＜prologue＞
I started a blog called “The Baby Boomer Generation’s Miscellaneous Blog”（Dankai-sedai no garakutatyou:団塊世代の我楽多（がらくた）帳） in July 2018, about a year before I fully retired. More than six years have passed since then, and the number of articles has increased considerably.
So, in order to make them accessible to people who don’t understand Japanese, I decided to translate my past articles into English and publish them.
It may sound a bit exaggerated, but I would like to make this my life’s work.
It should be noted that haiku and waka （Japanese short fixed form poems） are quite difficult to translate into English, so some parts are written in Japanese.
If you are interested in haiku or waka and would like to know more, please read introductory or specialized books on haiku or waka written in English.
I also write many articles about the Japanese language. I would be happy if these inspire more people to want to learn Japanese.
my blog’s URL:https://skawa68.com/
my X’s URL:団塊世代の我楽多帳（@historia49）さん / X
In an earlier article（＊）, I introduced “Age Diminal” until 120 years old, but this time I will talk about the units of numbers.
（＊）「年齢の異称」
In 2009, when the Democratic Party of Japan (DPJ) was in power, Renho asked at the “Project Sorting Meeting” about the research and development cost of the next-generation supercomputer project, the Kei(「京」) computer, “Is there any reason why it should definitely be the world’s best, or why not second place?”
・「京」も2020年ごろには撤去されて、性能が100倍程度に向上した新しい「次世代スーパーコンピュータ」に置き換えられる
As a result, the budget was cut by 11 billion yen. The “Kei computer” is scheduled to be removed around 2020 and replaced by a new “next-generation supercomputer” whose performance has been improved by about 100 times.
I am an amateur, so I cannot judge the extent to which the project sorting has caused delays in development and other negative effects, but in any case, supercomputers are used for simulation processing and analysis by computing vast amounts of data at ultra-high speeds, and I expect “concrete results” to emerge in the future.
1. units of large numbers
Let’s get back to the main topic.Thanks to the name of the supercomputer, the public is now aware of the number up to “「京」Kei (or Kyou)” after “「兆」trillion. So what about the numbers above that?
They are “gai（「垓（がい）」）,” “jo, shi（「秭（じょ、し）」）,” “jo（「穣（じょう）」）,” “kou（「溝（こう）」）,” “kan（「澗（かん）」）,” “sei（「正（せい）」）,” “sai（「載（さい）」）,” “goku（「極（ごく）」）,” “Gougasya（「恒河沙（ごうがしゃ）」）,” “Asogi（「阿僧祇（あそうぎ）」）,” “Nayuta（「那由他（なゆた）」）,” “Fukashigi（「不可思議（ふかしぎ）」）,” and “Muryotaisu（「無量大数（むりょうたいすう）」）.”
“Gougasya（「恒河沙（ごうがしゃ）」）” means the countless sands of the Ganges River. “Asogi（「阿僧祇（あそうぎ）」）” means the immeasurable, countless number in the Buddhist language. “Nayuta（「那由他（なゆた）」）” means an extremely large quantity in Sanskrit.
After all, even “Gougasya（「恒河沙（ごうがしゃ）」）” is 10 to the power of 52, and “Muryoutaisu（「無量大数（むりょうたいすう）」）” is 10 to the power of 68, which are both incredibly large numbers. However, it is surprising that people in ancient India and China, perhaps anticipating today’s computer age, even created units for such large numbers.
2. small number units
Next, let’s look at units of numbers smaller than 1. We’re all familiar with the unit of “batting average” for baseball players, which goes up to “〇％（割）△bu（分）□rin（厘）,” but what comes next?
