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Is "Ichibai" Really Two Times? How the Meaning of "Bai" Changed in Japanese Math in the Meiji Era

Category: History & Culture

When you say someone works "ichibai" (one-fold) harder than others, you mean they work more. But if you read "ichibai" literally as "one times," it means the same amount as everyone else, which is not a compliment. Historically, the Japanese word "ichibai" was said to represent what we now call two times. Some old commentaries even suggested it meant three times. In 1875, the government issued a decree to change "ichibai" to "nibai" (two times) in official documents. [2]

Why did the meaning of the word drift? And why can phrases like "three-fold increase" still be read in two different ways today? The answer lies in how people used to count and calculate. [1]

1. Why "Ichibai" in "Hito Ichibai" Does Not Simply Mean One Times

The phrase "hito ichibai ganbaru" means to try harder than other people. However, if you read "bai" (fold/times) according to standard arithmetic, "ichibai" (one fold) means the original size. Working the same amount as a normal person is not a compliment. This contradiction has a historical reason. According to JapanKnowledge, "ichibai" was originally an old way of saying "two times," referring to adding the same amount to a quantity again. [1] The oldest recorded use is said to be from the Nara period. [1]

However, whether "hito ichibai" currently means "two times a person" or just "more than a person" is split between dictionaries. [2] Was the old "ichibai" always exactly two times? The answer is not simple. [2]

2. "Ichibai Gane": An Edo-Period Loan Repaid at Two Times

In the Edo period, there appears to have been a type of loan called "ichibai gane" (one-fold silver). JapanKnowledge explains that this was a high-interest loan where the borrower returned two times the amount they borrowed. [1] However, since this is just one example, it cannot be said to have been a fixed system across the whole country. [1]

Another example where the numbers match is found in Ihara Saikaku’s novel *Nihon Eitaigura*. It describes 1 kan of money growing with "one year, two times calculation" until it reaches 8,192 kan. Since 2 multiplied by itself 13 times equals 8,192, the calculation is correct. A paper cites this as a clear example where "bai" was used as "×2." [2] People in the past naturally calculated things becoming two times their original size using the word "bai." But "ichibai" was not always strictly two times. [2]

3. How "Bai" Was Counted in Old Eastern Mathematics

One explanation of Eastern mathematics suggests that "bai" was viewed as "original number × (count + 1)." In this view, "ichibai" (one fold) equaled what we now call two times, and "hanbai" (half fold) equaled 1.5 times. [3] Western mathematics uses "original number × count," which is what schools teach today. [3]

However, old usages were not always consistent. In *Nihon Ryoiiki*, the phrase "sen ichibai ni shite" (money became one-fold) has a headnote in the Iwanami classical literature series stating: "Interest accrued, making it three times the original. Ichibai means three times." [2] Other views suggest that in *Konjaku Monogatari*, two meanings were used together, and that "ichibai" in ancient legal interest rules meant the same 100% increase as today. [3] This means the same word "ichibai" was read as either two times or three times. If money calculations could be read differently by different people, what would happen? [3]

4. Decree No. 183 of 1875: The Government Changes "Ichibai" to "Nibai" in Official Documents

How did the government address this confusion? The answer is Grand Council of State Decree No. 183, issued on December 2, 1875. It stated that in future official documents, the term "ichibai" should be discontinued in calculations, and existing rules using "ichibai" should be changed to "nibai." A note gave an example: if the original amount is 1 yen, two times is 2 yen, and ten times is 10 yen. [2] This text is cited from *Horei Zensho* (Complete Collection of Laws and Regulations). [2]

Changes are also visible in postal regulations. Regulations from 1873–1874 used "ichibai" frequently, which the paper interprets as meaning two times. By the regulations for 1876, it had changed to "nibai." [2] However, this change applied to official writing and rules, not everyday speech. Phrases like "hito ichibai" are said to retain the old meaning and are still used today. [2] So, is modern "bai" unambiguous? [2]

5. Why "Sanbai" and "200% Increase" Can Still Be Read Two Ways Today

If you see "sales increased sanbai (three-fold)" in the news, did the original 100 become 300 or 400? Many read it as becoming three times (300), but if read as "increased by three times the amount," you add three times the original to the original, making it 400. [4] Is there a correct way to read it? It seems there is no fixed answer. Dictionaries have an entry for "baizou" (doubling), but not for "△-baizou" (△-fold increase). A Nikkei article suggests writing "3 times ○○ yen" to avoid misunderstanding. [4]

Percentages follow the same logic. "○% increase" adds the increase to the original amount. If the original is 100, "100% increase" is 100 + 100 = 200, which is two times. "200% increase" is 100 + 200 = 300, which is three times. [5] "200%" alone is two times, so the word "increase" changes the answer. [5]

In school math, the concept of "bai" also expands. When dealing with decimal multiples, the meaning of "bai" is reinterpreted from "how many parts" to "how much it corresponds to when the standard amount is viewed as 1," according to an essay introducing the 2017 Course of Study commentary. [6] In this view, 1-fold is the same amount as the standard. The background of old "ichibai" being two times was a counting method of "adding the same number to the original." Modern math views "the original as 1." Even with the same word "bai," if what you count as 1 is different, the answer shifts. [6]

6. How to Check "Times" and "% Increase" by Setting the Original Number to 100

When you see "○ times," "○% increase," or "○-fold increase" in news or ads, write "original number is 100" on paper and calculate the result. "2 times" is 200. "100% increase" is also 200. "200% increase" is 300. For "3-fold increase," you can see that some people read it as 300 and others as 400, which shows the need for careful writing. [5]

Also, look up "hito ichibai" in your home dictionary. See if it is explained as "two times a person" or "more than a person." Since dictionaries are said to differ, if you have two or more, you can compare them. Reading the decree text cited in the paper with your own eyes is also a pleasure. [2]

Sources

  1. JapanKnowledge "Japanese, How About That?" https://japanknowledge.com/articles/blognihongo/entry.html?entryid=6 (Explains that "ichibai" was an old way of saying "two times" and introduces "ichibai gane.")
  2. Amanuma, N. "Ichibai = Nibai" (Otsuma Women's University Repository, 1985) https://otsuma.repo.nii.ac.jp/record/1592/files/OK16(001).pdf (Cites the Grand Council of State decree, postal rules, calculations in *Nihon Eitaigura*, notes in *Nihon Ryoiiki*, and dictionary differences for "hito ichibai.")
  3. 3rd-in Pedia Encyclopedia "Bai" https://pedia.3rd-in.co.jp/wiki/倍 (Explains Eastern vs. Western mathematical views on "bai" and introduces differing theories.)
  4. Nikkei "Is 'Sanbai-zo' 3 times or 4 times?" https://www.nikkei.com/article/DGXZZO06312190V20C10A4000000/ (Discusses the ambiguity in reading "△-fold increase.")
  5. Kousei Shiten "Confusion between % increase and bai" https://kousei.club/percent-increase-vs-times-confusion/ (Explains the relationship between "○% increase" and "bai," verified by calculation.)
  6. Nunokawa, K. "Extension of Meaning of Bai and Multiplication" https://www.juen.ac.jp/g_katei/nunokawa/IAQs/extension_of_meaning.pdf (Introduces the reinterpretation of "bai" in the 2017 Course of Study commentary.)