Providence in the Probabilistic: Faith and Non-Deterministic Systems

The early Church Fathers developed remarkably sophisticated frameworks for understanding how divine providence operates through genuine contingency. Modern theology has largely forgotten these frameworks. Modern computer science is independently rediscovering them.

That's not a metaphor. It's a structural observation grounded in information theory.

Maximus the Confessor described creation as unfolding through embedded rational principles he called logoi: patterns that allow for real variability within bounded possibility spaces. In modern technical terms, this is a latent space, the multidimensional manifold of all possible outputs that a system can generate. Gregory of Nyssa envisioned spiritual progress as directional but non-algorithmic, an iterative movement toward the infinite without a predetermined path. Origen argued that individual choices are genuinely unpredictable while the aggregate arc of creation bends toward restoration.

These aren't naive pre-scientific intuitions. They're nuanced positions on structured contingency that map with mathematical precision onto how modern stochastic systems actually work.

The Binary We're Stuck In

Both contemporary tech culture and contemporary Christianity operate with an impoverished binary: either outcomes are determined or they're random.

This is Boolean thinking applied to a Bayesian world.

The Enlightenment optimized for low-complexity, deterministic machines. It gave us a framework where truth exists in binary switches: true or false, real or superstition, determined or chaotic. That framework was useful for steam engines and clockwork. It breaks down completely when applied to systems where truth is found in probability distributions.

The Fathers refused the binary. So do probabilistic systems. So does quantum mechanics. The particle physicists figured this out when they discovered you can't know position and velocity simultaneously. The observational process itself constrains what's knowable. That's not a limitation of technique. It's fundamental to reality.

An LLM doesn't give you the same answer every time, but its outputs aren't arbitrary. They're shaped by training, constrained by probability distributions, and responsive to input in ways that are characterizable even when individual results aren't predictable. That's structurally identical to how the patristic tradition understood providence working through free will and natural processes.

The phrase I use is "variations on a theme." Yes, there's quite a bit of unpredictability, but it all falls within a bounded expectation of expression. This pattern shows up everywhere. And when we talk about probabilistic systems, that's exactly what we're talking about.

Three Indian Guys: A Case Study in Latent Space

Here's a story that demonstrates Maximus's theory in action.

I was doing image generation for my personal website. There's a section where I wanted professional-style family portraits, so I was using AI to take normal photos of my kids and pose them in that Sears portrait studio style.

I fed in pictures of my children. One time I got back an image of three Indian guys.

Totally bizarre. A wild left turn from the inputs. But here's what's interesting from an information theory perspective: the model found a local minimum within its latent space. The output satisfied the "portrait" constraints encoded in the training data but failed the "user intent" constraints that existed only in my head.

It didn't output random shapes and colors. It didn't output animals. It didn't crash my computer. It was still a portrait shot. Still people. Still in that professional studio style. The system navigated to a cluster within its weight space that met the formal requirements of the prompt while completely missing the semantic target.

That's not a glitch. That's structured contingency made visible. The bounded unpredictability was real on both ends: genuinely unpredictable within genuine bounds. The logoi held even when the specific output failed.

The Terminology Problem

People want to debate whether "non-deterministic" is even the right word for LLMs. Some engineers argue it's a misnomer that obscures the actual machinery.

Non-deterministic is a fine word. It's not deterministic. That's accurate.

The problem is when people conflate non-deterministic with totally random, with chaotic. That's a category error. The term "stochastic" is better because it describes something rather than just negating something else.

But here's where our language really breaks down. Think about things people consider quintessentially random: a roulette wheel, a dice toss. Even those are severely bounded. A roulette wheel will never land on 1,227,553. You're getting zero through 36. Two dice give you 2 through 12. The quintessential probabilistic thing is still operating within hard constraints.

And then people get confused by probability itself. They talk about being "due to win" after rolling five sixes, as if the dice remember what they did last time. It's the exact same chance as every other throw. Our intuitions around this stuff are terrible because the topic is genuinely hard to think about.

The shift we need is from Boolean logic to Bayesian inference. The Enlightenment gave us true/false. The Fathers and the LLMs give us probability distributions over possibility spaces.

The Asymptote: Gregory of Nyssa and Gradient Descent

Gregory of Nyssa's approach to spiritual progress is the strongest mathematical parallel in patristic thought.

Divine progress in the Patristic view is an asymptotic curve: constant movement toward a limit that is never reached. You know the direction you're moving. You know you're getting closer to something. But you don't know the exact shape of what you're approaching. You keep moving, adjusting as you go, converging on something without ever arriving at a final fixed point.

This is gradient descent with an infinite loss function.

In machine learning, we "descend" toward optimization by minimizing error. The loss function measures how far we are from the target. With each iteration, the system adjusts its weights to reduce the loss, moving incrementally toward better performance.

In Gregory's framework, the soul moves toward God through epektasis, an eternal stretching forward. But God is infinite. The loss can never reach zero. The asymptote extends forever.

That's not a loose analogy. That's the same geometric structure. An iterative process of error minimization moving toward a limit that, in a truly infinite system, can never be fully reached.

You're good at what you're doing. You don't know the exact destination. You don't even know the full shape of what you're trying to achieve. But you keep moving in a direction. That's spiritual progress. That's also how neural networks learn.

What the Fathers Understood That Enterprises Are Missing

Sequoia recently coined the phrase "stochastic mindset" as potentially the biggest shift in tool use since the computer itself. Moving from certainty to iterative development with probabilistic outcomes.

