Imagine all your neurons’ connections forming a graph.
How can we understand the insanely complex mess of information that’s constantly buzzing inside our brain? With 100 billion neurons in the average human brain, and 100 trillion connections between them, there isn’t an easy answer. Neuroscientists today use MRIs and other brain scans to see where blood and electrical impulses are flowing in the brain when people complete different tasks. But what combination of neurons are being activated specifically for that task? The PBS Infinite Series channel demonstrates one idea figuring this out, based in the mathematics of algebraic topology and the work of neuroscientists Kathryn Hess and the Bluebrain Project. They explored this idea in a three part series on the topic.
Algebraic topology is concerned with figuring out how many components, holes, and paths exist in a space. This is useful for all kinds of problems, but it’s particularly useful in the case of mapping the brain. These Infinite Series videos make a case for considering the brain as a graph, with neurons as points and whichever neurons are sending each other signals during a task as edges between the points. Things get more complicated when you factor in the direction of the impulses.
By using topology, and the concept of simplices, the videos show that our brains produce far more simplicies than a graph that represents random impulses. So, topology, must be telling us something about what the brain is actually doing. By doing tests on neural network models, scientists have determined that when the brain is stimulated, the number of holes and solids that exist within this framework skyrocket. You can think of it as the brain “creating” a higher dimensional solid, which disperses after the stimulus has dissipated (though this solid exists only in the realm of mathematical imagination). This is all pretty crazy and complex, but it’s a fascinating way to understand a little about our brains, and perhaps it’s how neuroscientists in the future will begin to pare down their knowledge into something legible.
Source: PBS Infinite Series