The mathematical framing — tasks on low-D manifolds

43:10imagine you've got a bunch of neurons. Okay, >> we've got about I think 80 billion neurons. We're not going to talk about that many neurons, but what you can think about when we think about what is a brain state. Okay. >> Okay. >> Let's let's first talk about what is a brain state. A brain state would be a description of all of your neurons and which ones are active and which ones are not active. Okay? >> For example, right? So like a zero one like a map of zero. >> Yeah, that's one way of thinking about it. Another way would be like um what's the firing rate of each of these neurons, right? And um is it it? Yeah. But at the end of the day, it's something like is this neuron active or not? And then how is it connected to all

43:51the other stuff? But the the state of the brain at any given point, like right now when I'm doing this podcast, there's certain neurons that are turning on and off, right? and my brain is moving from one state to the other as I speak, as I go through what I'm trying to talk about and things like that. Okay? And given we've got so many neurons, we run into this curse of dimensionality, >> right? >> And that means that if you've got a lot of neurons,