Our mental image of space appears to be expanding as the universe : ScienceAlert

Inside your brain is a map of every bedroom you’ve slept in. Every kitchen you’ve cooked in. Every city you’ve worked in, every country you’ve vacationed in. There’s even a worn-out map of every universe you’ve hair. have dreamed in.

Squeezing this huge amount of detailed information into a tiny blanket of neurons is possible thanks to some very clever math, according to a study on rat brains by researchers in the US.

These newly discovered patterns of brain cell arrangement that embody the mental representation of physical space not only reveal how our brain stores certain types of data, but may also provide insight into occasions when memory and mapping go awry.

Walk into a room for the first time and your brain will quickly recruit neurons that will outline the room. These place cells are not necessarily arranged in any way that mirrors space, but their coordinated blinking still serves as a way to place ourselves within a physical area.

Arranged in networks called place fields, these cells are repeatedly reorganized as we become accustomed to the space, contributing to an increasingly enriched network of cells that ripple with correlated responses as the space around you becomes more familiar.

Exactly how this hierarchy of correlated activity develops and functions has so far been mostly speculative, at least from a mathematical point of view.

In a new study led by computational neurobiologist Tatyana Sharpee of the Salk Institute for Biological Studies, researchers examined the activity of nerve cells in a part of the hippocampus of rats that is crucial for their memory of space.

Using a previously developed method to study place cells in rats as they run mazes, the researchers put a handful of adult rodents through their paces down a 48-meter (157-foot) straight track, where their neural activity was recorded as they completed the run.

There are a few ways a sequence of messages sent through a network can be modeled, depending on their physical proximity or the ways different cells match in response.

An analysis of the hierarchy of signals flickering across a network of place cells in the rats was best modeled by a type of geometry described as hyperbolic, which – ironically – is not the easiest geometry for our brains to image.

Imagine, if you will, a typical office building with a boss at the top, sitting alone on a floor all to himself. The managers below the boss all have luxurious offices. Below them, middle managers squeeze into slightly smaller suites. Further down, a whole lot of workers pile into a floor full of cubicles.

This ‘linear’ hierarchy quickly runs out of room for each individual as you descend through the floors and the additional departments add up.

However, an office tower constructed using hyperbolic geometry would have no problem accommodating new departments on the lower floors, which become exponentially larger, and obey a different set of rules for the angles that intersecting lines form when connecting different components.

flat circle hierarchy
A hyperbolic hierarchy, depicted as a flat circle. (Zhang et al., Nature communication2022)

Although we can use the example above to represent a hyperbolic hierarchy in flat space, in a full-dimensional reality, these triangles will all be the same size (yes, trying to imagine this will hurt your brain). So if this was a piece of material, the outer ends would curl with their excess circumference, like a floppy hat.

Hyperbolic hierarchies use similar mathematics to describe the relationships between different activity points in a cascade of operations, enabling a more efficient way of detailing distances and objects in our minds when we see ourselves in a space.

Here, the researchers observed the math in how small fields of place cells were quickly established when the rats were introduced to a new room, and grew into more complex fields according to a logarithmic expansion as time went on.

neuron group hierarchy
A hyperbolic hierarchy representing groups of neurons (nodes) mapped onto a place field, where different colors represent different properties of place cells. (Zhang et al., Nature communication2022)

“Our study shows that the brain does not always work in a linear fashion. Instead, neural networks work along an expanding curve, which can be analyzed and understood using hyperbolic geometry and information theory,” says Sharpee.

Recent studies found that olfactory systems in biology also follow a hyperbolic hierarchy, allowing animals to categorize odors in far more complex and varied ways than a linear way of grouping odors.

The researchers behind the new study argue that hyperbolic representations in our spatial awareness adapt better to the reorganization that comes with a growing mental map, relying only on the information that is available. Locating the body in space is also more accurate than if the map developed according to a linear model.

Measuring similar effects in humans can inform models of disease, particularly in neurology involved in memory and spatial awareness.

On a more poetic level, there is a beauty in knowing that the expansion of our mental universe mirrors the infinite expansion of our physical. While all signs so far point to our universe having a flat shape, there are models that speculate whether the overall geometry of space-time may yet have a subtle curvature.

“You would think that hyperbolic geometry only applies on a cosmic scale, but that’s not true,” says Sharpee.

“Our brains work much slower than the speed of light, which may be one reason why hyperbolic effects are observed in tangible spaces rather than astronomical ones. Next, we would like to learn more about how these dynamic hyperbolic representations in the brain grow, interact, and communicate with each other.”

This research was published in Nature Neuroscience.

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