We move along the surface of a doughnut: Researchers have gained a first insight into how the brain structures higher-level information. By extracting and analysing data from a neural network of grid cells, they found that the collective neural activity is shaped like the surface of a doughnut.

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If you take a 2D video game, and make your character wrap around the right and left of the screen, and also wrap around from top to bottom of the screen, visualizing the continuous 3D shape of the playfield is a torus (aka doughnut). This means reversing it – the surface could be mapped into a set of squares with the same rules. So I wonder if the shape derives from the nature of the setup of the grid cells.


This is super cool. I work in supercomputing and toroidal network topologies are sometimes used to connect individual computers (or cores within a single processor) because it can reduce the number of “hops” data has to make to travel between nodes, gives you flexibility to choose the fastest available path of many, and is resilient against failure. Of course it comes at the cost of higher complexity however. I admit I didn’t understand much of paper except the mathy bits. Can anyone chime in and say whether these neural networks might be arranged like so for similar reasons?


Homer Simpson was right.


Our mind is a torus? I’ve seen that somewhere else…


What does a 4d torus look like? Is it really the shape of space time?