Collection of quotes on interesting notations and how they affect thought

I especially like that Chiang's "Story of your Life" is included there. I found both the story and the movie personally significant, and the dance notation that Edward Tufte included in either, Envisioning Information and Quantitative Display is very good. Other examples might include how Feynman diagrams changed how we thought about atoms, state diagrams how we thought about algorithms. Sequence diagrams are vastly underappreciated for their expressive power.

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.

I was begging for something like this in ice skating class, where they would just be like "watch me do left foot, rotate shoulders, turn 180, extend leg". Too long of a sequence to remember without a reference, too hard recognize the long sequences as composed of the same basic movements.

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.

I just had a project where we need to keep track of changes to a string as a series of insertions, deletions and substitutions. We don't want the whole history, so if someone inserted then deleted the thing they inserted, we would track that there was no change. Using notation like that of an (abstract) algebra class computing "commutators" of the various operations (like D_n means "delete character at position n" or I_{n,string} means "insert 'string' before position n") helped me figure it out. This project is more complicated than it sounds: my earlier attempts had me repeatedly try to just intuitively write code but I kept running into problems and finding that my set-ups were insufficient and practically impossible to make bug-free. Having an algebraic notation made me make the order in which operations were performed explicit and helped finally give me a decent representation of them.

It should mention Geometric Algebra (also called Clifford Algebra) IMO.

In general: https://en.wikipedia.org/wiki/Geometric_algebra

And specifically: http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf

Abstract:

> 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.

Does anyone know of a notation for martial arts sequences ("kata").

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.

From the link, this is an absolutely fascinating discussion on Juggling notation.

Most notably it's "quantum mechanics" analogous interpretation about 2/3rd of the way through.

http://www.solipsys.co.uk/new/JugglingTalkSummary.html#toc_n...

The description says:

>>>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".

I'm looking for a search-engine that can explain notation that I encounter e.g. in scientific papers.

Would be interesting if he could add something about Feynman diagrams.