The brain may learn by building 11-dimensional "sandcastles"
We're all familiar with four dimensions – height, width, depth and time – but according to theoretical physics, the universe could be composed of as many as 11 dimensions. If you have a hard time wrapping your head around how those extra dimensions could possibly work, we've got news for you: your brain regularly makes use of these 11 dimensions to process information, according to a new study by the EPFL in Switzerland.
We use dimensions to describe where an object is in space, or properties like its size. In our everyday 3D world, that usually means the height, width and depth of something. Since things naturally change size, shape or location, time is considered a fourth dimension.
But that's not the end of it. According to various theories, physics only makes sense if there are other dimensions out there that we can't really picture or even perceive. They don't really have names since they're only used in somewhat specialized situations, but in addition to time there could be as many as 10 spatial dimensions.
A branch of mathematics called algebraic topology can help scientists understand complex systems, no matter how many dimensions they might be made up of. And in this study, the EPFL team applied that field to the network of neurons in the brain.
"Algebraic topology is like a telescope and microscope at the same time," says Kathryn Hess, co-author of the study. "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."
The trees in this metaphor are the neurons and the clearings are the spaces between them, as groups of neurons pass signals back and forth. The researchers found that neurons tend to form families (called "cliques"), where each neuron is connected to each other in the clique.
These cliques are hard to see in real brains: connected neurons are spread across different layers of the brain, and each neuron is a member of many cliques at once. So the team experimented with a virtual rat brain, watching as the neurons responded to stimuli by sending messages to each other through patterns that can be described as "multi-dimensional objects."
For example, two neurons connected to each other form a one-dimensional "rod." Three neurons all connected form a 2D triangle, while four create a 3D pyramid. The more neurons in a clique, the more dimensions the object has – but trying to picture a 7D object is a brain-breaking exercise. The researchers call these objects "multi-dimensional sandcastles," which does a decent job of describing a twisted complex shape that's somewhat fleeting.
"We found a world that we had never imagined," says Henry Markram, lead author on the study. "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."
The team calls the hollow shapes between neurons "cavities," and they could act as a new window into how the brain processes information. By stimulating the virtual brain, the team watched the cavities form in lower dimensions first, before moving into higher dimensions and eventually collapsing as a decision is made.
"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 Ran Levi, co-author of the study. "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 next step for the project is to study if brains that can build more complex "multi-dimensional sandcastles" are also capable of handling more complex tasks. The researchers even suggest that memory storage could be hiding between these multi-dimensional cracks.
"What is so amazing about this project is how relevant these techniques are to understanding both structure and function in the brain," says Levi. "The abundance of information we inferred from this approach is incredible."
The research was published in the journal Frontiers in Computational Neuroscience. The team explains the work in the video below.