They are “mou(hair,)（「毛（もう）」）” “shi(thread)（「糸（し）」）,” “kotu(instant)（「忽（こつ）」）,” “bi(tiny)（「微（び）」）,” “sen(fiber)（「繊（せん）」）,” “sya(sand)（「沙（しゃ）」）,” “jin(dust)（「塵（じん）」）,” “ai(dirt)（「埃（あい）」）,” “byou(vast)（「渺（びょう）」）,” “baku(vague)（「漠（ばく）」）,” “moko（「模糊（もこ）」）,” “syunjyun(hesitation)（「逡巡（しゅんじゅん）」）,” “syuyu(instant)（「須臾（しゅゆ）」）,” “syunsoku(breath)（「瞬息（しゅんそく）」）,” “danshi(striking finger)（「弾指（だんし）」）,” “setsuna(moment)（「刹那（せつな）」）,” “rittoku(six virtues)（「六徳（りっとく）」）,” “koku(void)（「虚空（こくう）」）,” “seijyou(purity)（「清浄（せいじょう/しょうじょう）」）,” “araya（「阿頼耶（あらや）」）,” “amara（「阿摩羅（あまら）」）,” and “nehanjyakujyou（Nirvana tranquility)（「涅槃寂静（ねはんじゃくじょう）」）.”
By the way, “Nirvana (tranquility)” is 10 to the power of minus 24. It is surprising that the ancient peoples of India and China created units for such small numbers as well as units for larger numbers.
3. The mysterious magic of numbers
What I will introduce here is an arithmetic magic trick that can easily surprise people by “using a calculator to make them line up their favorite numbers.
The procedure is as follows.
(1) Enter the 8-digit number “12345679”, skipping the “8” from the sequence of numbers 1 to 9.
(2) Multiply it by the other person’s favorite single-digit number.
(Example) If “7” is selected: 12345679 x 7 = 86,419,753
(3) Multiply this answer by “9
(Example) If “7” is selected: 86,419,753 x 9 = 777,777,777
Even if you try with other numbers, strangely enough, 9 “the other person’s favorite one-digit number” will always line up.
<Secret disclosure>
The trick becomes clearer when the order of (2) and (3) is reversed.
Let me explain with the example above.
(2) Multiply “original number” by “9”: 12345679 x 9 = 111,111,111
(3) Multiply it by “the other person’s favorite one-digit number”: 111,111,111 x 7 = 777,777,777
In other words, no matter what number the opponent chooses as his/her favorite number, the trick is always to line up 9 numbers of his/her favorite number.
4. How to read large numbers instantly
Now, let me change the subject. When you see a number with many “0’s” in a row, can you immediately say how much it is? I think it is quite difficult.
So, in this article, I will show you how you can easily answer at least “trillions”.
For example, suppose there is a number “10000000000000000”. How much is this?
An easy way to answer this question is to put “,” (comma) in each of the three digits. This would be “1,000,000,000,000,000”. Then, from right to left, read “thousand（千）,” “million（百万）,” “billion（十億）,” “trillion（一兆）,” and so on. In other words, the “unit of measure” goes up by three digits, but the number at the beginning of the “unit of measure” goes down one by one from “thousand,” “hundred,” “ten,” to “one.
After “one trillion（一兆）,” the next numbers are “one thousand trillion（千兆）,” “one hundred billion（「百京」）,” “ten trillion（「十垓」）,” and “one quadrillion（「一秭」）.
Adding three more digits to “one trillion（一兆）” gives you “1,000,000,000,000,000”, which is “one thousand trillion（千兆）”. Adding three more digits to “1,000,000,000,000,000,000” gives you “one hundred billion（「百京」）”. Was this helpful?
5. Mysterious Numbers
(1) Perfect numbers
A “perfect number” is “a natural number equal to the sum of all positive divisors except itself.”
Examples are “6”, “28”, “496”, etc.
6＝1+2+3
28＝1+2+4+7+14
496＝1+2+4+8+16+31+62+124+248
The term “perfect number” was named by the ancient Greek mathematician and philosopher Pythagoras, who believed that “all things are numbers（「万物は数なり」）”.
Medieval biblical scholars believed that “6 is the six days in which God created the world (creation) and 28 is the ‘orbital cycle of the moon,’ and that these two numbers symbolize the perfection of God on earth and in the heavens.
(2) Amicable Numbers
An “amicable number” is a pair of two different natural numbers whose sums of the divisors, excluding themselves, are equal to each other. They are also called “affinity numbers.”
The smallest amicable number combination is 220 and 284.
The divisors of 220, excluding itself, are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, and the sum is 284.
On the other hand, the divisors of 284 excluding itself are 1, 2, 4, 71, and 142, and the sum is 220.
