I don’t have coherent thoughts right now. But here are some misc vaguely related ideasposts I found while browsing around for inspiration from some of the commentary in this one I’m commenting on. This is me being a “related stuff online” search drone again (the results are my picks from a metaphor search of a paragraph from the post), so if this comment gets too far up the replies I may strong downvote myself. But if any of these things catch others’ eyes, please comment your takeaways, especially if there are action items for others.
I spent the last month wondering and investigating how we might design better workflows for creative work that meld the best of human intuition and machine intelligence. I think a promising path is in the design of notation. More explicitly, I believe inventing better notations can contribute far more than automated tools to our effective intelligence in understanding ourselves, the world, and our place in it
[...] to me the problem isn’t just that the first examples are badly formatted (missing spaces between operators, for example), or even that the environment isn’t rendering those equations using the traditional notation taught in grade school. The main problem is that the programming environment doesn’t give us any way of understanding what the symbols are doing.
3blue1brown’s videos about linear algebra are beautiful and likely improve mental imagery when thinking causally about things like linear transformations. However, Gilbert Strang’s notation-heavy lectures on the same subject are presented with the same interface learners use: chalkboards. When we have to actually factorize a matrix, the only way we can do that in our current media environment is by writing things down
Penrose is a platform that enables people to create beautiful diagrams just by typing mathematical notation in plain text.
Beautiful
The goal is to make it easy for non-experts to create and explore high-quality diagrams and provide deeper insight into challenging technical concepts.
Universal
We aim to democratize the process of creating visual intuition.
https://scholarphi.org/ is a research project that attempted something related for aiding paper skimming. It did not use ML. it doesn’t look ready to generalize. but it may be very useful for improving on basic multi-pass skimming. it apparently inspired semanticscholar’s semantic reader, which does not to my knowledge have this additional functionality?
The goal of the ScholarPhi project was to improve the reading of scientific papers by helping readers see the meanings of mathematical symbols, technical terms, and other information directly where they are used within the paper.
There were more results in the metaphor search, and tweaking the metaphor search (eg, using different paragraphs) may find more relevant stuff. Still, these results had some very interesting essays and so those are what I pasted. Hope this helps someone implement what John is thinking! Busy for 2h.
“Nota is a language for writing documents, like academic papers and blog posts. The goal of Nota is to bring documents into the 21st century.” https://nota-lang.org/
“Apparatus is a hybrid graphics editor and programming environment for creating interactive diagrams.” http://aprt.us/
“A Visual Programming Environment for Scientific Computing”—python visual programming with plotting https://mathinspector.com/
“Hazel is a live functional programming environment that is able to typecheck, manipulate, and even run incomplete programs, i.e. programs with holes. There are no meaningless editor states.” https://hazel.org/
windows only agpl math::topology of 3d::topology? I think? idk. “Topologic is a software development kit and plug-in that enables logical, hierarchical and topological representation of spaces and entities” https://topologic.app/
ordinary stuff
“Convert images and PDFs to LaTeX, DOCX, Overleaf, Markdown, Excel, ChemDraw and more, with our AI powered document conversion technology.” https://mathpix.com/
“Gridpaste is an online math tool to share computations, transformations, and annotations on geometric structures in a coordinate plane.” https://gridpaste.io/
For years, I’ve collected a MASSIVE number of links in a bookmark folder, about this exact cluster of topics. It started as “build a better wiki for maths, especially for AI alignment”, but now I’ve had a few different (not-very-workable) ideas for similar tools.
I don’t have coherent thoughts right now. But here are some misc vaguely related ideasposts I found while browsing around for inspiration from some of the commentary in this one I’m commenting on. This is me being a “related stuff online” search drone again (the results are my picks from a metaphor search of a paragraph from the post), so if this comment gets too far up the replies I may strong downvote myself. But if any of these things catch others’ eyes, please comment your takeaways, especially if there are action items for others.
https://thesephist.com/posts/notation/ is an interesting related essay. intro:
http://glench.com/LegibleMathematics/ is another interesting related essay. an intro paragraph:
https://a9.io/inquiry/notes/1rCLzzZwVdcOICn9eIrII/ is yet another related essay:
https://penrose.cs.cmu.edu/ seems interesting:
https://cognitivemedium.com/ has several related essays:
https://scholarphi.org/ is a research project that attempted something related for aiding paper skimming. It did not use ML. it doesn’t look ready to generalize. but it may be very useful for improving on basic multi-pass skimming. it apparently inspired semanticscholar’s semantic reader, which does not to my knowledge have this additional functionality?
There were more results in the metaphor search, and tweaking the metaphor search (eg, using different paragraphs) may find more relevant stuff. Still, these results had some very interesting essays and so those are what I pasted. Hope this helps someone implement what John is thinking! Busy for 2h.
more tidbits that could be part of or inspiration for an interesting tool
idk
“The goal of
curvenote.devis to provide open source tools to promote and enable interactive scientific writing, reactive documents and explorable explanations. These tools are used and supported by curvenote.com, which is an interactive scientific writing platform that integrates to Jupyter.” https://curvenote.dev/“Nota is a language for writing documents, like academic papers and blog posts. The goal of Nota is to bring documents into the 21st century.” https://nota-lang.org/
“Apparatus is a hybrid graphics editor and programming environment for creating interactive diagrams.” http://aprt.us/
“A Visual Programming Environment for Scientific Computing”—python visual programming with plotting https://mathinspector.com/
notebook with builtin desmos and latex https://themathist.com/app
“Hazel is a live functional programming environment that is able to typecheck, manipulate, and even run incomplete programs, i.e. programs with holes. There are no meaningless editor states.” https://hazel.org/
windows only agpl math::topology of 3d::topology? I think? idk. “Topologic is a software development kit and plug-in that enables logical, hierarchical and topological representation of spaces and entities” https://topologic.app/
ordinary stuff
“Convert images and PDFs to LaTeX, DOCX, Overleaf, Markdown, Excel, ChemDraw and more, with our AI powered document conversion technology.” https://mathpix.com/
“Gridpaste is an online math tool to share computations, transformations, and annotations on geometric structures in a coordinate plane.” https://gridpaste.io/
react libs and such
https://flume.dev/
https://mafs.dev/
https://github.com/unconed/mathbox
more blogs
https://mlajtos.mu/posts/new-kind-of-paper-1
https://mlajtos.mu/posts/new-kind-of-paper-2
https://mlajtos.mu/posts/new-kind-of-paper-3
https://mlajtos.mu/posts/new-kind-of-paper-4
https://www.inkandswitch.com/inkbase/
https://www.lesswrong.com/posts/ky988ePJvCRhmCwGo/using-vector-fields-to-visualise-preferences-and-make-them
a dataset: https://wellecks.com/naturalproofs/
For years, I’ve collected a MASSIVE number of links in a bookmark folder, about this exact cluster of topics. It started as “build a better wiki for maths, especially for AI alignment”, but now I’ve had a few different (not-very-workable) ideas for similar tools.
Here is a large dump of such links, in a similar vein: https://drive.google.com/file/d/1sFVb58wceAd_RoPqw_eGnA7K_wSIrziK/view?usp=sharing