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.
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!
> 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.