Post AUoggWa2Z4u6F5JxFQ by claire@bzh.social
(DIR) More posts by claire@bzh.social
(DIR) Post #AUkaow2oOgxDB2Z9xg by johncarlosbaez@mathstodon.xyz
2023-04-17T17:53:51Z
1 likes, 9 repeats
I'm fascinated by Eskimo-Aleut languages in Alaska, Canada and Greenland. There are many of these languages; they ring much of the Arctic Ocean. I just learned that they use a base 20 system for numbers, with a 'sub-base' of 5. That is, quantities are counted in 'scores' (twenties) with intermediate numerals for 5, 10, and 15. This makes a lot of sense if you look at your fingers and toes.But the Inuit didn't have a written form of their number system until the early 1990s, when nine high school students in a small northern Alaskan school invented one!They used 5 principles: • Visual simplicity: The symbols should be easy to remember. • Iconicity: There should be a clear relationship between the symbols and their meanings. • Efficiency: It should be easy to write the symbols without lifting the pencil from the paper. • Distinctiveness: There should be no confusion between this system and Arabic numerals. • Aesthetics: They should be pleasing to look at.They decided that the Kaktovik digit 0 should look like crossed arms, meaning that nothing was being counted.This was the start of quite a tale!(1/n)
(DIR) Post #AUkrcTwYkRsjlmHzc0 by johncarlosbaez@mathstodon.xyz
2023-04-17T17:57:49Z
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The students built base-20 abacuses. These were initially intended to help the conversion from decimal to base-20 and vice versa, but soon the students started using them to do arithmetic in base-20. The upper section of their abacus has 3 beads in each column for the values of the sub-base of 5, while the lower section has 4 beads in each column for the remaining units.(2/n)
(DIR) Post #AUkrcUVedxxFWci1JY by johncarlosbaez@mathstodon.xyz
2023-04-17T18:08:12Z
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The students discovered their new system was that arithmetic was easier than with the Arabic numerals. Adding two digits together often gives a result that *looks* like the combination of the two digits!(3/n)
(DIR) Post #AUkrcVDG1qphhr6qHI by johncarlosbaez@mathstodon.xyz
2023-04-17T18:17:56Z
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Students also found that long division was more fun with Kaktovik numerals! They noticed visually interesting patterns. They discovered that they could keep track of intermediate steps with colored pencils.(4/n)
(DIR) Post #AUkrcVmhu3BnTnh9X6 by johncarlosbaez@mathstodon.xyz
2023-04-17T18:24:51Z
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In the high school that used Kaktovik numerals, math scores on standardized tests improved dramatically! Before the new numerals, their average score was in the 20th percentile. Afterwards, their scores shot to above the national average. Some argue that being able to work in both base 10 and base 20 was helpful - much like being bilingual. I suspect that even more important was the sheer process of developing their own system of numerals! Getting engaged in mathematics is so much better than learning it passively.But this was just the start of the story. The new numerals began to catch on... but then:"Under the federal No Child Left Behind Act, from 2002 to 2015, schools faced severe sanctions—or even closure—for not meeting state standards, provoking a “scare” that some local educators say squeezed the Kaktovik numerals into a marginal role despite the system’s demonstrated educational impact."For more, read this:https://www.scientificamerican.com/article/a-number-system-invented-by-inuit-schoolchildren-will-make-its-silicon-valley-debut/(5/n)
(DIR) Post #AUkrcWNZgygDK8wazw by johncarlosbaez@mathstodon.xyz
2023-04-17T20:57:59Z
1 likes, 0 repeats
Why is Scientific American talking about Kaktovik numerals just *now*? It's because some linguists working with the Script Encoding Initiative at U.C Berkeley recently got them added to Unicode! See here:https://en.wikipedia.org/wiki/Kaktovik_Numerals_(Unicode_block)For more on the cool mathematical properties of Kaktovik numerals, try the Wikipedia article on them:https://en.wikipedia.org/wiki/Kaktovik_numeralsI suspect there's more to be said. Maybe someone has worked out all the details somewhere?Below is an example of long division.(5/n)
(DIR) Post #AUl5PLXK5oYXI07EnY by simon_brooke@mastodon.scot
2023-04-17T23:27:54Z
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@johncarlosbaez What I find interesting about this is that both English ('the years of a man's life are three score and ten') and French ('quatre vingt huit") traditionally used base twenty counting.
