3 The Relativity of Stained Glass and Math: Epilogue

A History (and Future) of Disbelief

Can literacy go too far? What happens when a system gets too large? What does this have to do with Singularity?

In the last post, we looked at how fluent literacy can lead to a type of authoritative rebirth that we called re+authoring. We discussed the end of the Dark Ages and the beginning of the a Renaissance. (The word, “renaissance,” literally means rebirth.) Marking this historic transition was the restoration of various types of literacy.

Since then, in the Western world, there has been a general increase in literacy. Paired with the ideas of the Enlightenment, naturalism and the birth of modern science, over time myriad doubts about the accuracy and viability of the Bible began to spring up, both from inside and outside the Church. (Speaking of Christianity after the Reformation, I feel like I should say “the Churches,” plural, but it just comes out awkwardly.)

Not only do we get skepticism and relativism from thinkers such as Hume and Kant, but we also get dog-piled by the loss of traditional authority in Kant, Hegel, Marx, and Nietzsche. In this same time frame, a budding new middle class was thirsty for status of any kind. This meant that ideas could spread rapidly by attaching the knowledge and understanding of such philosophies to aristocrat-like intellectual status. Further, the (semi-)dismantling of the feudal system gave many, if not most, some sense of hope for upward social mobility. As the traditional pairing of education and wealth persisted, each socially lower class reached upward, not just in the capitalist sense, but also “intellectually,” getting drunk on the trickle down of a more and more watered-down version of the newest ideas. In sequence, as a result of the spread of secular philosophy, we see a deterioration of the authority of the Church and Christian religion.

I could be wrong, but I think that each of these philosophers distanced themselves from Christianity in one way or another for the sheer fact that Christianity was failing to deliver on the goals and ideals put forth in the Gospel. I don’t think it was an impatience with the eschatological, but with the failure of the Church to exhibit, practically, the lessons of the Sermon on the Mount (among others). It’s as if these thinkers sought to scaffold the morality and metaphysics of Christianity without the mythology. For example, Nietzsche’s “Death of God” is as much a critique of the absence of activated belief and the lack of morality that logically follows, as it is a denial of an actual Being. (Tangentially, what purpose would an ubermensch serve if everyday Christians practiced the Golden Rule?)

The Two Barriers

…But I digress. When a young literate, but perhaps only semi-fluent, person who has not had their needs met by the Church reads or hears a phrase such as “God is dead,” it rings true without needing to inspect the details that lead to such a conclusion. These details were readily available to the one passing down such ideas, and because the messenger is inherently more fluent than the receiver, he/she is capable of choosing whether to re+author or re-write the text as he/she passes it down. To put it another way, the teacher always knows more than the student, therefore the teacher has the power to skew the lesson to his/her motives. This power dynamic can create a barrier to true fluency.

There seems to always be at least 2 barriers to fluent literacy: getting the illiterate literate, and finding benevolent authority for those who remain illiterate regardless of efforts to educate.

The remedy to the first issue, getting the illiterate literate, seems to be a no-brainier – education… … … But I’m just gonna leave that alone for now because of the mess that the American education system is. Maybe this isn’t even a barrier in other countries…

The second issue, which is really, ‘how do we govern the ignorant,” is even stickier. (Does a statement such as that provoke a fight in the comments section?) My original wording has my answer built in: the perpetually illiterate need a benevolent authority to guide them. The problem remains: where to find this ‘benevolent authority.’

The simple, Christian answer is, as always, Jesus! But because He is no longer physically present, finding a human proxy is quite the tall task. While no human is purely good or completely evil, the continuum of theologies developed from the mixture of re+authoring and re-writing the Gospel has divided Christianity into hundreds of denominations. The overlap and disagreement between any two could be both miniscule and infinite. Nowadays, to speak of the authority of the church could mean something different for almost everyone who speaks of it.

None the less, Christianity at least has a model for benevolent authority in its Christ. How about secularism?

How Science Will Fail.

Contemporary Science has as it’s biggest strength it’s biggest weakness: decentralization. Looking at the way that the Reformation took absolute (corrupting) power from the centralized Catholic Church’s hands, the decentralized nature of Science prevents such a circumstance from occurring in the first place. At the same time, the overwhelming project of science demands multiple authorities, each so specialized in increasingly siloed disciplines, that to make generalized practical statements, much less a coherent cosmology, is nearly impossible. Further, the limited resources for research grants has introduced capitalistic competition to the field, along with all its trappings and temptations.

All that aside, the literacy issue poses the largest threat to science as a cosmological competitor to religion. As Galileo would have it, mathematics is the language of science, and many of us do not have the ability to become literate enough in math on the scale necessary for full scientific understanding. Likewise, because of specialization, scientists from one discipline may be (are probably) only partially literate in another. A zoologist probably doesn’t fully grasp subatomic physics, and vice versa. To understand all of science, one must only understand the basics of most of it – any truly universal cosmology faces the challenge of not being an inch deep and a mile wide. So far, the solution to this problem has been to forgo a unified theory, and allow each discipline to be it’s own authority, because they seem to overlap decently. This potentially creates another problem: who gets to be the authority where disciplines overlap? What happens when two disciplines that should overlap don’t? What happens when the links in the chain of authors doesn’t hold together?

