Loops with Modifications
“I love you like this because I don’t know any other way,
except in this form in which I am not nor are you,
so close that your hand upon my chest is mine,
so close that your eyes close with my dreams.”
— Pablo Neruda
“History doesn’t repeat itself, but it often rhymes.”
— Mark Twain
Hello again,
It’s one of those years, you know, when suddenly everything’s different, even though nothing’s ever really changed.
You’ve been waiting for an eternity, it seems, waiting for something to happen or someone to come, waiting to be something more than you are.
And then you look up one day, and you take it all in — the sun in the field, the sweetness of the air, the stunning presence; and you breathe, you inhale your past, and all of sudden she’s there: your future, walking toward you like the pages of a good book turning slow.
She comes to you, glowing, and takes your hand in hers. Words are said, rings exchanged, and in that moment a union is formed.
Now freeze that moment right there. Freeze the embrace — the joining of two into one, the matrimonial convergence of self.
Freeze that moment.
Now zoom out.
We embrace by a meadow, at a charming French villa.
Zoom out again.
The villa is thirty miles from Byron Bay, just below the border of Queensland and New South Wales.
Zoom out again. We’re in Australia.
Again. We are swallowed by the Pacific, and the curve of the earth beyond it.
Keep zooming — we’re taking one of those journeys, you see — and soon our Earth gives way to the solar system, to the Milky Way, to galaxies beyond, the unimaginable expanse, all the way to the edge of the observable universe.
Out here there is no “you” and “me” to join, and no “we” for that matter. Our union is just as real as it was down by the meadow — just as true — but our very existence is so unutterably, insignificantly small at this scale that it hardly merits a status update.
It’s a nice place to honeymoon for a moment, up here at the forefront of time-space, but all honeymoons must end. What goes up, must come down; what expands — whether a universe or a perspective or a breathe — must round its cosmic corner and contract.
So in we go now.
Rushing back through the stars, the planets, the terra cognita, back to our island, our villa, my love in her dazzling dress… but we don’t stop there, we zoom in — to her precious hand, to a patch of her skin, tender and smooth. In, to her blood cells; to a strand of her DNA; her protons; her atoms fizzing.
We’re married here, too… whatever “we” means at a subatomic level, anyway.
Break us down into small enough bits and it is our fibers embracing, our molecular chemistry that is wed. Smaller still and we are quantum hitched — our particles as entangled as our fates are entwined.
But before we lose ourselves entirely, let’s talk about these photos for a second, shall we?
The first is, of course, from our elopement; a sweet, intimate affair held just a week before my birthday. Nothing compares to the beauty of your wedding day, of course, but in terms of scale perspective, this is pretty much how we all see things everyday as human-sized humans.
Most of the zoom-out and zoom-in images are cribbed from Powers of Ten — “a film dealing with the relative size of things in the universe.” It was made back in 1977, practically pre-historic as far as Youtube is concerned, but it’s a perennial favourite. (Wait But Why recently did a more modern and interactive take on the same journey).
Anyway, take a closer look at the images. Any patterns pop out at you?
Zoom out far enough and all we see are the circles.
When we look at things from a distance — all things, really, in space and in our lives, everything that happens, everything that is, everything that we know and do and experience, our selves and our relationships — it’s just loops around loops. It’s just hands circling clocks, planets circling stars, us circling each other, from birth to death, from love to loss, from wedding rings to Saturn’s rings out to the very boundaries of space and time.
The macro-perspective is cyclical. Everything that is, already has been and will be again. There’s nothing new under the sun, or beyond it. Sure, things change: oceans rise, empires fall, spring, summer, autumn, winter, political upheavals, technological breakthroughs… but they don’t call them “revolutions” for nothing. Sure you get the occasional black swan, the once-in-a-century storm; but zoom out a million years and ‘once-in-a-century’ is just clockwork for the gods.
It’s comforting, really, to live in the macro, where chaos itself is quilted — each missed stitch part of a grander pattern just waiting to emerge.
Distance insulates; it rounds out the harsh edges of reality.
But those same edges are sharpened by proximity.
Zoom out far enough and all we see are the circles.
Zoom in close enough, and all we see are lines.
