Blue Brain team discovers a multi-dimensional universe in brain networks

June 12, 2017
The image attempts to illustrate something that cannot be imaged -- a universe of multi-dimensional structures and spaces. On the left is a digital copy of a part of the neocortex, the most evolved part of the brain. On the right are shapes of different sizes and geometries in an attempt to represent structures ranging from 1 dimension to 7 dimensions and beyond. The "black-hole" in the middle is used to symbolize a complex of multi-dimensional spaces, or cavities. Researchers at Blue Brain Project report groups of neurons bound into such cavities provide the missing link between neural structure and function, in their new study published in Frontiers in Computational Neuroscience. Credit: Blue Brain Project

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 .

The research, published today in Frontiers in Computational Neuroscience, 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 of the geometric object.

"We found a world that we had never imagined," says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, 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 eleven dimensions."

Markram suggests this may explain why it has been so hard to understand the brain. "The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly."

If 4D worlds stretch our imagination, worlds with 5, 6 or more dimensions are too complex for most of us to comprehend. This is where algebraic topology comes in: a branch of mathematics that can describe systems with any number of dimensions. The mathematicians who brought algebraic topology to the study of brain networks in the Blue Brain Project were Kathryn Hess from EPFL and Ran Levi from Aberdeen University.

"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," explains Hess.

In 2015, Blue Brain published the first digital copy of a piece of the neocortex - the most evolved part of the brain and the seat of our sensations, actions, and consciousness. In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance. Experiments were then performed on real brain tissue in the Blue Brain's wet lab in Lausanne confirming that the earlier discoveries in the virtual tissue are biologically relevant and also suggesting that the brain constantly rewires during development to build a with as many high-dimensional structures as possible.

When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities. "The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner," says Levi. "It is as if the brain reacts to a stimulus by building 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. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates."

The big question these researchers are asking now is whether the intricacy of tasks we can perform depends on the complexity of the multi-dimensional "sandcastles" the brain can build. Neuroscience has also been struggling to find where the brain stores its memories. "They may be 'hiding' in high-dimensional cavities," Markram speculates.

Explore further: How the brain sees the world in 3-D

More information: Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function Frontiers in Computational Neuroscience (2017). DOI: 10.3389/fncom.2017.00048

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13 comments

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krundoloss
5 / 5 (2) Jun 12, 2017
Whoa! Can anyone make sense of this? I understand that the Blue Brain Project is a supercomputer simulation of the functions of a brain. Are they referring to Neurons themselves, and their interaction being in different shapes, that some how correlate to higher dimensional shapes? From what I have heard, we are finding that the brain is "encoded" with groups of neurons in complex, branch like groups, representing different Ideas, like "elephant" will cause certain neurons to fire, that are in a unique "shape", that represent that idea, unique to each person. However I find it difficult to connect that concept with the concept described here:

When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities.

dirk_bruere
5 / 5 (2) Jun 12, 2017
It's a variant on the way that multicomputer systems can be linked together in architecture such as linear (ethernet), rectangular (systolic arrays), cubic, and beyond. It is just a measure of how many computers are connected to any single computer. Most of this work in computer science was done in the 1970s.

Can't wait until the pseudoscience clickbait sites get hold of this one...
Nik_2213
5 / 5 (1) Jun 12, 2017
Not being a poly-dimensional topologist, this made my wits spin, too...

I think it means you have multiple 3D networks snugly interwoven and sparsely connected to each other in the same region of brain. If so, I'd call it highly parallel processing.
zorro6204
not rated yet Jun 12, 2017
Is this a real article or a hoax? My eleven dimension brain is twisted.

"It is just a measure of how many computers are connected to any single computer."

Yeah, but that could be diagrammed in two dimensions, just a lot of intersecting straight lines.
JayB
not rated yet Jun 12, 2017
I find it aggravating when fancy phrases like "multi-dimensional geometrical structures and spaces" are used to mean something simple like "groups of inter-connected neurons". So: 2D structure = a clique of 2 neurons, 3D = group of 3, ..., 11D = a small sub-circuit of 11 neurons.
c0y0te
not rated yet Jun 12, 2017
Of course it can be diagrammed. Brain is still three dimensional spatially.
c0y0te
5 / 5 (1) Jun 12, 2017
Actually, for n dimensional structure you need n+1 neurons, but yes, too much about (expected) interconnections, while to me the mentioned creating and disintegrating of such structures is what is really interesting. How long do those "sandcastles" last? How fast are they created? Why are they disingrated?
VOR_
not rated yet Jun 13, 2017
No matter how you slice it, referring to 3d things as having more dimensions than they do is just crappy. As interesting as the subject is, there is no need for the inappropriate geek-speak. More than 3 physical dimensions is not even known to exist. So why put people through this? Just stop.
antialias_physorg
not rated yet Jun 13, 2017
" More than 3 physical dimensions is not even known to exis"

Good thing they're not talking about *physical* dimensions anywhere in the article, then, is it? This is a science site. A modicum of education is expected. This includes knowing that the word dimensions need refer to space/time.
gaytanlu6
5 / 5 (1) Jun 13, 2017
Most of this work in computer science was done in the 1970s.
LariAnn
4 / 5 (1) Jun 18, 2017
I continue to be amazed at the idea that "higher" dimensions are thought to be so esoteric. It all has to do with what a "dimension" actually is. A dimension is simply a unique measurable parameter that is also a distinguishing characteristic of the object in question. You don't need to twist your brain into multidimensional knots in order to grasp higher dimensions. See my page http://fractalica...dims.htm for my descriptions of 11 dimensions in space-time. I also describe 11 temporal dimensions, which is a clue that "time" is not really a dimension.
johnqsmith
5 / 5 (1) Jun 19, 2017
11 dimensions. Hmmm. Any connection with 11 dimensional String Theory?
exequus
not rated yet Jul 01, 2017
reply to johnqsmith..."11 dimensions....Any connections with 11..."

What a coincidence, that's precisely what I thought

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