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Related work: * Penrose graphical notation. https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation
by kmill 10y ago
Related work:
* Penrose graphical notation. https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation
* Trace diagrams. https://en.wikipedia.org/wiki/Trace_diagram https://en.wikipedia.org/wiki/Trace_diagram
* Trace diagrams for Hopf algebras. http://tmp.esoteri.casa/hopf.pdf http://tmp.esoteri.casa/hopf.pdf
* Frobenius algebras. http://math.ucr.edu/home/baez/week299.html http://math.ucr.edu/home/baez/week299.html
* Temperley-Lieb algebras. https://en.wikipedia.org/wiki/Temperley%E2%80%93Lieb_algebra https://en.wikipedia.org/wiki/Temperley%E2%80%93Lieb_algebra
* Planar algebras. https://math.berkeley.edu/~vfr/VANDERBILT/pl21.pdf https://math.berkeley.edu/~vfr/VANDERBILT/pl21.pdf
* String diagrams for 2-categories. https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram
* Diagrammatic algebras in general. http://mathoverflow.net/questions/168888/who-invented-diagrammatic-algebra http://mathoverflow.net/questions/168888/who-invented-diagra...
* Begriffsschrift. https://i.ytimg.com/vi/KFYvF3t1xUM/hqdefault.jpg https://i.ytimg.com/vi/KFYvF3t1xUM/hqdefault.jpg
* Existential graphs. https://en.wikipedia.org/wiki/Existential_graph https://en.wikipedia.org/wiki/Existential_graph
* Laws of Form by Spencer-Brown. https://en.wikipedia.org/wiki/Laws_of_Form https://en.wikipedia.org/wiki/Laws_of_Form
* Opetopes. http://mat.uab.es/~kock/cat/zoom/scan.jpg http://mat.uab.es/~kock/cat/zoom/scan.jpg
- closed 10y agowell, there goes my Friday night. Cheers :)
- pizza 10y agoalso amplituhedra for computing particle interactions
- ramblenode 10y agoBob Coecke's "Kindergarten Quantum Mechanics": http://www.cs.ox.ac.uk/bob.coecke/VaxjoProc.pdf http://www.cs.ox.ac.uk/bob.coecke/VaxjoProc.pdf
- laingc 10y agoThere is precisely one person who can be productive with Penrose notation, and that's Roger Penrose. You should see him do it, though - very impressive.
- OscarCunningham 10y agoThis isn't true. I've personally found proofs in the diagrammatic notation that I wouldn't have found without it.
- sfgysfdyu 10y agoalso similar to work by Louis H. Kauffman in representing QM with knots & braids https://arxiv.org/pdf/0903.1376.pdf https://arxiv.org/pdf/0903.1376.pdf
- mathgenius 10y agoGlobular: https://ncatlab.org/nlab/show/Globular https://ncatlab.org/nlab/show/Globular
- trustthispost 10y agoThere's a history from the introduction of Tensor networks by Penrose to the 3D tensor networks, the quon language: https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamonte-1700736114.pdf https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamo...
- trustthispost 10y agoThis gives more of a physical development, and frames the context of the lego-like language in the cross-disciplinary field of quantum information