1/ Short thread on "big picture" visualization metaphors and why I've become increasingly interested in mazes thanks to
Conversation
2/ I grew up with "jigsaw puzzles" as my main metaphor for big picture viz, with "solving murder mysteries" as the prototypical example. You get a bunch of pieces, and you put them together to get a big picture. Jigsaw puzzles are a great metaphor for *static* big pictures
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3/ Somewhere in the course of engineering education, I picked up a bunch of graph theory (though I never took a course) for research purposes, and learned the basics of graph structure, search, their relationship to linear algebra etc.
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4/ Graphs are GREAT for computers (which basically can't really do big picture, though they can sort of pretend to...unless you throw in some deep learning/clustering to weakly imitate human big picture thinking).
Graphs are LOUSY for humans, but we don't realize it, why?
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5/ This is because graphs as defined in math and used by computers don't actually include a notion of space, geometry, orientation, or direction. When humans talk about graphs, they mean 2d graphs drawn on paper with a specific geometry. These are NOT GRAPHS, they are EMBEDDINGS
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6/ Humans think in graph embeddings, not graphs. In particular 2d ones. Any graph can be embedded in 3d, but humans suck at 3d, so we compromise by thinking in sort of 2.5 d, where the 0.5 is tunnels and bridges to prevent intersections.
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7/ Now, what's the difference between a graph and a 2.5d embedding of it with a specific geometry? Is it mere UI? NO!!! A classic 1978 paper by Blum and Kozen, "The Power of the Compass (or, why mazes are easier to search than graphs)" showed this dl.acm.org/citation.cfm?i
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8/ Slight tech aside: the popular A* algorithm (and derivatives like D* for incomplete info) as used for map navigation is technically a maze search, not a general graph search, because it relies on having a compass heading to work with. This requires an embedding.
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9/ Now we come to why mazes are better big picture visualizations than jigsaw puzzles. They not only provide a view of the whole, they have *paths* through them connecting points (shared with graphs). This opens a WHOLE NEW WAY of understanding them.
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10/ Many graph problems are also very interesting maze problems with very interesting properties, and are generally more tractable in their maze forms: all shortest paths, hamilton circuit, traveling salesman... all of them become easier if you have the power of the compass.
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But here's the BIGGEST reason this matters. A path through a graph, whether it is the shortest one, or a search-and-map one, or a visit-all-vertices one, is also a SERIALIZATION of a big picture. A path turns a maze into a STORY.
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Mazes therefore are at the heart of the connection between the two most important ways humans do big picture thinking: in SPACE (2d-2.5d MECE representations of a thing) and TIME (stories that evolve in 1d)
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Mazes are the corpus callosum of abstract human thought. They connect our spatial big picture thinking ability to our temporal big picture thinking ability, by providing a 1d view of a 2.5d and vice versa.
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My personal intellectual stake in the project I'm collaborating on with and is to really get at the heart of what's going on with mazes and getting better at using them to think. Follow if you want to keep up with our progress.
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Related to this, I'm using a "maze of time" to organize my thoughts on temporality in a spatial way. The masthead picture on the account is a portion of this maze, collaboratively developed by Dan and me. I'm using it to "serialize" my ideas about time... in time.
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One of the reasons I jumped on when I did is that it also seems to embody an understanding of "maze thinking" as opposed to "jigsaw thinking" or purely serial "narrative thinking". I'm using both Roam and mazes as prosthetics for my current multitemporality research
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Twitter is not quite maze-like, it is much more graph like, so it is less tractable, and it's easier to get lost in the forest of threads and quote tweet intersections.
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