Put anything under a microscope and it looks like it’s going somewhere. Day-to-day, minute-to-minute, things are changing right in front of our eyes! Look real close, blink real fast, and that change is linear, it has direction: progress or regress, growth or decline. Covid cases are ticking up; equities are trading down. This hashtag is trending up; this candidate is polling down. More breaking news — another tyranny, another protest. Each day feels like a movement is building; each new development feels raw, like it means something.
This rawness can make life painful in the micro — our differences look more fundamental, relationships more volatile. Blood runs hot in the moment, words cut like ice without context. The injustices of our age, big and small, are so real and so immediate, and they demand immediate and forceful response.
But the blessings of life are in sharper relief as well. Come in close, my love, and every gesture is a slow dance, every gaze a poem. Look close beyond our meadow and see not the forest, but the trees; each blade of grass a pillar; each drop of dew a pearl.
Inhale, and zoom in with me. Everything matters.
Exhale, and zoom out. Just not terribly.
Inhale, zoom in with me. We’re all special snowflakes.
Exhale, zoom out. We’re all just dust in space.
Shrewd readers of these birthday letters may have noted, over the years, that they tend to be variations on a theme.
The basic thesis is that human experience is wrought with dichotomy (self and society; progress and acceptance; loss and recovery) and that in the face of such dichotomies we must resist the urge to choose one side or the other, and instead seek to transcend — to reimagine each binary choice as a spectrum of possibility; to savour but not succumb to the tension of opposing forces pulling us toward the poles; and ultimately, as Thich Nhat Hanh suggests, to “dissolve false boundaries” and allow ourselves to experience life as fully as possible up and down the range of each spectrum — you, me, big, little, snowflake, dust, all of it.
So how do we transcend the macro- and micro- perspective on things: on life, on marriage, on the universe?
How do we zoom in and out? How can we see things as both circular and linear, repetitive and progressive?
How do we visualize existence as both a loop and a line?
Spirals are the most obvious answer. “Circles that go somewhere,” I like to call them.
I’m hardly the first to take note. Archimedes wrote a book about spirals in the 3rd century B.C.; a thousand years later, medieval Indian poets were writing spiral verse in Sanskrit; but it was Fibonacci’s famous attempt to plot the breeding of bunny rabbits in the 12th century that yielded the eponymous sequence and sparked a centuries-long enthusiasm for spiral occurrences in nature, from the helixes within us to the heavens beyond and everything in between.
It did not stop there (that’s the point, remember).
More modern thinkers became enamoured with the spirals’s capacity to represent not just physical nature but human behaviour. Because the spiral is both “repetitive and progressive,” it is especially well-suited to illustrating pathways of iterative growth. Spirals form the geometric backbone to contemporary models of personal and organizational development; narrative storytelling; software development; political history; art.
Good, good… all good stuff.
Well, not all good, of course. Like any responsible metaphor, spirals twist both ways.
A “downward spiral” indicates a loss of control; a descent into a repetitive and progressively hotter hell.
Markets spiral when a single sell-off event triggers a vicious cycle of investor confidence and realized losses.
Relationships go into a spiral when the same repetitive behaviour inflicts progressively worse damage on the trust between partners.
We see it in marriages — the same argument over the same differences, played out over and over again with a heavier and heavier cost, the mutual resentment magnified with each crank of the wheel. We see it in our politics and our geopolitics— the widening gyre of our culture wars and ideological crusades.
A spiral is when you can’t back down. You can’t turn the other cheek. You can’t help but take another swing, another hit, another loop but harder.
We spiral into violence; we spiral into depression; we spiral into substance abuse.
But those aren’t even the worst spirals.
The worst, of course, are the meta-spirals. Spiralling into your spirals, that is, or becoming so fixated with the geometry that you forget anything else is possible.
“If we’re built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?”
Okay, let’s pull ourselves out of that rabbit hole for a moment.
Inhale—lots of stuff looks like other stuff.
Exhale — it’s just stuff.
Breathe in, breathe out, zoom in, zoom out.
All good? Okay let’s jump into another rabbit hole!
I promise, this one will be cooler.
