Neuroscientist Henry Markram, director of the Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, said that the human brain is capable of building structures with up to 11 dimensions.
The structures of the human brain can operate in up to 11 dimensions, according to a little-known study (pdf below) that was published in Frontiers in Computational Neuroscience last year. The Blue Brain Project, a Swiss research effort, carried out the study.
“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 eleven dimensions.”
“We found a world that we had never imagined,” said neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland.
“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 eleven dimensions,” Markram added.
The scientists discovered that conventional mathematics were ineffective for studying the human brain, one of the most complex structures on Earth. The high-dimensional structures and spaces that we can now plainly perceive cannot be detected by the mathematics that is often used to study networks, according to Markram.
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In order to distinguish between them, the researchers made the decision to employ algebraic topology, a field of mathematics that deals with the creation of algebraic invariants connected to topological spaces. In order to apply this field, the Blue Brain Project requested the help of mathematicians Ran Levi from Aberdeen University and Kathryn Hess from EPFL.
“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,” explained Hess.
Using this method, the scientists conducted experiments on rat brain tissue and a neocortex model that was published by the Blue Brain Project in 2015. Using this method, they were able to examine the neural network of the brain in depth at both the level of the individual neurons and the level of the overall brain structure.
Cliques and cavities
They discovered that cliques, or groups of closely connected neurons, bind to enclose cavities, or high-dimensional holes, by stimulating the virtual brain tissue. “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 organised manner,” said Levi.
“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,” added Levi.
Up to 11 dimensions were used in the more complex geometries. According to the researchers, “the brain processes stimuli by forming increasingly complex functional cliques and cavities.”
The research may someday provide an answer to the long-standing mystery of where the brain stores memories. They could be “hiding” in high-dimensional cavities, according to Markram.
This is not the first time that researchers have examined the brain using algebraic topology. Comparable study has been done with somewhat similar results by a team at the University of Pennsylvania under the direction of Ann Sizemore.
Read the study given below: