Tried square Venn diagrams prior to habryka’s comment. Rejected them because they were worse pedagogically (despite being more accurate). Suspect rounded-corner quadrangles may actually be an optimal substitute.
Essentially, I found that they implied something much more specific and meaningful in the overlap. With circles, you’re just pushing centers together/overlapping radii, and the mind parses the overlap as perfect/symmetrical and therefore containing no semantic content other than size/area.
With the square or rectangular Venn diagrams, the creator starts making choices—should the overlap be center-to-center, center-to-corner, corner-to-corner, etc.? Should the overlap be “designed” to have a square aspect ratio, or to be golden, or to be long and narrow? If you’ve got a clear grid such that every background square is 1u^2, should you force the blocks to adhere evenly to that grid, or have them be off? What if your area doesn’t easily break down into X by X, or X-minus-a-little by X-plus-a-little? If your squares are e.g. 4x4 and 6x6 but you want the overlap to be 7 squares, what do?
I found that there was no “natural” answer to these questions; no Schelling layout that seemed zero-content. Instead, every arrangement invited the reader to try to actively parse it for additional meaning that wasn’t there, chewing up attention and bandwidth.
Here’s my take on a good Venn diagram layout that doesn’t try to convey extra information, and avoids the problems you and the parent mentioned: https://i.imgur.com/tKPzfLM.png. Make the rectangles full height, and give them rounded corners so it’s clear that these are subsets of a larger space and not just vertical bars (it’s unclear with square corners that there are 2 overlapping sets and not 3 adjacent). Only caveats are that this is not instantly recognizable like your standard Venn diagram, and is only really usable for 2 subsets.
Yeah. I hadn’t thought to go full column height, but this definitely resembles one of the options I thought was most promising. I think you may have identified the best option for square diagrams that match the use case in this post.
Tried square Venn diagrams prior to habryka’s comment. Rejected them because they were worse pedagogically (despite being more accurate). Suspect rounded-corner quadrangles may actually be an optimal substitute.
I’ve never actually tried square Venn Diagrams, so I would be interested in you unpacking the “they were worse pedagogically”.
Essentially, I found that they implied something much more specific and meaningful in the overlap. With circles, you’re just pushing centers together/overlapping radii, and the mind parses the overlap as perfect/symmetrical and therefore containing no semantic content other than size/area.
With the square or rectangular Venn diagrams, the creator starts making choices—should the overlap be center-to-center, center-to-corner, corner-to-corner, etc.? Should the overlap be “designed” to have a square aspect ratio, or to be golden, or to be long and narrow? If you’ve got a clear grid such that every background square is 1u^2, should you force the blocks to adhere evenly to that grid, or have them be off? What if your area doesn’t easily break down into X by X, or X-minus-a-little by X-plus-a-little? If your squares are e.g. 4x4 and 6x6 but you want the overlap to be 7 squares, what do?
I found that there was no “natural” answer to these questions; no Schelling layout that seemed zero-content. Instead, every arrangement invited the reader to try to actively parse it for additional meaning that wasn’t there, chewing up attention and bandwidth.
This was a great explanation, and now I want to try this out to see the same effect myself.
Alternative idea: Waterfall diagrams, which is what Eliezer uses sometimes in his latest Bayes Guide.
Here’s my take on a good Venn diagram layout that doesn’t try to convey extra information, and avoids the problems you and the parent mentioned: https://i.imgur.com/tKPzfLM.png. Make the rectangles full height, and give them rounded corners so it’s clear that these are subsets of a larger space and not just vertical bars (it’s unclear with square corners that there are 2 overlapping sets and not 3 adjacent). Only caveats are that this is not instantly recognizable like your standard Venn diagram, and is only really usable for 2 subsets.
Yeah. I hadn’t thought to go full column height, but this definitely resembles one of the options I thought was most promising. I think you may have identified the best option for square diagrams that match the use case in this post.