I want to talk about a topic that fascinates me: projections. The Wikipedia article is pretty dense and extremely math-focused which makes it a poor option for an introduction, particularly when there’s some very practical metaphors we can work with. In this article, I’d like to define ( in a broad sense ) what a projection is by way of example, and then talk a bit about how projections can be used as a mental model for organizing information.
The biggest assumption is that you can see. Most of these examples rely on vision-based sensory experiences. Beyond that, no technical knowledge is needed.
The technical term for a projection is a “mapping”; it relates an input to an output in a specific, consistent way. This is very abstract, but I hope some examples will provide some illumination.
Perhaps the most common projection you’ll meet is shadows. Let’s say we have an infinite void, empty except for a light source infinitely far away. Now let’s add a flat plane, just a nice featureless surface. Finally, put a sphere in between the light source and the plane.
Think about what happens with the shadow, as we change certain details about this scenario. Make sure to ask “What do I not see?” as well as “What do I see?”
Imagine that instead of a sphere, we placed a cylinder. Our two questions start getting a lot trickier now. What the shadow looks like depends on the orientation of the cylinder; if it’s pointed directly at the light source, its shadow would be indistinguishable from the shadow of a sphere, but rotate it so its long axis is facing the light source and now you have a shadow that looks like a rectangle.
The shadow of this object is a projection. It “maps” part of a three-dimensional objects onto a two-dimensional surface. In the simplest case, the sphere maps onto the plane as a circle. No matter how you rotate it or move the light source, it always comes out as a circle. But not all mappings are quite so trivial.
The cylinder does the best job illustrating both the utility and confusing nature of projections here. Here, the shadow, the projection, becomes far less reliable at telling us what we might be working with. If we only ever got to see a photograph of the cylinder’s shadow, it’s very reasonable that we might draw extremely false conclusions about the nature of this object. This is simply the nature of data and communication: if you fail to provide sufficient context your work can and probably will be misinterpreted.
The utility of projections, however, cannot be understated. This thought experiment was deliberately contrived, working with a small number of simple objects. It may not not be immediately obvious why it’s useful to create such an “incomplete copy” of a thing like this.
Until, that is, you begin to think about how complicated the real world is. It’s only very rarely that you’ll find yourself floating in an infinite, empty void kept company only by Platonic geometric figures. In the real world, accomplishing a task usually only demands a small subset of the information available to you about something.
If you’re trying to figure out the fastest way to get across town in time for happy hour at the buffet, you’d probably want a subway map. The subway map is a projection of a more complex object: the city and landscape it is embedded within. In this moment where you need to get across town, information about the sand/clay/loam ratio of a given area would not be helpful, nor would information about where sewage lines cross railroad tracks.
To this end, you can have dozens and dozens of different maps that all faithfully represent “the city” and look nothing alike, have no discernible shared qualities other than the name written on the piece of paper. Each one is correct, useful.
With the city/map metaphor, I hope I have brought the point home. Projections are a tool for taking complex, “higher dimensional” objects and laying them out on a surface that we can work with. Projections aren’t guaranteed to capture every piece of information about an object, and this is their strength; we already have the complex object in hand/brain. If we were able to work with it, it wouldn’t be an object so complex we have to create tools to assist us.
When I take notes on a subject, I never try to capture every imaginable detail about it. All of my notes are simply projections. They take some complex concept or object and project them onto a text file, capturing a “photo” of its “shadow”, specifically one suited to the problem this note is solving. My notes about work do not mention the weather, when I take notes about philosophy I don’t create notes defining concepts I already know, and so on.
Projections are also not limited to single notes. All of the notes in my Logs/Health are together a projection of my life: one that only reveals details about my health. My blog is another projection of my life, my knowledge. I haven’t written about recipes or tabletop gaming (yet) but I’ll get there.
And that brings us to the grand conclusion: your vault is a projection too. Layers and layers of projections, of “shadows”. Remember to ask yourself: “What can I see?”. “What can I not see?”