(NB: this approach to coding in Python won't suit most people, for many reasons - I wrote it because I had a lot of requests to document my approach, not because I want anyone else to do the same thing. But if you're curious about ways to lay out code that are rather different to PEP8, do check it out!)
> 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.
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)
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.
I've been working through "Seven Sketches in Composability" , posted here a few weeks ago, and thinking about how much math relies in diagrams which are somewhere between drawing and writing. In research meetings, I often see people reasoning with diagrams and mathematical notation. In the vein of this article, I wonder whether it would also be possible to formalize mathematical pictographs to the point where they could be computable--a not-strictly-textual programming language. iPython notebooks often toggle between symbolic expressions and their implementation in code.
One thing that might be missing is context. Diagrams are indexical (pointing to contextual meaning) even more than text, often illustrating a problem that has previously been defined. This feels to me like potentially-fruitful design problem.
It explains how Greeks began using various sorts of counters or tokens for currency, policy making, court judgments, food distribution, recreation, etc., and demonstrates that Greek numeracy was quite varied and sophisticated while remaining concrete/tangible.
http://prog21.dadgum.com/114.html - "Papers from the lost culture of Array Languages" - has links to this and a couple more interesting sounding things.
Thank you for the link to this other paper, I can branch out to discover related works. Just found this one, I'll chew it well: "Language as an intellectual tool: From hieroglyphics to APL" .