In what ways are functions useful (or not useful) in explaining spiritual conditions? What is the connection between the concept of rates of change and one's spiritual path?

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Math in general is fairly useful. In particular I use the concept of a hyperbolic space a lot to think about spiritual things. In normal Euclidian space, if you go North 10 yards, then West 10 yards, then South 10 yards, then East 10 yards, then you end up back where you started.

In hyperbolic space, you’re nowhere near your starting point. In fact, depending on the degree of curvature of the space, there’s a point at which you won’t ever be able to get back without some kind of help.

There’s this game called HyperRogue. You should try it some time, it warps your mind a bit. Your horizon in hyperbolic space has to be limited otherwise the space in the distance gets too crowded to be useful. But if you go past the horizon then you can’t get back. In theory you could retrace your steps, but if you miss even one step you’re in a totally new realm.

Why I like this is because the space of possibility can be expressed this way. Even the small space around you you can see doesn’t really mean a whole lot because the future exists in space of much greater dimension than the one you’re in.

But you asked about functions.

Functions are pretty neat. For me, what’s interesting about them is that you can operate on them just like numbers. You can add and subtract functions. It’s mildly interesting from a spiritual standpoint but functions have an important limitation, they’re only really useful for describing one-dimensional operations.

Math allows you to analogize spiritual concepts to space. This is important because we exist in 3 dimensions plus time, and so being able to see concepts in terms of space allows us to reuse our existing spatial processing abilities in our brain to make sense of those concepts.

One dimension doesn’t allow our brains to engage usefully. You’re too analytical. The lack of detail that the number line gives us makes you yearn for more. So you want to look at the actual math.

No! You’re not studying math, you’re studying Spirit!

Instead, you want two dimensions. A map. Functions pack dimensional information into strings of numbers. You can describe any 3 dimensional object using four numbers in a structure called a quaternion. Four numbers is not a map. Here’s a relevant YouTube vid:

I went through that entire presentation and couldn’t think of one spiritual usage for it. It just goes against intuition.

You want to invert that visualization. You want a map of all the interesting things that happen as you tweak the knobs. You’re not interested in the function at all, you want the graph. But you can’t graph multi-dimensional functions easily. So you’re in this awkward no-mans-land of too much information with not enough insight to make sense of it.