Nicholas Cooke in "Handbook of Musical Analysis" says something that has always influenced me very deeply:
> All notation is analysis
Obviously he's talking in the specific context of musical notation, but it seems true in other fields too. Choosing how to notate seems a very important analytical decision and certain forms of notation help or hinder analysis.
Feynman diagrams for example famously help to understand the maths underlying particle interactions.
Roman numerals (for a different example) make all kinds of arithmetic much harder than in Arabic notation.
> Roman numerals (for a different example) make all kinds of arithmetic much harder than in Arabic notation.
Definitely not for simple addition or subtraction, the kind you're likely to do every day haggling over prices or counting things - roman numerals work visually!
What is I + II? You just write them together -> III
What is VVVV - V? Take just one V away -> VVV.
Knowing that IIIII = V or X = VV = IIIIIIIIII only allows you to express things as a shorthand. Also, some numerals allow for a subtraction index, so: X - I = IX (take I from X)
>Roman numerals make all kinds of arithmetic much harder than in Arabic notation
Sure. But of course they made arithmetic easier than it was before ('tallying' I think, i.e. IIIIIII....)
It's interesting how notation and language, which arise to foster communication between different people, become the very things that make it possible for a lone individual to think. This is why I guess that a single artificial person (AI) couldn't be created in isolation.
> All notation is analysis
Obviously he's talking in the specific context of musical notation, but it seems true in other fields too. Choosing how to notate seems a very important analytical decision and certain forms of notation help or hinder analysis.
Feynman diagrams for example famously help to understand the maths underlying particle interactions.
Roman numerals (for a different example) make all kinds of arithmetic much harder than in Arabic notation.