Sunday, September 4, 2022

The human brain builds structures in 11 dimensions, discover scientists

The brain’s incredible complexity continues to amaze us. When our brain analyzes information, it generates neural structures with up to 11 dimensions, according to groundbreaking study that combines neuroscience and math.

They mean abstract mathematical spaces, not other physical realms, when they say “dimensions.” Nonetheless, the researchers “discovered a world we had never imagined,” according to Henry Markram, director of the Blue Brain Project, which made the finding.

The Blue Brain Project, based in Switzerland, aims to create a “biologically detailed” simulation of the human brain digitally. The scientists hope to increase our understanding of the extraordinarily complex human brain, which contains approximately 86 billion neurons, by building digital brains with “unprecedented” levels of biological information.

The scientists used supercomputers and a peculiar branch of math to gain a better understanding of how such a vast network works to form our ideas and actions. The team’s current study is based on a digital model of the neocortex that was completed in 2015.

Using the algebraic topology mathematical system, they investigated how this digital neocortex responded. It allowed them to discover that our brain constantly generates extremely intricate multidimensional mathematical forms and spaces that resemble “sandcastles.”


Visualizing the multi-dimensional network was difficult without the use of algebraic topology, an area of mathematics that describes systems with any number of dimensions.


Researchers were able to see the great degree of organization in what previously seemed to be “chaotic” patterns of neurons using the novel mathematical approach.


“Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures—the trees in the forest—and see the empty spaces—the clearings—all at the same time,” stated the study’s author Kathryn Hess.

The scientists first tested the virtual brain tissue they developed, then performed the tests on real brain tissue from rats to confirm the results.

When activated, virtual neurons create a clique, with each neuron connected to the next in such a way that a specific geometric object is formed. A huge number of neurons would provide extra dimensions, up to 11 in some situations. The structures would form around a high-dimensional hole known as a “cavity” by the researchers. The clique and cavity vanished when the brain processed the information.



Left: digital copy of a part of the neocortex, the most evolved part of the brain.
Right: shapes of different sizes and geometries that represent structures ranging from 1 dimension to 7 dimensions and more. The “black-hole” in the center represents a series of multi-dimensional regions known as cavities.

Ran Levi, a researcher, explained how this process works:
“The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner. It is as if the brain reacts to a stimulus by building 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. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates.”

The discovery is significant because it gives us a better grasp of “one of the fundamental mysteries of neuroscience – the link between the shape of the brain and how it processes information,” according to Kathryn Hess in an interview with Newsweek.

The scientists look to use algebraic topography to study the role of “plasticity” which is the process of strengthening and weakening of neural connections when stimulated – a key component in how our brains learn. They hope to use their findings to learn more about human intelligence and recollection formation.

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