Re: Chinese rod numerals
On 15/01/2004 11:50, Christopher Cullen wrote: I am grateful for all the advice I have received on this proposal, which I intend to pursue, time permitting. Meanwhile I am signing off to avoid a surfeit of Klingon, so please address me off-list if you wish to make any further suggestions. Thanks Christopher Cullen Understood. Perhaps there should be a separate list for Klingon and other ConScripts, just as there are for other languages and groups which generate a lot of correspondence which is not interesting to most of us. -- Peter Kirk [EMAIL PROTECTED] (personal) [EMAIL PROTECTED] (work) http://www.qaya.org/
Re: Chinese rod numerals
I am grateful for all the advice I have received on this proposal, which I intend to pursue, time permitting. Meanwhile I am signing off to avoid a surfeit of Klingon, so please address me off-list if you wish to make any further suggestions. Thanks Christopher Cullen
Re: Chinese rod numerals
Thus for example, referring to the page from a 13th century book reproduced in Needham (1959) p. 132, I would translate the passage from the bottom of the fourth column from the right (reading right to left) roughly as: ... having done that, multiply the breadth of the yellow hypotenuse by the unknown, to obtain (-2x^2 + 654x), then divide that by ... The expression shown here using algebra is set out in the original using rod numerals. If that is not writing, then algebra is not writing either. Nobody here is trying to prejudge the issue. The proposal for encoding these should simply cite some instances of Song dynasty alebraicists using the forms in writing. I revert again to the cross-cultural issue: why should modern western mathematicians have the privilege of finding everything they need in Unicode, whereas those who wish to write Chinese mathematics have to resort to pasting graphics into their texts, because someone decides that parts of those texts are not real writing? There is no need to go off down this garden path. Trying to accuse the committees of western mathematical bias (or any other cross-cultural bias) in choice of symbols is just going to get their backs up for no good reason. If you are looking for *any* character encoding without a cultural bias, then Unicode is your ticket. All you need to do is provide evidence in the summary proposal form of use of the symbols in writing (as opposed to laying out counting rods on tables to do calculations). That will cinch the case for them as characters. You (and John Jenkins) say such examples exist aplenty in the mathematical classics. O.k. just scan a few examples and provide those illustrations in the proposal. Incidentally, I do note that provision has been made to encode the 64 hexagrams of the Book of Change, and also the symbols used in Yang Xiong's Taixuan jing. See http://www.unicode.org/charts/ under Yi Jing hexagram symbols and Tai xuan jing symbols. While I think that the idea of writing may not be in the last analysis a helpful one to use as a demarcation criterion for Unicode, given that the home page does say The Unicode Standard defines codes for arrows, dingbats, etc., The home page is not the criterion. The text of the standard and the decision history of the encoding committees are. The Unicode Standard, Version 4.0, p. 1, first line: The Unicode Standard is the universal character encoding scheme for written characters and text. Scope statement of ISO/IEC 10646, 3rd edition (the International Standard that the Unicode Standard is synchronized with): ISO/IEC 10646 specifies the Universal Multiple-Octet Coded Character Set (UCS). It is applicable to the representation, transmission, interchange, processing, storage, input, and presentation of the written form of the languages of the world as well as of additional symbols. I would think that if the hexagrams etc. are in, then a fortiori so should rod numerals be. Much more if the Tai xuan jing symbols are in, which I personally have never seen used outside the context of the ancient book in which they occur Fine, make the case. The Unicode Technical Committee is not prejudiced against characters which occur only in ancient books (or even only on ancient tablets or incised in stone, for that matter). Witness the encoding of Linear B, of Ugaritic, and so on, or the imminent encoding of Sumero-Akkadian cuneiform. --Ken
Re: Chinese rod numerals
My suggestion would be to just give values 1-9, 10-90 for the Chinese rod numerals and be done with it, for the Unicode character properties. But the fact that the values are position dependent raises the suspicion that this really is a calculation system, rather than simply a set of 18 numeral characters, and as such, it may be over the edge of what is appropriate to encode in the Unicode Standard. --Ken Too bad it is over the edge, for if it wasn't it could have been encoded as follows: Supplementary characters for chinese rods base-100 digits 0-99. Left half of the glyph looks like space or 10-90. Right half looks like space or 1-9. Assigned in such a way that the 18 cinese rod numerals plus two extra spaces behave as if they were assigned to surrogate code points.
