Probability Collapse

Unsorted ruminations, a love letter

Fractal art by Ethan Smith

As far as I understand it, anything that is not precluded as a law of physics or some universal constant is on a spectrum of probability. Lately, everything seems like patterns and probabilities to me. I’ve been spending a little bit of time thinking about: chess, the ocean, the stock market, large language models, and writing.

In my free time I’ve been working on a stock-trading algorithm (this is an embarrassing admission for me, I’d really like not to be relegated to finance-bro territory.) This guilty pleasure of a hobby is a radical broach into a new world for me because I am not a math guy by any stretch of the imagination and I’m not really all that interested in becoming a millionaire by discovering some secret inefficiency in the market only I know about and can exploit for financial gain.

But I am interested in modeling market behavior (and yes, beating it as a measure of how much I can understand it). I won’t go into too much detail so as not to bore you, but this practice of analysing stock data and behaviors through a technical lens (using sometimes basic math, primarily, not candle-chart reading) has been a fascinating pursuit. How do you model something as complex as the financial market: the sum of all quantifiable value on Earth and in which all possibilities have more or less been accounted for? How can you model something so vast as the sum of most all human activity, hopes, fears? How can you model the roiling power of the deep ocean?

That’s what this endeavor feels like, honestly. A meager, uninformed, attempt to model the seas of the Earth. There’s myriad ways to go about it and different inefficiencies to capture. People successfully create algorithms to trade the market all the time, and they’re all unique and often ephemeral. An algorithm that works today might not work in a few years. It’s all about frameworks and philosophies.

It’s almost a pure, intellectual, pursuit. It reminds me of my time in University as an English major where I delighted in spending a semester talking about just a handful of books. The only class besides Calculus I ever got a C in during my time at school was actually an English class about Edmund Spencer’s Faerie Queene. Yet, I actually rather enjoyed the class. I enjoyed that my classmates and I got to throw our entire mental powers against a text older than our country and draw Insight from it through different critical analysis frameworks. We got nothing tangibly useful out of it except to deepen our ways of thinking about and seeing a fixed object. To widen our perspective, our worldview. It was almost meditative. I felt sharp and nimble back then. Modeling the market in my own amateur way feels akin to that. It doesn’t have to be fruitful to be worthwhile. Sometimes it’s okay just to do things even if you’re bad at them. Not even just because you want to improve at it, but because you want to improve as a person through the pursuit itself.

Another thing I’ve been more interested in lately, though I’ve long considered myself bad at it, is chess. My whole life I saw chess, like math, as an indominable thing outside of my reach. It just wasn’t for me. I have the flaw of being unable, or maybe unwilling, to strategize in games. I just can’t bring myself to do it. But my brother has lately gotten really into chess and even bought a real board to play on. Of course I am often his partner at this (reluctantly, perhaps). At first when I saw the chess board I was absolutely overwhelmed. Everything looked like chaos, even after I refreshed myself on the rules of each piece’s movement. But I played a few games and soon it didn’t look so much like chaos anymore. I sort of understood the game. I could play, really play. That’s one thing humans are incredibly gifted at: discerning signal from noise. Gaining insight from chaos. Seeing shapes in the stars. In many ways that is what learning is. We are pattern machines — possibility machines.

But my brother’s been playing chess longer than me, and my friend Tristan even moreso and they of course swiftly destroyed me in any game I played against them because they were beyond where I was: they were on Vienna Openings and London Systems. They were playing higher-order games than I was because chess is a game of patterns — of openings and ripple effects.

It’s worth noting that as a game developer I’ve really come to appreciate chess as the perfect game that it is. It’s totally balanced. The quintessence of a game. The most interesting thing about it is that it happens on a finite combinatorial space. Meaning that all information is known at all times throughout the game. There is no chance, no dice-rolling, no randomness. It’s computable. The combinatorial space of chess is admittedly large, however. In fact, according to the Shannon Number there are more possible games of chess than there are atoms in the Universe. This means, of course, you can’t just compute every chess game. Not because it’s not possible, but because it’s not practical.

Is chess like the ocean? Like the stock market? Maybe. Regardless, I found the development of these strategies, these openings and patterns, that more advanced chess players use really interesting because they’re not only strategies for winning but also means for restricting the possible patterns of a chess game. A reduction of the combinatorial space. When I played Tristan in particular the game felt less like an even match but a slow and steady reduction of my possibilities until all that was left was my inevitable failure.

It felt like something called Wave Function Collapse. It’s a term from quantum physics but I first learned about it in a totally different context: video games. One reason I love game development is that because it’s so multi-disciplinary and attractive to people like myself who are at the crossroads of many artforms it ends up surfacing really novel solutions to sometimes silly problems. One such problem: if I’m tired of developing all the levels for my 2D adventure game by hand, how can I speed up the process? It’d be nice to procedurally generate the whole game, but how can I do that in a way that doesn’t totally suck?

