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.
> I am not really sure what to do about this, except to maybe err on the side of using square Venn diagrams and flow diagrams when possible.
Strong support for square venn-diagrams.
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.