the average person and they’ll admit that they hated math in high school. Testing confirms Americans are only elementarily fluent in the subject: “In math, Americans with a high school diploma performed about the same as high school dropouts in other countries.” (Source)

Ultimately, very few people in the population at large understand the language of mathematics. To be generous, I’ll say we are, as a society, semi-literate in Math (thus Science).

We are, at best, semi-literate in the language of our dominant ideology.

Essentially everything we, as common folk, know of science, especially physics (even more so theoretical physics) is told to us through analogy and metaphor by an authority. This means we are only getting part of the picture when we watch YouTube videos about block holes, wormholes, string theory, or time travel. Ask anyone who really knows the math and they will tell you that even the best verbal analogies and computer generated visualizations do not accurately mimic the mathematics. It is only with a deep fluency in the language of math that we can accurately understand the descriptions and predictions that science makes about our world.

Math, such as the above examples, is the basis for all of the science that gives us all of our understanding of all existence, from quarks to multiverses, everything in between, and their origins. It is no coincidence that similar math and science make our mobile phones work. (Link1 and Link2 give us a glimpse into how.)

You are probably looking at your phone right this instant. Now, think about what you are actually looking at.

A piece of glass with light shining through it.

When illuminated, the light emitting diodes composing the images on your screen bring to life the forces and theories screen-watchers learn and hear about in their free time (because they didn’t care at school). The imagery not only sparks the imagination, but also informs ideology.

What screen-watchers learn is a story about an ultimate truth. A truth that has been reinforced by almost every authority they have known, reiterated from birth and passed down through the generations.  The ultimate authority on that truth has been the academic hierarchy of the sciences. And this hierarchy is intimately tied to a lineage of authority – and more specifically, a lineage of authors of mathematical models.

Your phone is kind of like a portable stained glass window; instead of colored glass backlit by the sun, it’s clear glass with colored light shining through. But just like a Medieval cathedral window, it is a visual plane where a semi-literate people look to fill the gap in their knowledge.

Authors vs Authorities

When we are illiterate, we must rely on authority to enlighten us. At the same time, we must always be weary of authority, because “absolute power corrupts absolutely.” Authority misusing it’s power is nothing new, it happens in every religion and in the sciences, too. Therefore, we must become literate so that we may not be reliant on authorities, but authors in our own right.

I will continue to build the case for self-authorship in the next post, as well as continue to compare and contrast our relationship to the authorities in science and religion.

If you were offended by one critique or the other, it is simply illustrating your epistemological bias. Unless you are an authority, or at least literate, you are at risk of being played by an authority.