On the Tactility of Equations and Diagrams

I have some difficulty with philosophy, because it's usually explained in words. Physics is my intellectual homeland, and it's built on simple equations. Imagine explaining all of electromagnetism in ordinary language... You could get the general ideas across, but without anywhere near the specificity and compactness of \( \partial F = j \) . (Of course, that specificity and compactness presents its own challenges to learning...)*

But even beyond that, mathematical theories have a certain tactility to them. Any equation can be analyzed by applying various algebraic tools, to pick apart its implications. It's a "model" not just in the sense that it represents some phenomena, but also in the sense that you can play with it. It's interactive. Poke it and see what happens. Set this value to zero, apply this identity, distribute these terms... and the theory will react, giving you some response.

This extends similarly to any sort of diagrammatic theory. Free-body diagrams, or circuits, for example. Unique systems of algebra or diagram particularly interest me, though I don't know very many. It's what motivated my spirit graphs concept, I wanted a concise way to "draw" a FNaF theory (And I wasn't satisfied with timelines).

I want more theories to come packaged with unique systems of symbols I can push around, or schematics I can doodle.

* This is Maxwell's equation, curtosy of spacetime algebra. It reduces 4 equations into just 4 symbols, provided we stick to natural units. Though technically you also need \( dp/d\tau = qF \cdot u \) . And maybe some (relativistic) fluid mechanics to relate p and u to j... Let's not worry about this.