The Calculus of Christmas
A Straight Line is a Godless Line
Rectangles
What’s the area of this shape?
… *crickets* …
Well. Reasons has its limits.
You know, if a dog or a rhesus monkey had designs on Universal Truth we’d rightly be skeptical. Dog Aquinas or Rhesus Monkey Nikola Tesla might, indeed, be very intelligent for their species, and they might even, in their own, limited way, say some real, true things.
Sure.
At the end of the day though, it would still just be the pontifications of a canine and the math formulas of a monkey. The brightest either of those two species could muster would top out at a level lower than the average human toddler.
And yet we think we can know everything.
We think we can understand.
Tell me reader… Where is it written that hairless apes can know the secrets of the Cosmos?
There.
That’s better.
We all know that one.
The area of a rectangle is Base x Height. Easy. Straight lines and right angles. Simple, smooth sailing.
That’s why we live in boxes.
Homes, offices buildings, schools, churches… almost everything people build is nothing but variations in the key of Square. Sure we might throw in a triangle here and there, use the odd hexagon. If we’re feeling saucy and have some extra cash we might even include a circle, such as with an arch or a dome.
Overall though, we are cubists.
Squares are what we can get our minds around, and all conceptions of Reality must collapse to the intelligence of the thinker.
It’s a real problem.
I mean, look. Here we are, men and women, smartest creatures ever observed in the known universe… and yet all we can really deal with in our heads are straight lines and regular shapes. It is a paucity. We are intellectual paupers.
It would be fine if the universe was made of straight lines and regular shapes but in actuality it’s hardly ever. In fact, just the opposite. Everywhere we look in nature we see curves and parabolas. Bends and angles. Twists and turns. A straight line is a godless line, and whoever made the universe wasn’t much into them. The actual shapes that make up plants and animals and mountains are so asymmetrical and serpentine that we can’t even hope to give them a name and yet we, like babies playing with puzzles, are only capable of dealing with what is regular and even.
So what are we to do?
Give up? Admit defeat? Throw up our hands and declare the universe fundamentally unknowable? Humble ourselves and admit that Reality is incomprehensible to our primate brains?
No.
No!
We force it.
We rape the universe.
…
Take that.
Congratulations.
You’ve just learned calculus.
In my experience teachers do a fairly poor job of explaining the concept but, at its core, Calculus is simply the mathematics of irregular shapes. That’s all. It is the math of plots that have curves in them. The math of graphs and movements which aren’t even. Long ago, clever people had the humility to admit that human brains weren’t capable of understanding much beyond squares and so they figured, “Hey… why not just cut everything up into squares?”
Makes sense, doesn’t it?
We can’t calculate the area under that curve outright, no, but we can calculate the area of each of those rectangles we broke it up into and then add them all together. That won’t be exactly correct, no, because as you can see here and there our rectangles overshoot the edges of our curve. However, if we stuff more and more rectangles under the curve by making each of them thinner and thinner and thinner such that the overshoot of each one becomes less and less, then, as the number of rectangles we use approaches infinity, the accuracy of our calculation will approach 100%.
That’s calculus.
Calculus is nothing more than a lot of clever tricks for doing exactly that.
That’s why in Calc 1 and Calc 2 they talked your ear off about “limits”. Because the accuracy of your estimation depends upon how far you go. On how many rectangles you’re willing to divvy the curve up into.
And all of human thought is like this.
All of it.
What we do to get by as a species is force things into boxes.
Music, Gays, and Keeping Time.
Noon isn’t really 12 p.m. you know. Years aren’t a neat and tidy 365 days. Speaking of, what is a day anyway and how do you define it? Are you talking about a solar day? Or sidereal? You realize too of course that things like “daylight savings” are entirely made up.
