We’re exploring the concept of overlap. Let’s start with one of the best science exhibits that fits in your pocket: three small LED flashlights of Red, Green, and Blue:
I’ve had a lot of fun in the office, whenever a few new people wander in, handing them each one of the flashlights and watching them play with the overlaps together. It’s one of those things that really wants to be real, and is satisfyingly simple. It seems obvious in retrospect, yet without the VR prototypes we did of Venn Diagram exhibits, I wouldn’t have thought of it.
Our virtual light exhibit used three virtual spotlights that turn on/off when you touch them, with the only interaction being which lights are on and which are off:
This virtual exhibit came about because it was “close to the surface” considering the capabilities of Anyland, the prototyping environment we were using. After creating a spotlight for use with a different exhibit, and given how easy it was to conjure up spotlights of any color with just a few hand motions, the design for the above exhibit was just a few steps down the path of possible creations.
My original thoughts for a real version would use three spotlights with color filters. But somewhere in my searches, I started looking for flashlights with color filters, and then just colored LED flashlights, which I hadn’t known existed before. And when I got the flashlights, I still thought I was going to mount them into a still and perfect Venn diagram arrangement, but it turned out that the embodied action of pointing the flashlights in different directions to overlap and un-overlap was much more compelling in real life than I could have imagined. Mixing and unmixing the light happens instantly, without rendering, without having to stir two paints and then reverse entropy to un-mix, they just overlap and un-overlap with perfect visual clarity and direct manipulation.
After making the prototype Venn diagram of light mixing in VR, which is additive mixing, I also made the companion subtractive mixing venn diagram, where the primary colors are red, yellow, and blue:
Unfortunately, the VR version is not interactive, beyond being able to pick it up and throw it around. Because while lights are a necessary part of any virtual environment and a standard part of computer graphics, the same is not true for fluid dynamics and mixable particulates. But the VR prototype suggested a much more compelling counterpart in reality, where you actually mix real colors and see real results.
First I invited people in the office to relax and take a break to draw a Venn diagram of overlapping colors, free to interpret that however they like:
All this brought to mind one of the fundamental ideas we’re researching, with all this Venn VR stuff, which has to do with different ideas of mixing and overlap, and how they relate to our embodied understanding of the world.
So I made up a worksheet that asks the user (player?) to create venn diagrams of mixing colors, but to think about that mix in a few different ways:
In the first, you literally overlap the colors, first coloring one circle, then the other. In the next, you try to be a little more careful with the mixing of your colors, to get what feels more like the right mix. In the last, the player is asked to color the overlap in what feels like the overlap color, even if it doesn’t actually use the same coloring implements as in the two circles.
Here’s some of the completed worksheets:
It’s interesting to see how sometimes our ideas of overlap aren’t better than the “real” thing, while in other cases, choosing different colors leads to a lighter more colory-feeling color than a literal mix of the initial pigments could create. Sometimes, when mixing real pigments, I’m disappointed by getting what I feel like is the “wrong” color, even though it is quite literally the correct result according to physics. But shouldn’t yellow and blue always mix to make green, not some muddy mess? In VR, we could make virtual paints always mix into what they “should” be. It’s not clear to me whether that’s a good or bad thing, but it’s a thing.
Let’s quickly document just a few other relevant creations and their relative reality:
The following color octahedron demonstrates three orthogonal axes of color overlapping into the 8 quadrants of 3D space, as related to the venn diagram. It’s nice that objects can float, animate, and do intersection-style overlap in VR.
Also related to the formal logic idea of Venn diagrams, I prototyped some physical octahedra, though I could do better on the color one:
This is related to the color cube, a solid cube that contains all colors by using the 3 axes R G and B. For the Venn museum I made a pile of discrete color cubes:
I’m totally into this relationship between the 3-circle Venn diagram, the octahedron, the 3 axes of 3D space, and 3 primary colors. I think something like the following could work, with bigger/thinner hemispheres with better translucent colors than my painted Christmas ornament balls:
Unlike in VR where solid hemispheres can intersect no problem, the above hemispherical shells overlap in a certain order, with no true overlap in one sense. In VR, two objects can be in exactly the same place, though with current graphics rendering there’s z-fighting and wonkiness with how it’s displayed, sometimes. Different graphics algorithms can create different visual results when two objects overlap, and it would be interesting to design a graphics engine meant for a virtual world where objects often overlap perfectly, as well as other feats natural to VR that don’t replicate real physics.
What I’d like to point out about these additive/subtractive color exercises is that there’s multiple ways to think about overlap, and that different ways can be equally valid. There’s one sort of thing we call “yellow” like the yellow we see on an rgb display, which is quite literally both red light and green light. Another kind of yellow is a pure yellow wavelength, neither red nor green. Our bodies experience these different yellows as the same because of the biology of our eyes, though our bodies also experience that if you physically mix red and green, you get a muddy brown that doesn’t look like yellow at all. It would be difficult indeed to apply the strict concept of logical categories onto a complicated experience like yellow. (See this piece on VR and the Philosophy of Color if you’re into that sort of thing.)
Speaking of categories, here’s a third Venn game we’ve been playing in the office: choose three labels for three overlapping circles, then go around the office trying to find things that fit in each section of the diagram. In the following picture, we chose the categories of writing implements, made of wood, and yellow things:
In this case, we’re applying not just the biology of our eyes and our experience of objects, but also our embodied experience with sorting objects into physical locations. And when it comes to sorting objects into places, our goals are less purely logical and more functional: what use is reserving a place for a category of object if nothing goes in it?
