We’ve grown used to a full-decimal system, but all kinds of weird stuff has existed in the past.
Telugu (a language of southern India) has an interesting traditional numeric system: base ten for integers, and base four for fractions.
U+0C78 "౸" TELUGU FRACTION DIGIT ZERO FOR ODD POWERS OF FOUR
U+0C79 "౹" TELUGU FRACTION DIGIT ONE FOR ODD POWERS OF FOUR
U+0C7A "౺" TELUGU FRACTION DIGIT TWO FOR ODD POWERS OF FOUR
U+0C7B "౻" TELUGU FRACTION DIGIT THREE FOR ODD POWERS OF FOUR
(U+0C66 "౦" TELUGU DIGIT ZERO is used for even powers of four too)
U+0C7C "౼" TELUGU FRACTION DIGIT ONE FOR EVEN POWERS OF FOUR
U+0C7D "౽" TELUGU FRACTION DIGIT TWO FOR EVEN POWERS OF FOUR
U+0C7E "౾" TELUGU FRACTION DIGIT THREE FOR EVEN POWERS OF FOUR
Few Telugu speakers even know about this any more—no one can read even the traditional integers (౦౧౨౩౪౫౬౭౮౯), because 0123456789 have replaced them. (This is the case in most but not all Indian languages. Bengali’s traditional digits are still common, so you can enjoy ৪ being four and ৭ seven.)
A couple of articles and discussions about it:
• https://www.unicode.org/wg2/docs/n3156.pdf is the best public resource I know of (Unicode proposals and related papers are often delightful for information on obscure written stuff, because they had to write down and publish the details to get the characters encoded). One tid-bit: NYSE used a similar decimal/quaternary system until early 2001.
• https://blog.plover.com/math/telugu.html from the same site as the current article, discussed in https://news.ycombinator.com/item?id=14683767 nine years ago.
Thanks for the callout to my Telugu fractions article!
If you enjoy ৪ being four and ৭ seven you will probably enjoy the thousand-year-old magic square inscribed at the Parshvanatha temple in Madhya Pradesh.
https://blog.plover.com/math/magic-square-puzzle.html
Shreevatsa R. tells me that the digit symbols are probably Nagari, which predates Devanagari.
> One tid-bit: NYSE used a similar decimal/quaternary system until early 2001.
Prior to decimal pricing, us exchanges priced in eighths. An article [1] I found from a source I don't recognize says that there was briefly trading in sixteenths, but I guess I wasn't following the stock markets that closely then and I missed it.
https://tontinecoffeehouse.com/2018/11/05/pricing-in-eighths...
Heh. I've seen the code in the codebase at my previous work that supported not only 1/8 and 1/16 price scales, but all the way up to 1/256... but I don't think I've ever seen a ticker with such price scale outside of unit tests.
> Telugu (a language of southern India) has an interesting traditional numeric system: base ten for integers, and base four for fractions.
If they do consistently that is not too bad. Compare that with imperial units, which, depending on the quantity and sometimes its magnitude, uses
- base 10 for integers and base 12 for fractions (lengths in feet and inches). Alternatively, base 10 for mikes, base 5,280 for feet’s in a mile, base 12 for inches in a foot.
- base 10 for integers and base 14 for fractions (weights in stone and pound). Alternatively, there’s a base 112 when measuring in long tons and stones or 1,016 when using long tons and pounds)
- base 10 for integers and base 4 for fractions (lengths in miles and quarter/half miles)
And that’s ignoring specific units for weighing gold, diamonds, etc.
You left out perhaps the most widespread and important example! Many western European cultures, going back I think to Charlemagne, had a monetary system in which a pound was divided into 20 shillings / solidi, and each shilling was divided into 12 pence / denarii. This system persisted in England into the 1970s but it was widespread before the 20th century. For example, in France each livre was divided into 20 sou, and each sou into 12 denier, until 1795.
Leonardo of Pisa's famous book "Liber Abaci" spends a lot of time showing how to do arithmetic on these complicated mixed units, and has an interesting notation for them. If you're interested see https://blog.plover.com/math/liber-abaci-fractions.html .
I actually made an app a few years ago that converts to the traditional Telugu style of decimals. Its interesting how the fractions in spoken Telugu are based around 1/4ths but few people know about the same applying for the written expression as you mentioned.
https://play.google.com/store/apps/details?id=com.telugu_num...
Mind blown, I had no idea about this, thx for sharing