TOPIC 5 · PHASE A COGNITION

Spatial Navigation & Cognitive Maps

Your skull really holds a map — with a hexagonal coordinate grid laid over it

2026-07-11 · BigCat

The machinery that keeps you from getting lost may be the same machinery you use to think a problem through.

You get up in the dark and reach the bathroom without a light — your feet know where to turn, how many steps to the door. Ask someone which way their hometown is and they'll point almost before thinking. That quiet certainty of "where I am, where things are, which way to go" is something you never give a second thought. Yet behind it is one of the brain's most astonishing tricks: there is an actual map inside your skull — not a metaphor, but a living map drawn by a crowd of cells that "light up" when you stand in a particular place. Stranger still, the brain lays a hexagonal coordinate grid over that map. This issue we go see how this "inner GPS" is built — why the people who found it won a Nobel Prize, and why it may not be for getting around at all.

// 01

There's a living "you are here" map inside your head

In 1971, scientists slid a hair-thin electrode into a rat's hippocampus and listened to single neurons fire. They found something odd: one cell fired furiously only when the rat was in one particular corner of the cage and went quiet everywhere else. A neighboring cell owned a different corner. These came to be called place cells — each one stakes a claim to a small patch of space, and the moment you step onto its patch it shouts "we're here."

If one cell covers one patch, then a whole crowd of place cells strung together makes a living map that tiles the entire space: which cells are lit right now amounts to "you are standing here." Walk a loop around a room and a chain of place cells lights up like a relay, faithfully tracking your feet.

a room (top view) · each patch = one place cell's turf cell A cell B cell C cell D cell E the path walked: step on a turf, that cell lights
Place cells each claim a patch; a whole crowd strung together is a living "you are here" map

This cracked an older puzzle. In 1948 the psychologist Tolman noticed that a rat running a maze does not carry a string of "turn left, then right" instructions. Block the usual route and it will instantly cut a brand-new shortcut straight to the goal — which has only one explanation: it holds a survey-style, bird's-eye map, not a memorized set of turns. Tolman named that map the cognitive map. The place cells found two decades later are its hardware.

// 02

The brain lays a hexagonal coordinate grid over the world

Place cells have a gap. Each one seems to recognize its patch by leaning on landmarks — "there's a table here, a window there." But what about a blank, featureless snowfield with no landmarks at all? You can still gauge roughly how far you've walked. The brain must have a second system that works purely from distance and direction, no landmarks needed.

In 2005 the Mosers found it right next door, in the entorhinal cortex, and it shook the whole field. The cells here are called grid cells, and their firing pattern is uncanny: a single cell fires at many locations, and those locations arrange themselves into a neat, regular pattern of equilateral triangles — a hexagonal lattice, as if someone took honeycomb graph paper and snapped it down over the whole room. Step onto any vertex of the grid and the cell pings once.

every spot one grid cell fires (top view of a room) hexagon
Grid cells: one cell fires at many spots, and those spots form a perfect hexagonal lattice — the brain's built-in graph paper

This fills in exactly what place cells were missing: grid cells keep ticking off space by "which way and how far you've moved", landmarks or not — a ruler laid across the whole room. With that ruler, place cells know where to light up. O'Keefe, who found place cells, and the Mosers, who found grid cells, together won the 2014 Nobel Prize in Physiology or Medicine for uncovering this positioning system in the brain. (For how the hippocampus–entorhinal circuit is wired and what each part does, see hippocampus & entorhinal.)

The AI reading

Let an AI learn navigation on its own and grid cells pop out — this isn't made up. In 2018 a team trained a network to do path estimation (feed it a stream of movements, ask it to report where it is at all times), telling it nothing about "hexagons"; to do the job well, the network spontaneously grew hexagonal, grid-cell-like codes inside itself. That hints at something deep: the hexagonal grid isn't a whim of evolution but the optimal solution forced out by the math of "efficiently representing position on a plane" — carbon brains and silicon networks pushed by the same problem to the same answer.

// 03

Knowing where you are even with no signal

There's a Saharan ant that leaves its nest, winds a hundred metres out on a foraging trek, finds food, and then — not by retracing its steps — turns and walks a dead-straight shortcut home. No breadcrumbs, no GPS. It manages this by quietly summing every step's direction and count along the way, computing in real time "how far I am from the nest and in which direction." This skill is called path integration — blindfold you, walk you a few steps around a room, ask where the door is, and you'll usually point pretty close, using the same trick.