You see, the problem with simple spirals as geometric metaphors for life is that they are a little too smooth — they are neat, clean, predictable abstractions of a universe that is anything but.
Yes, the simplification of complex things can be handy for building models, which can lead to understanding; but if we smooth away all the texture and bumps, all the variance from our curves, we are just as easily lead astray. If we smooth over the subtleties, the nuances and shades that lie along our spectrums, if we greyscale everything between black and white, we are not merely failing to transcend the dichotomies of life, we are actually reinforcing them. We are smoothing reality into a cartoon.
This does not serve us well.
Visualizing existence as a series of spirals is ultimately no less reductive than the loops and lines they were meant to transcend.
In their place, we need a geometry that can properly capture the “roughness” of things — the delightfully messy, spontaneous wonder of complex dynamics.
We need a geometry that does not flatten the bumps, but probes within them.
We need a geometry that can dissolve false boundaries without dissolving the nuance on either side.
We need a geometry that can illustrate transcendence at a nearly infinite scale.
We need fractals.
The rabbit hole you see above is the world’s most famous fractal — the Mandelbrot Set, named after the 20th century “father of fractals” and self-described “scientific maverick,” Benoit Mandelbrot.
Apparently, many decades ago, my mother stumbled upon these same images and was so taken with their beauty and their philosophical implications that she cold-called Mandelbrot at his office and started randomly picking his brain.
(I would give literally anything for a record of their conversation, but sadly they have both since died, both of pancreatic cancer. Researchers have subsequently discovered fractal patterns both within the pancreas and in tumor growth).
I don’t know what drew my mother to fractals. She never mentioned her interest to me, though she did once give me a glass ball with a mysteriously fractal depth which I cherish to this day.
It is possible she just liked the pretty shapes and colours; more likely she was intrigued by the promise of a grand unifying structure. There are certainly plenty of “fractals in nature” to point to, but we’ve been through this with the spirals so I’ll spare you the whole refrain.
The key point here is that fractal patterns are self-similar and recursive; that is, you can zoom in on any portion and find within it an approximation of the whole.
This self-similar recursiveness can be very basic — you can easily draw more triangles within triangles, for example, or squares within squares; or it can be very complex — the tension-release patterns in Beethoven’s symphonies and Jackson Pollack’s poured paintings are astonishing if unwitting examples of fractal patterns in human composition.
So you can see why I’m into it, right? The whole zooming in / zooming out thing, the whole “variations on a theme.” It’s 100% on brand.
But remember: fractals aren’t just a series of shapes or patterns. Fractal geometry is a whole new geometry, with a whole new set of powers. And transcending the macro- and micro-perspective… why that’s just the beginning.
Here’s what’s really cool:
Fractals have the power to transcend dichotomy itself; they dissolve the false boundaries between seemingly distinct things, and reveal the infinite richness of what lies in the in-between.
Mathematically speaking, a fractal is an object that literally exists in-between two dimensions: a “fractal dimension” is a non-integer usually between 1.0 and 2.0, “too detailed to be one-dimensional, too simple to be two-dimensional.”
Where an object falls on this inter-dimensional scale measures its complexity —in a sense, a fractal is the measure of how some things change, and some things never do. Mandelbrot himself described the science he invented as a “middle ground’ between order and chaos.
A middle ground between the repressiveness of total order and the madness of total chaos — I imagine a lot of us have pined for such a middle ground this year. We pine for it in our macro public lives — in our social distancing; our policing; our voting laws — as well as in our micro private lives — in our marriages, in our work-from-home routines. We want a space in-between order and chaos, in-between opportunity and security, in-between constancy and change.
Fractal geometry describes that in-betweenness.
And in doing so, it reveals the infinite possibilities that lie within apparent dichotomies, at any and every scale along the way.
How?
Let’s take a trip to the beach.
Not a very nice beach, I’m afraid.
England.
This is where Mandelbrot first identified fractal patterns in nature, years before he even coined the term. Here he describes the coastline paradox: if you zoom way out and roughly measure the coastline of Britain in 250 km lengths, you’ll find the total perimeter of the island is 2,500 km (ten such lengths). But of course by measuring in chunks of 250 km, you’ve simplified out a lot of the complexity of the coastline — cut some corners here and there, lopped off the peninsulas, rounded off all the zigs and zags of Britain’s bluffs and bays.
