For most people, it is a stretch
of the imagination to understand the world in four dimensions but a new study
has discovered structures in the brain with up to eleven dimensions -
ground-breaking work that is beginning to reveal the brain's deepest architectural
secrets. Using algebraic topology in a way that it has never been used before
in neuroscience, a team from the Blue Brain Project has uncovered a universe of
multi-dimensional geometrical structures and spaces within the networks of the
brain.
The research shows that these
structures arise when a group of neurons forms a clique: each neuron connects
to every other neuron in the group in a very specific way that generates a
precise geometric object. The more neurons there are in a clique, the higher
the dimension of the geometric object. Since 5, 6 or more dimensions are too
complex for most of us to comprehend, algebraic topology comes in: a branch of
mathematics that can describe systems with any number of dimensions.
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