Inspired by Chiang, I think tree graphs as taxonomies can massively accelerate how quickly people can absorb concepts. As a notation, it allows for breadth-first understanding of linked ideas and the 'whys', instead of patching together bits of depth-first competence. I've played with them for introducing complex topics and people are shocked at being able to absorb things that took others years to apprehend. The knowledge is not competence, just as the map is not the territory, but exploring territory with a map is very efficient.
My own interest in representing concepts led me to my current project where, I found that the poor quality of security assessments was more an artifact of how we represent systems and risk, and not the knowledge of the person doing it.
Like Wolfram, Chiang's story, and others in the OPs list, or even the Luther Bible, a translation from Greek and Latin to regional German, notation can have the same effect as automation, and the challenge of a new notation is that it disrupts the equilibrium in the economy of people who were gatekeepers to the previous one.
In this way, notations aren't just a detail, I'd say they are technologies themselves. It's such an important area.
A taxonomy is right in the middle of an unstructured mind map, and a logically parseable ontology. So maybe, a directed acyclic mindmap?:)
The practical parts of this are in the "Movements" branch of the tree, and when you have expanded it, consider that most people learn this topic from right to left, instead of left to right.
It uses code directly from the d3 example pages. I just wrote something for parsing a csv file into a tree, which I think is now native to a few packages.
It doesn't give you physical competence (which can take decades), but a map of the logic of categories is useful.
This seems to tie into the old debate of top-down versus bottom-up pedagogies. A high-level map of a topic is indisputably valuable, but I personally find it most useful as a guide for where to dive deep and back out, to make concrete the abstractions; a more directed patching-together of competencies, as you put it.
The reason I use these is I think a lot of suffering comes from (or can be defined as) churning on deep-node problems without information from higher level concepts, and a notation that "locates" meaning in an broader ontology can relieve some of it, and yield new understanding.
I think this is a theme Ted Chiang is on to as well, as it appears in the literary world as well as STEM.
The Global Dynamics of Cellular Automata:
An Atlas of Basin of Attraction Fields of
One-Dimensional Cellular Automata.
By Andrew Wuensche (Santa Fe Institute, Santa Fe, New Mexico) and Mike Lesser (International Ecotechnology Research Center, Bedford, United Kingdom). Published by Addison-Wesley in 1992. ISBN 0-201-55704-1.
Author's web page: http://uncomp.uwe.ac.uk/wuensche/gdca.html
PDF file: http://uncomp.uwe.ac.uk/wuensche/downloads/papers/global_dyn...
This is a beautiful geeky coffee table book! They've developed a wonderful way to graphically display the converging state space topologies of cellular automata basin of attraction fields. It shows basins of attraction as loops, and garden of eden nodes at the tips of dendrites.
The book includes some intriguing black and white illustrations and color plates, as well as a floppy disk with software to generate your own images on an IBM-PC.
Key to Basin Field Presentation:
I liked the discussion of how Chinese symbols remain readable even when pronunciation shifts, while phonetic alphabets become unclear -- helping Chinese culture be more rooted in the past.
This is, in part, why we ended up developing SiteSwap. Being able to communicate and remember juggling sequences was really hard, and the notation made a huge difference. The emergence of the underlying mathematics was a bonus.
In general: https://en.wikipedia.org/wiki/Geometric_algebra
And specifically: http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf
> This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends and integrates the mathematical methods of classical, relativistic and quantum physics while elucidating geometric structure of the theory. For example, STA provides a single, matrix-free spinor method for rotational dynamics with applications from classical rigid body mechanics to relativistic quantum theory – thus significantly reducing the mathematical and conceptual barriers between classical and quantum mechanics. The entire physics curriculum can be unified and simplified by adopting STA as the standard mathematical language. This would enable early infusion of spacetime physics and give it the prominent place it deserves in the curriculum.
I'm thinking of making one, but if there's one already I'll probably just use that.
It would I feel be similar to car rally course notations that co-drivers create/use.
Most notably it's "quantum mechanics" analogous interpretation about 2/3rd of the way through.
>>>This list focuses on notation as "a series or system of written symbols used to represent numbers, amounts, or elements in something such as music or mathematics." This is distinct from a language (computer or natural), interface, diagram, visualization, or tool, but may overlap with them.
Not sure how this is distinct from a language. She has an example of a notation for knots. This is a way to describe knots. Now, consider for example a notation for describing binary valued functions of a binary arguments. We have tables, the boolean algebra, with DNF and CNF, decision tree representation, and for larger functions - VHDL, for example. All are languages.
In fact, distinguishing between "language" and "notation" looks like a good example of "bad notation".