It's Fractals All the Way to Infinity
The Grandeur Just Keeps Getting Grander & The Most Terrifying Thought Ever
Physicist Hans G. Schantz and philosophical/political writer extraordinare John Carter recently had a wild conversation about physics, its unanswered problems, and deeper symmetries that are out there, that got me thinking some wild thoughts, or, at least, wilder than normal, about the nature and orderliness of the physical universe. Check out the Dirac large numbers hypothesis or the single electron theory if you really want to blow your mind.
As much as we do think about the mysteries of the world, we’re often too busy, at least in our current age (the one coming to a close, modernity), to really really ponder how extravagantly wild existence is.
Existentialist Terror
Don’t misunderstand me here, but I kind of can’t understand why God—or the world—exists.
This question is not what it seems. No, I’m not denying the world, I’m not denying God. Other than a weird brief period as a young child where the fiction somehow seemed more imminently (and threateningly) real than the First Cause, who is pure being itself/Himself, I’ve never struggled with the fact of God’s existence, or the world’s.
But my question is one more of the type of “why?” known as “propter quid” versus the more humdrum one that’s always been obvious to me of “quia.”
Because I see the world, I know that it has a Creator. Why is there a God? Behold the world, quia (because) all this contingent being needs a Creator. The more confusing thing to me, as I presume it is to many of us if we ever stumble upon the other question somewhat weirdly, for some reason, is not whether God has to exist, but why, on account of what, for what reason, or by what cause does He exist.
Now, of course, I’m not God, so that’s probably the reason why I can’t answer this question. But the weirdest thing to me about this question is the fact that it’s always been a scary question, or, as I’ve imagined it, the scariest thought imaginable.
Imagine for yourself absolute emptiness. Not empty space, no. Nothing. Nothing from which nothing proceedeth, nor can proceed. Not blackness. Just nothing. No God, no world, no you, no thing, and no nothing. For a moment, as I’ve imagined this scene again and again for close to two decades now, nothingness just makes a lot more sense than there being any being (or beings).
And then reality flashes back to life in my imagination. There is being. There is God. There is a created world.
But my imagination from a moment before argues back. Why? Why not nothing? WHY? Isn’t it all too weird? Isn’t it all just too plain wasteful? Wouldn’t it all be simpler if there just weren’t any such thing as being?
The contrast, as I shock myself with the discordant, infinite difference between being and non-being, is something I can only describe as about the scariest thought I’ve ever thought.
I think of the expressionist Edvard Munch’s 1893 portrait of man’s existential dread, “The Scream,” when I think about these moments of my thinking about nothingness.
Other than a little Kafka, my portrait of the existentialists or absurdists like Sartre and Camus comes only in bits and pieces. I’m a little interested in melting the conveniences of ordered reason remain within my mind any more than they’ve already been scrambled, preposterous thoughts. But, under the surface, as much as we use busy work and distractions to ignore existential questions in our (temporary and about to be over) age of Modernity, we’re all hanging under the shadow of them, whether or not we want to admit it.
And the World Just Keeps Getting Grander…
Reality is weird. The fact that we exist is weird. The fact that God exists, and deigned it fitting to create us, and this massive world that keeps getting larger and more complex, and also, simultaneously more and more ordered, symmetrical, and—dare I say?—simple at the same time, just makes these existential questions more and more potent.
The grandeur just keeps getting grander…
Two thousand years ago, contrary to what Richard Dawkins and Company (Atheist Inc.) have claimed, it was possible to be an “intellectually fulfilled atheist.” There wasn’t all too much universe to explain back then, and one of those could pretty convincingly argue that it was just a chaotic mess filled with meaty blobs, watery blobs, earthy blobs, airy blobs, and maybe aetheral blobs, and a little bit of a mystical swerve if you were one of these “materialist” proto-atheists like Democritus and Lucretius.
Of course, there was glory and beauty to be seen if you dared to look, and mystery probably captivated the human imagination more than it does for our distracted selves.
But there was less existential dread in the cozy little universe that was neat, tidy, and not so mind-shatteringly detailed nor absolutely massive as the ever-expanding mysteries of science (as continually neat and tidy as our authorities may claim to the contrary) are revealing themselves more and more to be.
I’m not just focused on the size, every increasing orderliness (and mysteriousness) of the physical laws, or how just about everything new we encounter, as Hans G. Schantz and John Carter discuss, subverts our current models, replacing them with something even more detailed, mysterious, and ordered, all at the same time.
