Brain Talk

Our thoughts aren't just data; they might be complex geometric shapes. This post explores the revolutionary idea of modeling the mind with high-dimensional manifolds, where memories and concepts exist as intricate structures in a vast mental space.

7/24/2025

Right then. Let’s pour a nice cup of darjeeling tea, sit down, and talk about the universe I’ve got squirreled away between my ears. Because honestly, the stuff going on out in space with galaxies and whatnot has got nothing on the sheer, beautiful madness happening inside my own noggin—and it’s not because I am bipolar.

Trying to Read the Jelly That Thinks

Picture this. I’ve got the most mad object in the known universe sitting on my shoulders. It’s a three-pound lump of wobbly, pinkish-grey jelly that learned and understood how scientists split atoms, which writes bad doggerels, and remembers the precise smell of the sintheemore street-side urinals I’ve encountered on a rainy Tuesday many decades back. And I, clever clogs that I am, want to understand how it pulls off this magic trick.

For the longest time, I’ve been approaching it a bit like a mechanic trying to understand a Honda by just listening to the engine. I stick little probes in, I watch bits light up on a doctor’s MRI scan when I think about my dog, the black one, and I say, “Aha! That bit there is the ‘melancholic’ bit!” It’s all very clever, but it’s a bit like trying to appreciate the Mona Lisa by analyzing the chemical composition of the paint. I’m, or in this case the doctor who treated me (trabscranial magnetic stimulation in Sam Antonio), cataloguing the ingredients, but he hasn’t got the faintest clue about the recipe, let alone the art.

This is what is called the “language issue.” If I am trying to understand my brain, I am basically a tourist in the country of my own mind. I can point at things and learn a few nouns—“this is a neuron,” “that’s the hippocampus”—but I can’t speak a lick of the local dialect. I can’t hold a conversation. I don’t understand the grammar, the poetry, the idioms of thought itself. Not just me I mean, no one can.

And that’s because we might have been using the wrong kind of dictionary all along. The brain doesn’t speak in words or in computer code. The new, slightly bonkers, and utterly brilliant idea is that the brain speaks in shapes.

The Spacetime of a Memory

Okay, stay with me. This is where it gets fun.

Think about a single, simple concept. Let’s say, “my neighbor’s cat.” Now, that isn’t one little nugget of information stored in one little brain cell. It’s a whole constellation of things, isn’t it?

It’s the name of my neighbor’s cat (Taklu Babu). It’s the colour of its fur (white with a sort of splotch of black). It’s the specific sound of its meow (sweetly grumbling). It’s the feeling of its fur under my hand (surprisingly coarse). It’s the emotion it triggers (a mix of affection and remembering how it always wants to urinate on things—male cat thing). It’s the memory of the only creature in the world visiting me everyday, who’d worry if I’m dead.

Each one of these things—the name, the colour, the sound, the feeling, the place, the emotion—is a separate piece of data. Now, in mathematics, when I have a bunch of separate variables that all describe one thing, I can think of each variable as a dimension.

I know, I know, “dimension” is a word that immediately makes me think of wormholes and sci-fi. But hang on. A line on a page is one-dimensional (length). A piece of paper is two-dimensional (length and width). A box is three-dimensional (length, width, height). All a dimension is, really, is another direction to move in, another quality I can measure.

So what if the concept of “my neighbor’s cat” doesn’t exist in 3 dimensions, but in, say, 20? Or 200? What if it’s a single point in a vast, multi-dimensional space? And the thought isn’t just the point itself, but a shape—a sort of complex, shimmering, mathematical ghost that connects all those different dimensions into one coherent idea. This is the wild and wonderful world of manifolds.

A manifold is just a fancy word for a shape that, if I zoom in really close, looks a bit flat and normal. The Earth is a perfect example. It’s a giant 3D sphere, but for me walking down to the shops in Calcutta, it feels perfectly flat. My immediate experience is a 2D-ish one. What if a thought is like that? What if it’s a “walk” across a stupendously complex surface—a manifold with thousands of dimensions—that my consciousness experiences as a simple, single idea?

The Ultimate Mapmakers

This is the mathematical frontier I’m talking about. The “neural correlate” of an idea—the physical thing in the brain that corresponds to the thought—might not be a location, but a piece of geometry. An impossibly intricate piece of hyper-dimensional origami.

When I learn something new, I’m not just storing a file. I am, quite literally, changing the shape of the universe inside my head. I’m adding a new fold, a new wrinkle, a new dimension to this internal manifold. The accumulated wisdom of my fifty years isn’t a library of books; it’s an impossibly complex cathedral of geometric relationships. My “neural capital” is the architecture of this cathedral.

Suddenly, the task becomes clear, and gloriously so. The folks trying to solve this—the neuroscientists with their scanners, the mathematicians with their topology, the AI gurus with their network theories—they’re not just engineers. They are cartographers. They are setting out on the greatest exploration in human history: to map the hyper-dimensional landscape of a single mind. To learn the language of its geometry.

If they can do that—if they can figure out the mathematics of these inner shapes—then the dream I speak of isn’t science fiction. Preserving the intricate latticework of a mind, the neural connections honed over a lifetime, becomes a real possibility. It’s not about trapping a ghost in a machine. It’s about translating a masterpiece of geometric art from one medium (squishy biological stuff) to another (a more durable, perhaps silicon-based, canvas). Then me and my cat memory will live on. It’s a staggering thought. Everything I’ve ever felt, learned, or loved might not be a fleeting spark, but an enduring, beautiful, and mind-bogglingly complex shape.