What do a developing embryo, an ant colony, and the latest version of ChatGPT have in common? At first glance, it may seem that there is nothing connecting them, but an interdisciplinary group of scientists has uncovered a hidden algorithm that unites all these systems. They concluded that any intelligence, whether it be a cell or a complex computer, does not merely process information but "navigates" through imaginary maps of meanings and forms. We often consider intelligence to be solely a product of brain function; however, biology and artificial intelligence demonstrate that thinking is navigation in a space of abstract coordinates. Understanding this internal compass opens new horizons in cognitive science, allowing us to view the world not as a random set of events but as a complex geometric problem, as noted by Hi-Tech+.
Who is the initiator of this discovery?
Michael Levin from Tufts University, the lead author of the study, is today renowned as one of the boldest innovators in biology. He is often referred to as the "hacker of the code of life" due to his experiments in creating xenobots — the world's first living robots made from frog cells. Levin asserts that even the tissues of our body possess intelligence and can "reprogram" themselves. The team also includes Benedict Hartl, a physicist and complex systems specialist who translates biological concepts into the language of mathematical models. Their collaborative work is creating a universal theory of how any matter can think.
Below is a popular summary of their new paper titled "Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems," which was recently published on arxiv.org.
Imagine that you are lost in an unfamiliar city. To find your way out, you need two things: a map to understand where you are and a navigator to guide you to your destination.
In their work, Levin and his team argue that this duo — creating a map and navigating it — is the fundamental law of the mind. Regardless of whether it concerns a human, a tiny cell of an embryo, or artificial intelligence, they all solve the same problem: transforming the chaos of external signals into a convenient internal "map" and striving to minimize errors as they move toward their goal.
1. Cognitive invariant: the mind as a universal program
Traditionally, we view intelligence as a "brain-centric" process: neurons are thoughts, and their absence is merely mechanical responses to stimuli. Levin and Hartl dismantle this notion by introducing the concept of cognitive invariant — a fundamental principle of information processing that remains unchanged regardless of whether it operates on carbon cells or silicon chips.
Every living system faces similar challenges: the world is too complex and chaotic to respond to each stimulus separately. To survive, a system must evolve from a mere "set of parts" into a cognitive agent.
- For an embryonic cell, "intelligence" is the knowledge of how to create an eye without a blueprint, relying on interactions with neighbors.
- For AI, it is the ability to predict the next word based on the context of all literature.
The authors of the paper argue that the mind is not a "bonus" for brain owners but a fundamental property of organized matter. Every system striving to maintain its integrity must engage in cognitive activity, constantly predicting the future and adjusting its state, which shifts biology from the realm of "chemistry" to that of "informatics."
2. Embedding space: the secret map of meanings
If the cognitive invariant is the driving force of thought, then the embedding space is the "road" along which it travels. This can be envisioned as an extensive system of metaphors.
In a computer or a cluster of cells, there are no "apples," "fear," or "liver shapes." There are only signals. The embedding space is a mathematical concept that allows qualitative notions to be transformed into numerical coordinates.
How it works in detail:
- Multidimensionality. Each concept is a point in space, but not in traditional 3D space; rather, in a multidimensional space where there can be thousands of dimensions. For example, the word "dog" has coordinates along the axes of "alive/inanimate," "size," "loyalty," and others.
- Proximity as meaning. The key point here is that the distance between points corresponds to their meaning. In this space, "dog" and "puppy" will be close to each other, while "dog" and "cryptocurrency" will be at a significant distance.
- Biological embeddings. Levin applies this logic to biology, asserting that cells also have their own "embedding space," where the coordinates are the levels of electrical tension across membranes and the concentration of proteins. The cell "perceives" its position in this space and understands that it needs to move towards "healthy tissue" for restoration.
Thus, thinking represents not manipulation of objects in reality but navigation within this vast mathematical map. All systems, including ourselves, our cells, and AI, are always searching for the "right address" on this map, constantly recalculating the route to minimize the distance to the goal.
3. Remapping: when the world changes
If navigation is moving along familiar routes, then remapping is a kind of earthquake that alters the landscape. In Hartl and Levin's work, this is the key idea of adaptation.
The system does not merely move toward a goal; it constantly checks: "Does my map correspond to reality?"
- In learning: When you suddenly grasp a complex metaphor, your "embedding space" experiences a tectonic shift. Points that were far apart suddenly become close. Your internal space reorganizes for more efficient error minimization in the future.
