6 ms·

Penrose: From mathematical notation to beautiful diagrams

176 points by amazing_stories 6y ago

dunefox 6y ago
That is a beautiful document!
2sk21 6y ago
So this is written in Haskell - very impressive demo of the languages capabilities.
- hbogert 6y ago
  You mean that it can create decent parsers?
mark_l_watson 6y ago
It is ready for public use yet - I wish they had put that information sooner in the article. That said, looks cool and it is written in Haskell and React: https://github.com/penrose/penrose https://github.com/penrose/penrose
- sealjam 6y ago
  I assume you mean "it is not ready for public use yet"?
  - mark_l_watson 6y ago
    Yes, thanks.
Xophmeister 6y ago
As a recovering mathematician, this fills me with joy. It would be great if it were implemented as, say, a LaTeX package, so the code to your diagrams could sit right in your documents (like how TikZ works). Still, either way, amazing work!
- Myrmornis 6y ago
  It will be great to include Penrose diagrams in LaTeX documents. But Penrose is implemented in Haskell and I'm pretty sure no-one would want to see what it would look like were it implemented in TeX!
  - a-nikolaev 6y ago
    I agree that rendering graphics as a separate file is fine. I think, if one wants to get better interoperability with TeX, they can try to make Penrose produce TikZ, which can be then embedded into the TeX document.
  - Xophmeister 6y ago
    Oh sure, reimplementing in TeX would not be worth thinking about! I'm not familiar with exactly how TeX packages work, but I assumed they could call out to external tools that return the necessary (La)TeX commands (e.g., code syntax highlighters work like this, IIRC).
    - Myrmornis 6y ago
      OK, I see. Sorry yes I agree what you're saying is sensible and what I said was silly. Yes, minted works like that -- it starts a python child process to use pygments to do the syntax highlighting. But with minted and TikZ there's a single element of "source code" in the LaTeX file (a code listing or tikz code fragment respectively) that maps to a single element in the output (syntax-highlighted code, or a TiKZ image). Whereas with Penrose, there would be multiple source code files (the style and substance code). I'm not sure it quite fits the native LaTeX model does it? Maybe it's better just to use Make to generate the Penrose diagram for inclusion via \includegraphics?
- abdullahkhalids 6y ago
  Yeah. That would be really nice. I think all that is needed is a wrapper package. https://tex.stackexchange.com/questions/92691/is-it-possible-to-call-external-programs-from-latex https://tex.stackexchange.com/questions/92691/is-it-possible...
stared 6y ago
In this line - I enjoyed playing Euclidea (https://www.euclidea.xyz/ https://www.euclidea.xyz/) a minimalistic game on Euclidean geometry. The specification of geometry looks similar to the one from the game. ... Side note: when I hear "Penrose diagrams" I have in mind Penrose tensor notation, as in https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams https://www.math3ma.com/blog/matrices-as-tensor-network-diag....
nsajko 6y ago
The Byrne they mention is Oliver Byrne, who made a book of Elements of Euclid including colored graphics for the geometry. https://en.wikipedia.org/wiki/Oliver_Byrne_(mathematician) https://en.wikipedia.org/wiki/Oliver_Byrne_(mathematician) Archive.org, print: https://news.ycombinator.com/item?id=11628606 https://news.ycombinator.com/item?id=11628606 In TeX: https://github.com/jemmybutton/byrne-euclid https://github.com/jemmybutton/byrne-euclid
layoutIfNeeded 6y ago
Oh, I thought this was about the Penrose graphical notation for tensors: https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation
6gvONxR4sf7o 6y ago
Stuff like this could be amazing for pedagogy. It’s automatically generating different ways of looking at a topic. I’m sure authors would love to include these different viewpoints were it not for the effort involved, so making it easy could be great!
peter_d_sherman 6y ago
This looks beautiful! And strange! And beautiful! Like the diagrams for an entire Calculus textbook could be created with it...(!) Penrose, for mathematical drawings, might very well become what TeX, LaTeX, and Desktop Publishing programs are, to text! I think you are on the right track to something grand! Wishing you a lot of luck in this endeavor!

dunefox 6y ago

That is a beautiful document!