Re: Chinese rod numerals
I am very grateful to those who have devoted time to discussing the suggestion I made about encoding Chinese rod numerals. Leaving to one side technical points about where in Unicode any new encodings might be placed ( I don't know enough) may I make some points on John Jenkins' useful contribution - which asks in effect whether the rod numerals are actually characters rather than graphics. To this I would reply: (1) The web page I cited was chosen purely in order to let list members see what the rod numerals looked like. Its statements about the nature and usage of these numerals should not be taken as authoritative. Better accounts are to be found in Chinese histories of mathematics, such as that of Li Di Zhongguo shuxue tongshi Nanjing 1997, pp 53 ff., in which their origins and early usage are discussed. Accessible and readily available English language discussions include HO Peng-Yoke, Li Qi and Shu: an Introduction to Science and Civilisation in China, Hong Kong 1985 rep. New York 2000, 55-58, and 92-104, and as part of the magisterial work by Joseph Needham, Science and Civilisation in China, volume 3, Cambridge 1959, pp 5-17, 45, 62 and 129-133. (2) The Unicode home page says: The Unicode Standard defines codes for characters used in all the major languages written today. Scripts include the European alphabetic scripts, Middle Eastern right-to-left scripts, and many scripts of Asia. The Unicode Standard further includes punctuation marks, diacritics, mathematical symbols, technical symbols, arrows, dingbats, etc.. I suggest that in an enterprise so universal and cross-cultural as Unicode, the definition of what counts as a mathematical symbol has to be conditioned by actual mathematical practice in the culture whose script is being encoded. We cannot simply take modern western mathematics as the standard. This means we have to look at the usage of Chinese mathematical writers in the periods in which rod numerals are used (and indeed this is the implication of John Jenkins' very sensible approach in his message). (3) The most sophisticated indigenous Chinese mathematical texts before contacts with Western techniques (which did not, by the by appear obviously superior when the Chinese first met them in the 17th century) come from the algebraists of the late Song and Yuan periods (13th-14th centuries AD). The historian of science George Sarton characterised one of these, Qin Jiushao, as one of the greatest mathematicians ... of all times. Qin developed methods for solving problems which would in western terms involve equations of up to the power 10. To do this he made use of a matrix notation in which rod numerals were essential. Needham (p. 131,132) reproduces pages from the work of two of Qin's contemporaries in which rod numerals appear in the text: the second example is particularly striking as showing a sequence of normal written characters with the rod numerals used as ordinary numbers. At a much more demotic level, Li Di (pp. 389 ff discusses and illustrates a mathematical MS from the Dunhuang cave shrines (possibly dating 7th-10th C.) in which rod numerals and common characters are mixed. On this basis, I suggest it is reasonable to allow that in Chinese terms the rod numerals should at the very least be admitted into the category of mathematical symbols, technical symbols, arrows, dingbats, etc. , and personally I should urge that they should be accepted as a technical way of writing numbers - which is how they frequently functioned. I hope this helps to advance the discussion. Further comments would be welcome. Christopher Cullen On 13 Jan 2004, at 01:45, Kenneth Whistler wrote: John Jenkins responded: Personally, I think it's an excellent idea. I have my doubts, personally, but concur that getting a proposal together to debate the merits is a good idea. It'd be good to get it on the UTC agenda for next month, so if you could start on the form. I can give you any help you need. On Jan 10, 2004, at 5:23 AM, Christopher Cullen wrote: These represent the arrays of counting rods on a counting board as used in China for complex calculations before the invention of the abacus. There are eighteen forms in all, representing the numerals one to nine in two forms which are basically versions of each other with a 90 degrees rotation. One form is used for units, the the other for tens, then back to the first form for hundreds, and so on. A zero is represented by a gap in the array. For pictures of these and an explanatory text, see: http://www.math.sfu.ca/histmath/China/Beginning/Rod.html This page does show a few exhibits of tally marks scratched on earthenware, presumably using the same system as the counting rods. But what is lacking here are actual instances of these rod numerals used as characters in writing. The claim is that Computations were actually done using rod numerals. But these are only shown in summary
RE: Chinese rod numerals
