Talk:Suanpan

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Contents 1 Origins and the Roman abacus 2 Confusing paragraph in Beads section 3 Confusing sentence 4 number of beads

[edit] Origins and the Roman abacus

Its similarity to the Roman abacus suggests that that was the ultimate source, and this was very possible, since there were direct trade relations between the classical world and China, and Mongol traders along the Silk Route were a bridge between East and West. It could even have been introduced by the Roman soldiers captured by the Persians and sold to the Chinese emperor as engineers. Most were later ransomed, but many found China much to their liking.

This connection is way too far-fetched in my opinion for several reasons:

• There are more dissimilarities than similarities.
• Roman uses removable beads
• Chinese uses sliding beads
• Roman abacus uses 1-plus-4 beads to represent decimal numbers
• Chinese abacus uses 2-plus-5 beads to represent either decimal or hexadecimal numbers
• Roman used the abacus purely as a counting tool.
• Chinese used it as a calculating device by developing advanced computation techniques to do multiplication, divison, square root and cubic root on the abacus.

Such claim needs more evidence than just pure speculations. Kowloonese 01:14, 2 Sep 2004 (UTC)

This is not pure speculation. Claiming the Mayans were influenced by the Egyptians solely because of a similarity of large buildings that exist in both civilization is an example of PURE speculation. There was no opportunity for the two cultures to come into contact.

The Roman abacus dates back to at least 100 BCE.

The well-known version of the Chinese abacus, the Suan Pan, emerged in the 13th century, when most of the cultures in the world were using the 10-digit positional notation system which, almost one thousand years earlier, the Romans lacked.

The Yuan Dynasty (1271-1368) was when the Mongols rule China. It was a period of cultural enlightenment. The Mongols replaced the Han Chinese bureaucrats and all important central and regional posts within China were monopolized by Mongols, who also preferred employing non-Chinese from other parts of the Mongol domain--Central Asia, the Middle East, and even Europe to fill positions for which no Mongol could be found. Scientic education, literacy, and public works florished under Mongols. It was in this melting pot of cultures and enlightenment, that the Suan Pan leaped into existance as a fully formed two-deck abacus in the 13th century.

Admittedly, as far back at 190 CE, there were references to abaci in China. It was mentioned in a book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue in that year. Of course, this was at the height of the Roman Empire. In addition to trading via the Mongols along the Silk Road, there is proof of direct contact between the cultures. Hou Hanshu (History of the Later Han) recounts that a Roman convoy set out by emperor Antoninus Pius reached the Chinese capital Luoyang in 166 CE and was greeted by Emperor Huan.

Chinese Trade in the Tang Dynasty (618-907) along the Indian Ocean and the Middle East would have provided direct contact with India and Islam allowing them to accquire the concept of Zero and the decimal point from Indian and Islamic merchants and mathematicians.

Another reference to an abacus in China occurred at the latest during the Song Dynasty (960-1297), when Zhang Zeduan painted his Riverside Scenes at Qingming Festival. In this famous long scroll, an abacus is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao). Worthy of note is the increased Mongol influences as Song Dynasty collapsed under Mongol incursions.

By the 13th century, the Chinese numeral system is a fully expressed 10-digit system with positional notation, so it is not unreasonable to expect the Chinese to have developed computing techniques for the abacus that are readily expressed as algorisms under a positional notation system.

Any form of advanced arithmetic is extremely difficult using Roman numerals which lacked the Zero and positional notation. Before an arithmetic operation could be transfered to an abacus, someone had to develop the algorism for the operation. The complexity of multiplication and division under Roman arithmetic did not mean they were limited to only counting on an abacus. The limitation of the advanced arithmetic operations is a function of limitations of the Roman numeral system and not their abaci.

The adaption of the Roman abacus to the needs of the Chinese numeral system could be the cause of the mutation from 1/4 to 2/5 beads. I have found no evidence for or against early Chinese abaci having other than the 2/5 configuration. If a Roman abacus was presented to the Han Emperor in 166 CE, (no doubt the staff and merchants whom accompanied the envoy would have had abaci as well) then the intervening centuries were sufficently long enough for the Chinese to make the abacus their 'own' by adapting to their needs.