To do that running sum, the brain first has to know "which way am I facing right now." That job goes to head direction cells: like a built-in compass, one cell fires when you face north, another takes over when you turn east, locked to the heading of your head. Add border cells, which watch walls and boundaries — they fire as you near a wall, driving a few pins into this floating map so it doesn't drift ever more crooked with use.

nest food foraging: winding out return: a straight-line shortcut heading
Path integration: sum a trek's direction × distance and out falls the straight line home — head direction cells as compass, border cells pinning the reference
// 04

This map may draw your thoughts too

Here a thought becomes hard to resist: did this elaborate machine — part map, part coordinate grid — evolve only to keep you from getting lost in the woods? That would be a waste. The most thrilling finding of the last decade is that the same machine also draws "maps" of things that aren't spatial at all.

In one experiment people learned a set of abstract relations — say birds varying in neck length and leg length, combined into a "concept space." Scans then showed that as the brain "moved" thoughts through this purely abstract space, the entorhinal cortex threw off the same hexagonal grid signal it uses when you walk. As if the brain handles "how far is this bird from that one" with the very method it uses for "how far is this intersection from that one." This echoes the strange fact that the hippocampus does both maps and memory — to remember something is, in a sense, to give it a place on some map. Space may just be the scaffolding the brain learned first, and then reached for again and again, to organize every kind of relation.

real space concept space intersections · places leg neck different birds same grid
One hexagonal coordinate system measures both distances between real intersections and "distances" between abstract concepts

The AI reading

The tightest AI parallel is the successor representation in reinforcement learning. An ordinary navigation map records "what each place looks like"; the successor representation goes further and records "starting from here, which places am I likely to reach next" — not static terrain, but a predictive map. And the activity of hippocampal place cells looks strikingly like exactly this: it encodes not just "where you are" but a quiet forecast of "where you're likely to head." A more recent model — the Tolman-Eichenbaum Machine (the name a tribute to the two figures above) — has a single network grow grid cells, place cells, and relational memory all at once, stitching navigation and memory into one thing — the very theme this issue keeps running into.

🌀 Border-crossings · cross-disciplinary echoes

"The brain is born with a spatial coordinate frame, and reuses it to hold abstract thoughts" — several old disciplines bumped into this from different doors:

// Going deeper

Does leaning on turn-by-turn apps let this inner map waste away?
There's a clue worth heeding. Studies found that veteran London cab drivers — the ones who have to cram the whole city into their heads and pass "the Knowledge" exam — have a markedly larger posterior hippocampus, and the longer they drive the larger it grows, like a muscle bulked up by use. Run that backwards: when you only stare at an arrow saying "right at the next junction," you're using the memorized-route machinery and barely engaging the map-drawing kind. That doesn't mean navigation apps make you dumb, but it does suggest your sense of direction is trained — switching the app off now and then and finding your own way is probably not a loss.
Why are some people born with a great sense of direction and others lost the moment they leave the metro?
The difference is real, and partly tied to how stable this system runs — how accurately head direction and grid signals stay calibrated, how much they lean on landmarks. It's not fixed, though: direction sense responds strongly to practice and strategy (people who actively build a "global map" get lost less than those who memorize "route recipes"). Tellingly, decline in spatial navigation is one of the earliest signs of Alzheimer's — because the entorhinal cortex is exactly where that disease strikes first, a thread Topics 25 and 28 will pick back up.
If space and abstract thought really share one map, is "can't figure out a problem" the same kind of stuck as "lost"?
This is still an open conjecture, but a weightier one all the time. If reasoning is, in some sense, "finding a path" through concept space, then "getting stuck" may genuinely resemble "lost in a region with no good map" — and "figuring it out" is like suddenly seeing the whole layout and cutting a shortcut. It could even explain why we love diagrams and mind maps: turning an abstract problem back into space hands it to the navigation circuitry the brain is best at. This thread quietly connects to later issues on creativity and insight.
What is this map doing while you sleep?
Picking up last issue's replay: in deep sleep the hippocampus replays the routes you walked, time-compressed, over and over, a chain of place cells flashing in their original order. Better still, it sometimes replays paths you never actually took — as if rehearsing tomorrow's possible moves. The map isn't only used to remember the way you came; it's used to simulate the way ahead. Space, memory, imagination — at the hippocampus they look more and more like facets of one thing.

// Further reading