Imagine three neurons, each with a firing speed at a time called τ: a₁(τ), a₂(τ), and a₃(τ). Together, these three firing speeds make a group: A(τ) = [a₁(τ), a₂(τ), a₃(τ)]. This group shows how active the three neurons are at that moment. You can think of this group as a point in space with three directions, one for each neuron’s activity. This helps us see what the brain is doing when a ball flies through the air.

It doesn't mean the brain is articulating the language of math behind the scenes.

You simply remember (record/store) values of where the ball was last time you saw it fly through the air. You get better at modeling the trajectory because the neurons physically move closer together as you learn. We can and do represent this with math.

These linear algebra vectors and algorithms are math/compsci that can represent the branching nature of firing neurons in the same way it can be applied to how a river winds through a landscape, and other things. (this does not mean "the river is doing math" btw).

That's why in neuroscience, linear algebra is so widely used to represent firing rates of neurons, coordinate systems in sensory spaces, and multi-channel neuroimaging data matrices (like fMRI or EEG). Also PCA (dimensionality reduction) relies solely on it since you are representing actual brain cells with elements in Arrays.

> not supported by the data

Entire fields exist, you're just ignorant beyond belief.