Christopher Cullen wrote: (2) The Unicode home page says: The Unicode Standard defines codes for characters used in all the major languages [...] mathematical symbols, technical symbols, [...]. I suggest that in an enterprise so universal and cross-cultural as Unicode, the definition of what counts as a mathematical symbol has to be conditioned by actual mathematical practice in the culture whose script is being encoded. I think that Ken Whistler point was simply this: OK, Chinese rod numerals may be symbols, but were these symbols used in *writing*? Not all symbols are used in writing, and only symbols used in writing are suitable to be part of a repertoire of, well, encoding symbols used in writing... A flag, a medal, a tattoo, T-shirt may definitely be calle4d symbols, yet Unicode does not need a code point for Union Jack or Che Guevara T-Shirt. To stick to mathematics, a pellet on an abacus, a key on an electronic calculator, or a curve drawn on a whiteboard may legitimately be considered symbols for numbers or other mathematical concepts. Yet, Unicode does not need a code point for abacus pellet, or memory recall key, or hyperbola with horizontal axis, because these symbols are not elements of writing. IMHO, in your proposal you should provide evidence that the answer to the above question is yes. I.e., you don't need to prove that these symbols were used in Chinese mathematics, but rather that they were used to *write* something (numbers, arguably, or arithmetical operations, etc.). _ Marco
Re: Chinese rod numerals
On Jan 12, 2004, at 6:45 PM, Kenneth Whistler wrote: The issue comes down to whether we are talking about characters in text, or whether we are talking about some glyphs representing the usage of counting rods, which might be more convenient if available in fonts, rather than being manipulated as graphics embedded in text. The proposal will need to make the case for encoding *as characters*. *sigh* You're just trying to make me dig out my copy of Needham, aren't you? The counting-rod forms are an outgrowth of (ultimately) oracle bone forms (see Needham, vol. 3, pp. 6-7 for a chart). The forms for 1-4 on the oracle bones pretty much match the later counting-rod forms, and by the time of Zhou dynasty coinage, the forms for 5-9 do, as well. The main difference between the Zhou coins and the counting rods is the use of alternating orientations for different decimal places. Certainly, then, these symbols are part of a family of symbols used to actually represent numbers in earlier Chinese texts in a context separate from diagrams. Unfortunately, the only actual copy of the Chinese mathematical classics I've got is a fairly recent edition of the Jiuzhang Suanshu, which was published in the PRC and actually uses simplified forms throughout, so it's not a reliable indication of what the text would originally have. My copy of Libbrecht seems to be AWOL. I'll see if I can dig up a copy of the Sunzi Suanshu or any of the works of the great Song mathematicians. (Oh, if only there were somebody I knew with access to Berkeley's Far Eastern Library!) Meanwhile, the point you raise is a fairly subtle one. I've seen books, for example, with pictures of slide rules or abaci illustrating their use. I think here, however, although there is in the mind of the Chinese mathematicians an inextricable link between the two, it's rather on the order of our using Arabic numerals on our calculators and in our math books. That is, they not only used them to illustrate how to uses the instruments, but also in tables of numerals with mathematical interest. (E.g., the famous diagram of Pascal's triangle in the Siyuan Yujian.) John H. Jenkins [EMAIL PROTECTED] [EMAIL PROTECTED] http://homepage..mac.com/jhjenkins/
Re: Chinese rod numerals
My submission is that the evidence I cite does show that the rod numerals were used in writing. Of course some forms of writing are more technical than others, and mathematics is a particularly technical form of writing. Rod numerals functioned in the work of the Song/Yuan algebraists in the same way that algebraic notation does for a modern mathematician. Thus for example, referring to the page from a 13th century book reproduced in Needham (1959) p. 132, I would translate the passage from the bottom of the fourth column from the right (reading right to left) roughly as: ... having done that, multiply the breadth of the yellow hypotenuse by the unknown, to obtain (-2x^2 + 654x), then divide that by ... The expression shown here using algebra is set out in the original using rod numerals. If that is not writing, then algebra is not writing either. I revert again to the cross-cultural issue: why should modern western mathematicians have the privilege of finding everything they need in Unicode, whereas those who wish to write Chinese mathematics have to resort to pasting graphics into their texts, because someone decides that parts of those texts are not real writing? Incidentally, I do note that provision has been made to encode the 64 hexagrams of the Book of Change, and also the symbols used in Yang Xiong's Taixuan jing. See http://www.unicode.org/charts/ under Yi Jing hexagram symbols and Tai xuan jing symbols. While I think that the idea of writing may not be in the last analysis a helpful one to use as a demarcation criterion for Unicode, given that the home page does say The Unicode Standard defines codes for arrows, dingbats, etc., I would think that if the hexagrams etc. are in, then a fortiori so should rod numerals be. Much more if the Tai xuan jing symbols are in, which I personally have never seen used outside the context of the ancient book in which they occur (maybe I'm just ignorant. Yes, I probably am). Christopher On 13 Jan 2004, at 16:05, Marco Cimarosti wrote: Christopher Cullen wrote: (2) The Unicode home page says: The Unicode Standard defines codes for characters used in all the major languages [...] mathematical symbols, technical symbols, [...]