Cherokee Numerals

It's also interesting how history has taken us to the point that an anthropologist names a numeral system invented in India and brought to Europe via Africa "Western", because readers will understand that name, and uses that name in contrast to a system that was invented in the actual West.

Also, not enough is made of the fact that the numeral system was based upon United States decimal coinage. Viewed in terms of 1 cent, 5 cent, and 10 cent coins, with the added notion of a barred gate for 1 to 5 (as explained), the numerals actually make a lot of sense; especially if one considers them as erosions into arcs and squiggles caused by rapidly drawing the original full circles and bars.

* 1 to 5 are the five-barred gate with the downward bars mostly elided or reduced to squiggles for speed and the pen not removed from the paper in between bars.

* 6 to 10 are a 5 cent piece reduced to an arc plus one to five 1 cent pieces as bars, again mostly elided.

* 11 to 15 are a 10 cent piece still mostly a circle plus one to five 1 cent pieces.

* The 30 to 90 symbols are the superscript notation described in Lowery's biography, but prefixed instead of suffixed. 50, for example, is a prefixed 5, as reduced to a squiggle, before a 10 cent piece.

The text states that numerals above 20 had the numerals from 1 to 9 appended. By implication, therefore: 16 to 25 are a 10 cent piece, plus a 5 cent piece, plus one or two barred gates of 1 cent pieces; and 26 to 29 are a 10 cent piece, plus two 5 cent pieces, plus some 1 cent pieces.

It would appear that Sequoyah didn't encounter 25 cent pieces often enough to warrant retaining them in the system as it evolved.

> It's also interesting how history has taken us to the point that an anthropologist names a numeral system invented in India and brought to Europe via Africa "Western", because readers will understand that name, and uses that name in contrast to a system that was invented in the actual West.

It is true that place value systems originated in India, but I would personally say that calling our numeral system ‘Indian’ would be no less incorrect than calling it ‘Western’. The history is more complicated (and more interesting!) than such names would imply:

• The shapes of our modern numerals originated in the Brāhmi script of ancient India, around 300 BCE (𑁦𑁧𑁨𑁩𑁪𑁫𑁬𑁭𑁮𑁯).

• Place-value systems are much younger; the first date from around 500 CE. By this time the original shapes of the numerals had already been heavily altered, becoming more similar to the modern Hindu numerals (०१२३४५६७८९).

• These systems were then transmitted to Persia, where they evolved into the numeral system used in Persian (۰۱۲۳۴۵۶۷۸۹) and thence Arabic (٠١٢٣٤٥٦٧٨٩).

• It was only at this point that the Arabic numerals were transmitted to Europe primarily via Fibonacci; over a few centuries they evolved into their modern forms (0123456789). Wikipedia calls this numeral set ‘Western Arabic’, and I do think this is a more correct name than either ‘Western’ or ‘Indian’.

Curiously I have never heard of it as Western numerals, but only as Arabic, and that's how I learned at school.

I rather thought this stupid:

> We don’t know what impetus exists for developing a ciphered-additive system where the signs for 20 through 90 have their own distinct signs, and where there is a multiplier for 10 in place of a zero

Romantic languages have an obvious difference when reading the words representing them when in comes to numbers under ten, 11-15, and multiples of ten to 90. English’s 11-12 differs from other teens. 20-90 may perhaps be hybrids of words and numerals to eliminate confusion or seem more familiar to speakers.

It’s also obvious why a multiplier for 10 would replace zero, as that’s what it does.

Am I missing something here??

To make matters more confusing, modern Arabs don't use the numerals we call "Arabic": https://en.wikipedia.org/wiki/Eastern_Arabic_numerals

There are however Arab regions where it is more common to see so-called "Western/Arabic" numerals used instead of the native-Arabic-script numerals. This is the case of Morocco, for instance.

This is mostly correct and very interesting, but I'd like to correct a couple of errors:

> Place-value systems are much younger; the first date from around 500 CE

No, although place-value systems do seem to be younger than the non-place-value system the article calls "ciphered-additive", place-value numerals date from 02000 BCE: https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals#...

However, there seems to be no line of descent from Babylonian numerals, which used an empty space to represent zero, to the Hindu numerals about 2000 years later. (The oldest occurrence of zero is actually at Gwalior, somewhat later than the Brahmi script.) Similarly, the Maya vigesimal place-value numeral system dates from the first century BCE, and the decimal place-value numeral system of the khipu is normally considered to date from around the same time, although Ruth Shady has reported a tantalizing "proto-khipu" find that may predate even the Babylonian system. However, there is no plausible route of cultural transmission from these systems to Classical India.

Even the Hindu decimal place-value numeral system is likely older than 00500 CE; the Bakhshali manuscript, which uses a dot for zero like modern Eastern Arabic numerals, probably dates from about 00300 CE. https://en.wikipedia.org/wiki/Bakhshali_manuscript#Contents

> they evolved into the numeral system used in Persian (۰۱۲۳۴۵۶۷۸۹) and thence Arabic (٠١٢٣٤٥٦٧٨٩) ... It was only at this point that the Arabic numerals were transmitted to Europe primarily via Fibonacci; over a few centuries they evolved into their modern forms (0123456789).

It turns out that Arabic-speakers in Africa were using a divergent set of digits for the Hindu–Arabic place-value system, not descended from ٠١٢٣٤٥٦٧٨٩, and these are entirely readable to modern European-educated eyes, except for the 4, which is rotated 90° and has a tail: https://en.wikipedia.org/wiki/Arabic_numerals#Adoption_in_Eu... https://commons.wikimedia.org/wiki/File:The_Brahmi_numeral_s...