Long ago, in ancient empires, Astronomers and Mathematicians went to great trouble trying to keep time. I mean, think about it. How long should an hour be? What about a minute, and how many of those ought we stuff inside an hour? If you’re trying to describe reality, to make a time system that tracks with the movements of the heavens, then you’re going to have quite a bit of trouble because the heavens rotate in pretty complex ways. The sun moves around throughout the year and the amount of daylight hours varies constantly, so if you want to tie a specific celestial happening (sunrise or sunset or noon) to a specific time on the clock then you’re going to face real challenges. For example, if you want a clock that keeps Sunrise constant, let’s say, every day at exactly 6 a.m., then you need a system that either varies the number of hours and minutes each day has, or else changes the length of those hours and minutes throughout the year. Pretty hard! If you instead belong to a lunar culture and want to line your clocks up with the motions of the moon, then you face an even bigger challenge. Your clocks will have to be set to match a celestial body which changes even more rapidly than the sun… and which on some nights isn’t even there! Worse, even if you do go through all these calculations and deliberations to craft some semblance of a system that works… simply moving a few hundred miles north or south completely negates it, as the length of day varies considerably based upon your distance from the poles. In an age before computers it was a simply impossible task, indeed, it’s barely possible now. The end result therefore was that Time was simply local. The idea of “universal time” or “global time” simply didn’t exist. Every city went by its own sundial. Every community kept a variation of its own calendar.
Madness.
Anarchy.
It was a tangled mess of non-standardization that required Order, and the Fascist Fist of the Germans would come to beat Time into submission.
Though they’d been around for a while and (as with most things) were first invented in China, in the 1300s the Germans really started going hog wild with mechanical clocks. Sundials, astronomical clocks, and local calendars were out. Not cool. Modern life required uniformity and standardization and the King and the Pope and the Whoever Else needed to be able to coordinate across the realm. “We’re all meeting at ten.” “Church starts at seven.” “Have your kit and be ready to go to war by lunch.”
Of course, cogs and gears and mainsprings aren’t, as a rule, very flexible. They do what they do, pretty much exactly the same way every time. Such rigid instruments didn’t mesh well with Reality, with a solar system constantly changing everything depending on latitude and time of year. Okay. So… just redefine Reality. If you can’t make a clock that strikes twelve every day at Noon (when the sun is directly overhead), just change the word “Noon” to mean, “when my clock reads twelve.” Turns out, the only thing holding The Ancients back was a lack of hubris. Just force the minutes and hours to be regular. Make the days even. Declare, by fiat, that every year is uniform.
…
Just do a Calculus.
Impose it.
Put time into bins, into regular, easy to understand rectangles and squares. It may not be True, no. But it’s close enough on average. We’ll hit 12 p.m. when the sun is pretty much overhead and sunrise and sunset will usually land within a two hour window. Call it good. It’s a system we can wrap our minds around and, more importantly, it’s a system simple enough that we can replicate it with our technology.
It’s this:
I’m telling you. This is all we ever do.
…
Music too.
Our instruments, most of them anyway, are square. They’re regular. Quantized. A guitar string for example, is fretted. This means that the number of tones it is capable of producing is limited by the number of frets upon the neck. A guitarist can’t play between those tones. Notes between the frets are not possible. In like manner pianos have discrete notes too, each assigned to a separate button (a separate key). Most wind and chromatic percussion instruments (xylophone, etc) are likewise restricted to a set of discrete, noncontinuous tones wherein the musician simply can’t play between the available notes.
All such instruments, by necessity, are slightly out of tune.
Admittedly, unless you’re an audiophile and familiar with the finer points of music you’ve probably never noticed this. In fact, it’s likely that you’ve grown accustomed to the “unpleasantness” of modern tuning and consider it normal, this being almost all you’ve ever heard in commercially produced music. Perfect Tuning however, Just Intonation, is better, and sounds cleaner and more pure than what you’re used to. It’s just not possible on our instruments. It’s not possible with musical technologies that divide sound up into separate, distinct bits.
On the other hand, organic instruments made by God (e.g. the human voice) are not restricted to discrete sets of sounds and can change intonation on the fly. These (and fretless stringed instruments like violins) therefore have no need for tonal compromises, and if playing in ensembles by themselves often don’t make them. For everything else though?
