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The Brain Can Think In 11 Dimensions

Using a branch of math known as algebraic topology, scientists have discovered that the human brain can operate in 11 dimensions.

By Hugh Finlay

Using a branch of math, neuroscientists have discovered that the brain can operate in 11 dimensions. This latest picture of the brain found by a Swiss research project called Blue Brain Project, was aiming to build a super-computer image of the human brain.

Algebraic Topology

They used a branch of math called algebraic topology, which is designed to describe the properties of spaces and objects, regardless of whether they change shape. As one of the team described it “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.”
Algebraic topology allowed the project to discover that groups of closely connected neurons, or cliques, and the spaces in between, created high-dimensional geometric networks in the brain. Algebraic topology has the capability to discover details of neural networks in the brain, both on the level of individual neurons, and on the level of the whole brain, and connect these two levels to give a picture of what is going on in the brain.

Cliques

The project discovered that groups of neurons collect into ‘cliques’. The number of neurons that gather in a clique led to what size it would be as a high-dimensional geometric shape. These shapes are mathematical dimensional concepts, not the space-time dimensions that we are usually acquainted with.
What they discovered is described by the lead researcher of the project, Henry Markram of the EPFL institute “We found a world that we never imagined. 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 11 dimensions. Networks are often analyzed in terms of groups of nodes that are all-to-all connected, known as cliques. The number of neurons in a clique determines its size, or more formally, its dimension.”

Networks

The brain has 86 billion neurons, and these neurons can connect with each other in any direction, forming webs which creates the cellular network that allows our brain to operate in a complex way. The number of connections that can be made is huge, and the Blue Brain project was designed to help understand the complex network of the brain, by creating a digital picture of how the networks works. The area that the project chose to focus on was an area of the brain known as the neocortex, said to be one of the most advanced parts of the brain. Once they had their picture of the brain they verified it on a virtual level, and then also on the physical level, with experiments on the brain tissue of rats.

Multi-Dimensional Sandcastle

As the project team put it “We found a remarkably high number and variety of high-dimensional directed cliques and cavities, which had not been seen before in neural networks, either biological or artificial. It is as if the brain reacts to a stimulus by building and raising a tower of multi-dimensional blocks, starting with rods (1 dimensional), then planks (2 dimensional) then cubes (3 dimensional), 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.”

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