2700: The Non-Roman Origins of Roman Numerals | May 12, 2024

Unlike other letter-based numerals that use the letters in ascending order of the alphabet, like Greek or Hebrew, Roman numerals are more abstracted, and somewhat systematic. For instance, X is 10, and take ½ of that for V (5), which is the top half of X. The X is probably derived from adding on an extra line at the end of a set in an early tally marks system. This works the same in M (1,000) and D (500), but not in the way that you might think. 

These letters are not tied to words, though M was reinforced by Latin ‘mille’ for ‘thousand’, and the original form of M in numerals was ↀ, half of which is D. This originated in pre-Roman Etruscan numerals, that used C (100), IↃ (500), and CIↃ (1,000) and these bracketed-I forms then were written as similar looking letters, and C reinforced by ‘centum’. In fact, though not as typically used, other forms ↁ (10,000) and ↂ (50,000) exist from this system of adding brackets. The shapes of the letters, and some Latin words may have slightly influenced the form of Roman numerals as in the case of ↀ→M, but in almost all other cases (I,V,X,L,D) these symbols only coincidentally looked like letters and have nothing to do with the words they represented.

2531: Order in Welsh Numbers Nov 17, 2021

Welsh numbers are already very complex with two different systems, but part of the complexity is the variation. Celtic languages have many sounds which mutate and different adjectival forms for these numbers, but on top of that the order of the words is not necessarily set. The numbers are stated with prepositions, such as "un ar ddeg ar hugain" (one on ten on twenty) to say '31'. When this is used as a modifier, the noun can be put in the middle of the phrase as well such as "un ar ddeg ar hugain o gŵn" (31 dogs) literally "one on ten on twenty of dogs" which can be reordered as "Un ci ddeg ar hugain", literally "one dog ten on twenty".

2530: Welsh Numbers Nov 16, 2021

People may be aware that French numbers use somewhat mathematical descriptions, like soixante-dix for 70 meaning sixty-ten, and 'quatre-vingts' for 80 meaning 'four-twenties' but Welsh numbers are even more extreme. Indeed, there are actually two different systems, one decimal and one vigesimal. The decimal system operates similarly to English's decimal system, but the vigesimal is base-20 for all numbers so to say '30' it is 'deg ar hugain' (ten on twenty), '40' is 'deugain' (two twenty) and likewise for 60 and 80. To say ‘70’ is 'deg a thrigain' (ten and three twenty) and likewise for 90, but 50 is 'hanner cant’ (half a hundred) which also does not exist in the decimal system. The vigesimal system is more common when talking about dates and ages etc. and people may switch back-and-forth. There are many internal variations as well, including dropping the prepositions, or adjectival forms.

2299: Hebrew's Alternative Plus Sign: ﬩ Apr 2, 2021

Numbers in modern Hebrew writings, including in math equations, are written left-to-right, even though Hebrew is written right-to-left. This means that math and numerals in general are exactly the same as in Europe for instance, with one exception. The plus-sign, conventionally + for most places, is often written ﬩ as a sort of inverted capital T. This is because historically, the Jews using the symbol wanted to avoid writing something that resembled a Christian cross but even in secular settings now the symbol remains present.

2271: Zwei...Zwene, & Zwo? Mar 5, 2021

The German word for 2, 'zwei' is not declined like a regular adjective in German. Historically, all three grammatical genders were used, including 'zwene' or 'zween' for the masculine which has entirely dropped out, and the feminine 'zwo' which is a variant sometimes used for clarity with 'drei' (three), such as in military radio transmissions. This loss of gender in cardinal numbers is not universal in German with 'eins' (one) declined normally; moreover, Luxembourgish and certain Swiss German dialects still feature variants like 'zwou' and 'zwéin' [Luxembourgish]. It does elucidate the connection to the English 'twain'—also historically the masculine form of 'twā' [feminine]—but in the case of 'twain' this was later used more broadly before certain types of words such as nouns as to disambiguate between it and 'to' or 'too', thus outlasting the general breakdown of English's grammatical gender.

2236: Why Tu BShvat is called 'Tu' Jan 28, 2021

The Jewish holiday of Tu B'Shvat—which just ended if you read this at the time of publication—is named for the date: the 15th of the month of Shvat (שבט‎). 'Tu' (ט״ו) is not a number however though it is seen here and also in the holiday Tu B’Av. Indeed, Hebrew uses a quasi-decimalized numerical system for writing numbers based off the order of the alphabet, as with Greek numerals, but while numbers from ten (י), eleven (יא or 10+1), twelve (יב or 10+2) etc. just go in order that way with addition, 15 and 16 are represented ט״ו‎‎ (9 + 6) and ט״ז‎‎ (9 + 7) as to avoid writing out one of the spellings for a name of Gd. It just so happens טו would be pronounced 'tu', but in normal speech the word would be חמש-עשרה (chamesh-esre).

2203: French Revolutionary Calendar: Months Dec 26, 2020

The French Revolution saw a lot of societal change, including an attempted change of the calendar. Everything was decimalized from the number of days of the week to hours in a day etc. but there were still twelve months. These months fell out on different days but roughly followed the seasons. The names are:

In Autumn: Vendémiaire, Brumaire, and Frimaire

In Winter: Nivôse, Pluviôse, and Ventôse

In Spring: Germinal, Floréal, and Prairial

In Summer: Messidor, Thermidor (or Fervidor*), Fructidor

These were all invented words meant to convey a meaning about the time. In order it would be:

vintage, mist, and frost; snow, rain, and wind; germination flowers and meadow; and harvest, summer-heat, and fruit, which would for the most part be recognizable for French speakers. This system had with it associated with produce, animals, minerals (for the winter) in order to counter the Catholic Church who had associated a saint with each day of the year. Likewise, the years and weeks ('décades') had similar systems of associated things meant to celebrate France and French culture.