Furthermore, I did find an obscure reference that there was a Roman abacus with 2/5 configuration, but I am not sure if the author was correct. The author of the article cites K. Menninger, Number Words and Number Symbols (New York: Dover, 1992) as the source.

Note that the text of the article did not assert the connection was proven. However, I believe that there is more than enough evidence to suggest such a connection and that such a connection is not pure speculation as you claim. If more evidence presents itself, I am sure references will be cited and proofs offered.

--Denise Norris 13:39, Sep 2, 2004 (UTC)

Two brief insertions into this discussion:

I checked the Menninger book; I can find no reference to Roman abaci having the 2/5 configuration. Page 305 near bottom he mentions 5 counters in one groove used for counting unciae (fractions); perhaps this is the source of the misunderstanding.

Is it true that the Chinese abacus is used for hexadecimal arithmetics too? At what time is this use likely to have begun?

PS. I firmly support the mentioning of both possibilities (Roman abacus inspiring the Chinese, as well as independent development).--Niels Ø 13:54, August 7, 2005 (UTC)

I am not convinced despite everything you quoted here. There were many similar inventions in Chinese and Western culture that were proven to be developed independently. Almost all cultures around the world figured out what a year and a month is because they all looked at the same sky, not because they made contact and shared notes. Almost all cultures around the world figured out how to count in ten. Not because the cultures had contact with each other, it was because human beings have the common physiology, the ten fingers. The 1/4 bead counting came naturally when people used one hand to count while the other hand was busy sorting things. People count in ten because of ten fingers in two hands, people modified it into 1/4 counting because one hand got busy and then they figured out that they can count using the thumb to represent 5 and the fingers to represents ones. The abacus could very well be a natural extention to finger counting. Chinese and Roman could easily come up with the same idea independently.

You could believe Mayan and Egyptian could came up with large buildings independently because you couldn't find any evidence that the two cultures made contact. What if the evidence show up tomorrow, will you then claim Mayan and Egyptian learned their building technique from each others? Substitute buildings with abaci, then the same argument becomes very weak. Proving Chinese and Roman had contact does not prove their abaci are related.

In my opinion, the 1/4 and 2/5 design of the abaci were developed independently. And Chinese stuck with the same design all along because they used it for both decimal and hexadecimal calculation. The Japanese adopted the Chinese abacus, but they didn't use them for hexadecimal calculation, and they removed the two redundent beads and resulted to a design very similar to the Roman abacus.

Another example is the weighing unit in China and the Imperial weighing unit from England. Chinese had one jin for 16 liang while the English had one pound for 16 ounces. You can argue they learned from each other because they made contact and the hexadecimal approaches are strikingly similar. However, when you understand the 16 based unit were natural result from using a beam balance scale to make division. For example, you spit one pound of your grains into two piles until the scale balances on both side, you repeat it 4 times and you get an ounce. The Chinese did the same with their grain to come up with the similar 16 base units. Whether the two cultures made contact or not is irrelevant.

Unless you have found literature that explained the origin of the abaci, the claim in the article is baseless and should be removed. Kowloonese 07:59, 3 Sep 2004 (UTC)

Hmmmm, I wonder how Needham treated this controversy. I wish I were back in Montreal, I would have access to his publications right away. AlainV 06:29, 5 Sep 2004 (UTC)

I am working on getting the sources from the various authors as well as starting orginal research were opportunity exists. I believe it is unlikely that a definitive answer will emerge. --Denise Norris 12:07, Sep 5, 2004 (UTC)

The claim of a Roman origin is mere speculation. If it does not stand on fairly firm ground, it should be removed. Shorne 01:03, 3 Oct 2004 (UTC)

I was under the impression that the current wording of the text was acceptable to all. If you have specific suggestions to resolve a perceived NPOV issues, please feel free to discuss them here.

--Denise Norris 16:46, Oct 4, 2004 (UTC)

You knew my opinion from the start. Since wikipedia is a collaboration, my opinion only count for one vote. I still think the Roman connection is extremely weak. Though it does not hurt to include the possiblity in the article, but in my opinion it is so unlikely that the inclusion is irrelevant. I don't really like the current wording personally, because it sounded like the Roman connection was more likely than the independent development theory. I'd prefer the two emphasis swapped around instead. Kowloonese 17:50, 4 Oct 2004 (UTC)

I agree that the article as written gives too much weight to the dubious claim of a Roman origin. That position comes across as stronger than it is. Shorne 18:27, 4 Oct 2004 (UTC)

As I said on the Abacus discussion page, feel free to suggest alternatives for compromise or submit this article to mediation. Since there is strong evidence that the Chinese were exposed to the Roman abacus in 166 CE - 24 years prior to the earliest mention of an abacus in any Chinese literature and almost 1000 years before the developement of the modern Chinese abacus.

