Hieroglyphs

I only have 1 big diagram in my thesis

I looks like a pre-computer form of VPL

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

Looks like a wiring diagram or function block code, cool.

Penrose Tensor Notation

What exactly is it, user?

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.

Actually Frege, not Gentzen

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

Ehat the heck is that

>wagon wheels

what the actual fuck

?

OP said outlandish, not difficult.

those sums look like they're about to murder their entire clan

Frege made everything unnecessarily difficult

aaaaaaaaaa

[math]i^{2}[/math]
No idea what it means.

>there are brainlets ITT right now that don't understand graphical calculus
Are you serious?

is that like where you look for the max or min

not necessarily notation but it looks cool

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

hairer.org/notes/Regularity.pdf

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

Diagrammatic algebra. Diagrammatic algebra everywhere.

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.

可愛い

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].

i want this in not shit res

>tfw trancended formal proofs and now pictures are the new numbers

cc.gatech.edu/~turk/bio_sim/articles/metabolic_pathways.png

This is almost like proof via interpretive dancing.

I've seen it so many times but I still don't know how it works.

Nice.

>cc.gatech.edu/~turk/bio_sim/articles/metabolic_pathways.png
cheers mate

you could also just flip the head over right

why are there so many theoretical physics touhouposters on Veeky Forums

There's only one.

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