In the case of physical sorting, we tend to flex our definitions of categories to fit the things we’d like to put in them. The yellow pencil in the above photo is both yellow, a writing implement, and pencils are generally made of wood… except this one isn’t, it’s a plastic mechanical pencil designed to look like a wooden pencil. But as we didn’t have any wooden pencils, it seemed like the right place to put this conceptually wooden yellow writing implement. And we didn’t have any non-yellow wooden pencils, but as they’re not that uncommon, leaving a space for them seemed fine. We didn’t have any in the office, but it’s plausible that we could have. And the yellow book and post-it-notes are made of paper, not wood, but as paper is made of wood, there’s an argument that yellow paper things are both yellow things and wooden things. This argument wins in an office context where there’s lots of yellow paper things but no yellow solid-wood things.
So what if we played the Venn diagram sorting game with one category for red things and one category for green things? We might fill the center section using one of the following ideas of red/green overlap:
- Things that are partly red and partly green
- Things that are either green or red at different times
- Yellow things
- Muddy brown things
- Things that are the kind of yellow made up of both green and red frequencies, but not yellow things that are the kind of yellow that is only yellow frequencies
- Things that appear red or green depending on the angle you look at them, or other external factors
- Things that are completely red and completely green all over at the same time (Interestingly, there’s a few rare phenomenological experiences where people can see something as both red and green all over at the same time [which I believe you can read about in C. L. Hardin’s “Color for Philosophers”].)
The practical results of the red/green sorting game would probably depend on the context. If you’re in a room being decorated for Christmas that has lots of things that are solid red, solid green, and also lots of things that are partly red and partly green, those would probably go in the overlap. If you’re outside in a place with apples ripening and leaves turning, then the concept of being both red and green through time might seem like the right thing. And your overlap might look similarly different depending on whether you’re in a painter’s studio, a lab for studying rare perceptual phenomena, or Styria (where pumpkin seed oil, a delicious red/green dichromatic liquid, is quite common).
The human tendency to fit things into categories that seem practical, even when the evidence shows the categories to be technically wrong, is extremely useful if you’re storing things in limited physical space. These different ideas about categories help us keep track of the overwhelmingly huge array of people, places, and things we have to interact with on a daily basis. And according to one theory, it’s our bodies’ experience sorting physical things that creates the concept of categories that we use to sort ideas in conceptual space, so more flexible categories means more ability to keep track of many abstract ideas. So, as the concept of categories is fairly essential to mathematics, science, and technology, I do wonder what other concepts our bodies could learn and apply with the help of VR, that aren’t possible to experience in the physical world!
Unfortunately, our functional categorization ability when used unawares in some contexts can be problematic, as when we stubbornly sort people into the mental categories we’ve made mental space for in accordance with cultural biases, despite evidence to the contrary. Also unfortunately, people are often turned off by mathematics and formal logic when they are told their very reasonable intuitions for how categories should work are flat out wrong with no room for interpretation.
Anyway. Inspired by this work, I played with a couple different ideas of mixing and overlap in this year’s Pi Day video “Venn Piagram”. One idea of overlap might lead the overlap of a peach pie and blackberry pie to be a blackberry-peach pie, which mixes the two fillings to get something that’s both. But another idea of category would say that each thing in that section of the diagram is either a peach or a blackberry, but none of those things are both peaches and blackberries at the same time, and so the overlap of a peach pie and blackberry pie should have no filling at all (or you should choose categories with better filling overlap, such as yellow fruits and stone fruits, or berries and red fruits).
So basically, we’ve been exploring the idea of overlap, as felt through embodied action. VR is just one tool we’ve been using to do this, but it’s a very useful one, especially as the rules of overlap are different when physics can’t get in the way.
Oh, and speaking of physics one last time, I’d like to add an overlap comment to our previous Venn post about the Venn piano, in which we poked a Venn diagram to play overlapping notes. Let us consider what happens when we hear notes overlap into chords and harmonies. What reaches our ears isn’t two separate sound waves, but one single linear wave, with no actual overlap happening if you think about it one way, but obviously overlapping as far as the listener’s experience is concerned. We perceive overlapping sounds almost constantly throughout our lives, which perhaps reflects a truth about a world where things can make noises simultaneously, as overlapping events in time. I think our experience of a linear time that has multiple things going on at once is actually pretty remarkable.
When we see the overlapping section of Venn diagrams being used in different ways, especially in ways that seem contrary to logical purity, rather than chalk it up to pure opinion or interpretation I want to understand how different ideas of category mixing might fall naturally out of different embodied interactions with the world. An overlap between categories might represent something abstract, but the very idea of overlap comes with the baggage of embodied experience. In different contexts, we know how overlap feels, looks, tastes, sounds, and functions, regardless of what logical categories would tell us. And perhaps by further studying the kind of overlaps we can experience, both real and virtual, we can create new formal structures that allow us to use our intuitive embodied knowledge as a powerful tool for understanding wholly new things.
P.S. You can see the virtual Venn museum in the “Venn Diagram Museum” area in Anyland, which is now free to play, if you have access to a Vive VR headset.
P.P.S. Our old email address is still broken and you should still email our “elevirtual” gmail instead.
Previous Venn posts discuss the creation of a virtual Venn Diagram Museum of Mathematics, Venn diagrams as applied to music theory, venn pianos, programming, and things where VR is better than real life, and the creation of a Venn Diagram House. Also relevant are previous posts on Container Schema and Embodied Cognition. Oh and don’t forget the Venn Diagram Museum project page, which keeps a running list of these posts and things.