That’s according to a new study published in the journal Frontiers in Computational Neuroscience. It uses algebraic topology (what else?) to show how the structures in the brain react when information is processed. And, as it turns out, that means a whole lot more dimensions than your run-of-the-mill height, width, depth, and time.
“How the structure of the brain shapes its function is one of the central mysteries of neuroscience,” Kathryn Hess Bellwald, a professor in the Laboratory for Topology and Neuroscience at Switzerland’s École Polytechnique Fédérale de Lausanne, told Digital Trends. “The connections among the neurons in the brain form an incredibly rich and intricate structure, of which it is difficult to provide a quantitative global description. The firing patterns of neurons in reaction to stimuli are, if anything, even more complex. By examining structure and activity through the filter of algebraic topology, we were able to provide quantitative descriptions of both and to discern a reflection of the connectivity structure of a neural circuit in the shape of its response to stimuli.”
The paper is pretty mind-bending stuff (no pun intended) that helps unpack some of the enormous complexity in the brain. For example, one of its interesting points is about the neural “sand castles,” referring to the fantastically complex structures that the brain constructs as it processes information. This is a geometric reflection of the increasing degree of coordination and organization in neuronal firing that takes place as the brain reacts to a stimulus, which vanishes abruptly once the processing ends.
This is where the multidimensional stuff comes into play, since it relates to how neurons connect to one another. For instance, two neurons connect to make a one-dimensional “rod,” while three make a 2D triangle, four make a 3D pyramid, and so on. As you can imagine, when you get to possible 11D objects, things get all sorts of crazy. And that’s without even worrying about the math.
It might sound like densely abstract research (and it kind of is), but according to Hess Bellwald, there are potential real-world applications to the discovery.
“In the long run, if we develop a deep understanding of what a normal pattern of response to a given input stimulus looks like, expressed in the language of algebraic topology, then we could perhaps use this knowledge to detect and quantify brain pathology, such as that arising in neurodegenerative diseases,” she said.
Since mind-reading tech is currently all the rage for everything from predicting movie box office numbers to helping paralyzed individuals move again, this could turn out to be incredibly useful research.