With the help of mathematical methods of algebraic topology, scientists have found structures and multidimensional geometric spaces in human brain networks. A new study has demonstrated that the human brain contains structures and shapes that may have up to 11 dimensions.
Experts have previously stated how human brains are estimated to contain a staggering 86 billion neurons, including several connections from each cell, expanding and connecting in every possible direction, producing a super-vast cellular network that somehow makes us capable of thought and consciousness, reports an article at Science Alert.
Now, an international team of researchers gathered around the Blue Brain Project has obtained results that have never before been observed in the world of neuroscience, according to the research written in the journal Frontiers in Computational Neuroscience.
Mathematics Reveals the Unimaginable
Scientists managed to locate structures in the human brain that display a multi-dimensional universe, revealing the very first geometric design of neural connections and how they react to different stimuli.
Researchers utilized in-depth computer modeling methods in order to understand how human brain cells can adapt themselves in order to carry out extremely complex tasks.
Scientists made use of mathematical models of algebraic topology in order to describe different structures and multidimensional geometric spaces in human brain networks.
In the study, scientists note how structures are formed at the same time that they are interlaced in a ‘unity’ that creates a precise geometric structure.
Henry Markram, a neuroscientist and the director of Blue Brain Project in Lausanne, Switzerland said:
We have found a world that we had never imagined before. We’ve uncovered tens of millions of these objects, even in a small speck of the brain, up through seven dimensions. However, in some networks, we even discovered structures with up to 11 dimensions.
As explained by scientists, every single neuron within our brain can interconnect to an adjacent one in a particular way, in order to form an object with intricate connections. Interestingly, the more neurons join in with the clique; the more dimensions that are joined to the object.
With the help of algebraic topology, experts were able to model the structure within a virtual brain, produced with the aid of computers. Later, experts carried out tests on real brain tissue to verify the results.,
After researchers included stimulus into the virtual brain tissue, they found that cliques of progressively higher dimensions compiled. They discovered that in between these cliques were empty spaces, like holes or cavities.
Ran Levi from Aberdeen University, who worked on the paper, said:
The presence of high-dimensional cavities when the brain is processing information indicates that the neurons in the network respond to stimuli in a remarkably organized manner.
It is as if the brain responds to an inducement by constructing then smashing a tower of multi-dimensional blocks, starting with rods (1D), planks (2D), cubes (3D), and then more complex geometries with 4D, 5D, etc. The sequence of activity throughout the brain resembles a multi-dimensional sandcastle that has the ability to materialize out of the sand and then disintegrate.
Furthermore, experts note that while shapes that are three-dimensional in nature have height, width, and depth, the objects uncovered by experts in the study don’t exist in more than three dimensions in our reality. However, the mathematics used to define them may contain as many as 5, 6, 7 or up to 11 dimensions.
Professor Cees van Leeuwen, from KU Leuven, Belgium, said:
Outside of physics, high-dimensional spaces are commonly used to represent complex data structures or conditions of systems. For example, the state of a dynamical system in state space… The space is simply the combination of all the degrees of freedom the system has, and its state represents the values these degrees of freedom are actually assuming.
This research was published in Frontiers in Computational Neuroscience.