What are the most outlandish notations you have ever encountered Veeky Forums?

take your Standard Model Lagrangian outta here

# Hieroglyphs

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Mechanical Notation, Charle's Babbage's crazy way of drawing machines. We still don't understand it.

to this day we don't have verilog for mechanical systems, cause gears and shit actually have to go places.

Gentzen's way of writing proofs

This is actually just a (big) commutative diagram, like when you write [math]A \overset{f}{\longrightarrow} B[/math] to say f is a map from A to B.

Another use of that notation in some John Baez book about higher dimensional algebra

there are brainlets ITT right now that don't understand graphical calculus

Are you serious?

tfw your branch of mathematics is closer to transplantational surgery than to calculus

I'm a mathematician but I bow before the might and complexity of biochemical pathways.

i just find it incredible that string diagrams and graphical calculus exist, much less actually work and be useful for stuff like QFT

what is the name of that theorem that guarantees the existence of these diagrams

this is some black magic shit

If someone knows this, please tell me. I found a pdf about it in 2013 but at the time couldn't understand it, and I cant find anything about it now.

These 6j symbols are what's more generally referred to as fusion matrices for a conformal field theory. Let [math](\mathscr{V},\{V_i\}_i)[/math] be a simple modular category with simple objects [math]V_i[/math] and some fixed set of fusion rules, then there exists a covariant functor [math]F:\text{Rib}_\mathscr{V} \rightarrow \mathscr{V}[/math] from the ribbon category based on [math]\mathscr{V}[/math] to [math]\mathscr{V}[/math] called the operator invariant. This functor allows you to cast fusion rules in the form of ribbon graphs as well as express some results regarding the dimensions and traces of objects in [math]\mathscr{V}[/math] as knot invariants. This allows you to prove fusion relations such as the pentagon/hexagon relations, Verlinde-Seiberg formula and Vafa's theorem with braids and knots. In addition if [math]\mathscr{V}[/math] is unitary metaplectic then these fusion matrices form a [math]\mathbb{C}[/math]-vector space called the space of conformal blocks. In this case the 6j-symbols are basically instructions for fusing the simple objects of [math]\mathscr{V}[/math] as Hilbert spaces and you can consider it as relations between knots or ribbon graphs WLOG. For instance, the fusion matrix [math] F_{pq}\left[\begin{bmatrix} i & j \\ k & l\end{bmatrix}\right] [/math] can be considered as a consistency condition between fusing objects [math]i,j,k[/math] by fusing [math]i,j[/math] first into [math]p[/math] and then fusing [math]p,k[/math] into [math]l[/math] or first fusing [math]j,k[/math] into [math]q[/math] then fusing [math]i,q[/math] into [math]l[/math].

Game theory

Being so autistic that you need trigonometry to simulate a negotiation process