A sandbox you can play with, and a plain walkthrough of what it shows.

The one idea

No mind sees all of reality. Your eyes take in a sliver of the light in a room, your brain throws most of it away, and what is left is a compressed, useful sketch you act on. Any observer that is part of the world, whether a cell, a brain, a computer, or an AI, faces the same problem: there is far more going on than it can track, so it must compress.

This page lets you measure that. It builds a tiny, fully known toy world, drops a deliberately limited observer inside it, and asks three questions: how much can the observer predict, does changing its viewpoint change what is knowable, and if you run it forward where does the arrow of time come from? The surprise is that the answers are not about the world alone. They are about the fit between the world and the observer looking at it. Run the experiment below...

It is often said that the human brain is the most complex object in the known universe. While incredibly intricate, with nearly 100 billion neurons forming trillions of connections, it remains, of course, far less complex than the universe itself. The universe contains billions of galaxies, each with billions of stars, planets, and plenty of brains. Even just on this planet we have quite a few billion. Logically, our brains, incredible as they are, must be simpler than the universe they aim to comprehend. We can't model every atom in a glass of water, much less the larger picture. We model what's necessary to survive and thrive and move on.

We are bounded observers, constrained by the limits of our senses, memory, and processing power. These constraints shape how we experience the universe as well as the patterns we see within it. This may seem obvious, still only recently have the deeper impacts of boundedness been explored across wider areas of knowledge.

A Bounded Brain in an Irreducible Universe

Advances in neuroscience and artificial intelligence have brought renewed focus to the limits of our ability to model and understand the universe. To perceive a pattern is to create an abstraction. An abstraction is a loss of information, but it's a necessary loss. To have any perspective means that some information is more available than other information.

These constraints are of course limits, but they are also the story of human progress. Necessity is the mother of invention, and constraints, while limiting, drive the need to access new ways of looking at the world, new perspectives. We have developed tools, from the written word to artificial intelligence, to continually expand our awareness and capacity. This iterative process, reaching the limits of our boundedness then expanding capacity through discovery of new patterns and new tools, is at the heart of value creation. Now, perhaps ironically, there's value to be gained from understanding a perspective that includes these constraints and what it means for how science models reality.

From Philosophy to Hard Science

The tension between subjective experience ("in here") and objective reality ("out there") has been a cornerstone of philosophy for millennia. From Plato’s Allegory of the Cave to Zen koans, thinkers have grappled with questions like: If a tree falls, does it make a sound if no one is there to hear it? Such questions are intended to test the boundaries of the objective in light of our subjective limits.

While science has historically focused on the "objective" view, the rise of quantum mechanics over the past century began to emphasize the observer's role. This shift has been slow to influence other fields of study, until now.

Swimming Against Entropy

Einstein said of the Second Law of Thermodynamics that it is:

"the only physical theory... I am convinced... it will never be overthrown.”

But now the role of bounded observers is calling the second law into question from multiple leading voices.

Could the second law be merely a matter of perspective? And, as time is largely defined by increasing entropy that the second law describes, is time itself a matter of perspective? Physicists have long been puzzled that at the most elementary level, there is no direction to time. The subjective perspective may explain in part why we perceive one.

In Carlo Rovelli’s bestseller The Order of Time, he explores this notion of perspective being deeply tied to time itself: “We must not, in short, confuse the temporal structures that belong to the world ‘as seen from the outside’ with the aspects of the world we observe and which depend on our being part of it...” In other words, how we see things, and how our sciences and philosophies model things, depends wholly on who we are as observers. Rovelli goes on to show how this includes the Second Law and the flow of time. We are programmed to recognize patterns and order. It is driven by the fact that we must abstract away complexity from our "view." We have blurred vision of the elementary levels. This necessary abstraction may lead to the perception of time. We'll explore this deeply in future posts, particularly related to a new but rapidly accepted theory called causal emergence, but Rovelli is not alone.

Adam Frank, a leading astrophysicist, talks about this in a recent Lex Fridman podcast (great explanation) and in his recent book: The Blind Spot. He argues that modern science overlooks subjective experience and it's a huge problem in our view of the universe. "The Blinds Spot" he refers to, is the subjective experience that has led to misunderstandings across many disciplines. We can never take the observer, and therefore our abstractions, out of the experiments.

Decades ago, biologist E.O. Wilson, in his seminal work Consilience, anticipated parts of this trajectory. Wilson posited that brain science could unify all other sciences because every discipline, from physics to art, ultimately stems from the operations of the human brain and our subjective experience therein.

This isn't true solely related to the limits of human cognition. The bounded observer is true for any system trying to understand the system it resides in, including AI. Any limited perspective runs up against something called computational irreducibility.

The Irreducible Universe

In the previous post I referenced Wolfram Physics. Stephen Wolfram, the author of A New Kind of Science and creator of Wolfram Alpha, has been leading calls for pulling the observer into our models across many areas of science. His post on Observer Theory is well worth the rather long read, as is a more recent one on the nature of time.

Wolfram sees the universe as computational, meaning that it follows very simple rules that ultimately lead to very complex phenomena. This happens in simple systems like his cellular automata ,and perhaps as he believes, the universe itself. It's deeper level of quantum systems where simple rules govern relationships at the smallest levels, the compounding of the ongoing activation of these rules leads to the complex world we see. A corollary to this computational view is computational irreducibility, the idea that you can't run a simulation of the system any faster than it runs itself.

Computational irreducibility is core to Wolfram Physics and Wolfram’s work over the last 30 years. Computational irreducibility simply means, given even a very simple rule, like rule 30, you can’t jump forward and make predictions about what a state of the system will be without just letting the rule run. The result of this recursion (where the answer at each step feeds back into the rule) is unpredictable without actually just running the rule repeatedly to see the result. You can't predict what will happen unless you just run the program. There are no shortcuts to a future state. Our universe and the nature of time may be similar. There are always some prediction errors.

Bounded Brains (and other kinds of observers)

The core of many mysteries in science seems to be pointing to the limit of being bounded observers making predictions in this sea of computational irreducibility. Bounded observers, because they are part of a universe which is computationally irreducible, are necessarily a subset of the entire universe. An observer within a system could never fully model the system it/he/she is in. As we simply can’t run the same program the entire universe is running, we must take shortcuts that can never tell the whole story. There will always be uncertainty and unpredictability, even if there are pockets of near perfect reducibility, like the sun will come up tomorrow. Black swans will forever lurk at the fringes.

As bounded observers, we each create a model of the universe based on the limited access to information through our senses and limited processing capacity for processing what comes in. We distill things into patterns, and collections of patterns that make things like the computer and desk and coffee cup appear as concepts we put into categories of experience.

We can make “good enough” predictions about the world. Information is always lost out of necessity, based on constraints and limited models and reference frames. Therefore the patterns we see, which is really everything we experience, is a condition of being constrained and limited, and that includes the flow of time. Still, you and I can "experience" presumably much more than an amoeba. That's because of expanded reference frames throughout evolution and learning, which are essentially two sides of the same process.

Framing the Bounded Experience

Because we have these limitations, in order to match our model of the world to a future context and make predictions, we need reference frames. Reference frames are kind of like working memory and context windows. They are a set of spaces, a library of internal models, which we can match to a limited problem space (like our current environment) to act and make decisions accordingly, stored solutions to given contexts. Consciousness may be driven by the experience of moving across reference frames as need to match the required context that fits the moment.

The architecture of the cerebral cortical columns, which repeat through the cortex, are possibly a repeatable architecture of reference frames that are repurposed for many kinds of problems. Jeff Hawkins discusses this in A Thousand Brains.

Think of it this way, we or any bounded system like a cell or an AI, has only certain storage and processing capacity. There are only so many variables, locations and relationships that can be tracked at once. In essence, we have limited space or resources to track these. So we create mini spaces that reflect sets of relationships and bring them up as needed to match the context we find ourselves in, whether it's a pattern on a chess board or navigating the streets of Manhattan.

Finding Causal Models

A key to expanding reference frames, expanding expertise, learning to play a new song, these all come when we find causal models within a reference frame, then compress that causal model into something more manageable. A causal model is also an abstraction, and is never perfectly predictive, but it allows us to compress our experience and make good enough predictions, then freeing up more space for novel information within the reference frame, like when a musician no longer thinks about a chord that fits. She just plays it. As soon as we can identify something that happens 99.9% (or whatever probability matters) of the time based on a set of inputs, we can free up space in the relationship map or reference frame by moving the recognition down out of conscious awareness. It frees up power.

We can live in the flow of the moment in these frames. The flow state is likely indicative of being at the limits of a reference frame, yet finely tuned to it.

This is why you can catch a ball or read a word without thinking about it. You’ve done it enough times that it becomes automated to your subconscious, out of your currently needed reference frame. The causal models have moved to new frames, below conscious experience. You may be able to carry on a conversation while playing catch. Your reference frame has found space beyond the causal model of catching the ball.

This process is true for consciousness, but it’s also true for computer programming, such as when someone creates a useful open source library, or when genes encode an improved regulatory enzyme that helps an animal run faster. Expanding context windows by finding and storing causal relationships means we can expand what we know and what we can deal with. We see the same thing now with AI. AI's answers are 'good enough' yet the context windows continue to expand.