6. A simple way to convert “tsubo（「坪」）” to “㎡”
In Japan, the unit of land area used to be “tsubo”, but now it is mostly “㎡”
For an old-fashioned person like me, “㎡” doesn’t give a clear idea of how much area it represents. I would like to think of it in “tsubo” instead, but I think many people find it troublesome to calculate, saying things like “It’s impossible to divide by 3.3 in your head.”
So, here is a simple conversion method. Just multiply the square meters by 0.3 (you can also multiply the square meters by 3 and divide by 10 (drop one digit)).
For example, for 100 square meters, 100 x 0.3 = 30 (tsubo).
<Secret disclosure>
Strictly speaking, the correct answer is to multiply by “0.3025”. The reason for this is as follows. It is derived from the relationship between the shakkanho system（「尺貫法」） and the metric system（「メートル法」）.
1 shaku（尺） = 10/33m 1 ken（間） = 6 shaku = 60/33m
1 tsubo（坪） = 1 ken x 1 ken = 60/33 x 60/33 square meters (㎡) = 3600/1089 square meters (㎡)
1 square meter (㎡) = 1089/3600 tsubo = 0.3025 tsubo
Conversely, to convert from tsubo to square meters, you multiply the number of tsubo by 3.3, as you know. The reason for this is as follows:
1 tsubo = 3600/1089 square meters (㎡) = 3.3057 square meters (㎡)
7. “「大字（だいじ）」Daiji(large character)” and “「小字（しょうじ）」Shoji(small character)” in Chinese numerals（漢数字）
Did you know that there are “large characters” and “small characters” in Chinese numerals?
The “large characters” of numbers are a type of Chinese numerals that use a different Chinese character with the same sound instead of the normally used “small characters” (Chinese numerals with simpler shapes).
In the past, all banknotes were printed in large characters, and even today, large characters are used on the 10,000 yen and 2,000 yen bills.
I think it would be easier to understand if I give a concrete example.
(1) What is a “small character”?
These are the Chinese numerals that are usually used, such as one（一）, two（ニ）, three（三）, four（四）, five（五）, six（六）, seven（七）, eight（八）, nine（九）, ten（十）, one hundred（百）, one thousand（千）, and ten thousand（万）.
(2) What is a “large character”?
The large characters that correspond to the small characters in the Chinese numerals above are as follows:
The following are the numbers: 壱 (or 壹, 弌), 弐 (or 貳, 貮, 弍), 参 (or 參, 弎), 肆, 伍, 陸, 漆 (or 質, 柒), 捌, 玖, 拾 (or 什),陌 (or 佰), 阡 (or 仟), and 萬.
Kanji numerals are usually written in small characters, but because they have few strokes and are prone to tampering, large characters are sometimes used to write important numbers.
Specifically, they are used in legal documents and accounting documents (such as family registers, receipts, and registrations). They are also used for handwritten promissory notes and amounts in loan agreements that are not written using a checkwriter.
For example, if “金一万円” is written on a receipt, it can easily be falsified later by adding “丨” or “L” or “イ” or “二” to make it “十万円”（100,000 yen） or “廿万円” (200,000 yen) or “千万円”（10 million yen） or ”三万円”（30,000 yen）.
Similarly, if you write “6,000 yen” in messy handwriting, it is possible for the other person to mistake it for “大干円(Daikan yen).” Furthermore, by adding “丶” to “九百円(900 yen)” or “九万円(90,000 yen),” it is possible to falsify it into “丸百円(Maru 100 yen)” or “丸万円(Maru 10,000 yen).”
Conversely, when we receive a receipt that says “金三万円（30,000 yen） ” or “金七万円（70,000 yen ）” or “金百万円（1 million yen）,” we may be tempted to suspect that what was originally “金一万円（10,000 yen ）” was “padded (by adding 「一」（one） or「ニ」（ two） or 「し」or「白」) to ‘金三万円（30,000 yen）’ or ‘金七万円（70,000 yen）’ or ‘金百万円(1 million yen)” when submitted.
The reason for the existence of large characters is to prevent falsification by using difficult kanji with a large number of strokes.
As a side note, please read the article 「少額紙幣の思い出とお札の肖像になった歴代の人物にまつわる話を紹介」“Memories of Small Denomination Banknotes and Stories about the People of the Past Who Became Portraits on the Bills” for an introduction to old banknotes, if you are interested.
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