Suppose a level only has a certain amount of total tiles: 256. And a tile could be a sand tile, water tile, grass tile, or stone tile. That leaves a lot of potential configurations of what a level might look like. Let’s come up with some rules. A water tile could only go next to a sand tile, and a sand tile can only be between a water and grass tile. Stone tiles can only show up next to grass tiles or other stone tiles. Grass tiles can be next to any tile except water tiles.

With this simple ruleset we can generate our worlds by simply setting down a tile of our choosing anywhere. The constraints of the rules and the possible tile types allow you to generate a not-quite-infinite-but-definitely-a-lot number of worlds.

The origin of the term comes from the way that, in quantum physics, everything lives in a state of simultaneous probabilities until acted upon by an external factor like mere observation. In our day to day lives we are constantly collapsing probabilities into our current reality merely by existing, by being conscious. We are the ruleset, we are the tiles, we are our own world.

Part of what makes writing so intimidating for me is that I’m not sure it’s a combinatorial space. It feels infinite, even though it is numerically constrained to the possible words I can use in a sentence and the grammar rules by which I’m allowed to place certain words next to each other. How can I guarantee I will choose the right path? The path of possible words, aligned just so, to create something you’ll like? Something good, valuable? I’ve written before about how writing is difficult because of its many possibilities (and the decision fatigue that comes with making so many choices consecutively).

Anyways, the essence of writing is this: you have an infinite canvas to play with, and it is so blank it's blinding. You have no brush, no string, no materials except a spell book called a dictionary and a syntax of incantation called grammar. These incantations of yours are shaky vessels for something potent and infinite: your imagination. Your only job, really, is to use your spells in such a way that you reduce the infiniteness of possibility into something more concrete and coherent. If you're skilled then it's something beautiful.

Writing functions a little bit like wave function collapse: anything is possible until you put a word down, and then that constrains the next potential word. Which means it does get easier to do over time. But boy is it hard at the start.

But then again — isn’t life like this? I guess that’s why I sympathize with people who are frozen up because they don’t know what they’re doing, they don’t know where to go. They’re just overwhelmed by the possibilities and terrorized by all the ways they could choose wrong. It shouldn’t stop us from just getting on with it, but it does. It stops me from writing. But the cure is the fear itself. We must just get on with it.

A chart depicting a guassian random walk at 100 steps of simulation

In a simplified way, this is what each moment of your life looks like. Near infinite branching paths of possibilities that we collapse in every consecutive moment into absolute certainty — and then fractures again into myriad possibilities. This chart is a random walk, and it is what our past looks like, and our present, and our future. It’s terrifying, indiscernable noise. It’s vast, inscrutable, near-infinite in scale. We are so small, as humans. So, so small. And yet one single person, in even as paltry an amount of time as an hour, is the begetter of more possibilities than even a celestial body as large as Saturn itself.

So when I think of all the superpositions that had to harmonize, all the probabilities that collapsed, the lives that passed, the hearts that touched, the stars that aligned, for me to be with you — I am awed. I feel fortunate. I am instantly religious: humbled, uplifted. What grace has befallen me that I should be so improbably lucky to know you and love you? The sequence of blessings must be larger than all the stars there ever were for me to be besides you.

I love the way you scrunch your nose at me, your quips, the words you make up. I love that you make me laugh so much, even when you’re not being funny. Not just because I’m amused but because you are, to me, an endless stream of little delights. You surprise me even when I know you like I know my way home. You are the rhythm of the very best stories. Everything you do works out just how it’s supposed to, even when I don’t expect it. You make me happy in that way.

But what I really love about you is that it feels like, luck beyond luck, you are just right for me. I’m a hungry sort of man and constantly I feel the drive to create and do and take action at all times. Perhaps it’s because I feel subconciously that I must do something or be something that justifies my own existence. To collapse as many possibilities as I can in the pursuit of concreteness. But with you, not because of anything you say or do but just because of who you are, I don’t feel that way. With you I just feel like all I have to do is to breathe, besides you, to justify all I’ve ever done or been or will be. With you I feel that nothing more needs to come to pass for it all to have been worth it.

You are the shade of a grand oak tree in which I may take respite after a long day in the blazing sun. With you I could watch clouds pass by and the bees land on flowers, and the wind play on leaves, and everything is just as it should be. You are the gift of gravity that binds me to the soft grassy Earth when so much of my world is weightless and ethereal and uncertain. And I am so lucky to rest in the shade of the long delight of your love.

And if I had to do it again, if everything collapsed into itself and the universe turned into nothingness, I would tell the Progenitor of worlds to put into play that exact sequence of probabilities that led me to being with you. And I’m excited, absolutely joyous, that I can go on this random walk with you into the boundless future. You know I’ve always loved a good walk.

With love as always,
Juan