Talk:Hindu–Arabic numeral system

message: I bring to your notice that I insist on adding an image of the Hindu Numeral Image that has reference to the evolution from the Brahmi Script to Gwalior to Devanagari Script. I also insist on adding the names of the books of Al-Khwarizmi and Al-Kindi in their native language. I also insist on bringing the Evolution of the Number System Image to the top section. GurkhanofAsia (talk) 20:23, 7 January 2024 (UTC)
replies: text: I see no reason why you shouldnt. adding images would be good for this. H20346 (talk) 22:49, 21 January 2024 (UTC)

text: Can you be specific about which image you mean? You also don't need to speak so formally ("bring to your notice" etc.). Note that :File:Evolution_of_Hindu-Arabic_numerals.jpg is actually a copyright violation and should be removed from Wikipedia/Wikimedia commons; it was copied from Karl Menninger's 1969 book (page 418) without attribution. If you would be able to carefully draw a replacement image that conveys the same information without being a ripoff of Menninger's original diagram that would be a big help. –jacobolus (t) 23:26, 21 January 2024 (UTC)
thread_title:  Addition of Hindu Numerals Image of Brahmi Script and its evolution 

message: @Paul August, let met try to give a summary for you. The original speculation comes from Joseph Needham (Science and Civilisation in China, vol. 3), and is pretty thin. Needham valuably piles up a lot of material related to China (it would be great if Wikipedia could cover some of this in greater detail), but in his eagerness to credit China with "more advanced and scientific" mathematics than other contemporary civilizations throughout history, unfortunately mischaracterizes the numerical systems and mathematical accomplishments of ancient Mesopotamia and the Mediterranean (and perhaps Egypt), and of medieval India and the Arab world, even as they were known 60 years ago; in the past half-century these have all been studied further, and his presentation is now quite dated. Needham is also pretty free mixing speculation with fact, which sometimes makes it hard to figure out precisely what he is claiming is known vs. conjectured. It makes a potential good starting point, but should be read with some healthy skepticism.
Here's most of the specifically relevant bit:
: 
You can see that this doesn't present any particular evidence, and is explicitly speculative.
Lam Lay Yong, I believe at some point a student of Needham's, took the idea and elaborated it into a paper (or a few?) and a book Fleeting Footsteps with coauthor Ang Tian Se, which includes an English translation of the Sunzi Suanjing (a Chinese book of unknown original date and unknown original author, the main part of which probably dates from the 5th century or before and which was eventually included among the canon of "ten mathematical manuals" during the Tang dynasty in the 7th century). Lam analyses the counting-rod-based arithmetical procedures described in the available copy of the Sunzi Suanjing, and finds that a variety of arithmetical algorithms are similar to those found in medieval arithmetic sources written in Arabic. Noting that there was cultural contact between India and China at the time, e.g. the transmission of Buddhism from India to China, Lam therefore claims that Indian arithmetic must have come from China.
The problem with the book is that (a) Lam does not have any direct evidence whatsoever for her main theory, and (b) Lam does not address the several most obvious criticisms of her theory:
First, Chinese counting rods are in many ways similar to counting boards used in Egypt, Greece, Rome, and Mesopotamia, which were even older than Chinese counting rods, and used across a wide geographical area over long periods of time by civilizations with even more cultural contact with India. Unfortunately our knowledge of the precise methods used with these is somewhat scanty because we don't have any contemporary written manuals. I'm not enough of an expert to immediatly do it myself but I'd love to see improvement of our articles abacus and counting board, among others. Lam does not consider that Indian and/or Chinese arithmetic may have been influenced by these other tools/systems, a speculative conjecture which also has no direct evidence but is just as plausible as Lam's own. Positional numbering is also similar in many ways to the Mesopotamian positional (base sixty) system, to the Greek numeral system, etc.; the Chinese counting rod system is not particularly more similar to Indian arithmetic than these other previous systems, and there's nothing obvious about the relationship between Indian and Chinese systems.
Second, Lam doesn't consider, as Martzloff points out, that the copy of the Sunzi Suanjing she translated might have been modified or extended by copyists later than its original date. Indeed there is explicit historical documentation of such modification in the 7th century, not discussed by Lam's book ("the biography of Li Chunfeng (602-670) [...] states that Li Chunfeng and others reedited the SZSJ because 'the text was very erroneous (or contradictory) from the point of view of the principles'"). It is hard to firmly date the various pieces of the Sunzi Suanjing or figure out precisely when the methods described developed, but it is entirely plausible that methods described by Lam were even brought to China from outside. (It is also entirely plausible that they developed independently.) We have explicit evidence of the use of Indian numerals in China as early as the 8th century, and considering the cultural contact Lam stresses, it is entirely plausible that their influence was felt centuries earlier than that. But again this is all pure speculation, and any comments about it in Wikipedia should be described as such.
Third, Lam does not address the clear structural differences between Indian and counting-rod number systems. The counting-rod system uses a 5 × 2 structure also found in the Roman counting board but not found at all in the Indian arithmetic system. Lam puts great emphasis on the use of a blank space for zero in computing with counting rods, but this is a prominent feature of every kind of counting board. Lam hangs much of her theory on the claim that counting rods were used in a strictly positional way, unlike Greek, Mesopotamian, Egyptian, or other < 0 BCE written numeral systems, which involved various irregularities. She assumes that this purported feature couldn't have developed independently. But as Marzloff points out, this is not even an accurate summary of the actual use of counting rods, noting that for example blank spaces for "zeros" were not uniformly preserved, and that "irregular forms [...] were rather common in [Chinese] mathematical texts. [...] in practice, the counting-rod system was not as perfectly decimal and positional as the descriptions in Fleeting Footsteps would imply." The counting rod system is very concrete, almost identical in basic format to the Mayan (base twenty) or Sumerian (base sixty) systems, whereas Indian arithmetic uses symbols which are substantially abstract, more comparable to Greek alphabetic numerals. Neither counting rods nor Chinese written numbers of the time were discernably similar to the symbols adopted in India, which likely developed indigenously from earlier Indian symbols; nobody has even speculated that the symbols themselves originated in any Chinese system. Martzloff's summary is that "examples of Chinese written numerals from sources anterior to the tenth century do exist, and the structure of these militates against the idea of the Chinese origin of the Hindu-Arabic numerals."
Finally, Lam does not sufficiently address the lack of any direct or textual evidence, and does not surface any with her book. No numerically related words were adopted from Chinese into Indian languages (however, several were transmitted in the other direction). No extant Indian sources mention Chinese number systems. There are no examples of counting rods found in India. Etc. Etc.
Note again that Marzloff is one of the preeminent historians of Chinese mathematics; this is not some kind of politically motivated position. Indeed, I imagine the journal editors chose to have Martzloff write a review specifically to forestall any accusation of political motivation, as might arise if a scholar focusing on e.g. Greece, Persia, or Southeast Asia wrote a review. –jacobolus (t) 19:25, 23 February 2024 (UTC)
replies: text: Thank's for this. I have a few questions but they'll have to wait. Paul August ☎ 19:54, 23 February 2024 (UTC)
thread_title:  A sketch of Needham/Lam's theory and criticism thereof 