There’s Equal Temperament.
A system in which all the intervals (save the octave), are just a little bit wrong.
…
In other words, it’s this:
Everything is this. Over and over again.
In the same way, we as individuals almost never fit into the boxes society puts us in. Actual people always exist on a continuous spectrum, on a curve, and regardless of our skin color, ethnic background, religion, gender, or sexuality, I’m confident almost none of us are well described or understood by labels like “white”, “black”, “Muslim”, “Swedish”, “gay”, “female”, or “Jew.” Indeed, most people find such labels offensive, if not oppressive, since such categorizations cannot help but attach stereotypes to individuals based on the biased public perception of groups.
Of course.
…
… …
But what do you want?
Mankind is cubist. We literally think in boxes. We have to put things in bins.
Asking a man or a woman not to categorize and label Reality is futile. As futile as asking Dog Aquinas to stop allegorizing everything with bones and head scratches, or Rhesus Tesla to stop counting with bananas. All of human thought is always some variation of trying to throw a “Net” over Reality. Trying to force it into the framework of a lattice. Into squares. We lay our streets out in blocks and mark our maps up into grids. We do our agriculture in rows and hold our roofs up with columns. We make our images with pixels and polygons. We count in whole numbers. We categorize and designate and classify. We divide into districts. We draw lines and borders. We think problem solving involves breaking an issue down into discrete pieces and we take living organisms and only declare them understood after we’ve killed them and cut them up into little parts.
…
… … …
And.
All this is well and good.
It is.
It’s okay.
It’s all okay so long as we remember. So long as we don’t forget that that’s what we’re doing. That we’re dividing the world up.
But…
We do forget.
We forget that our rectangles aren’t the Curve. We forget that our gridlines don’t actually exist in the world. We come to believe our categorizations are the Gospel Truth, and we forget that Reality, by definition, is always Uncontained.
Holy Night. As in Whole. Not Broken up Into Bits.
I don’t think the people who encountered Christ knew their categories were breaking. I doubt strongly that they suspected that the baby born within a manger was destined to overturn the entire social order. I don’t think they knew they were witnessing the birth of an entirely new calendar and dating system, or a new religion, or a new metaphysics of the divine. I think they probably came to him believing they understood the world. That their mental boxes were neat and tidy, in need of no reshuffling. Yet, even if you don’t believe in Jesus, it seems fairly undeniable that he was the most impactful person to ever live. Why is another question, but the fact that the knock-on effects of his life and teaching eventually brought down the Roman Empire, started the two most popular religions, forever altered Judaism, and inspired the philosophy, politics, and policy of several continents for centuries is indisputable. Christ has entered the ranks of the deities of Hinduism, he’s influenced countless Buddhists. People have debated his historicity and his divinity, and fought great wars over same. His image has been depicted more than any other human’s, and billions of pages have been written trying to explain him. He has been invoked by Kings, Presidents, and Emperors, and he has lambasted by crooks, liars, and thieves. The world’s great musicians have dedicated odes to him, countries and cities have been named after his saints, and Buzz Aldrin, one of the apollo astronauts, believes he ate his body on the moon.
Why?
Because Christmas is a haunting holiday.
Because, even more than Halloween, it is a time for ghosts.
The Christmas Story is one of the Remainder. It’s a story of what’s left out. What’s forgotten. The Christmas story is an intrusion of the line upon the grid. It is a reassertion of Absolute Reality against the fraud of all our categories. The birth of God into animal life, into human life, stands as an eternal proof and reminder that all of our models of reality aren’t True.
They’re just “true.”
They’re approximations. Guesses. Something kind of sort of approaching the real thing. During Christmas we’re allowed to remember that our nets don’t catch Everything and that something, something vital, always evades us. Like the magi, we’re reminded that the only hope we have of finding what’s truly important, is to follow the brightest star.
Wise Men still seek him. Merry Christmas to all, and to all a good night.
Brilliant.
Didn't have time to read this as deeply as I'd like - but this is good. Keep up the good, happy new year.