Did you know that the Milky Way flaps its wings, by the way?
No, I’m not just thinking about this, but also about some of the other weird things, like just how orderly, simple, and yet capable of ever further abstraction and expansion something like mathematics is.
Fractals All the Way Up (And Down)
Whatever’s going on in mathematics, regardless of how hardened an atheist’s heart is, it’s powerful enough to break even that if he really stares at one of these Mandelbrot set visualizations long enough.
It will certainly break your mind too if you stare at it for too long.
Leave aside the visual stunningness of what is literally in these visualizations, a plunge into infinity, and just think about what number is. In my new job as a math teacher, I certainly do so a lot, and can’t help noticing how mathematics (and its applied version, geometry), while each having depths deeper than any I’d noticed growing up, is also a whole lot more ordered than I’d ever noticed before.1
It’s not about manipulation and change as much as it seems like a cacophony of disparate operations of just that sort on the outside. Rather, a single reality, a single unity, a gem is looked at from multiple angles, peered at, rotated, but remains the same in itself. Even as our abstraction to higher and higher heights of analysis, it gives us both a clearer image of a single gem, yet also increasing detail.2
Math is really just about how oneness relates to infinitude, geometry is about how the infinitely small and simple (a point) relates to itself, and even calculus is just about figuring out how to transcend finitude and approach a reality that is present, ordered, and simultaneously always just beyond reach.3
Mathematics, like the cool visualizations that can be made with it, and like our ever increasingly mind-breaking models of reality, is fractal, with an infinitely complex, never-ending pattern that repeats itself across different scales of analysis but reveals, again and again, simpler principles that underly and cause the outwardly revealed complexity.
Perhaps, as with Mark Bisone’s theory of everything in his essay “What Reaches Back,” reality as a whole is like this, with ever-increasing complexity, bounded and determined by ever-increasing order at larger and smaller scales of size (and abstraction).
If we dared to look, that is, opposed to the stultified state of modern scientism’s dogmatism, dead set on perpetuating the line that the world is meaningless, boring rocks made out of boring blobs, that-may-or-may-not-be-made-out-of-anything-but-please-just-keep-paying-us-to-work-on-string-theory-forever…4 Just as occurred with the transition from Newtonian to Einsteinian paradigms, the World is far more ordered than the current models, and each scientific regime fails and needs replacement because the model is just too small, too clunky, too ad hoc and has to small of an imagination.
For Mark and the neuroscientist and philosopher Iain McGilchrist who’s strongly influenced his views, the world, like the old adage, is turtles all the way down (and up), fractals on top of (and below) fractals, complexity in every direction, but ordered complexity. The world is a nested hierarchy of beings, laws, and principles, each governed by some other principle above them and each unifying those below them.
For the Christian, this is the kind of thing we would expect in a created world, and Mark/Iain sound a lot like the Medieval Model of the Great Chain of Being, but one, this time, that due both too all the discoveries over the last centuries and the whole lot more that we also don’t yet know about,5 is a little too complex and perfect to fit into a human drawn sketch:
The chain, of course, can’t go on forever. The created world is held in existence by the Creator at the top, with the activities of the angels in the middle, but above us, while, at the bottom, below the lowest being, lies absolute non-being, that-which-is-not. And the average physicist, for all his probable stuffiness and materialism, agrees with the Medieval. There is some reason, some ratio/Logos lying causally primal to the world, and there is, on the other end of the rope, nothing smaller and simpler than the smallest particle (besides maybe the potency and fuzziness of the quantum foam).
What’s At the End of the Chain?
But this image, beautiful as it is for the believer by the increased grandeur it gives to God’s work, will, absent correction, give us a false, and in some ways falsely terrifying view of God, as with my aforementioned moments of experience of existential dread, a feeling I’ve found best encapsulated in this video combining Zbigniew Preisner’s rendition of Mozart’s “Lacrimosa” with space telescope imagery of the grandeur of creation:
The God who created all this—and you, could very easily appear to be a scrupulous micromanager on one hand, who’s using you to fulfill some impossible to understand master plan, or an ethereal and distant cosmic force who barely notices you. It’s a plausible dichotomy, and as our knowledge of the world’s complexity—and order—builds over time, the problem becomes worse. It’s as if all of history is a journey bringing us from the outposts of a civilization to its capital city, or from the antechambers of a king’s castle to his throne room, but we keep on discovering that the king is further away. The castle is larger, the kingdom grander, the throne room another two flights of stairs away, separated from us by another moat.