Show me a reference to an abacus in China prior to the opening of the Silk Road in 119 BCE by Zhang Qian under Emperor Wu and I will gladly relinquish the point.

Otherwise, I will stand my ground that cultural contacts (direct and indirect) via the Silk Road allowed for technology exchanges between the Roman Empire and China and that these exchanges would have included the concept of abacus as an advanced form of counting device, superior to the counting sticks in use by China at the time.

--Denise Norris 21:20, Oct 4, 2004 (UTC)

Forgive me for being so blunt, but presenting a theory and then asking peers to disprove it is not the proper academic process.

"Its similarity to the Roman abacus suggests that that WAS the ultimate source, and this was possible"

This is very strong wording which implies that a conclusion can be drawn but the article presents only very vague circumstantial evidence with no direct link whatsover. The smoking gun is simply not there and I don't believe the wording is appropriate. A better wording would be "Its similarity to the Roman abacus suggests that that was POSSIBLY the ultimate source." but I myself wouldn't present the theory without more direct evidence. CW 17:26, 28 May 2005 (UTC)

To comment on Mr Norris' claims, there is no "strong evidence that the Chinese were exposed to the Roman abacus in 166 CE - 24 years prior to the earliest mention of an abacus in any Chinese literature and almost 1000 years before the developement of the modern Chinese abacus." and I defy Mr Norris to produce any. At most there are spurious claims that Romans may have ended up in China. There are also less spurious claims that some people claiming to be Roman envoys from Antonius Pius ended up in Vietnam. With a stress on the word claim. But neither accounts suggest they brought the Roman counting table with them - because after all the Romans did not have an abacus. Ever. The Silk Road is a myth and was certainly not opened during Han Wudi's reign. Admittedly Chinese soldiers may have met Roman soldiers wandering around the Caspian (or even Black) Sea. But again no evidence of transmission. You can stand by the claim if you like but it remains without any sort of evidence or source. It is your opinion and little better than that. Why should it be included? Lao Wai 14:29, 7 August 2005 (UTC)

Mr Norris, during The Han Dynasty the silk road only reached the western region or central Asia it was not until the Tang dynasty that the Chinese came in contact with the declining roman empire. Also your statement about the romans sending a convoy to china was sent by Marcus Aurelius Antoninus Augustus NOT Antoninus Pius but still contemporary Roman chronicles make no mention of any attempts to contact the Chinese. Thus there is no or little evidence that what you say is ture

The other think is that The Roman Abacus use metal, while that of Chinese use wood and bamboo. The metallurgy allow at that time do have iron, if Chinese abacus originates from Roman Abacus, then the Chinese abacus would be made of metal, say bronze or copper, at least.

See the two following sections for detail Punkymonkeypun 16:06, 10 April 2007 (UTC)

[edit] Confusing paragraph in Beads section

"This Chinese division method [i.e. with division table (归除)] was not used when the Japanese changed their abacus to 1 upper bead and 4 lower beads in about 1920's. So, without a clear knowledge of division table, the trail of history, many have the wrong perception that Chinese abacus was from Roman Grooved Abacus."

This paragraph makes no semantic sense. Could the original author clarify it? I can't correct it myself since I'm not sure I understand what it means to say.

It was because in 1958, two japanese (山崎 and 右衞門) quote some ancient script and, mentioned that Chinese Abacus was evolved from Roman Abacus. In their passage, they (the two Japanese) deliberately omitted two very important idea, (i) according to the first written discription of "bead arithmatics" in 数书记遗

珠算，控带四时，经纬三才

甄鸾法：刻板为三分，其上下二分以停游珠，中间一分以定算位，位各五珠，上一珠与下四珠色别，其上别色之珠当五，其下四珠，珠各当一，至下四珠所领，故云控带四时．其珠游于三方之中，故云经纬三才。

No matter how the ancient chinese abacus re-made, NONE was like the Roman Abacus.

