Multi-Dimensional Geometry Found In The Brain
Scientists from the Blue Brain Project are now finding the same multi-dimensional geometry described by mathematician Euclid two millenia ago in the behaviour of information flow in the brain. Indeed, the ancient Greek philosopher first hypothesised about their existence in his mathematical treatise Elements in 300 BC.
Some convex regular 4 dimensional polytopes from least to most complex
5 cell pentachoron, 8 cell tesseract, 16 cell hexadecachoron
The former images are a conceptional tool for grasping regular convex polyhedra (platonic solids) in 4 dimensional space. In reality what scientists are finding is that the brain encodes information in up to 11 dimensions. Far beyond our ability to grasp or model consciously. Up until relatively recently scientists did not understand how complex neural networks in the brain coalesce to form emergent properties. It’s always been a mystery as too how these cellular conduits of electricity end up co-operating across distances separated by space and time. Now a group of them think they are much closer to answering this question than ever before.
The reason that this discovery is so important is because the brain is one of the most complex and powerful things science has come to know. The potential for revealing some sort of underlying structure is extremely valuable to just about every field of human ingenuity. In the future for example, they may be able to reverse certain perturbations in multidimensional geometry that lead to instances of psycho-pathology, or perhaps modify procedures in non-invasive brain stimulation to increase intelligence and compassion.
Most of the activity in our brain is a black box to scientists. They can make assumptions based on dissection and surgery but our technology does not allow us to see what is going on in the deeper evolutionary layers. However, what we can do is track the activity of electromagnetism on the surface of the scalp. This superficial layer of the brain beneath the scalp is called the Neo-cortex and is responsible for higher levels of human cognition we often attribute to sentient organisms.
Using algebraic topology scientists from the Blue Brain project, among other credible institutions began mapping abstract symbols on to the neo-cortex in an attempt to reveal some sort of patterm. They began by analysing the direction of synaptic transmissions i.e. signals that are transmitted from point a to b and back or from a to b to c on the neo-cortex. What they found is that smaller, simpler cliques of neurons organise themselves in to chronomes i.e structures in time that resemble multi-dimensional geometry. The former is a conceptual tool for visualising the latter image in 4 dimensions, which was taken from the video above.
“what i think we’re seeing here is a way of interpreting or visualizing the brains OWN code for what it’s doing.
It is generally understood how local activity in the brain influences closer local areas, as well as to how the sensitivity of neurons on a macroscopic scale can effect network dynamics, but until now there has been no successful attempts at bridging the micro and macro scales of the brain.
Furthermore most studies have neglected the direction of information flow, instead focusing on undirected graphs. Now that scientists understand the place of geometry in neuropsychology they’re beginning to explore how this multidimensional complexity effects our behaviour.
For example, does the orchestration of a vast symphony rely on sophisticated geometry in the brain?
Reimann MW, Nolte M, Scolamiero M, Turner K, Perin R, Chindemi G, Dłotko P, Levi R, Hess K and Markram H (2017) Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function. Front. Comput. Neurosci. 11:48. doi: 10.3389/fncom.2017.00048