What sort of king is this? What sort of a creator is this, we ponder to ourselves? What sort of world were we brought into existence within? What sort of ineffable Creator exists, and why did this sort of Creator have to exist?
Now the king’s enemies have one answer that they whisper in our ear as we make the ascent: “The king is not good. The king is using you. At the end of the stairway, you will find a tyrant. Come, join our effort to build a kingdom for ourselves off to the North.”
Or perhaps it’s the other, more subtle Siren song, is whispered in our ear: “Nothing you can do will be enough for him. Give up now. Whimper before his grandeur. Dare not to make the climb.”
The Catholic Thomistic view of God (as with the rest of the Church Fathers) cut through this dichotomy, but the answer proposed about the nature of the King, Creator is also so odd to our small imaginations as to be mind-breaking.
Though God (again in a way that we cannot imagine nor comprehend) exists of Himself of necessity, God creates and created from an absolute lack of natural necessity, either of nature or will. It means that anything and everything held into existence by God has been done so freely and undeservedly. The universe is a free, unnecessary, and superfluous gift to itself, not owed to anything or anybody, not even to God himself, but proceeding forth from Him in such a manner so unnecessary so as to seem almost useless. But it is not, for love gives it both its being and its meaning. Love desires the increase of the beloved. God makes the cosmos because He desires to make it desirable and Divine-like.
See my senior thesis on St. Thomas’s arguments for how creation involves no necessity on God’s part:6
God loves it into existence. He loves it into being lovable. As St. Thomas writes that “everything that is generated, whether by art or by nature, is in some way rendered similar to the agent in virtue of its form, since every agent produces an effect that has some resemblance to the agent himself,” everything in creation bears in some way an imitation of the Divine perfection. God creates, then, by freely bestowing imitations of Himself, sharings of Divinity with existence. These imitations refer back to God in their being and also have him as the end.
Though not Catholic, the image provided by St. Thomas is, I believe, best put into prose by C.S. Lewis in his book on love, The Four Loves:
In God there is no hunger that needs to be filled, only plentiousness that desires to give. The doctrine that God was under no necessity to create is not a piece of dry scholastic speculation. It is essential. Without it, we can hardly avoid the conception of what we might call a “managerial” God; a being whose function or nature is to “run” the universe, who stands to it as as a head-master to a school or a hotelier to a hotel. But to be sovereign of the universe is no great matter for God. In Himself, at home in “the land of the Trinity,” he is Sovereign of a far greater realm… God, who needs nothing, loves into existence wholly superfluous creatures that He may love and perfect them… If I may dare the biological image, God is a “host” who deliberately creates His own parasites, causes us to be that we may exploit and take advantage of Him. Herein is love. This is the diagram of Love Himself. The inventor of all loves.7
God doesn’t care about the cosmos because He has to, or even because it gives Him pleasure or happiness. Unlike a “managerial” God (Richard Dawkins’ view, for one), our God doesn’t have to care about us. The glorious thing about Christ the King, “Love Himself,” is that as “The inventor of all loves,” He simply decides to love what is not lovable into being lovable, and that is the origin of all love outside of God. God creates not out of a hunger to receive, but a “plentiousness that desires to give.”
Lewis’ bold analogy, that “God is a ‘host’ who deliberately creates His own parasites, causes us to be that we may exploit and take advantage of Him” is striking to the point of repulsiveness, but is, at core, quite true. God creates only to let us share in His existence and “take advantage of Him”, to come into existence and receive a participation in Him. Herein, in creation, the greatest and first self-sacrifice of love, the origin of all loves, God shares His existence and perfections with other creatures by calling them into existence. God shares being God-like with what has no right or debt to be in existence without His call, His will, His love. God is not a manager nor an impersonal force, but a lover:
But the wilder part of this way of breaking the aforementioned existentialist dichotomy that tells us to fear God is how it increases His grandeur even more. For God to be sovereign of the universe, as grand, ordered, and magnificent as it may be, is “no great matter” for Him. For God, in Himself, in “the land of the Trinity,” He is “Sovereign of a Far Greater Realm,” just as, if you don’t believe Aquinas/Lewis, God Himself in the Book of Job also says:
“Where were you when I laid the foundation of the earth?
Tell me, if you have understanding.
Who determined its measurements—surely you know!
