**With about 86 billion neurons, the human brain is the most complex structure in nature that we still don’t fully understand.**

Since 2017, neuroscientists have refined a classical mathematical method of describing the structure of our brains. This method shows that the brain is filled with multi-dimensional geometric structures operating in 11-dimensional space.

We often think that the world has only 3 dimensions (length, width, height), so it is quite difficult to describe the 11-dimensional structure. However, this research could be the next important step in understanding the human brain – the most complex structure we have ever known.

A mathematical model for the brain described by a team of researchers from Switzerland’s **Blue Brain Project** , dedicated to building supercomputers based on the human brain.

The team used algebraic topology, a branch of mathematics used to describe the properties of objects and spaces, regardless of how they change shape.

This image illustrates a multidimensional spatial structure, below is an illustration of the cerebral cortex – the most evolved region of the brain, while above are different geometric structures representing spatial dimensions. The black hole in the middle represents the complex of multidimensional spaces. (Photo: Blue Brain Project).

They found that groups of neurons connect into ‘clusters’, the number of neurons in a cluster determines the number of dimensions of that cluster (mathematical dimension, not space or *time).*

*“We found a world that no one could have imagined before,”* said neuroscientist Henry Markram from the EPFL Institute in Switzerland. *“There are tens of millions of clusters of neurons in a small piece of the brain, up to seven dimensions in size. In some networks we even find 11-dimensional structures.”*

This is not the dimension of space (Our Universe has three spatial dimensions plus one time dimension), instead it refers to the number of ways clusters of neurons connect to each other, each of which is 1 dimension.

*“ Neural networks are analyzed based on groups of fully connected neurons. Each of these groups is called a cluster, and there are connections between these clusters in the brain. The number of neurons in a cluster determines its size, in other words, its dimension,”* the team explains.

The human brain is estimated to have about 86 billion neurons, nerve cell connections growing in all directions forming the neural network that allows us to think and perceive.

Because of the huge number of connections, we still don’t fully understand how the brain works. However, mathematical modeling can help us create a “digital” brain that mimics our own.

To test the accuracy of the math model, the team used a detailed model of the cortex that was published by the Blue Brain Project in 2015. The cerebral cortex is believed to be the most developed part of our brain and is involved involved in some higher-order functions such as perception and sensation.

An American warrior brain simulation. (Photo: The Atlantic).

After developing a mathematical model and testing it on a number of computer simulations, the team confirmed their results were true in mouse brain tissue. According to them, mathematical tools and simulations allow us to see closely at the cellular level individual neurons and the entire brain structure.

Using mathematical simulations, the team saw links between clusters and their gaps in our brains. *“We found a remarkable amount of diversity of multidimensional groups and holes, which has never been seen before in neural networks, whether biological or artificial,” the team said.*

*“Algebraic topology is like a microscope and a telescope combined into one,”* says mathematician Kathryn Hess from EPFL: *“It can look deeply into the microscopic structures that lie within, like every leaf on the tree, even the gaps, the larger structure.”*

Gaps in the brain can play a very important role. When the scientists ran a numerical simulation, they found that the neurons responded to these gaps in a very organized way.

*“It’s like our brains respond to a signal by creating multiple multi-dimensional structures that represent that signal, and then destroying those structures. Multidimensional blocks start with bars (1Dimension) , then planes (2D), cubes (3D), more complex geometries with 4D, 5D, …”* , said mathematician Ran Levi from the University of Aberdeen, Scotland.

Gaps in the brain can play a very important role that we don’t fully understand. (Photo: Itsastrangeworld).

*“The brain works like it’s constantly building multidimensional ‘sand castles’, a way of materializing information, then processing and destroying it. This process repeats itself over and over again.”* he said.

These findings provide a fascinating new picture of how the brain processes information, but the researchers point out that it remains unclear what drives clusters and holes to form.

More work will be needed to determine how the complexity of the multidimensional geometrical structures formed by our neurons corresponds to the complexity of various cognitive tasks, but here certainly a new step towards understanding the human *“soul” –* the brain.