message: Does anyone have recommended sources to examine while trying to draw a replacement for scans of Menninger's glyph evolution image? I mentioned Chrisomalis (2010) Numerical Notation: A Comparative History as one fairly comprehensive scholarly survey by a career expert. Are there other relatively recent surveys with decent coverage of this topic? –jacobolus (t) 02:10, 25 February 2024 (UTC)
thread_title:  Sources for a better glyph evolution image 

message: Can you please explain why you chose to not use the short form cites I introduced into the "Origins" section? Paul August ☎ 15:22, 26 February 2024 (UTC)
replies: text: This article has previously had a convention of putting citations to short articles/chapters into footnotes, and citations to full books which needed page numbers specified in multiple different places into a list at the end, with short references including the page numbers in footnotes. I don't see a clear reason for adopting a mishmash of mixed conventions. –jacobolus (t) 15:26, 26 February 2024 (UTC)

text: I could imagine adopting some other style convention though; this article is (and has been) generally mediocre and inconsistent in scope, organization, content, sourcing, and style, and the citation style is no exception, with lots of incomplete and poorly formatted references and lots of unsourced claims. If the defenders of this article would stop deleting every attempt at improvement (including the sources), it would be theoretically possible to substantially fix, expand, and improve the article, including adopting some different citation style. There are high-quality Wikipedia articles which adopt a variety of different styles for sources. –jacobolus (t) 15:33, 26 February 2024 (UTC)
replies: text: I think it's very useful to have page numbers (with links) whenever possible, for all citations, with full bibliographic info in a separate section. So unless you object I would like to return to using short form cites. Paul August ☎ 15:45, 26 February 2024 (UTC)
replies: text: I object to having an inconsistent mishmash of different citation styles within an article, and I don't think it's worth cleaning up and globally restyling the current citations in this article unless we're going to actually commit to making a substantial rewrite/improvement, since many of the current citations are not very good. Specific page numbers aren't really necessary for sources which are shorter than about 30 pages, though they can be fine to include also. One way to add both the full page numbers of a book chapter or paper and also a specific page number is to include a quotation along with the "quote page" parameter. It's also probably fine to specify the page number range and then explicitly call out one page, something like "pp. 45–75, specifically p. 62". –jacobolus (t) 16:03, 26 February 2024 (UTC)
thread_title:  Citation style