How does it not fit in our quantitative descriptions?
I mean it just kinda fucking doesn't. Our physical model of reality is a bunch of mathematical models and there's no mathematical formula for consciousness yet.
I'd love for some mystical thing to exist, but literally every mystical thing people have believed for tens of thousands of years has been wrong.
But you're literally experiencing the "mystical thing" right now. The mystical part is the part where you don't really have a mathematical equation for it and yet it exists. Think of it like "dark matter" where you know it probably exists but you can't really model it properly.