I think for maximum uselessness, they should not be overlapping spheres, but deform at the interface, like soap bubbles or rubber balls. As long as the spheres are the same size and modelled with the same “surface tension” or “elasticity”, the “intersection” of two sets would then be a circular interface with an area proportional to what would otherwise be an overlap (I think). If the spheres have different sizes or are modelled with different surface tension or elasticity, one would “intrude” into the other.
Multiple sets would have increasingly complex shapes that may or not also create volumes external to the deformed spheres but still surrounded by the various interfaces.
Time to break out the mathematics of bubbles and foam. This data ain’t gonna obscure itself!
Might there actually be utility to something like this? Scrunch the spheres together but make invisible everything that is not an interface and label the faces accordingly. I suppose the same could be said of the shape described by overlapping. (Jesus, you’d think I was high or something. Just riffing.)
What about 3D Venn diagrams, but the sets are spheres?
I think for maximum uselessness, they should not be overlapping spheres, but deform at the interface, like soap bubbles or rubber balls. As long as the spheres are the same size and modelled with the same “surface tension” or “elasticity”, the “intersection” of two sets would then be a circular interface with an area proportional to what would otherwise be an overlap (I think). If the spheres have different sizes or are modelled with different surface tension or elasticity, one would “intrude” into the other.
Multiple sets would have increasingly complex shapes that may or not also create volumes external to the deformed spheres but still surrounded by the various interfaces.
Time to break out the mathematics of bubbles and foam. This data ain’t gonna obscure itself!
Might there actually be utility to something like this? Scrunch the spheres together but make invisible everything that is not an interface and label the faces accordingly. I suppose the same could be said of the shape described by overlapping. (Jesus, you’d think I was high or something. Just riffing.)
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No, that’s not what I was thinking, but that sounds like a decent idea. Maybe a better idea than just simple labels representing the facing sphere.
Venn diagrams, but the sets represent whatever the diagram is about (like houses for housing markets).
So something like this? I love that idea!
Projected on a 2D screen, it’d look more like a normal venn diagram.
That’s what 3D printing is for…
How about 4D Venn diagrams?
One might even go as far as 5D
When I read your comment, my monocle popped right off!
Volumetric Herbert space diagram.
Why limit it to 3 dimensions?
Why limit it to an integer number of dimensions?
Because I’m not sure how to make it work in non integer dimensions.
Open your mind