Sheng Li (gmachine1729) wrote,
Sheng Li

Solid evidence that Hindu-Arabic decimal system was copied from Chinese counting rods

Originally published at 狗和留美者不得入内. You can comment here or there.

PDF of book: Lam Lay Yong, Ang Tian Se – Fleeting Footsteps_ Tracing the Concepti_ Tracing the Conception of Arithmetic and Algebra in Ancient China-World Scientific Pub Co ( (2008)

A book by Lam Lay Yong (蓝丽蓉) gave solid evidence that the Hindu-Arabic decimal system was with near full probability copied from Chinese counting rods. To get an instant idea of what counting rods are like, here is an example of subtraction using rod calculus, with three steps.

Rod subtraction.jpg

Below is an example of a number with a zero digit in rod calculus, which represents it with a blank.


For examples of multiplication, division, square root extraction, etc using rod calculus, see

Algorithms using rods for multiplication and division were first explicitly described in a book written between 3rd to 5th century AD called Sunzi Suanjing. This was before Indian mathematician Aryabhata. There is also archaeological evidence of counting rods before the birth of Christ, and moreover, explicit mention of them in the ancient mathematical text Nine Chapters of Mathematical Art much of which was likely written before 0 AD, with commentary of it by 3rd century mathematician Liu Hui.

Solid evidence that decimal arithmetic in Middle East and India almost certainly came from China

  • On the Calculation with Hindu Numerals by Muhammad ibn M usa al-Khwarizmi in 825 AD, the algorithms for multiplication, division, etc are pretty much identical to the ones given in Sunzi Suanjing but executed with numerals on a dust board. The difference was they were done with Hindu-Arabic numerals.
  • With counting rods as opposed to writing, it’s easy to remove a rod by hand; on the other hand, using writing, it would be quite inconvenient to execute those algorithms for arithmetic.
  • Sunzi Suanjing mentioned a Buddhist sutra, and indeed exchange via Buddhist monks between China and India, and also between the Sinosphere countries China, Vietnam, Korea, Japan around the same time is well documented.
  • There was identical notation for fractions, identical procedures for arrangement of digits.
  • The early Hindu-Arab numerals also used a blank for a zero digit, but later on introduced the zero symbol or sometimes a dot. Even in the very statistical significant case that the same algorithms with identical arrangement of digits were independently invented in India via Hindu numerals, the use of a blank in writing for zero would have been extremely unnatural, whereas it is natural in the medium of counting rods.
  • Counting rods and even explicit mention of arithmetic algorithms through them in Sunzi Suanjing vastly predates 7th century Indian mathematician Brahmagupta who did some work regarding zero and negative numbers.
  • Indian Brahmi numerals in the 2nd century AD were still using separate symbols for the tens, hundreds, thousands.
  • In Lam’s book, search the word “identical” and read up on the linked Wikipedia pages and other relevant ones to verify yourself.



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