Neuroscientists have used classical mathematics to look into the structure of our brains. They found that it is full of multidimensional geometric shapes working in 11 dimensions!
The Swiss research group Blue Brain has set itself the goal of a non-trivial task - to completely reconstruct the human brain based on a supercomputer. To do this, scientists have created a special model using algebraic topology - a branch of mathematics that describes the properties of objects and spaces, regardless of the change in their shape. They found that groups of neurons are connected in "clicks", and that the number of neurons in a clique depends on its size as a multidimensional geometric object (this is a mathematical, not a space-time concept of measurement - this is important).
"We found a world we never dreamed of," said lead researcher, neuroscientist Henry Markram of the EPFL Institute in Switzerland. “Even in the smallest part of the brain there are tens of millions of such objects, and their dimension ranges up to seven dimensions. In some networks, we even found structures with up to 11 dimensions.”
For those who did not understand, we explain: we are not talking about spatial dimensions (we, for example, perceive the Universe only in three spatial dimensions + one temporal). Instead, researchers note the degree to which neurons are connected to each other. Connection nodes are "clicks". The more there are, the higher the dimension.
According to neuroscientists, our brain is made up of 86 billion neurons, closely related to each other. They form a vast cellular network that somehow empowers us with the ability to actively think and act consciously. Given the enormous amount of connections this complex structure contains, it is not surprising that scientists still do not have a clear understanding of how it all works.
However, the mathematical framework developed by Swiss scientists brings us one step closer to the day when the brain will be completely digitalized.
To run the tests, the team used a detailed neocortex model that the Blue Brain Project published back in 2015. The neocortex is believed to be a part of our brain that is involved in some of the higher-order functions such as cognition and sensory perception.
After developing the mathematical structure and testing it on some virtual stimuli, the team also confirmed their results on real brain tissue in rats.
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According to the researchers, algebraic topology provides mathematical tools for recognizing the details of a neural network, both in close-up mode at the level of individual neurons, and on a wider scale of the structure of the brain as a whole. By connecting these two levels, the researchers could distinguish multidimensional geometric structures in the brain, formed by collections of closely related neurons (clicks) and empty spaces (cavities) between them.
“We found a surprisingly large number and variety of clicks and large cavities that were not previously found in neural networks, neither biological nor artificial,” the team wrote in the new study. "Algebraic topology is like a telescope and a microscope at the same time," explained one of the team members, mathematician Catherine Hess of EPFL. “It helps you get closer to networks to find hidden structures and at the same time see empty spaces. It's like looking for trees and clearings in a single forest,”he said.
These gaps, or "cavities," seem to be critical to the functioning of the brain. When the researchers stimulated virtual brain tissue, they saw that neurons respond to it in a highly organized way.
“It's as if the brain reacted to the stimulus by building and then destroying a tower of multidimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D) and then more complex geometries - 4D, 5D, etc. etc.,”explains mathematician Ran Levy of the University of Aberdeen in Scotland. "The development of activity through the brain is like a multidimensional sand castle that materializes out of sand and then disintegrates."
The results of the work gave the world a stunning and fresh picture of how the brain processes information. However, the researchers note that they have not yet figured out the reason why cliques and cavities are formed in very specific ways. More work will be required to determine how the complexity of these multidimensional geometric shapes formed by our neurons relates to the complexity of various cognitive tasks.
Vasily Makarov