Our most successful scientific theories reflect this constraint. Newton's laws don't capture quantum details, but they provide remarkably useful predictions at human scales. Our theories represent compressed patterns we've discovered - patterns that match our brain's ability to recognize and use them and then allow us to expand our context to bigger problems and more complex scenarios. Modeling the universe revolving around the Earth isn't necessarily wrong, but it's much harder to model than what we believe today. What's "true" scientifically, is often just the simplest, most easily compressed, model that fits. That frees up space for expanding the context window and expanding our models and creating value.

Looking Ahead

The goal of this post was to introduce some fundamental concepts. I'll explore the interplay of context windows, causal models, bounded observers and computational irreducibility in future posts, ultimately describing how they seem to form repeating patterns of progress across scales, from the subatomic to economics.

In this work, The Mirror and the Loom, we'll explore the processes that have brought us to this point and how they might guide us forward. By examining evolution, programming, economics, and AI through the lens of bounded observers and recursive pattern compression, we can better understand how systems—from human cognition to entire civilizations—discover and leverage patterns to progress.

Next we'll delve into these concepts with mathematical models and simulations. As a preview, I recently ran a simulation of Wolfram's Rule 30 to demonstrate computational irreducibility. Let me know in the comments if you'd like to see the code or learn more about these simulations.

This act of seeing, how we go about trusting the scene in our mind's eye, depends on layers upon layers of pattern processing of which we are blissfully unaware. From the retinas in our eyes distinguishing wavelengths of light to the visual cortex detecting edges and building shapes, our minds are performing immense pattern recognition and pulling it into a scene. Our minds do it so well that we just see the world as if it’s “out there,” even though all of this happens between our ears. Close your eyes, it mostly disappears. Eastern mystics may say the world is an "illusion" and it sounds compelling ("is nothing real?") yet it is not an illusion so much as a really good representation based on these filters. Like Plato's cave, the shadows we see are interpretations of reality, not reality itself.

(A future questions we'll grapple with in this series is what can be said of a reality beyond perspective, if anything. This isn't solipsism (nothing exists but me) so much as an impossible question. What can be said about what is if it's not said from a perspective?)

We arrived where we are in nature at this moment because whether or not these representations are “true” is far less important than the fact that they are useful. Our systems evolved for survival, not adherence to any one model but the one that works. Survival isn't helped when we treat the world as illusion. Survival dictates we treat our best current model as real. If it sounds like a lion in the bushes, best to err on the side of caution, even it's just a rustling branch.

Today, as we teach machines to “see” and act in the world, we are beginning to understand just how layered and complex this process of perception really is, just how much our representations determine not only what we see, but what we see in ourselves. We have an intimate relationship between ourselves and our representations. Can we say an observation exists without an observer? What would that mean? The tree in the forest may not, in fact, make a sound unless there is someone to hear it. This may seem like semantics, but this basic idea is starting to have repercussions across science beyond just quantum physics.

What Is a Pattern?

The word “pattern” originates from the Latin patron, meaning protector or guide. Why? A patron was a model for society to emulate. Similarly a pattern is a model, but more in the sense of an abstraction, a core set of similarity across individual occurrences. The pattern "triangle" comes in many shapes and sizes that still retain certain features.

Because of the regularity that exists in any pattern, either due to repeating in time or similarity across individual occurrences, we might say a pattern guides us away from uncertainty and toward predictability. Patterns repeat and thus have some level of predictability to be useful. They are regularities in the world that can be described more simply than listing all of their elements. If you say something is a triangle, you can immediately know it is not a circle. Patterns simplify, compress, and guide action that can be quick when a pattern becomes more recognizable.

The Greeks had a word for this too: idea (ἰδέα), meaning form or pattern. Plato’s "ideal" forms were thought to be the purest patterns: mental representations of perfect objects. Once again, patterns link to representation. But here lies a chicken and egg problem, which came first, the pattern or the pattern recognizer (aka the observer)?

The Role of Observers

Patterns require observers. An observation, by definition, requires someone or something to observe it. Without an observer, something capable of detecting regularities, what can we say of the world? Every observation is an interplay between observer and observed.

In order to create something called an observation, the observer must compress raw information into a meaningful pattern or patterns. If an observer could process everything in the world, it would be as large and complex as the world itself. The Observer would quickly become enveloped into the world of the observation. Every observation of a finite mind is a small slice of the observable world, and a compressed slice at that.

Observers, as they are a part of the universe and necessarily a subset of it, are not just constrained by, but are defined by computational boundedness: we call them "bounded observers." Any slice or sample of the world you try to take, you'll have way more information than it is possible to analyze, so we must take only abstractions or compressions.

So, we, as cognitive agents by definition as observers must be computationally smaller than the systems they observe. Yet to survive we must make sense of a world much more complex and vast than they are. How do we play this game? If we can expand our context window, the size of our model the world, perhaps we can better predict the world around us? In many ways, this is how we have arrived at this level of evolution, and now creating AI with potentially even larger processing power than the human brain. That will mean larger context windows and better predictive power, but never without limits.

