A map of each bedroom you’ve slept in is stored in your brain. each of the kitchens you’ve worked in. Every place you have lived, every place you have worked. There is even a worn-out chart of every **universe** you have ever dreamed of.

According to a study on rat brains carried out by academics in the US, some extremely brilliant mathematics allows for the compression of this tremendous store of precise information into a little tapestry of neurons.

These recently identified patterns of brain cell organization that describe the mental image of physical space not only show how our brain stores specific types of data, but they may also provide light on instances in which memory and mapping go wrong.

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**Brain’s Authorization**

When you first enter a room, your brain will quickly draw the room’s layout in your brain’s neural network. The synchronised flashing of these place cells allows us to locate ourselves within a physical space even though they are not always arranged in a way that mirrors the room.

As we become accustomed to the environment, those cells, which are arranged into networks called place fields, are repeatedly reorganised. This results in an increasingly enriched network of cells that ripple with correlated responses.

**Mathematical Standpoint**

From a Mathematical perspective, it has been mostly theoretical how this hierarchy of connected activity evolves and functions up until now. In a recent study, Tatyana Sharpee, a computational neurobiologist at the Salk Institute for Biological Studies, and her team looked at the activity of nerve cells in a region of the rat’s hippocampus that’s important for the memory of spatial locations.

The researchers put a few adult rodents through their paces down a straight, 48-meter (157-foot) track, while their neural activity was recorded as they finished runs. They did this using a previously developed method for studying where cells are placed in rats as they run mazes.

**Cells Retaliation**

Depending on their physical proximity or how distinct cells respond to one another, a series of signals transmitted over a network could be depicted in a variety of ways.

A sort of geometry known as hyperbolic, which is ironically not the easiest geometry for our brains to envision, was shown to be the best model for a study of the hierarchy of signals flickering through a network of place cells in the rats.

If you will, picture a standard office building with a boss at the top, sitting by themselves on the floor. Each executive below the CEO has a plush office. The middle managers below them cram into slightly smaller suites. A floor full of cubicles is further down where a huge group of employees cram.

**Hyperbolic Grading**

The triangles in the aforementioned example can be used to illustrate a hyperbolic hierarchy in flat space, but in three-dimensional reality, they would all be the same size (yes, trying to imagine this will hurt your brain). Consequently, if this were a piece of fabric, the outside ends would curl from their extra diameter, like a floppy hat.

In order to more effectively express distances and things in our brains as we visualise ourselves in space, hyperbolic hierarchies employ comparable mathematics to describe the relationships between various points of activity in a cascade of operations.

When the rats were introduced to a new location, the researchers studied the math of how simple fields of place cells quickly formed and quickly expanded into more complicated fields over time in accordance with a logarithmic expansion.

**Upshot On The Research**

“The results of our study show that the brain does not always function in a linear fashion.” “Hyperbolic geometry and information theory can be used to understand and comprehend the growing curve along which neural networks operate,” asserts Sharpee.

Recent research has revealed that olfactory systems in biology also follow a hyperbolic hierarchy, enabling animals to classify odors in much more complicated and varied ways than would be possible with a linear system of scent classification.

**Extension Of Mind**

The authors of the current study contend that because we only use the information that is immediately available, hyperbolic representations in our spatial awareness are better able to adapt to the restructuring that results from an expanding mental map.

Measuring similar effects in humans could inform models of disease, especially in fields of neurology involved with memory and spatial awareness. On a more poetic level, there’s a beauty in knowing the expansion of our mental Universe reflects the infinite expansion of our physical one.

**Conclusion**

While all signs so far point to our Universe having a flat shape, there are models that speculate whether the total geometry of space-time might yet have a subtle curvature to it.It would seem that hyperbolic geometry would only be applicable on a cosmic scale, but Sharpee argues that this is untrue.

“This is because our brains process information far more slowly than light travels through space. It’s possible that graspable spaces rather than astronomical ones are where hyperbolic effects are seen. The process by which these dynamic hyperbolic representations develop, interact, and communicate with one another in the brain is what we’d like to learn more about next.”