Re: Low FPS webcam - here's an approach that attempts to analyze coin tossing data from the _sound_ rather than the _video_, since sound is typically recorded at a much higher sampling rate (high enough to "hear" the spinning of the coin). https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...
A lot of replies here are missing the key idea behind Penrose: that the "substance" and "style" of any mathematical diagram are separable. For example, the "substance" of a diagram might be a collection of sets with known subset relationships:
Set A, B, C
IsSubset(B, A)
IsSubset(C, A)
That same substance can then be rendered in many different styles, e.g. as a Venn diagram or as a tree diagram (substance vs. style is a lot like HTML vs. CSS). Importantly, Penrose's vision is that experts will author libraries of domains and styles, and end-users need only express the substance of their diagrams (i.e. the three lines of code above).
The second beautiful idea in Penrose is that diagram generation is expressed as a constrained optimization problem. This lets you easily experiment with layouts by writing constraints and sampling a variety of potential diagrams via stochastic search.
These two ideas set Penrose apart from most other diagram software out there. I really hope it gains wider adoption. Give it a try!
Given the popularity of frameworks like TailwindCSS, it seems that people here don’t understand the advantage of separating HTML and CSS either, so I’m not sure if this analogy is helpful…
> Importantly, Penrose's vision is that experts will author libraries of domains and styles, and end-users need only express the substance of their diagrams (i.e. the three lines of code above).
In that case, would it be a good idea to start the tutorial with some predefined domains and styles? Part of the intimidation factor here is not just the programming language, but also the abstraction one is faced with using and trying to understand before seeing their first picture. If the goal is to have predefined libraries, then why not start with pre-defined domains and styles and first teach people only how to do the substance, and leave domain & style definitions for advanced tutorials?
What are the advantages of making everything a constrained optimization problem? I like the idea that I can experiment with layouts sometimes, but I don’t really want a random diagram all the time. I realize it doesn’t have to be random, I have the choice to explicitly pin things down, but that takes extra work with Penrose, I’m asking why random is the default. Having done a lot of technical diagramming in papers and books, I would expect to almost always pin things down, and maybe once in a while free up a few elements to move around. Letting the whole thing go random is rarely if ever something I’d choose, especially near the end of making a more complicated diagram. What I’m wondering is whether this design is good for experts, and why, or if it mostly helps beginners.
I recently discovered GeoGebra, and would love to hear some compare & contrast notes. It doesn’t use constrained optimization, and it does separate style from substance as needed, but in a different way than Penrose. The important feature seems to be that it lets you define the relationships between elements of the diagram, so if you move a point, the line attached follows, and then parallel and perpendicular lines attached follow, and so on, everything in the diagram becomes responsive to adapt to the change while letting you put something right where you want it. This way I still get to experiment with layouts, but nothing in the construction needs to be random. Most of the style definitions are point & click GUI actions. Are there reasons that workflow is inferior to Penrose?
Yeah, exactly! Also, possibly a third idea of Penrose is the way the selector matching blocks in the Style language can be used to construct the constrained optimization problem as you mention. This is inspired by CSS, but there are a lot of differences too.
With regard to the separation of substance and style, I think that idea can be profitably applied in other settings as well. For instance, Graphviz, tikz-cd, and Mermaid are all fairly declarative. But also, I feel like this idea could be even more profitably applied by building a diagramming library inside of a general-purpose programming language like Python.
However, as I've commented on other software like this, why are none of the examples style-free Venn diagrams? That is, black on white 3 circle overlapping each other in pairs with a single shared triangle intersection at center? I apologize if one of these is already present. Style has little value there since it may obscure reality.
Thanks so much for sharing upset given the context of my question!
Their explication of Venn diagrams is exemplary and compelling, particularly the banana and the way the Venn is elucidated and visualized through the accompanying meta-detail, for lack of a better phrase.
I cannot thank you enough. This will literally propel much of my work on data going forward.
This reminds me of a small experiment I did with a friend, where we asked different people to independently write the HTML and CSS for a website (without communicating), and then put the HTML and CSS files together to see how well they worked. https://kach.github.io/generative-adversarial-web-developmen...
If you liked this, you might enjoy this little trick you can do with moiré patterns -- near the end of the post, I talk a little bit about the math behind the FFT connection. https://hardmath123.github.io/moire.html
