Why Intelligence Depends on Navigating Spaces Not Brain Size

The Octopus That Made Me Question Everything

A few years ago, a researcher named Michael Levin watched an octopus solve a puzzle that should have been impossible for it. The animal had to open a childproof pill bottle to get food inside. The octopus had never seen a pill bottle before. It had no hands, no opposable thumbs, no frontal cortex. Yet within minutes, it twisted the cap off.

Levin, a biologist at Tufts University, had seen something that the standard model of intelligence cannot explain. If intelligence lives in the brain, and bigger brains mean more intelligence, then an octopus with its distributed nervous system and tiny central brain should be a dim-witted invertebrate. But octopuses solve mazes, recognize individual humans, and use tools. They navigate spaces they have never encountered before.

That last part, the navigating of unfamiliar spaces, is what matters. It is what Chris Fields, an independent cognitive scientist, and Levin argue is the real measure of intelligence. In their 2022 paper "Competency in Navigating Arbitrary Spaces as an Invariant for Analyzing Cognition in Diverse Embodiments," published in Entropy, they propose that intelligence is not about brain size or neuron count. It is about how well an agent can move through any kind of space, whether physical, metabolic, or conceptual, and find what it needs (Fields & Levin, 2022).

This is not a metaphor. They mean it literally.

What Do You Mean by "Space"?

When you hear "navigating space," you probably think of a rat running a maze or a bird migrating south. Fields and Levin are after something bigger. They define space as any set of possibilities that an agent can explore. A bacterium navigating a chemical gradient is moving through metabolic space. A cell deciding whether to become a neuron or a skin cell is navigating developmental space. An entrepreneur figuring out how to launch a product is navigating market space.

The authors call this "competent navigation in arbitrary spaces." The key word is arbitrary. It does not matter what the space is made of. It does not matter what the agent is made of. What matters is whether the agent can enter an unfamiliar space, figure out its structure, and find a path to a goal (Fields & Levin, 2022).

This framework has a radical implication: intelligence is not a property of brains. It is a property of systems that can solve problems across different types of spaces. A cell that repairs a damaged organ is doing the same kind of thing as a person solving a math problem. Both are navigating an abstract space of possibilities.

The Evidence Is Everywhere If You Look

Fields and Levin do not just propose this idea. They show it at work across biology. They point to planarian flatworms, which can be cut into pieces and regenerate an entire body, including a brain, from any fragment. The worm navigates the space of body morphology. It knows what shape it needs to be and how to get there.

They point to slime molds, single-celled organisms that can solve mazes and anticipate periodic events. A slime mold has no neurons. It has no brain. Yet it navigates physical space better than many robots.

They point to cancer cells, which navigate the space of tissue architecture. When cancer cells metastasize, they are not just growing. They are moving through a body, finding new territories to colonize. This is a form of navigation, and it is intelligent in the same way that a foraging animal is intelligent.

The authors argue that the ability to navigate arbitrary spaces is an invariant of cognition. It is the one thing that all intelligent systems, from bacteria to humans to AI, must be able to do. If a system can do this, it is intelligent, regardless of its physical substrate (Fields & Levin, 2022).

Why Brain Size Misses the Point

The standard view in neuroscience is that intelligence scales with brain size, at least roughly. Humans have big brains relative to body size, and we are smart. Elephants have bigger brains than humans, but they are not smarter. The correlation is messy.

But the deeper problem is that brain size assumes intelligence is located in the brain. Fields and Levin argue this is a category error. Intelligence is not a thing that lives inside a skull. It is a relationship between an agent and its environment. It is the capacity to solve problems in spaces that the agent has not been programmed to handle.

This is why the octopus is so instructive. An octopus has a donut-shaped brain that wraps around its esophagus. It also has two-thirds of its neurons distributed throughout its arms. Each arm can taste, touch, and make decisions independently. The octopus does not have a central command center. It has a network.

Yet the octopus navigates physical space, social space (it recognizes individual humans), and problem space (it opens jars, solves puzzles). By Fields and Levin's measure, the octopus is highly intelligent. By the brain size measure, it should be a dim-witted blob.

The octopus is not an anomaly. It is a clue that we have been measuring the wrong thing.

How They Tested This

Fields and Levin do not present a single experiment. Their paper is a theoretical framework that synthesizes evidence from multiple fields: developmental biology, evolutionary theory, artificial life, and cognitive science. They use case studies to illustrate their claims.

One case study involves chimeric organisms, which are created by combining cells from different species. Levin's lab has created "xenobots," which are living robots made from frog skin cells. These xenobots can move through their environment, heal themselves, and even reproduce. They have no brains. They have no nervous systems. But they navigate physical space and solve problems.