. I suggest that in an enterprise so universal and cross-cultural as Unicode, the definition of what counts as a mathematical symbol has to be conditioned by actual mathematical practice in the culture whose script is being encoded. I think that Ken Whistler point was simply this: OK, Chinese rod numerals may be symbols, but were these symbols used in *writing*? Not all symbols are used in writing, and only symbols used in writing are suitable to be part of a repertoire of, well, encoding symbols used in writing... A flag, a medal, a tattoo, T-shirt may definitely be calle4d symbols, yet Unicode does not need a code point for Union Jack or Che Guevara T-Shirt. To stick to mathematics, a pellet on an abacus, a key on an electronic calculator, or a curve drawn on a whiteboard may legitimately be considered symbols for numbers or other mathematical concepts. Yet, Unicode does not need a code point for abacus pellet, or memory recall key, or hyperbola with horizontal axis, because these symbols are not elements of writing. IMHO, in your proposal you should provide evidence that the answer to the above question is yes. I.e., you don't need to prove that these symbols were used in Chinese mathematics, but rather that they were used to *write* something (numbers, arguably, or arithmetical operations, etc.). _ Marco
Re: Chinese rod numerals
John Jenkins responded: Personally, I think it's an excellent idea. I have my doubts, personally, but concur that getting a proposal together to debate the merits is a good idea. It'd be good to get it on the UTC agenda for next month, so if you could start on the form. I can give you any help you need. On Jan 10, 2004, at 5:23 AM, Christopher Cullen wrote: These represent the arrays of counting rods on a counting board as used in China for complex calculations before the invention of the abacus. There are eighteen forms in all, representing the numerals one to nine in two forms which are basically versions of each other with a 90 degrees rotation. One form is used for units, the the other for tens, then back to the first form for hundreds, and so on. A zero is represented by a gap in the array. For pictures of these and an explanatory text, see: http://www.math.sfu.ca/histmath/China/Beginning/Rod.html This page does show a few exhibits of tally marks scratched on earthenware, presumably using the same system as the counting rods. But what is lacking here are actual instances of these rod numerals used as characters in writing. The claim is that Computations were actually done using rod numerals. But these are only shown in summary figures demonstrating the rod numerals used. Such figures are arguably graphics, not characters. The numerals are mathematical entities in the calculation method, to be sure, but the cited Sun Tzu Suan Ching talks about the calculations using rods, but doesn't actually *write* them in text. The discussion of the calculations is in terms of the ordinary Chinese number characters. It would be a great convenience to have these as a standard resource rather than having to create a special private font in order to represent them. The issue comes down to whether we are talking about characters in text, or whether we are talking about some glyphs representing the usage of counting rods, which might be more convenient if available in fonts, rather than being manipulated as graphics embedded in text. The proposal will need to make the case for encoding *as characters*. That said, clearly space for encoding is not an issue, of course, for a set of 18 of these things. Character properties, however, may be a problem, and should also be taken into account in any proposal. The obvious precedent for a set of numerals like this are the Aegean numerals, U+10107..U+10118, which are also quite obviously derived from layouts of tallying sticks, and which have a units set 1-9 and a tens set 10-90 oriented at right angles to the 1-9 set. But the Aegean system used other counters for 100 and up, so there is not a problem of alternating values. My suggestion would be to just give values 1-9, 10-90 for the Chinese rod numerals and be done with it, for the Unicode character properties. But the fact that the values are position dependent raises the suspicion that this really is a calculation system, rather than simply a set of 18 numeral characters, and as such, it may be over the edge of what is appropriate to encode in the Unicode Standard. --Ken From a private source, I have been told that these forms are neither in any current Unicode encoding initiative, nor indeed anywhere in the proposal pipeline. I should therefore be grateful for any comments or advice that might guide me towards making a formal submission.
