Hidden Geometry in the Brain: How We Build Mental Maps to Navigate the World

Web Editor

September 13, 2025

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Neural Activity in Circular Patterns

When we first enter a room, our mind effortlessly activates an internal representation system that not only allows us to locate ourselves in space but also relates everything happening at the moment with our memory of past events. The windows, doors, furniture orientation, and book arrangement on a table are all registered instantly in our brain.

As we leave the room through a corridor, a mental map emerges in our consciousness, much like Alice in Wonderland navigating the rabbit hole. We traverse the corridor by touching walls, feeling changes in roughness, and picking up small cues to understand our location. At the end of the corridor, we find a door that leads back into the original room on the opposite side. Suddenly, we realize the corridor is circular, and our brain has closed a loop by creating a mental map connecting the start and end of the journey.

In a recent study published in Neuron, we demonstrated for the first time that our environmental information is organized in the brain using geometric shapes. We achieved this by analyzing the activity records of hundreds of neurons in the hippocampus, a crucial brain region for memory and navigation. In the case of the room and corridor, this representation takes the form of three-dimensional ring structures.

In our lab, we observed that each time a mouse navigates the maze’s corridors, its neurons activate in a trajectory that completes a full loop in an abstract space—a ring representing the entire experience of traversing the maze.

What’s fascinating is that not all neurons participate equally. Some encode very specific sensory information, like floor texture, reward presence, or turning directions in the maze. Others record and utilize external information unrelated to the maze, relying on broader environmental cues like room location or reference object position to maintain orientation stability.

These distinct neural populations form parallel rings in the neuronal activity space but serve different functions. When everything goes well, they work together to stabilize the experience. However, if something disorients us (e.g., someone spinning or guiding us blindfolded to another location), other mechanisms are deployed.

In that case, one representation remains fixed like an internal compass, helping maintain the perception of the environment. Other neurons reorient themselves to represent the change, providing mental certainty that we are oriented.

The Geometry of Brain Activity

Space is typically the container for our experiences. Understanding that the brain encodes its structure with precise geometric shapes opens new doors to comprehend how we think, remember, and navigate the world.

The study of the geometry and topology of brain activity is an emerging field that combines mathematics, data science, and sophisticated bioengineering tools applied to brain research. Today, we can identify subtypes of neurons based on their genetic profiles—excitatory, inhibitory, and dopamine-producing neurons are genetically distinct—and modify them to express fluorescent proteins that allow us to visualize and control their activity in real-time.

These approaches are advancing our understanding of how the brain builds its internal maps. Each discovery not only helps decipher the biological foundations of memory and orientation but also paves the way for new applications in neurotechnology, artificial intelligence, and potentially treating neurological disorders where these maps deteriorate, such as Alzheimer’s disease.

Key Questions and Answers

  • What is the main finding of the study? The research demonstrates that our environmental information is organized in the brain using geometric shapes, specifically circular patterns.
  • How does this discovery impact our understanding of the brain? This finding contributes to a deeper comprehension of how the brain constructs its internal maps, with potential applications in neurotechnology and artificial intelligence.
  • What are the implications for treating neurological disorders? Understanding these geometric representations in the brain may lead to new approaches for treating disorders where these maps deteriorate, such as Alzheimer’s disease.