This divergent evolution is why many of "0123456789" bear a closer resemblance to the numerals from Gwalior and in one case the Brahmi script you see in that graphic than to the Eastern Arabic "٠١٢٣٤٥٦٧٨٩". It's not that the Europeans evolved "٣" and "٦" back into the Gwalior "3" and the Brahmi "6" by coincidence; it's that the Africans they copied their numbers from were already using numerals that looked like "3" and "6".

These numerals are called "Western Arabic" because the Western Arabs in the Maghreb used them, as opposed to the Eastern Arabs in Arabia itself. It's not a juxtaposition of the names of two separate polities, "Western" and "Arabic".

I agree with the grandparent that it's terribly amusing that an anthropologist railing against "coopt[ing] Native American accomplishments by claiming them as generically American", "American imperial project[s]", and "the dominant American narrative of the primitivity of indigenous Americans" would so completely erase the African origin of what he repeatedly calls "Western numerals" in a region recently invaded and currently partly occupied by the US Air Force.

As I explained in more detail in https://news.ycombinator.com/item?id=26525109, those are "Western Arabic" numerals, not "Western/Arabic" numerals, because they were invented by the Arabs in Morocco and thereabouts, which is to the west of the Arabs in, for example, Syria.

Morocco today doesn’t use its native Arabic numeral system that diverged from that used in other Arab countries to the east, it uses the European system borrowed wholesale.

It's just a minor typographical variation, similar to how some lowercase "g" glyphs have a closed loop while others have just a hook, or how some Latin fonts have serifs and others don't. It's not a totally different numeral system like the Greek or Maya systems, or even a dramatically different set of glyphs like the Eastern Arabic or Brahmi numerals.

The old African numeral glyphs resemble today's European styles more closely than Caslon resembles blackletter, more closely than either resembles Palmer cursive, and more closely than any of the three resembles Roman monumental inscriptions (except, of course, for the upper case of Caslon). Yet we consider Caslon, blackletter, Palmer, and the inscriptions all to be the same Latin alphabet.

Again, Morocco uses the European system wholesale, not just local glyphs that bear a great resemblance to European glyphs. This development is a consequence of the French colonial era and the fact that most serious printing in the country is done in French, while Arabic is mainly (though not exclusively) treated as a language only of speaking and non-serious writing. Thus, even when Moroccans do write in Arabic, they use the same numbers known from French-language publications.

Sure, but French uses the Moroccan† system wholesale, a consequence of developments predating the French colonial era. So Moroccans writing in Arabic have been using the same numbers known from French-language publications for some five centuries longer than the French-language publications have been using them, and some seven centuries longer than the cultural hegemony of French in the country. There wasn't some time in between when Moroccans were using Eastern Arabic numerals or classical Greek numerals or something.

Suppose you find that an Italian professor of computer science has published a computer science paper in Italian using Knuth's cmr10 font from California. Moreover, he has previously published papers in English, some also using cmr10, in part because he wants people in California to be able to read them, and Italian is mainly treated as a language of speaking and non-serious writing — or at any rate not for computer science.

Would you therefore say, "Italy today doesn't use its own native Latin alphabet that diverged from that used in Greece; it uses the Californian system borrowed wholesale, not just local glyphs that bear a great resemblance to Californian glyphs"? To me this sounds absurd, even though the cmr10 glyphs being used were designed in California.

(Perhaps the answer in this case is too obvious because "cmr10" is an abbreviation for "Computer Modern Roman 10 point", and Rome is in Italy, but on the other hand, we are discussing a system of numerals almost universally known as "Arabic".)

_______

†At the time that the French adopted it, political boundaries in the Maghreb were of course very different, so at the time Fibonacci might have said his numbers were the numbers used in the Almohad Caliphate; but before the Almohads conquered the Maghreb and al-Andalus, they were the Berber rulers of Tinmel, so I don't think it's a stretch to call them Moroccan. The numerals were already in use throughout the Maghreb before the Almohad conquest, though.

> No, although place-value systems do seem to be younger than the non-place-value system the article calls "ciphered-additive", place-value numerals date from 02000 BCE

This is of course correct; I should have mentioned it. (Though I was specifically talking about the numeral system 0123456789, which has no direct connection to the Babylonian numerals.)

> Even the Hindu decimal place-value numeral system is likely older than 00500 CE; the Bakhshali manuscript, which uses a dot for zero like modern Eastern Arabic numerals, probably dates from about 00300 CE.

As it happens, an earlier draft of my post did indeed say ‘300–500 CE’, but I cut it out because I figured the extra precision didn’t really add anything to the post. (Also, because no-one would care about exact dates; looks like I was wrong there!)

> It turns out that Arabic-speakers in Africa were using a divergent set of digits for the Hindu–Arabic place-value system, not descended from ٠١٢٣٤٥٦٧٨٩, and these are entirely readable to modern European-educated eyes, except for the 4, which is rotated 90° and has a tail

Interesting, I hadn’t known this — thanks for the correction!

> These numerals are called "Western Arabic" because the Western Arabs in the Maghreb used them, as opposed to the Eastern Arabs in Arabia itself. It's not a juxtaposition of the names of two separate polities, "Western" and "Arabic".

I am aware of this, and I never meant to imply otherwise.

> Also, because no-one would care about exact dates; looks like I was wrong there!

You can always count on me to be a gigantic pedant! That was a really important time in mathematics—that's when we invented the Pulverizer Algorithm, for example.

> I am aware of this, and I never meant to imply otherwise.

I'm sorry I misread your comment!