Mathematics is like a big building with many apartments. We have at least Arithmetic and Analysis, Algebra and Topology – and we have Geometry and Probability-Theory. Very often the tenants of these different apartments seem not to understand each other.
Paul Lorenzen, “Constructive and Axiomatic Method.” Protophysics of Time: Constructive Foundation and History of Time Measurement (Boston Studies in the Philosophy and History of Science Book 30)

Although the quote is about math, it also highlights the current problem of macro and quantum physics. The scientists understand each other, but their equations don’t – the equations that work for large objects don’t work for small objects. Currently, all attempts to create a Unified Theory have resorted to a sort of metaphysics (ahem, I’m looking at you, multi-verse). Interestingly, most people don’t recognize it as a metaphysics because the language is advanced mathematics, which is not easily comprehended. And when it get translated to literature, something gets lost in translation.

While there are numerous important and critical scientists in every field, the names we all know – Arthur Eddington, Stephen Hawking, Brian Greene, Neil deGrasse Tyson, etc. – are mainly popular because of their ability to translate such math into the language of the laity. They have become the apparent authority not only for their scientific achievement, but because they are so fluent in their language that they can translate/re+author, it into another. These authors give their subject new life; in their re+authoring, their subjects are reborn.

But up to what level can we trust these authorities? If we do not, cannot, read the language of their ideological foundation, what is to stop them from misusing the trust and power we give them? Could the limited number of them precipitate into a scientific oligarchy? Can the peer review process prevent a conspiracy toward malevolent authorship?

Just as the overreach of papal power was prevented from within the church, science might just take care of itself.

The Cyborg Reformation

If human-machine integration is to truly take place – if the augmentation of humans with computers is to reach it’s full potential – then one day, our brains will be bio-digitally synchronized with the complete catalogue of scientific information.

But will we be able to glean meaning from it? Will there be any meaning left- or just information?

Just as verbal literacy led to widespread critical viewing of the Biblical text, will universal mathematical literacy promote cynicism toward the lack of a unified Science? Will there be a unified science by then? Is unification and/or computational singularity an eschatological dream?

Let’s examine the problem of cyborgism – augmentation of computers into the human animal – for just a moment. When humans have a supercomputer in/with/as their brain, everyone should be fluent enough in mathematics to translate the various math equations that explain the big bang, or Higgs Bozon Particles, or gravity, etc. Once fluent, what if we can all easily deconstruct the construct of physics, what if we can all find the inconsistencies that derail any unification theory? What if we find out the multi-verse was all just a mathematical metaphor, equational poetry for the actual physical world? What if it’s just a “play on numbers” that tricks our logic into following a valid syllogism based on false premises? What if we recognize that the numbers still don’t add up to our conscious experience?

Will the same system that created the technology create a technology that undermines that system?

You may recognize these proposed questions as slight variations of the criticism of Christianity (or any religion.) The analogy only works if one accepts math as an actual language, just as Hebrew, Greek, Latin or English are. Many people, especially mathematicians and scientists, believe that math is more than a language; they see it as the essence of reality. Some believe that we can break down the physical world to a point where only numbers would remain. To an extent, many believe that underneath everything, there is (only) math.

I disagree. I don’t believe there is an “underneath.” More precisely, I think the physical world is the underneath. Not necessarily in a fully Platonic way, but in that if physical matter is broken down, I think one will only find more physical matter. I believe that only when physical matter is added together do we get something more.

The physical must be added to in order to get a metaphysics!

‘Meta’ + ‘physics’ literally means “after the physical.” One must have a “protophysics” to be under or before the physical. But before we get too deep into a discussion about if Math is a first principle, or whether the chicken or the egg came first, let us just look at what makes a chicken come from an egg, and what makes a viable egg come from a chicken…

Here, unfortunately and for many reasons, I must leave you with a cliffhanger. First off, I’m not sure how to wrap this up quickly and neatly, if at all. Second, this is a good place to launch into a much larger discussion of emergence.

The next posts will begin a sort of typological cosmology that I am still working out. It will try to explain how singularity is synonymous with non-being, while at the same time claiming that a trinity (the Trinity) is the bare minimum for existence – an existence that goes from zero to infinity instantly. For now, a respite…

“The Lord brought me forth as the first of his works, before his deeds of old; I was formed long ages ago, at the very beginning, when the world came to be. When there were no watery depths, I was given birth, when there were no springs overflowing with water; before the mountains were settled in place, before the hills, I was given birth, before he made the world or its fields or any of the dust of the earth. I was there when he set the heavens in place, when he marked out the horizon on the face of the deep, when he established the clouds above and fixed securely the fountains of the deep, when he gave the sea its boundary so the waters would not overstep his command, and when he marked out the foundations of the earth. Then I was constantly at his side. I was filled with delight day after day, rejoicing always in his presence, rejoicing in his whole world and delighting in mankind. “Now then, my children, listen to me; blessed are those who keep my ways. Listen to my instruction and be wise; do not disregard it. Blessed are those who listen to me, watching daily at my doors, waiting at my doorway. For those who find me find life and receive favor from the Lord . But those who fail to find me harm themselves; all who hate me love death.”
Proverbs 8:22‭-‬36 NIV

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.”

(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.