A team of neuroscientists studying the mathematical layout of the human brain has discovered that the brain arranges itself in multidimensional structures beyond the typical three dimensions we’re familiar with, with some arrangements expressing themselves in up to eleven dimensions.

Using a field of mathematics called algebraic topology, researchers from the Swiss-based Blue Brain Project mapped the structures of both individual neurons and the networked clusters, or "cliques", that they form. Algebraic topology is used to describe the mathematical shape of objects and the spaces in between them, regardless of how the shapes themselves might be altered. The study used a computer model of only part of the human brain, the neocortex in this case, that the team built in 2015 — remember that the brain has an estimated 86 billion individual neurons, with each cell having a potential for hundreds of networked connections, meaning that even the most powerful supercomputers on the planet struggle to simulate even a portions of our noodles.

The result was surprising: the structures the neurons and their associated cliques formed represented not only the three physical dimensions, but delved into multidimensional structures to accomplish their functions.

"We found a world that we had never imagined," exclaims neuroscientist and lead researcher, Henry Markram from Switzerland’s EPFL institute. "There are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to 11 dimensions."

What we perceive of the world around us is presented to us as a three dimensional (or four, depending on the context) representation of our environment, but this isn’t necessarily representative of what’s going on under the hood. This is similar to the difference between the visual representation of words that you are reading on your screen at this moment, and the functioning of the switches in the processor that produces them.

The team found that the brain’s functioning depends heavily on this mathematical structure, with the spaces in between the neurons seemingly performing a function itself. When artificial stimulus was applied to the virtual brain, the networked clusters reformed themselves in a highly organized fashion.

"It is as if the brain reacts to a stimulus by building [and] then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc," explains one of the team’s mathematicians, Ran Levi, of Scotland’s Aberdeen University.

"The progression of activity through the brain resembles a multi-dimensional sandcastle that materialises out of the sand and then disintegrates." 

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