Meanwhile, nearly two-thirds of organizations are stuck in "pilot purgatory," unable to deploy AI because of trust issues.

The diagnosis is simple: enterprises are applying Deist theology to stochastic tools.

Deism imagines God as a clockmaker who builds a perfect machine and walks away. The clock ticks predictably forever. Any deviation is a malfunction, a betrayal of the design.

The Fathers held no such view. They understood that doing the right things doesn't guarantee good outcomes. It makes good outcomes more likely. The sun shines on the good and the evil equally. Look at Ecclesiastes. Look at the early Christians getting martyred while living in subsistence conditions. Material outcomes weren't correlated with virtue in any guaranteed way.

The so-called prosperity gospel has it exactly backwards. The view that following the right path means good things will happen to you is not what the Fathers taught. They understood something closer to probability distributions: virtue increases the likelihood of flourishing, but the correlation isn't deterministic.

The transformation is in you, not in your life circumstances.

This maps directly to the enterprise failure mode:

Feature | Deterministic Bias (Modern Enterprise) | Stochastic Providence (Patristic/AI)
Output | Guaranteed Result | Bounded Variation
Process | Algorithmic / Linear | Iterative / Emergent
Failure | System Crash / Betrayal of Trust | Out-of-bounds "Hallucination"
Trust Model | Absence of Variance | Management of Bounds

Organizations want the left column. Reality offers the right column. The mismatch creates pilot purgatory.

The Human-in-the-Loop Fallacy

You can't solve the trust problem by eliminating hallucinations. You can minimize them. You can bound them. But the possibility of stochastic outputs creating issues is inherent to the system.

Someone recently argued that human-in-the-loop isn't scalable, that what we need instead is guardrails for the AI where humans only intervene when outputs go outside the guardrails.

Who creates the guardrails?

That's human-in-the-loop with extra steps. The argument annoyed me because it was really just a reframe dressed up as a hot take. The fundamental reality hasn't changed: if your system can produce problematic outputs, verifying and bounding those outputs requires human judgment somewhere in the chain.

All you can do is verify that you've properly bounded the results and handle out-of-bounds cases appropriately. That's not a failure of AI. That's the nature of stochastic systems. The Fathers would have recognized it immediately.

Logoi and System Design

Maximus's concept of logoi, embedded rational principles allowing real variability within bounded possibility spaces, has practical implications for how you actually build things.

Early in my career, my mentor taught me about finite state machines. We needed to manage communication between concurrent processes that had to coordinate without fully synchronous socket communication. The solution was a state machine managing connection status. No connection. Connection initiating. Good connection. The various shutdown states in reverse.

The insight was about bounded possibility within a latent space of system states.

There could be up to ten processes talking to the main application. The combinatorial explosion of possible states was massive. But by defining a finite set of valid states and valid transitions between them, we could reason about the system. We could prove things about its behavior without having to trace every possible execution path.

That's what logoi are in system design. Embedded rational principles that allow real variability while keeping the possibility space bounded enough to be comprehensible and manageable.

When you think about systems modularly, where everything doesn't have to know about everything else, you're applying this pattern. The individual components have real freedom within their bounded domains. The overall system behavior emerges from those bounded freedoms interacting according to defined interfaces.

It's the same structure the Fathers saw in creation. Local contingency within global teleology. Real variance at the component level, coherent direction at the system level.

The Re-Enchantment

We're in a period of re-enchantment.

The virality of social media content, the emergence of trends without any committee deciding them, the way ideas propagate mimetically through culture. None of this fits the Enlightenment model of mechanistic causation. People are recognizing that there's more to life than base matter and Boolean switches.

The Fathers had observational data about human nature and social dynamics, knowledge passed down from antiquity. They were working with real patterns even if they couldn't quantify them the way we'd want to now. They understood that there's an unseen world that interacts with the visible world, influences it, is part of it. Not real versus superstition. Visible versus invisible. Measurable versus unmeasurable.

The shift from Boolean to Bayesian isn't just a technical upgrade. It's a return to a richer ontology.

Not Guarantees, But Direction

Recovering the patristic vocabulary for structured contingency has concrete implications.

For system design: The outputs won't be deterministic, but they'll be bounded. Design for that reality instead of pretending you can eliminate variance. Define your latent space. Understand what clusters exist within it. Build for graceful handling of local minima that satisfy formal constraints while missing semantic targets.

For expectations: These tools don't offer guarantees. Neither does providence. What they offer is direction within bounded possibility spaces. Movement along an asymptotic curve toward optimization that may never fully arrive.

For trust: Trust in stochastic systems, divine or digital, is not the absence of variance. It's the management of bounds. To deploy AI, you must adopt a Patristic view of risk.

On average, following the Christian path makes your life better. The probability is high that it increases joy, peace, love, fulfillment, purpose. But it's not guaranteed. The early martyrs were virtuous and they died horribly. When we downplay that aspect, we create a prosperity gospel that turns people off, especially people going through hard times who don't see a way out.

The stochastic insight applies to faith as much as to technology. You're not promised specific outcomes. You're given bounded possibility spaces that tend in certain directions over time.

That's not a lesser kind of providence. That's what providence through genuine contingency actually looks like.

Conclusion

The connection between patristic theology and probabilistic systems is real. Both theologians and technologists would benefit from recognizing what the Fathers figured out seventeen centuries ago: that structured contingency is not a problem to be solved but a feature of reality to be understood.

We are not discovering a new way of thinking. We are remembering an old one.