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by skadamat·7y ago·view on hn ↗
The first 20 mins of Bret's talk (https://www.youtube.com/watch?v=agOdP2Bmieg) discusses representations quite well in a very similar context / framing.

The challenge with roman numerals was definitely computing with them and really "thinking with them". Abacuses helped, but it was still a poor UX in many ways and it took lots of training & practice to get familiar.

Algebraic notation also requires training & practice but has a much quicker learning curve. Almost every literate adult uses equations in some form or another on a weekly basis. Both the medium (pencil & paper) as well as the representation (algebraic notation) were critical to this (as well as other things like education system / literacy, etc).

The benefits & disadvantages of different representations is massively understudied and misunderstood. Data visualization, semiotics, and some other fields focus a bit on this but still fall short in many ways.

1 comments
> Algebraic notation ... has a much quicker learning curve

Not true - many people still struggle with algebraic notation.