Now, if you zoom in by an order of magnitude and measure the same coastline in 25 km units, you’ll find the coast has almost doubled to 4,225 km! Zoom in more — measure in kilometers; meters; micrometers — and the total length of the coastline keeps growing with each magnification of scale.
So, how long is the coast of Britain?
As your measuring stick gets smaller, the thing you are measuring gets longer. Break something down into small enough pieces and you have an infinite supply of it. Only eat half the cake, and you will always have cake.
“In daylights, in sunsets
In midnights, in cups of coffee
In inches, in miles, in laughter, in strife
In five hundred twenty-five thousand six hundred minutes
How do you measure, a year in the life?”— Rent (1994)
Fractals remind us that how you measure matters. If you live in years, you probably get less than a hundred years. If you could live in breathes, in heartbeats, if you could break time down into infinitely small flickers of consciousness — what we sometimes refer to so casually as living in the present— it would be fair to say you would be living an infinite life.
Of course, empirically, you won’t live forever; at some point you will die. Similarly, Britain’s coastline does not go on forever; you can kayak around it if you are so inclined. You can take all these theoretically infinite micro-measurements and fit them all very neatly into a finite macro box: a hundred years should do the trick for a human life, in most cases; a thousand square-mile rectangle on a map will easily hold Her Majesty’s rock.
But don’t be disappointed… for this is precisely what’s so exciting about fractals: they allow the infinite to exist within the finite!
Infinite time and infinite space—and with it, infinite potential! — all can exist within our familiar boundaries and constraints.
My friends, look around you. Look closely at the fractal threads of your bed quilt, and discover that your little apartment has limitless depth to explore. Breathe a bit slower, a bit deeper, and consider how many countless moments would fit into this one hour if you could but be aware of them all.
Yes, our mortal lives can seem so squalidly Euclidean and square; but despite our boundaries—indeed, within them — we are all of us so infinitely rich.
So this is my fractal life.
2020 has been a year of incredibly finite space. Travel bans, quarantines, lockdown, shelter in place. My love and I have been stuck in Australia living out of suitcases since March, almost entirely cut off from our friends, family, jobs, and community. For the last several months we have been living a tiny life on a tiny island off the Gold Coast. Our newlywed routine is wholesome, boring, blissful: wake, walk, coffee, run, wash, work, eat, work, walk, coffee, work, eat, watch, walk, sleep. We cross the same bridge six times a day. Our physical lives fit neatly into a kilometer-long box.
But within the unprecedented constraints of this year, I’ve experienced unprecedented progress and growth.
I hit a number of macro-milestones between 35 and 36: I got engaged; started a new business; married my best friend. These are the milestones we often use to mark the curvature of our lives.
But finer still are the micro-maturities: the daily practice of patience; the calm pursuit of peace; the tectonic plates of habit grinding to align with the wants and needs of another.
It is these more infinitesimal moments that make us who we are.
I meditate more often these days, and feel within each breathe a dimension folding and unfolding, a tiny fractal universe expanding and contracting in my lungs.
If the birth, life, and death of such a universe could transpire in a single breathe of mine, then surely my tiny universe — my birth, life, and death — are but a breathe in some larger divine lung, all of this but the idle meditation of a god at rest. All of this but a god at rest — can you imagine if the god went jogging?
Within our bounded space and time, a boundlessness takes hold; and within our mortal bodies, immortality unfolds.
My friends,
Some of you are concerned, no doubt, that your very finite time may collapse into the endlessly self-similar recursiveness of this letter.
Allow me then this final modification of the loop:
The fractal abundance of the in-between lies between you and I, as well, dear friend. Yes, you: you who have stayed with me so long, through long letter and long life; you by my side a million miles apart; you who have known but an instant of me, and I an instant of you, and yet who hold the whole of me within you, just as I hold you each moment within me.
Breathe me a breathe for my birthday — a whole little universe as a gift.
Dissolve the false boundaries between us, and here we are once more.
Hello again,
Jonathan
