Your Brain's GPS Is Also a Dictionary

Here's something that should bother you more than it currently does: the neurons your brain uses to track where you are in a room are mathematically related to the neurons it uses to organize what a concept means. Not metaphorically. The same underlying computational geometry, possibly the same physical cells, doing double duty across two completely different cognitive jobs.

I'd say this sounds like the kind of thing a philosophy undergrad says at 2am, but two rigorously peer-reviewed papers published in 2024 and 2025 make the case with actual math. And the AI angle is even weirder.

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First, the GPS

Grid cells live in the medial entorhinal cortex — a region that feeds directly into the hippocampus. When you move through physical space, they fire in a pattern so mathematically striking that when John O'Keefe and the Mosers won the Nobel Prize for discovering them, the committee basically called it the brain's GPS.

Here's the thing that still gets me: the firing pattern is hexagonal. Not circular, not random, not a messy blob. Hexagonal grids, like bathroom tiles scaled to the room you're in, tiling the environment with neural activity. Each cell has preferred locations arranged in that lattice, and together they create a coordinate system that updates as you move.

According to Dong and Fiete (2024) in their comprehensive review in the Annual Review of Neuroscience, this hexagonal code turns out to be near-optimal for path integration — the process of tracking your position by accumulating movement signals without GPS, without landmarks, just dead reckoning through space. The brain, through however many millions of years of evolution, converged on essentially the best possible mathematical solution for keeping track of where you are.

That's already impressive. But it's not the part I want to talk about.

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Now, the Dictionary Part

Haga et al. (2025) published a paper in PNAS proposing a unified computational model — they call it Disentangled Successor Information, which is simultaneously a great prog-rock band name and a genuinely important theoretical contribution — that explains both spatial navigation and abstract conceptual representation within a single mathematical framework.

The central claim is this: there is a formal mathematical correspondence between how hippocampal neurons encode your location in physical space and how they encode abstract semantic meaning.

Same geometry. Same code. Different territory.

The model produces something remarkable in simulations: population-level representations that look like grid codes in navigation tasks and word-embedding geometry in semantic tasks (Haga et al., 2025). If you've ever heard of word embeddings — the vectors that NLP systems use to represent word meaning, where "king minus man plus woman equals queen" — you've encountered the conceptual-space cousin of the brain's spatial grid. What this paper suggests is that the brain may literally be using navigation machinery to organize what things mean.

"Justice" and "the corner by the bookshelf" might live in maps that share an architecture.

I'll pause here to register my own skepticism: this is a theoretical model, not a direct recording of neurons organizing concepts in hexagonal patterns. Computational neuroscience is full of elegant models that turn out to be too clever by half. But the mathematical correspondence is clean, it generates testable predictions, and it lines up with a surprising amount of other evidence about the hippocampus as a general-purpose relational map-maker — not just a spatial specialist.

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The Part Where AI Accidentally Confirms It

Here's where it gets genuinely strange.

In 2018, DeepMind trained a deep reinforcement learning agent to navigate a virtual environment. They gave it no architectural bias toward hexagonal codes. They just optimized it for navigation performance.

It spontaneously developed grid-cell-like representations (Dong and Fiete, 2024).

Sit with that for a second. Two completely different optimization processes — biological evolution across millions of years and gradient descent across thousands of training iterations — independently converged on a hexagonal coordinate code for space. Not because anyone told them to. Because that code is apparently just the right answer to the problem of spatial navigation, and both processes found it without being pointed in that direction.

This is the kind of convergence that actually means something. Not "AI thinks like a brain" vibes-posting — actual mathematical structure, appearing independently in both systems, for the same computational reasons.

I want to be careful here, because this is exactly the kind of result that gets overclaimed. The fact that evolution and gradient descent both found hexagonal grid codes doesn't mean the brain and AI are "doing the same thing" in any deep sense. When convergent evolution independently produces wings in birds and bats, it doesn't mean bats and birds are equivalent — it means flying imposes specific physical constraints that push solutions toward similar shapes. The grid code convergence tells us the problem has a near-unique best solution. It doesn't tell us the underlying implementations are alike in the ways that matter for understanding intelligence.

That said — it's a genuinely interesting result. One worth taking seriously rather than either breathlessly overgeneralizing or defensively dismissing.

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The Calibrating Gut-Punch

And now, just to make sure we don't drift too far into "biology and AI are beautiful mirror images" territory, I want to introduce the finding that should be making a lot more noise than it is.

Jansen et al. (2025) published a paper in Nature showing that tiny recurrent neural networks — sometimes with as few as one to four units — outperform both classical Bayesian models and large-scale neural networks at predicting human and animal behavior across six reward-learning tasks and eight datasets.

One to four units. Not one to four billion. One to four.

These microscopic networks discover interpretable cognitive strategies that capture individual behavioral quirks, biases, and learning idiosyncrasies better than the sophisticated models researchers usually reach for. The implication cuts against a lot of current AI discourse: intelligence doesn't scale the way the press releases suggest. Sometimes the right circuit is tiny. Sometimes the right algorithm is embarrassingly simple.

Castro et al. (2025) from Google DeepMind pushed this further in an ICML Spotlight paper. Using a system called FunSearch — an LLM-powered evolutionary search — they automatically discovered symbolic cognitive models that outperform hand-crafted state-of-the-art models at predicting reward-learning behavior. The kicker: this worked across three species. Humans, mice, and flies.

AI discovering the mathematical algorithms that describe how animals learn from feedback. The discovered programs are human-readable — scientists can actually look at what FunSearch found and say, "oh, that's an interesting algorithm, I hadn't thought of that one." It's AI doing cognitive science, and occasionally getting further than the cognitive scientists did by hand.

So we have: AI rediscovering the brain's spatial code. AI discovering the cognitive algorithms that describe how organisms learn. AI being used to show that spatial and conceptual representation share geometry. These are genuine convergences. They're not evidence that AI "understands" or "thinks." They're evidence that certain computational problems have elegant solutions, and both biological brains and machine learning are finding them.

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What This Means If You're Raising a Brain

Here's the part that keeps nagging at me.

If the brain really does use spatial navigation machinery to organize conceptual space — and the evidence is pointing that way — then the question of how children build rich conceptual repertoires looks a little different.

The grid cell system isn't mature at birth. In rodents, grid cells achieve their characteristic hexagonal patterning around the time of eye-opening — a major developmental milestone. The full development of hippocampal and entorhinal circuits in humans extends well into adolescence. The substrate for both spatial and conceptual mapping is under construction during exactly the years when we're making decisions about how much unstructured outdoor play to schedule versus how much structured screen time to allow.

Physical exploration — running through spaces, building block towers, navigating neighborhoods, making spatial maps through play — may not be separate from abstract reasoning. It may be training the architecture that later handles conceptual navigation too.

I want to be clear: I'm not saying "go outside and your kid will think better." That's exactly the kind of causal overclaim I find irritating when other people make it, and I'm not going to make it here. The neuroscience doesn't yet support a clean "spatial play → grid cell development → better concept learning" story with anything like interventional evidence.

But I am saying: the machinery for space and the machinery for meaning appear to share a lot more than we thought. A childhood that builds spatial competence — that gives the hippocampal-entorhinal system real environments to map and navigate — probably isn't wasted on "just play." It may be building the geometry of thought itself.

The brain didn't evolve a GPS and then bolt a thesaurus onto the side. It seems to have built one system for navigating any landscape, physical or conceptual, and then used it for everything. If that's right, the line between "playing in the park" and "learning to reason" is a lot blurrier than the school curriculum suggests.

That's worth sitting with — even if the full picture isn't in yet.