To finish, a fun question: is there some way to improve still further on arabic numerals? I believe the answer is almost certainly yes! But that's a thread for another day.
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A few addenda: (1) as lots of people have pointed out, it'd have been more accurate to name them Hindu-Arabic numerals; (2) the ancient Greeks seem to have known much of this (which I didn't know);
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(3) the ancient Babylonians ditto (which I did know - it was meant as a thought experiment about discovery and lines of insight, not history); (4)
@DavidDeutschOxf has a lovely discussion of number systems in chapter 6 of "The Beginning of Infinity".3 replies 0 retweets 16 likesShow this thread -
(5) Via
@CXGonzalez_, a paper arguing that for educated romans, the computational difficulty of working with roman numerals was comparable to us working with Hindu-Arabic: http://csjarchive.cogsci.rpi.edu/Proceedings/2008/pdfs/p2097.pdf …3 replies 4 retweets 12 likesShow this thread -
(6) I haven't published anything specifically on improving Hindu-Arabic numerals. But here's some related work inspired in part by that problem: on "Magic Paper" (new interfaces for mathematics) http://cognitivemedium.com/magic_paper/index.html …
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"Toward an Exploratory Medium for Mathematics" (on developing a logic of heuristic discovery, to underly creative exploration) http://cognitivemedium.com/emm/emm.html
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And "Thought as a Technology" (about the idea that we internalize the interfaces we use as part of our thinking; interface designers actually help us think new thoughts): http://cognitivemedium.com/tat/index.html
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Replying to @michael_nielsen
1/ One issue here, speaking of the cognitive aspects of this, is the cognitive LOAD involved in learning both systems. If you are not using numbers much above 100, then, arguably the Roman numeral system is easier
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Replying to @adamdavidlong @michael_nielsen
2/ i.e. I only have to learn 3 symbols, rather than 10 of them, and the symbols (kind of) relate to each other. I = 1. Crossed Is = 10. Half of X is V.
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Very true. Another example in this vein: @andy_matuschak has pointed out to me (and I vaguely recall from childhood) how complex & hard to learn children often find the place-number concept. @farrarscott made the same point above.
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Replying to @michael_nielsen @adamdavidlong and
I like Engelbart's parable of the tricycle versus the bicycle: the tricycle is much easier to learn, but eventually most of us want to learn the bicycle. On the other hand, there's only so much time to invest in tool-learning.
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Replying to @michael_nielsen @adamdavidlong and
A fun problem - maybe a nice essay - would be to figure out how to make those tradeoffs. It's a kind of multi-arm bandit, exploration-exploitation problem, with highly uncertain payoffs. Nice problem!
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