2sk21 6y ago

So this is written in Haskell - very impressive demo of the languages capabilities.

hbogert 6y ago
You mean that it can create decent parsers?

mark_l_watson 6y ago

It is ready for public use yet - I wish they had put that information sooner in the article. That said, looks cool and it is written in Haskell and React: https://github.com/penrose/penrose https://github.com/penrose/penrose

sealjam 6y ago
I assume you mean "it is not ready for public use yet"?
- mark_l_watson 6y ago
  Yes, thanks.

Xophmeister 6y ago

As a recovering mathematician, this fills me with joy. It would be great if it were implemented as, say, a LaTeX package, so the code to your diagrams could sit right in your documents (like how TikZ works). Still, either way, amazing work!

Myrmornis 6y ago
It will be great to include Penrose diagrams in LaTeX documents. But Penrose is implemented in Haskell and I'm pretty sure no-one would want to see what it would look like were it implemented in TeX!
- a-nikolaev 6y ago
  I agree that rendering graphics as a separate file is fine. I think, if one wants to get better interoperability with TeX, they can try to make Penrose produce TikZ, which can be then embedded into the TeX document.
- Xophmeister 6y ago
  Oh sure, reimplementing in TeX would not be worth thinking about! I'm not familiar with exactly how TeX packages work, but I assumed they could call out to external tools that return the necessary (La)TeX commands (e.g., code syntax highlighters work like this, IIRC).
  - Myrmornis 6y ago
    OK, I see. Sorry yes I agree what you're saying is sensible and what I said was silly. Yes, minted works like that -- it starts a python child process to use pygments to do the syntax highlighting. But with minted and TikZ there's a single element of "source code" in the LaTeX file (a code listing or tikz code fragment respectively) that maps to a single element in the output (syntax-highlighted code, or a TiKZ image). Whereas with Penrose, there would be multiple source code files (the style and substance code). I'm not sure it quite fits the native LaTeX model does it? Maybe it's better just to use Make to generate the Penrose diagram for inclusion via \includegraphics?
abdullahkhalids 6y ago
Yeah. That would be really nice. I think all that is needed is a wrapper package. https://tex.stackexchange.com/questions/92691/is-it-possible-to-call-external-programs-from-latex https://tex.stackexchange.com/questions/92691/is-it-possible...

stared 6y ago

In this line - I enjoyed playing Euclidea (https://www.euclidea.xyz/ https://www.euclidea.xyz/) a minimalistic game on Euclidean geometry. The specification of geometry looks similar to the one from the game. ... Side note: when I hear "Penrose diagrams" I have in mind Penrose tensor notation, as in https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams https://www.math3ma.com/blog/matrices-as-tensor-network-diag....

nsajko 6y ago

The Byrne they mention is Oliver Byrne, who made a book of Elements of Euclid including colored graphics for the geometry. https://en.wikipedia.org/wiki/Oliver_Byrne_(mathematician) https://en.wikipedia.org/wiki/Oliver_Byrne_(mathematician) Archive.org, print: https://news.ycombinator.com/item?id=11628606 https://news.ycombinator.com/item?id=11628606 In TeX: https://github.com/jemmybutton/byrne-euclid https://github.com/jemmybutton/byrne-euclid

layoutIfNeeded 6y ago

Oh, I thought this was about the Penrose graphical notation for tensors: https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation

6gvONxR4sf7o 6y ago

Stuff like this could be amazing for pedagogy. It’s automatically generating different ways of looking at a topic. I’m sure authors would love to include these different viewpoints were it not for the effort involved, so making it easy could be great!

peter_d_sherman 6y ago

This looks beautiful! And strange! And beautiful! Like the diagrams for an entire Calculus textbook could be created with it...(!) Penrose, for mathematical drawings, might very well become what TeX, LaTeX, and Desktop Publishing programs are, to text! I think you are on the right track to something grand! Wishing you a lot of luck in this endeavor!