Biology

The brain may learn by building 11-dimensional "sandcastles"

The brain may learn by buildin...
Algebraic topography  has been used to better understand the neurons in the brain – which may be making use of 11 dimensions
Algebraic topography  has been used to better understand the neurons in the brain – which may be making use of 11 dimensions
View 3 Images
On the left is a digital representation of the neocortex in the brain, and on the right is a series of shapes and structures that represent objects of between 1D and 7D – the black hole is the cavity
1/3
On the left is a digital representation of the neocortex in the brain, and on the right is a series of shapes and structures that represent objects of between 1D and 7D – the black hole is the cavity
The mess of neurons in the brain connect with each other in unfathomable ways, but the researchers were able to make more sense of the structure by applying the mathematics of algebraic topology
2/3
The mess of neurons in the brain connect with each other in unfathomable ways, but the researchers were able to make more sense of the structure by applying the mathematics of algebraic topology
Algebraic topography  has been used to better understand the neurons in the brain – which may be making use of 11 dimensions
3/3
Algebraic topography  has been used to better understand the neurons in the brain – which may be making use of 11 dimensions
View gallery - 3 images

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.

The mess of neurons in the brain connect with each other in unfathomable ways, but the researchers were able to make more sense of the structure by applying the mathematics of algebraic topology
The mess of neurons in the brain connect with each other in unfathomable ways, but the researchers were able to make more sense of the structure by applying the mathematics of algebraic topology

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."

On the left is a digital representation of the neocortex in the brain, and on the right is a series of shapes and structures that represent objects of between 1D and 7D – the black hole is the cavity
On the left is a digital representation of the neocortex in the brain, and on the right is a series of shapes and structures that represent objects of between 1D and 7D – the black hole is the cavity

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.

Sources: EPFL, Frontiers

Scientists discover hidden patterns of brain activity

View gallery - 3 images
7 comments
Ken Brody
It's interesting that the association structures can be best described in 11 dimensions. One can't help thinking that string theory (M-theory) is also described in 11-dimensions. Coincidence?
S Michael
Interesting concept. IMHO the brain has no time constraints, except those that are place on it by the "owner." And it is the "owner" that gives the brain the conscripts to work within. If the "owner" has no constraints, well you might be looking at a social pathological deviate. If the "owner" has moral, ethical and other restraints then you might have some other behavior. Environmental and DNA disruptions or mutations may also affect the brains thought process.
Douglas Bennett Rogers
I am tired of hearing people use the word "dimension" interchangeably with "universe". "...a being from another dimension..."
Racqia Dvorak
Ok, so, here's my question. This is a study done using "virtual rat brains."
What exactly are virtual rat brains and how well does this really inform us about how normal brains operate? Is it even wet ware, or is it just simulated? This whole 11 dimensions business sounds really neat, but it's also coming from mathematicians and, no offense to any mathematicians, but sometimes they exist in another world where numbers and words mean different things. Words like "real" "practical" fun" and "important."
They're practically not even human.
Ralf Biernacki
@Ken: I wouldn't read too much into this. The article says the cliques typically work up to 7 dimensions, with the highest outlier observed at 11. It seems like just a statistical long tail, not a "best" description. Besides, what they are describing is virtual rat brains. Leaving aside the question of how well they model a real rat brain, I would think that the human brain would tend to have more complex cliques.
JohnLauricella
Here's my theory: It seems to me we're beginning to understand the 4th dimension. Time has always been a complex subject. If these clusters, or "cliques", are being formed as a result of prior events, similar in nature, not only does that prove the old saying "practice makes perfect", but in ways we just never imagined. Picture this:
When learning to ride a bike, the clock moves slower. Every single happening is being recorded in the brain. Your increased heart rate supplies a flood of oxygen to keep up with the brain's increased processing. Once a bit of information is recorded into the brain, such as balance, the brain stores the "clique" used, into some sort of directory, so that next time you need to "balance on a bike", your brain just needs to find and use the same cluster it used before, causing the adaptation time to lessen each time. This leads me to believe that time flows differently for everyone, and that our perception of time is directly related to our previous experiences and how they relate to our current situation.
MEME401SUN
@Racqia
It's by EPFL Blue Brain--they're building on the neural model Henry Markram's team developed. It was created using automated observation of connection formation in rat cortical neurons in vivo, though the jury is still out on just how closely it approximates actual rat neurons.