Re: Chinese rod numerals
on 2004-01-12 17:45 Kenneth Whistler wrote: The obvious precedent for a set of numerals like this are the Aegean numerals, U+10107..U+10118, which are also quite obviously derived from layouts of tallying sticks, and which have a units set 1-9 and a tens set 10-90 oriented at right angles to the 1-9 set. But the Aegean system used other counters for 100 and up, so there is not a problem of alternating values. And historical examples of the Aegean numbers exist *primarily* (if not exclusively?) in written form, on clay tablets. -- Curtis Clark http://www.csupomona.edu/~jcclark/ Mockingbird Font Works http://www.mockfont.com/
Re: Chinese rod numerals
One very interesting thing I noted on the page: Negative numbers were usually represented using distinguisable features like color. Positive rods were usually colored red while negative rods were usually colored black. Wasn't there a really long thread not very long ago about whether color was ever a distinguishing characteristic of two otherwise identical characters? -- Elliotte Rusty Harold [EMAIL PROTECTED] Effective XML (Addison-Wesley, 2003) http://www.cafeconleche.org/books/effectivexml http://www.amazon.com/exec/obidos/ISBN%3D0321150406/ref%3Dnosim/cafeaulaitA
Re: Chinese rod numerals
Christopher, This is an excellent suggestion. A submission can be made using n2352-form.pdf that you can get from this site. http://www.dkuug.dk/JTC1/SC2/WG2/docs/summaryform.html Raymond Mercier - Original Message - From: Christopher Cullen [EMAIL PROTECTED] To: Unicode list [EMAIL PROTECTED] Sent: Saturday, January 10, 2004 12:23 PM Subject: Chinese rod numerals I am an academic with research interests in the history of ancient Chinese mathematics, and I should like to propose the encoding of traditional Chinese rod numerals. These represent the arrays of counting rods on a counting board as used in China for complex calculations before the invention of the abacus. There are eighteen forms in all, representing the numerals one to nine in two forms which are basically versions of each other with a 90 degrees rotation. One form is used for units, the the other for tens, then back to the first form for hundreds, and so on. A zero is represented by a gap in the array. For pictures of these and an explanatory text, see: http://www.math.sfu.ca/histmath/China/Beginning/Rod.html These forms appear in pre-modern mathematical books in China, and in modern books discussing ancient mathematics. They are not to be confused with the the related Hangzhou numerals, which are already encoded at 3021-303a. It would be a great convenience to have these as a standard resource rather than having to create a special private font in order to represent them. From a private source, I have been told that these forms are neither in any current Unicode encoding initiative, nor indeed anywhere in the proposal pipeline. I should therefore be grateful for any comments or advice that might guide me towards making a formal submission. Christopher Cullen
Re: Chinese rod numerals
On 10/01/2004 07:25, Elliotte Rusty Harold wrote: One very interesting thing I noted on the page: Negative numbers were usually represented using distinguisable features like color. Positive rods were usually colored red while negative rods were usually colored black. Wasn't there a really long thread not very long ago about whether color was ever a distinguishing characteristic of two otherwise identical characters? Sounds like the numerals on my bank statements, except the other way round. But I don't think that would justify encoding as separate characters red negative Arabic digits, or red positive Chinese rod digits. -- Peter Kirk [EMAIL PROTECTED] (personal) [EMAIL PROTECTED] (work) http://www.qaya.org/
Re: Chinese rod numerals
The earliest statement on this point is that of Liu Hui around AD 263, who says: (Jiu zhang suan shu, chapter 8 p. 175 in Guo Liu (eds) Suan jing shi shu, Taibei 2001.) Which means that the positive rods are red and the negative black, but adds that when this is not the case (presumably because one does not have coloured rods) one makes a difference by means of the inclined and straight. No further explanation is given in Liu Hui's text, but In later practice (as evidenced in the 13th C.) this appears to have meant that one set out the number as usual, but with an extra rod laid diagonally across the right-hand numeral of a given number. I do not recall having heard of any excavated sets of counting-rods showing signs of having been coloured, but I have not checked this. For completeness, perhaps one should also ask for the