Another case study involves planarian regeneration. When a planarian is cut, the fragments do not just grow back randomly. They coordinate to rebuild a complete body. The fragments navigate morphological space, the space of possible body shapes, and find the correct form.

The authors also discuss artificial intelligence. They note that current AI systems are good at navigating the spaces they were trained on but terrible at handling novelty. A chess AI cannot play checkers. A language model cannot tie a shoe. This is because these systems are not navigating arbitrary spaces. They are executing fixed programs in narrow domains.

By contrast, living systems routinely handle novelty. A bacterium encountering a new chemical can evolve a pathway to metabolize it. A human encountering a new problem can invent a solution. This is the hallmark of intelligence, and it is missing from most AI (Fields & Levin, 2022).

What This Changes About How We See Life

The most provocative implication of Fields and Levin's work is that intelligence is everywhere. It is not a rare property that emerged with humans or even with animals. It is a fundamental feature of life.

Consider a cell deciding whether to divide. It must sense its environment, process information about nutrient availability and chemical signals, and choose a course of action. This is navigation through the space of possible cell fates. The cell is making a decision, and that decision is intelligent.

Consider a plant growing toward sunlight. It is navigating physical space and light gradient space. It does not have a brain, but it solves the problem of finding energy.

Consider your immune system. It identifies pathogens it has never seen before and mounts a response. It navigates the space of molecular shapes and finds the right antibodies.

Fields and Levin call this "multi scale competency." Intelligence exists at every level of biology, from molecules to ecosystems. The same principles of navigation apply at each level. The tools are different, but the logic is the same (Fields & Levin, 2022).

This changes how we think about evolution. Evolution is not just about genes changing over time. It is about the emergence of systems that can navigate increasingly complex spaces. The first cells navigated metabolic space. Later organisms navigated morphological space. Animals navigated physical space. Humans navigate conceptual space. Each step is a scaling up of navigational competency.

What This Does Not Prove

Fields and Levin are careful about what they claim. They do not say that all living things are conscious. They do not say that bacteria have feelings or that plants suffer. They are talking about intelligence as problem solving capacity, not as subjective experience.

They also do not claim that navigation is the only thing that matters. They call it an invariant, meaning it is always present in intelligent systems. But there may be other invariants they have not identified.

The biggest open question is how to measure navigational competency. Brain size is easy to measure. You weigh a brain. But how do you measure a system's ability to navigate arbitrary spaces? Fields and Levin do not provide a simple metric. They provide a framework for thinking about the problem.

Another open question is whether all navigation is the same. Is a bacterium navigating a chemical gradient doing the same thing as a human navigating a social situation? Fields and Levin argue that the abstract structure is the same, but the implementations are wildly different. The bacterium does not have a self concept. The human does. The difference matters, even if the underlying logic is similar.

The Practical Payoff

This framework is not just philosophical. It has concrete applications.

In regenerative medicine, understanding that cells navigate morphological space changes how we approach injury repair. Instead of trying to micromanage every cell, we can provide the right signals and let the system navigate to the correct form. This is the approach Levin's lab uses to regenerate frog limbs. They do not build the limb cell by cell. They create conditions that allow the cells to figure out the shape themselves.

In artificial intelligence, the framework suggests that current approaches are missing something fundamental. Most AI systems are trained on fixed datasets and cannot handle novelty. Fields and Levin argue that true AI will require systems that can navigate arbitrary spaces, not just perform well on training data. This means building agents that can explore, learn, and adapt in real time.

In evolutionary biology, the framework explains how complex intelligence can emerge from simple beginnings. It is not a leap. It is a gradual scaling of navigational competency. The same principles that allow a bacterium to find food allow a human to find meaning.

What This Actually Means

• ▸Stop measuring intelligence by brain size. The octopus, the slime mold, and the planarian all demonstrate that problem solving capacity does not correlate with neuron count. Measure what matters: the ability to handle novelty across different types of spaces.

• ▸Recognize intelligence in unfamiliar forms. When a cell repairs a wound, it is solving a problem. When a plant grows toward light, it is navigating. These are not metaphors. They are forms of cognition that use the same abstract logic as human reasoning.

• ▸Build AI that can handle novelty. Current AI systems are brittle because they cannot navigate arbitrary spaces. The next generation of AI should be designed to explore and adapt, not just to optimize within fixed parameters.

• ▸Let biology do the work. In medicine, instead of trying to control every variable, create conditions that allow the system to navigate to health. The cells know what to do if you give them the right signals.

• ▸See evolution as a story of navigation. Life did not evolve to be smarter in some abstract sense. It evolved to navigate more complex spaces. That is the arc of evolution, from bacteria to Beethoven.

The octopus does not care about brain size. It cares about getting the food out of the bottle. And it does. That is intelligence. Everything else is just measurement.