Me and my friend were just talking and accidentally created a field of mathematics to model the behaviour and interactions of people's vibes.
We call it vibe theory and through it have established that the interaction of vibes can be thought of as an operation acting on two vibes, which we called the product, that behaves similarly, though not identically to the addition of sine waves. This thereby implies that for every vibe v, there exists a multiplicative inverse vibe v⁻¹ such that vv⁻¹ = o, or the zero vibe or identity vibe which behaves analogously under multiplication to a sine wave with zero amplitude. It also implies that multiplication of vibes is a closed operation. On top of this, it means that for any vibe v, vo = v, and you know what that means...
THAT'S RIGHT! Vibes form a group! Which allows us to use many of the useful theorems of group theory in vibe theory!
Furthermore, we established that a particular individual's vibe can be modelled as a set theoretic function of time f, such that for any time t, f(t) returns the vibe given off by that person at t. Since vibes can also be visually represented as combinations of sine waves, this means a person's vibe can be represented as a function f(x, t), where f is a real-valued function that is periodic in x, or alternatively as a 3D parametric function with 2 spatial and 1 temporal dimension, allowing the use of differential and multivariable calculus on vibes!
