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It is often said that the human brain is the most complex object in the known universe. While incredibly intricate—with its 86 billion neurons forming trillions of connections—it remains far less complex than the universe itself. The universe contains billions of galaxies, each with billions of stars, planets, and possibly many other brains. 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 to science and ontology.

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 the subjective.

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 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 the 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.

And it's not just about 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 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.

The need for the observer comes out of viewing the universe as computational, meaning that it follows very simple rules that ultimately lead to very complex phenomena in cellular automata and perhaps the universe 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 time may be similar.

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 be 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 need 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 come up with an improved regulatory enzyme that works better and 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. AIs 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.