# Scientists Discover That Our Brains Can Process The World In 11 Dimensions

Neuro-scientists
have used a classic branch of maths in a totally new way to peer into the
structure of our brains. What they’ve discovered is that the brain is full of
multi-dimensional geometrical structures operating in as many as 11 dimensions.

We’re used
to thinking of the world from a 3-D perspective, so this may sound a bit
tricky, but the results of this new study could be the next major step in
understanding the fabric of the human brain – the most complex structure we
know of.

This latest
brain model was produced by a team of researchers from the Blue Brain Project,
a Swiss research initiative devoted to building a supercomputer-powered
reconstruction of 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. They
found that groups of neurons connect into ‘cliques’, and that the number of
neurons in a clique would lead to its size as a high-dimensional geometric
object.

“We found a
world that we had never imagined,” says lead researcher, neuroscientist Henry
Markram from the EPFL institute in 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 11 dimensions.”

Human brains
are estimated to have a staggering 86 billion neurons, with multiple
connections from each cell webbing in every possible direction, forming the
vast cellular network that somehow makes us capable of thought and consciousness.

With such a
huge number of connections to work with, it’s no wonder we still don’t have a
thorough understanding of how the brain’s neural network operates. But the new
mathematical framework built by the team takes us one step closer to one day
having a digital brain model.

To perform
the mathematical tests, the team used a detailed model of the neocortex the
Blue Brain Project team published back in 2015. The neocortex is thought to be
the most recently evolved part of our brains, and the one involved in some of
our higher-order functions like cognition and sensory perception.

After
developing their mathematical framework and testing it on some virtual stimuli,
the team also confirmed their results on real brain tissue in rats.

According to
the researchers, algebraic topology provides mathematical tools for discerning
details of the neural network both in a close-up view at the level of
individual neurons, and a grander scale of the brain structure as a whole.

By
connecting these two levels, the researchers could discern high-dimensional
geometric structures in the brain, formed by collections of tightly connected
neurons (cliques) and the empty spaces (cavities) between them.

“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,” the team writes in the study.

“Algebraic
topology is like a telescope and microscope at the same time,” says one of the
team, mathematician Kathryn Hess from EPFL.

“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.”

Those
clearings or cavities seem to be critically important for brain function. When
researchers gave their virtual brain tissue a stimulus, they saw that neurons
were reacting to it in a highly organised manner.

“It is as if
the brain reacts to a stimulus by building [and] 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,” says one of the team,
mathematician Ran Levi from Aberdeen University in Scotland.

“The
progression of activity through the brain resembles a multi-dimensional
sandcastle that materializes out of the sand and then disintegrates.”

These
findings provide a tantalizing new picture of how the brain processes
information, but the researchers point out that it’s not yet clear what makes
the cliques and cavities form in their highly specific ways.

And more
work will be needed to determine how the complexity of these multi-dimensional
geometric shapes formed by our neurons correlates with the complexity of
various cognitive tasks.

But this is
definitely not the last we’ll be hearing of insights that algebraic topology
can give us on this most mysterious of human organs – the brain.

The study
was published in

**.***Frontiers of Computational Neuroscience*
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