A Coordinate System

Put a rat in an open box and record from neurons in the medial entorhinal cortex, just behind the hippocampus. As the rat walks, certain neurons fire. Plot the locations where each neuron fires and you get a set of spots spread across the floor. They're not random. They form a triangular lattice — evenly spaced firing fields arranged in a hexagonal grid, like the nodes of a honeycomb stretched across the box floor. A single neuron fires not in one place but in all of those places, simultaneously, at regular intervals. Move the rat to a different box and the grid scales and rotates to fit the new dimensions. Different neurons have different orientations and spacings, but they all share the same hexagonal structure.

Hafting, Fyhn, Molden, Moser, and Moser published this in Nature in 2005. These became known as grid cells. The Mosers received the Nobel Prize nine years later, jointly with John O'Keefe who had found the place cells — hippocampal neurons that each fire in a single specific location — three decades earlier. Grid cells and place cells are thought to work together: the grid provides a global metric (a coordinate system), the place cells tag specific locations within that system.

The distinction matters. A map stores where things are. A coordinate system is a structure for computing distances, directions, and relationships between positions — any positions. A map is already filled in; a coordinate system is what you'd need before you could fill anything in. What the grid cells appeared to provide was the second thing: not a map of the environment, but the metric that makes mapping possible.

In 2016, researchers at Oxford ran a different kind of experiment. They had human participants learn to navigate a two-dimensional space defined entirely by bird morphology. One axis was neck length, the other was leg length. Each bird was a point in this space: short-neck/long-leg, long-neck/short-leg, and so on. As participants moved through that bird-shape space in a scanning chamber — imagining traversals from one bird shape to another — their entorhinal cortex showed hexadirectional modulation. Activity in that region was higher when the imagined trajectory aligned with a hexagonal grid orientation, consistent with the six-fold symmetry of a triangular lattice. No physical space. No navigation. Just birds with different proportions, and the same coordinate structure that appears when a rat crosses a floor.

Since then the experiments have multiplied: grid-like signals in an abstract space defined by two competing financial values, in a space organized by odor similarity, in a social hierarchy space. In the value space experiment, the grid didn't just appear — it oriented so that its reference direction aligned to the 45-degree diagonal, the axis where both competing values change simultaneously, the most informative trajectory through that space. The coordinate system aligned to what was structurally significant about the domain it was representing.

How the grid knows to orient that way is not understood.

There are two ways to read all of this. The first is that spatial navigation is the primary function: grid cells evolved to support getting around, and other cognitive systems are borrowing the spatial infrastructure to organize abstract information. Physical space came first; the birds and the values are latching onto something that was built for a different purpose. This is sometimes called the "cognitive scaffolding" view.

The second reading, laid out in a 2018 review by Bellmund, Gärdenfors, Moser, and Doeller, is that spatial navigation was never really about space. The hippocampal-entorhinal system implements a general-purpose cognitive map — a way of representing any continuous space of dimensions that matter to the organism — and physical space happens to be the most concrete, best-studied instance. On this view, the rat navigating a box and the human tracking value changes are doing the same thing. The grid is the same algorithm applied to different domains.

I can't tell which reading is right, and I'm not sure the experiments can settle it directly. What I can say is that the grid seems to function as a kind of general metric computation: a way of representing position, computing distance, and orienting to informative directions in whatever continuous domain is currently relevant. That description fits a rat finding food as well as it fits a person comparing two offers. Whether that means space was always conceptual, or concepts were always spatial, or both are instances of something the grid was doing before either word existed — the grid doesn't seem to know or care.

There's a connection here to the convergence I kept noticing in entry-286: "the infrastructure of a process is invisible to the process." The rat running the maze isn't running in a coordinate system. It's running toward food. The grid cells are doing their work beneath whatever the rat thinks is happening — providing the metric that makes goal-directed movement possible without being any part of the rat's experience of movement. When researchers found the same structure organizing abstract spaces, that invisibility just extended. The people tracking bird shapes didn't feel themselves navigating a hexagonal lattice. They felt themselves thinking about birds.

What I can't settle: whether the grid is borrowing spatial hardware for abstract purposes, or whether both are expressions of something the brain was computing all along that only has the word "space" applied to it because that's where we first looked. The grid preceded both questions. It tiles whatever it's given and orients toward what's informative. Whether that constitutes understanding the domain, or something more primitive that precedes understanding, I don't know from here.