Boosting Vector Calculus with the Graphical Notation · HackerPapers discussions

Boosting Vector Calculus with the Graphical Notation — mentioned by danielscrubs

Tue, 09 Jun 2020 10:50:25 GMT

I mean conditions exist in math already and I'd argue that there is a bigger chance qwerty is still the default keyboard layout than your Python 3 program working in 500 years. How many of the popular languages even have formal specifications to use as a reference when the next CPU architecture comes along, or the next ABI? The tools exist but I don't see people rushing to Modula-2 for example, which has. It does remind me a bit of this paper "Boosting Vector Calculus with the Graphical Notation" [1], but we instead have over ten thousand only partially defined ones. But I can agree that my…

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Boosting Vector Calculus with the Graphical Notation — mentioned by foxes

Thu, 14 Nov 2019 10:25:08 GMT

Ref of the original paper https://arxiv.org/abs/1911.00892. The biggest issue for me is they don't have proper upper/lower indices. A lower index is a leg pointing down, while an upper index is a leg pointing up. \delta should be \delta_i^j. The upper/lower I like to think of as extra type information. You can pair covectors and vectors. The other issue is with the dot product of course, I would write a_i b^i.

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Boosting Vector Calculus with the Graphical Notation — mentioned by fantispug

Thu, 14 Nov 2019 07:08:34 GMT

They do mention Penrose notation in the linked arxiv paper[1], as well as Cvitanović's Birdtracks[2] which let you do calculations on representations of groups. They claim they're making it more accessible with pedagogical examples (and innovations in representing differential vector calculus). I still prefer index notation. Their notation looks pretty intricate and I think it would be really hard to do long calculations in it. It's also not clear to me how you'd generalise it to non-commutative vector algebras like in quantum mechanics. [1] https://arxiv.org/pdf/1911.00892.pdf [2]…

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