The Observer Effect in Everyday Life

Most know about the Observer Effect, where the act of measurement affects the outcome in quantum mechanics. Yet science is just coming around to the idea that the act of observing is never passive. An observer is always engaged in selecting, compressing, and abstracting information.

It’s true of all observation:

1. The eye detects light waves and edges of light and dark and recombines and compresses them into shapes.

2. The mind abstracts collections of shapes into objects.

3. We act on those objects, trusting that the patterns we’ve detected are reliable.

It’s so seamless we forget we’re doing it. It's that good. This process of 'observation, compression, action' is the foundation of how any bounded system interacts with its environment, and this is one of the core concepts of the Mirror-Loom, we weave our reflections of the world into a tapestry by which we then continue creating our world.

Emergence of Patterns: A Self-Reinforcing Loop

So it may be starting to become obvious, but patterns can only be detected by other patterns. To observe a regularity, the observer itself must exhibit a kind of regularity, a structure tuned to behave in a regular way to specific inputs. Your retina detects patterns in light because it evolved as a biological pattern recognizer. A neuron fires because it “sees” a particular input as significant. Facial recognition systems identify faces because they’ve been trained on patterns of data.

Which brings us back to the chicken-and-egg problem: where did the first patterns come from? How did the first “observers” emerge to detect anything at all? How deep is this particular rabbit hole?

To answer this, we must look for the simplest systems possible. Stephen Wolfram suggests that simple nodes and rules in his computational universe, akin to cellular automata, might be the first pattern recognizers. For instance:

• Node A gives rise to Node B.

• Node B gives rise back to Node A.

This simple alternation is a pattern. An observer at this level just looks like simple cause and effect. Action-reaction following simple rules generates regularity. From such primitive processes, more complex patterns and observers can emerge. Observers detect patterns, compress them, and validate them. Trust in those patterns allows them to expand their scope, their “context windows,”and recognize more sophisticated patterns. For more on Wolfram and Observer Theory from a computational perspective, check out Wolfram Physics and his article on Observer Theory. The concept of computational boundedness as a structural feature of observers comes from Stephen Wolfram's Observer Theory. What we'll explore in this series is what that boundedness generates. The limits, the bounds, are counterintuitively a prerequisite for the intelligence we know and the order we see.

Time and Patterns

Interestingly, even the dimension of time may emerge from this process. Time, as we perceive it, is not an independent reality but a byproduct of observing causal patterns. How is this so? The arrow of time is defined by the flow from order to chaos, an increase in entropy.

But what is entropy? It's a lack of reducibility, a lack of an ability to find a pattern. Computational irreducibility says that all computational slices of the universe are essentially equal in complexity. If that's true then the second law is telling us is that we generally go from scenarios where we can recognize patterns to scenarios where we cannot. See Wolfram. When a coffee cup breaks on the floor, there are many more states states available than the intact cup before it fell. We can describe the unbroken cup easily, but we have a hard time describing the mess on the floor in a simple way.

Observers are necessarily finite. We cannot perceive all interactions at once, so we observe sequences instead, and therefore we are able to pick out causal patterns by how we detect changing patterns. The “arrow of time” may simply reflect the order in which a bounded observer is able to detect and relate patterns in its environment. Our ability to detect causal relationships builds from our pattern recognition systems.

Modern AI and the Observer Paradox

As we build artificial systems to recognize patterns, we see these principles in action. Modern AI models like Large Language Models (LLMs) or knowledge graphs are designed to compress and abstract vast amounts of data into representations.

• LLMs compress patterns in language to generate coherent text.

• Knowledge graphs link concepts and relationships to create high-level representations of information.

Still, AI is also a bounded observer. AI's ability to detect patterns is limited by computational resources, training data, information interfaces and design constraints. Like us, they see a subset of the world, compresses what it can, and trusts the patterns it has learned.

This brings us full circle: patterns require observers, and observers are bounded systems navigating a complex world through the act of compression. Compression brings speed and faster decisions.

Where Does This Lead Us?

The Observer Paradox shows us that the ability to see, know, and act depends on the ability to compress reality into patterns we can act on with enough speed and accuracy to ensure our survival. Without computational bounds, and the associated compression, there would be no observation, no pattern, no time, no anything as we know it.

We are participants in this recursive process, much like AI systems and the simplest rules governing particles or nodes. The patterns we see are driven as much by who we are as observers as by what we perceive.

As we explore this further, across physics, biology, cognition, and artificial intelligence, we will find that the act of recognizing patterns is a universal principle of existence for things we recognize as, well, things, repeated at every scale. We have dug ourselves into a deep nest of ordered structures. We are just scratching an enormous surface here with a few of these ideas and how we have arrived here, but we will have a much clearer picture by the end of this series.

Where and how far can this nested recursive perspective take us?