Also from the structure of Roman Grooved Abacus is far different from Chinese abacus:-

The groove marked I indicates units(i.e. 7th from left, or 3rd from the right, the 2nd LONG column from right), X tens, and so on up to millions. The beads in the shorter grooves denote fives—five units, five tens, etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals.

The eighth column (right 2nd, i.e. the rightmost LONG column) and ninth column (right most) are for 1/12 (one twelveth) and fraction of 1/12.

On the eighth column (right 2nd ) there are 5 balls (not 4) in lower groove, each represents 1/12 (one twelveth), and one ball in upper groove that represents for 6/12. (6 twelevth, i.e. half).

On the ninth column (right most) there are three grooves, the only ball (one only) in the upper groove represents 1/24 (i.e. half of 1/12), the only ball (one only) in the middle groove represents 1/48 (i.e. one fourth of 1/12). In the lower groove there are (two balls) each represents 1/72. (2 times one quarter of 1/12). Thus values ranges from 1/144 to 1+1/144.

The number to be denoted are represented by balls that are move upward (as there are 3 grooves on the right column), unlike that of Chinese abacus that move towards the central beam.

(ii) In the document quoted (original written by F cajori and G. Friedlein), they also [deliberately] omitted another important fact..

(translate back from chinese)珠算与实用算数 pp430 - 431 ISBN 7-5375-1891-2/O

No matter which method...multiplication and division of comparatively large numbers are beyond the average power of ordinary calculator (the one who calculates), sometimes (the user) have to consult the 'table of sum' and 'table of difference' and 'multiplication table' in order to minimize such difficulties (in order words unlike the chinese abacus which mnemonics are suffice to operate the abacus, even for ordinary people.

The modern Japanse abacus (soroban) do not use division table (归除) and the multiplication (隔位乘) is not that like the Tradition Chinese abacus (留头乘法), and the USA follows that of Japanese, so they draw the wrong/misleading conclusion.Punkymonkeypun 15:31, 10 April 2007 (UTC)

[edit] Confusing sentence

"The earth beads and heaven beads are usually not used in addition and subtraction." What is this sentence trying to say? The earth and heaven beads are the only beads there are; how can they not be used in addition and subtraction? --Allen 20:20, 14 March 2007 (UTC)

Yes, the earth beads and heaven beads are NOT used in addition and subtraction. Many believe that heaven beads and earth beads are used just because they did NOT learn the multiplication and division method pertaining to Chinese abacus. Most Western people, ASSUMES, the multiplication and division are nearly or exactly the same as those with pen and paper. Actually not.

In Traditional multiplication and division, earth beads and heaven beads are required to sum the intermediate result. Had they known the unique method peculiar to Chinese abaci, they would never have said that Chinese abacus are from Roman Abacus. There are also some documents showing that there was no direct trade between Ancient China and Europe in the first century, but only indirectly through Arabia, (called 大食) at that time.

Also the Romans, EVEN in usually addition, requires consultation to 'addition table' and 'subtraction table' in addition to mental manipulation (just can't believe so clumsy), Roman Abacus do NOT have the mnemonics for addition and subtracation like the Chinese abacus. In fact, when manipulate many times with Chinese abacus, your finger can react just like touch typist.Punkymonkeypun 15:31, 10 April 2007 (UTC)

Concerning modern learning/usage of abaci/soroban The method that the Japanese learning is basically the abacus method on 1 + 4 configuraton. And they try to develop into a skill call 'anzan' which is basically move the mental beads in a mental soroban, when once mastered/developed.

However, the technique outside Japan is another world - completely different.

Before that, the sentence "to preseve culture" is totally wrong.

The abaci they (children) used are (i) no longer 2 + 5 in configuration. And, astonishing, (ii) the abaci they use are neither as small as the 'soroban' (Japanese abacus). Rather, the beads are of 1.9 mm in diameter. The most important thing is, aslo, the algorithm they are learning is not abacus technique at all, neither the Japanese method, nor the Traditional Chinese method, but, a just a combination of speedy calculation (with abacus, acutually can be done with paper, just that the beads are easy to maniuplate.

Some school teaches using both hands on the same abacus.

