The brain’s magnificent complexity continues to astound us. When our brain analyzes information, it generates neural structures with up to 11 dimensions, according to groundbreaking research that merges neuroscience and math. They mean abstract mathematical spaces, not other physical realms, when they say “dimensions.” Still, the researchers “found a world that we had never imagined,” said Henry Markram, director of the Blue Brain Project, which made the discovery.

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” amounts of biological information.

The scientists used supercomputers and a strange branch of math to gain a better understanding of how such a massive network operates to generate our ideas and actions. The team’s current study is based on a computerized model of the neocortex that was created in 2015. Using the algebraic topology mathematical system, they examined how this digital neocortex responded. It allowed them to discover that our brain constantly generates extremely sophisticated multidimensional geometrical forms and spaces that like “sandcastles.”

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

Researchers were able to see the high degree of organization in what previously seemed to be “chaotic” patterns of neurons using the unique 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 repeated the tests on real brain tissue from rats to confirm the results.

When stimulated, virtual neurons create a clique, with each neuron linked to the next in such a way that a specific geometric object is formed. A large number of neurons would provide extra dimensions, up to 11 in some cases. 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 middle symbolizes a complex of multi-dimensional spaces aka cavities.

The researcher Ran Levi detailed how this process is working:

“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 important because it gives us a better understanding of “one of the fundamental mysteries of neuroscience – the link between the structure 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 see further application of their findings in studying human intelligence and formation of memories.