- In evolution and development: If an organ is damaged to the extent that old regeneration pathways no longer work, cells can "remap" their signaling pathways, finding entirely new ways to restore function.
Thus, this explains the remarkable plasticity of life. We are not rigidly programmed automatons but rather systems that can change the scale and structure of their "internal navigation" on the fly.
4. Navigation: how abstract thought translates into action
If the embedding space is a map, then navigation is life itself. In traditional biology, it is believed that everything happens in a chain: "stimulus — response." But Hartl and Levin propose a different model: "state — goal — maneuver."
Navigation in biology. Imagine that cells need to create an eye. They do not follow a strict instruction from DNA like a cookbook. Rather, they act like an experienced driver. If a blockage arises on the path (for example, an injury or mutation), the driver does not stop but looks for a detour to still reach the destination. This is navigation: the system knows the "coordinates" of a healthy organ in the state space and constantly adjusts its course. This is why embryos are so resilient to damage — they can "navigate around" obstacles on their way to their final form.
Navigation in AI. When a neural network generates text, it does not simply produce random words. It makes micro-movements in its space of meanings. Each subsequent word is a step toward the most logical and coherent completion of your thought. AI "scans" the space ahead and selects the trajectory that seems most appropriate.
5. Error minimization: the fuel and compass of knowledge
This is the most technical yet simultaneously fascinating part of the theory. Why does a system move at all? The answer lies in free energy or "prediction error."
From a mathematical perspective, this looks like the desire to reduce the gap between current and target coordinates, which any cognitive system attempts to bring to zero.
The system constantly compares its current coordinates with the goal. This gap creates "tension." Just as a ball seeks to roll into a hole, an intelligent system seeks to "roll" into a state of zero error.
We always have two paths:
- Change the world (Navigation): act in such a way that reality matches our map (for example, grow a tail or finish writing a text).
- Change ourselves (Remapping): acknowledge that the map was incorrect and redraw it (learning).
6. Biological mind in action: how cells "agree" on shape
Michael Levin is not only a theorist but also a practitioner who has observed for many years how living matter solves geometric problems. Examples from his research confirm that navigation in state space is not just a metaphor but a reality.
Case #1: Regeneration as the search for the "right address"
The most famous example from Levin's work is the flatworms of planaria. If you cut such a worm into 200 pieces, each piece "knows" where it was and restores the missing part. From the perspective of the embedding theory, each cell has its coordinates on the overall map of the body. When the worm is cut, the system registers a significant "error": the current coordinates (a piece of the tail) do not match the target (a whole worm). The cells begin to alter their bioelectrical parameters, charting a route to the point "whole organism." Once the "address" is reached, growth stops.
Case #2: Xenobots — intelligence without ancestors
Levin creates xenobots — tiny organisms made from frog skin and heart cells. Lacking a brain and neurons, as well as millions of years of evolution behind them (they have never existed in nature in this form), these cells exhibit a remarkable ability to navigate:
- They group together.
- They "find" ways to move in space.
- They can collaboratively perform tasks, such as cleaning surfaces. This confirms that cells possess an "innate navigator": when faced with a new situation (a new embedding space), they can remap on the fly and find ways to survive and work together.
Case #3: Bioelectrical memory
The article mentions an experiment that seems fantastic: scientists altered the bioelectrical code on a worm's body without touching its DNA. As a result, the worm grew two heads. The most astonishing thing happened later: when this two-headed worm had its heads cut off again, it... grew two heads again! Although the worm's DNA was set for one head, the cognitive map of the system had been rewritten. The cells "remembered" the new coordinates in the embedding space and now strive for this state as their target.
Why this is so important
These examples show that life does not function as a rigidly programmed conveyor but as a dynamic agent. Cells are not just bricks but builders with a tablet containing a map. If the tablet is changed, the builders will revise the entire project. This opens new horizons for the medicine of the future: instead of trying to rewrite DNA (changing the bricks), we could simply alter the map in the "mind" of tissues, prompting them to heal cancer or restore organs on their own.
The paper by Hartl and Levin represents an attempt to create a "unified field theory" for intelligence, integrating developmental biology, cognitive psychology, and computer science. It emphasizes that thought processes do not depend on the presence of a brain but are a result of systems' ability to navigate their state maps.