Some other school combines with speed calculation, (may or may not with mental abacus). Some school requires the children to recite (extend) the multiplication table to 9 x 99 (instead of the usual 9 x 9 multiplication we learn in Elementary/Primary School). Some other school requires to use the method '一口清' (no English Transaltion) which is always add, subtract, multiply and divide from the larger digit. And dealing with the 'carry' from lower digits (adjustment of hundred digit beacuse of the 'carry' from the tenth-digit), according to certain rules. This method was merged with speedy calculation eversince, in the last 20 years, and very popular in mainland China, private sector.

In the Japanese system, as they use the 1 + 4 configuration, their method of deciding decimal points are different from that of Traditional Chinese Abacus (The Traditional Chinese Abaci is more consistent in deciding decimal points).

In order to preseve the advantage of using Chinese Traditional Abaci, e.g. in deciding the decimal points, but on a 1 + 4 configuration abaci, purely as a calculating tool, some of the abacus experts, in mainland China, (a) creates the 增商口诀, but that requires more memorization.

(b) some use the 改商法 method, in opposite to the Japanese method which puts (trial) quotient on the rod left (side) to the dividend. This method eiliminates the use chinese division table (归除法). But the intermediate sum can be more than 10 so the operator (the one who calcualtes) either memorize the intermediate result or use the method below.

An order to gain speed and to minimize the change of 试商 ('trial' quotient) , the concept of 负餘数 was used. In this case the 试商 (trial quotient, if, usually, too large) can be adjusted easily without thinking, and this methods enable getting several digits of answer with one manipulation of answer. (simply speaking, get 2, 3 or even 4 digits in answer with one single manipulation, the Traditional Chinese / Japanese method / pen and paper calcualtion only get one digit (dividend) in calculation).

N.B. The mnemonics for 归除 and 撞归 in Chinese always starts from the divisor, then followed by the dividend, and final with the quotient, as the divisor is, usually, put on the left side of the abacus, and the dividend is put on the middle or right hand side of the abacus. It is natural for the user to operate. But when translated to English (don't know who), the one who translates reverse the order that follows the mathematical equation. So it seems strange/stupid to the user when s/he recites the mnemonics as this is reverse to the operation of the Chinese abacus, and unnatural. The worse thing is the mnemonics for 撞归 is not translated, which makes the Chinese division table (to foreigners) in complete at all.

Finally, that, Chinese abaci are no longer used as handheld calculators are affordable and, using abaci and passing with graded exam is no longer a compulsory requirement in Business Studies in Universities or Colleges in mainland China, as bead-arithmatics are superseded by "computer studies" in Business Studies starting from 2003 (may be 2004, unsure). Punkymonkeypun 16:56, 12 April 2007 (UTC)

Thank you for this detailed response; however, I don't see how most of it pertains to my question. According to our article and all other sources I've seen (which admittedly are not many), the only moving parts of the Chinese abacus are the earth beads and the heaven beads. If neither earth beads nor heaven beads are used for addition and subtraction, then addition and subtraction must be performed without using any beads at all. Without beads, the abacus is simply an immobile wood frame, seemingly useless for calculations. --Allen 21:29, 14 April 2007 (UTC)

It seems that you misunderstand the meaning of 'heaven bead' and 'earth bead' and mix them up with 'upper beads' and 'lower beads':-

There 2 beads above the central horizontal/reckoning bar and both of them (2 beads) are called 'upper beads'. However, in the same column, only the upper one of the two upper beads is called 'heaven bead'. There are 5 beads below the central horizontal/reckoning bar. All five of them are called 'lower beads'. But only the lowest one of that five beads is called the 'earth bead'. So the most top (heaven bead) and most bottom (earth) beads are not used during addition and subtraction. These two beads are used in the traditional Chinese method of multiplication and division. Punkymonkeypun 15:09, 16 April 2007 (UTC)

[edit] number of beads

I don't understand why everyone thinks the Chinese abacus always has 2 beads on the top and 5 beads on the bottom. I'm Chinese and my Chinese abacus has 1 bead on the top and 4 beads on the bottom. Almost all new abacuses have one bead on the top and 4 beads on the bottom. Chenhsi (talk) 18:29, 16 December 2007 (UTC)

That is because China now uses the Japanese abacus.—Preceding unsigned comment added by My Love For Info (talk • contribs) 5 June 2008

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