(DIR) Post #AUlQiN6eZv98hJYRM0 by johncarlosbaez@mathstodon.xyz
2023-04-17T21:08:39Z
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Finally, here's a map of Eskimo-Aleut languages! The Kaktovik numerals were invented by high school students in northern Alaska who spoke Iñupiaq, one of these languages.For more on Iñupiaq:https://en.wikipedia.org/wiki/I%C3%B1upiaq_languageFor more on Inuit-Yupik-Unangan languages, try this:https://en.wikipedia.org/wiki/Eskaleut_languages(6/n, n = 6)
(DIR) Post #AUlR77oeZ3omVzwEuO by PawelK@noagendasocial.com
2023-04-18T03:41:03Z
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@johncarlosbaez Thats how some Slavs measure and estimate lengths and weights of material things of near-human scale, and that is likely how some of British measurements of lengths and weights got invented (see feet and stones).
(DIR) Post #AUlRkvWvf85BzicvvU by PawelK@noagendasocial.com
2023-04-18T03:48:14Z
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@johncarlosbaez The "visual" element od Kaktovik numerals and arithmetics could prove very useful to getting some autists of Temple Grandin type, as well as, perhaps kids overstimulated visually by blinking screens, ie many in the era od computers, intetested with basic maths.
(DIR) Post #AUoggWa2Z4u6F5JxFQ by claire@bzh.social
2023-04-18T12:36:02Z
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@johncarlosbaez french people also use the base 20 when they name their numbers as did the Gauls who counted on their fingers and toes 😉 (80 = quatre vingts = four twenty , 90 = quatre vingt dix = four twenty ten , 70 = soixante dix = sixty ten ) ...
(DIR) Post #AUoggXHdwxmYQJimDA by IronCurtain@mstdn.social
2023-04-18T12:49:02Z
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@claire @johncarlosbaez English used to do that with the word “score”, such as “four score and twenty” in the Gettysburg address to mean “87”.
(DIR) Post #AUoggXiEM737kmA0eW by Hyolobrika@berserker.town
2023-04-19T17:19:38Z
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@IronCurtainWouldn't that make 4 * 20 + 20 = 100?@claire @johncarlosbaez
(DIR) Post #AUogkgqGM1BBE6tYLw by wolfnowl@universeodon.com
2023-04-18T05:04:45Z
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@johncarlosbaez This might interest you: https://www.goodreads.com/book/show/2606485-twenty-countThere Was a small tribe of people in South America who for milennia had no concept of numbers. They understood few, and many, but had no idea of four, or thirteen. The anthropologist who discovered this was fascinated by them, but his attempts to discuss this with his colleagues and others led to a HUGE controversy. Finally their government decided it was incumbent upon them to Educate these people and bring them modern technology and... 🤦
(DIR) Post #AUogkhW5qUdjJqSxYO by Hyolobrika@berserker.town
2023-04-19T17:20:24Z
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@wolfnowlAre you talking about the Pirahã?@johncarlosbaez
(DIR) Post #AUogki2LuYRavtYips by wolfnowl@universeodon.com
2023-04-18T05:23:20Z
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@johncarlosbaez There's also ogham, but that's a completely different culture: https://en.m.wikipedia.org/wiki/Ogham
(DIR) Post #AUorATMC72bITTlOnA by IronCurtain@mstdn.social
2023-04-19T19:17:05Z
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@Hyolobrika @claire @johncarlosbaez Derp. Fixed! Thank you!
(DIR) Post #AUox0TFqEpLozBPEtk by Hyolobrika@berserker.town
2023-04-19T20:22:32Z
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@IronCurtainYw@claire @johncarlosbaez
(DIR) Post #AVbqMwybibSnAdRUrQ by strypey@mastodon.nzoss.nz
2023-05-13T10:28:57Z
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@johsvogelThat's #NumberWang! 😆@johncarlosbaez