encoding of a set of diagonally cancelled rod numerals so that the second style for negative numbers could be represented. Christopher Cullen On 10 Jan 2004, at 15:25, Elliotte Rusty Harold wrote: One very interesting thing I noted on the page: Negative numbers were usually represented using distinguisable features like color. Positive rods were usually colored red while negative rods were usually colored black. Wasn't there a really long thread not very long ago about whether color was ever a distinguishing characteristic of two otherwise identical characters? -- Elliotte Rusty Harold [EMAIL PROTECTED] Effective XML (Addison-Wesley, 2003) http://www.cafeconleche.org/books/effectivexml http://www.amazon.com/exec/obidos/ISBN%3D0321150406/ref%3Dnosim/cafeaulaitA
[OT] Legacy encodings (was: Re: Chinese rod numerals)
Christopher Cullen wrote: The earliest statement on this point is that of Liu Hui around AD 263, who says: One of the things I like about the Unicode list is that people have, and use, the freedom to post in different scripts instead of ASCII-fying everything. Hopefully, one day, it will become more common to actually post these items *in* Unicode, instead of resorting to legacy encodings like Big5. I understand that the current situation, whereby e-mail clients choose fonts on the basis of encodings rather than character content, makes this difficult. -Doug Ewell Fullerton, California http://users.adelphia.net/~dewell/
Re: Chinese rod numerals
Personally, I think it's an excellent idea. It'd be good to get it on the UTC agenda for next month, so if you could start on the form. I can give you any help you need. On Jan 10, 2004, at 5:23 AM, Christopher Cullen wrote: I am an academic with research interests in the history of ancient Chinese mathematics, and I should like to propose the encoding of traditional Chinese rod numerals. These represent the arrays of counting rods on a counting board as used in China for complex calculations before the invention of the abacus. There are eighteen forms in all, representing the numerals one to nine in two forms which are basically versions of each other with a 90 degrees rotation. One form is used for units, the the other for tens, then back to the first form for hundreds, and so on. A zero is represented by a gap in the array. For pictures of these and an explanatory text, see: http://www.math.sfu.ca/histmath/China/Beginning/Rod.html These forms appear in pre-modern mathematical books in China, and in modern books discussing ancient mathematics. They are not to be confused with the the related Hangzhou numerals, which are already encoded at 3021-303a. It would be a great convenience to have these as a standard resource rather than having to create a special private font in order to represent them. From a private source, I have been told that these forms are neither in any current Unicode encoding initiative, nor indeed anywhere in the proposal pipeline. I should therefore be grateful for any comments or advice that might guide me towards making a formal submission. Christopher Cullen John H. Jenkins [EMAIL PROTECTED] [EMAIL PROTECTED] http://homepage..mac.com/jhjenkins/
[OT] Legacy encodings (was: Re: Chinese rod numerals)
Sorry - actually my mail client (Mac Mail for OS X Panther) gives me a choice of encodings, but I just did not remember to select Unicode, as would I agree have been more respectful of the context. Here it is re-coded. Begin forwarded message: From: Christopher Cullen [EMAIL PROTECTED] Date: 10 January 2004 18:06:31 GMT To: Elliotte Rusty Harold [EMAIL PROTECTED] Cc: Unicode list [EMAIL PROTECTED] Subject: Re: Chinese rod numerals The earliest statement on this point is that of Liu Hui around AD 263, who says: (Jiu zhang suan shu, chapter 8 p. 175 in Guo Liu (eds) Suan jing shi shu, Taibei 2001.) Which means that the positive rods are red and the negative black, but adds that when this is not the case (presumably because one does not have coloured rods) one makes a difference by means of the inclined and straight. No further explanation is given in Liu Hui's text, but In later practice (as evidenced in the 13th C.) this appears to have meant that one set out the number as usual, but with an extra rod laid diagonally across the right-hand numeral of a given number. I do not recall having heard of any excavated sets of counting-rods showing signs of having been coloured, but I have not checked this. For completeness, perhaps one should also ask for the encoding of a set of diagonally cancelled rod numerals so that the second style for negative numbers could be represented. Christopher Cullen