Or who stretched the line upon it?
On what were its bases sunk,
or who laid its cornerstone,
when the morning stars sang together,
and all the sons of God shouted for joy?
[ … ]
“Can you bind the chains of the Plei′ades,
or loose the cords of Orion?
Can you lead forth the Maz′zaroth in their season,
or can you guide the Bear with its children?
Do you know the ordinances of the heavens?
Can you establish their rule on the earth?8
As great as we think God is, He’s unimaginably greater than the biggest image we can conceive. I’m purely speculating here, so take this as a poetic metaphor, but perhaps the fractal symmetry does go on forever, beyond the world and man made in the image of God, all the way up the ladder to Him and through Him and in Him. And, in Him, in His infinity, the ladder, the fractal continues.
The Actually Scariest Thought Ever
This image (by analogy), like staring into one of the Mandelbrot Fractal Zoom videos (but infinitely more so), should be mind-breaking. Perhaps my existential dread at nothingness compared to the minor majesty that is existence and the infinite majesty of the Divine is not completely ill-founded. Until we’re on the other side of the veil in the Beatific Vision, we’ll never be able to explain why there is anything at all, and even then, our understanding of that reason, of the Logos, will only be by unity to it.
Yet dread should fill us of the Judge for our failure to live up to the finite majesty and grandeur of our own being. Minute it as it is compared to infinity, it is, as with my moments of pondering the gulf between nothingness and my own existence, an infinite gap in itself that God brought us across in bringing us freely into existence. Dread should fill us if we misuse and abuse our place in this cosmic hierarchy of beautiful order out of fear, turning inward, or worse, turning aside from fulfilling our station.
For us, the scariest thought ever shouldn’t be nothingness, as God’s already brought us past that. The scariest thought ever should not be the thought of pondering God’s existence, nor that of not wanting to ascend the rest of the way up the ladder to meeting Him. No, the scariest thought ever should be dread at the thought of not wanting to meet Him.
And when He returns, and we meet Him, will He find faith (and joy) on Earth, and in us?
Thank you for allowing me the chance to satisfy some of my other interests, other than merely the dark news of our current age and the scandals and craziness in the Church. I don’t want to only be a downer, but there is more on those matters to come.
More on this after I’ve written the next test.
I see (properly understood) St. John Henry Newman’s idea of the truth as a gem remaining inviolable and unchanged, but capable of being better understood to be true in other areas than just theology.
To be fully justified in a future essay.
Check out Hans G. Schantz or Eric Weinstein for the receipts.
Lewis, C. S. The Four Loves, (New York: Harcourt, 1960), 175-176.
Job 38
A lot to digest in the opening line of St. Bonaventure’s post-Communion prayer…
“Pierced with the dart of Your love, O Lord,
and inflamed with the desire of enjoying You, I long to be dissolved and to be with You.”
Beautiful words of union with our God and Creator of the universe. Right? Wait. Not so fast. Read them in the context of a sinner, a narcissist, an atheist… they become the pinnacle of terror. As C.S. Lewis points out in one of my go-to CSL reads, “The Problem of Pain,” God casts no one into the fiery pits of hell. We go there, or into the suffering of Purgatory, of our own free will, terrified at the awesomeness of His infinite love that requires our complete surrender. I don’t know about anybody else, but I, for one, am a sinful coward with no hope in my own pitiful effort towards saintliness. I look forward to perhaps someday not being afraid of the idea of being “dissolved” in the Lord. To ponder it fills me with the humility of knowing God’s infinite mercy is my only hope.
With regard to the question of why does existence exist…. it’s always fun to ponder and roll around in our heads with our algorithms and theories. But God explained it to Moses in the simplest way our feeble human minds could comprehend… He *is* Existence. Was it Aquinas who said that what is meant by our being made in His “image and likeness” is our very own existence? Not sure, but, if not, I know I heard it or read it in some very Catholic literature.
Thanks for the thought provoking article. Jesus be blessed.
Beautifully written!
It brought me back to the 80s when I was a Systems Engineer for IBM. We were testing the newest and most powerful computer to date. Our top guy in Systems suddenly got interested in fractal geometry and was running these computer generated images all day and into the night! He created some gorgeous graphics like the ones above.
The most interesting thing about it is that, even with the top of the line machine, he would start the process and let it run through the night before it was complete. What I am holding in my hand is more powerful and can complete in seconds what that massive machine would take many hours to do!
Have a great and blessed day!