2201: farthing Dec 24, 2020

In old British currency a farthing was a fraction of a penny, but also happens to be somewhat related to a 'riding' as in the divisions of land in Yorkshire. This is because one can understand 'farthing' as 'fourth-ing' (i.e. 1/4 of a penny or in other words 1 / 960th of a pound) from the Old English 'fēorðing', and a 'riding' is from 'trithing' (i.e. a third) in Old English. As a point of information, there were different types and subdivisions of a farthing, including 'third farthings' (1/12 of a penny) and 'quarter farthings' (1/16 of penny). Farthings also referred to divisions of land in places like Gloucestershire.

2174: Why Merchants Prefered Roman Numerals Nov 27, 2020

While Arabic numerals eventually won out (or one out, some might say), for most of European history Roman numerals were used. Part of the reason that a few centuries ago Roman numerals were prefered was that the most common need for writing them was not with mathematics per se but with commerce. Merchants prefered to use Roman numerals because they are not so easy to counterfeit because they fall into a particular order, whereas in Arabic numerals someone could just add more digits. Moreover there were actual anti-counterfeit measures built in, such as how the terminal I (representing 1) would be written as a J for instance: XXIIJ (23) so that no one could just add extra digits.

1850: Math in Right-to-Left Scripts Jan 8, 2020

Just as languages written right-to-left present problems for sheet-music, math presents similar challenges. Indeed, while a great deal of math, including 'algebra' and 'Arabic numerals' were originally often right-to-left, Western dominance (and its own version of those numerals) has changed this. So, these days, many cultures will continue to write numbers and equations etc. left-to-right even if it appears in a right-to-left sentence like in Hebrew, whereas in other cultures, especially with Arabic, Persian etc. which have their own numerals and other symbols, they can do both. Generally however, they will use the Western numerals and work left-to-right.

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1747: eleven (and twelve) Sep 26, 2019

The word 'eleven' comes from a root meaning 'one left', or 'one after'. This is not a reference to numerals—that wouldn't make sense anyway—or subtraction, but rather just from an old way of speaking. Most of the numbers follow a base-ten pattern, but 'eleven' from the Old English 'enleofan' (literally "one leaving") follows a more colloquial pattern. Old English kennings were euphemistic idioms made from compounding nouns, so like how "darotha laf" (lit. "spear leavings") connoted 'retreating warriors', the roots for 'eleven' and 'twelve' both just meant "one/two after ten". This is the same for most Germanic languages. There will be more on this tomorrow.

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1668: 2 and ב Jul 9, 2019

While the numerals used in Western society, are from India , there are some links to closer cultures. For instance, many systems use letters, such as Roman numerals or Hebrew numerals. For instance, the second letter in the Hebrew is ב. This historically was used to represent 2, and many believe it also had an influence on the development of the numeral. Although they are called Arabic numerals by some, the Arabic version for 2 is much different: ٢.

Check out the new video that's out today on grammaticality: https://youtu.be/g-6K99Jz9hY

1648: Origin of ∞ Jun 19, 20109

The infinity symbol ∞ may appear to have been chosen as it loops, and therefore doesn't have an end, but this wouldn't be the full story. The first time it was published in math was 1655 by John Wallis, though it was used in Christian symbolism long before then. There are a number of theories as to why ∞ came to be, including that it looks like the Greek letter ω—the final letter in the alphabet—and that it looks like the Roman numeral for 1,000 (i.e. many), which is now thought of as an M, but in the medieval period was written curved almost like a sideways Theta θ, or even just CIƆ. In the former case, ω is used for certain sets in set-theory, and many cultures have used big numbers to signify 'countless' (like 'myriad') so both theories are sensible really.

See more about symbols of infinity here.

1493: Thai Numerals Jan 13, 2019

Thai, like many other East Asian languages has its own writing system, but unlike many other writing systems all over the world that do not have distinct symbols for numerals, the Thai system does. The numerals follow a base-ten system with the Arabic numerals, but this should not be surprising since they both followed from the same Hindu origins. However, while not represented in the numeration, the name for the number 1, nèung, changes to become èt when it is at the end of other numbers, like 11, or sìp èt (literally: ten-one).

0: ๐
1:๑
2:๒
3: ๓
4: ๔
5: ๕
6: ๖
7: ๗
8: ๘
9: ๙

931: Number-Arrangement Jun 27, 2017

Above the number twelve, all numbers in English are a combination of different numbers raised to multiples of ten, e.g. four-hundred-thirty is four times ten raised to the power of two, plus three times ten raised to the power of one. Almost all numbers in English are said with the highest place first, and then all smaller values next. The exception to this is with the -teens: thirteen through nineteen. While those terms no longer contain the word 'ten', the ending '-teen' used to be just that, so fourteen would be, in essence, like 'four-ten'; notably however 'forty' would as well. This style of forming cardinal numbers, by putting the number in the ones place first, is increasingly rare in Modern English, but in Old English and Middle English it was quite common, or even standard to form number like this, such as the line in Chaucer's Canterbury Tales: "Wel nyne and twenty in a compaignye" ("Some nine and twenty in a company") meaning 'twenty-nine' as we would say now. In German, and plenty of other languages, this is still the way that numbers are formed, such as "ninety-nine balloons" which is "neunundneunzig luftballons" (a famous song released in 1983), literally "nine and ninety".

899: Greek Numerals May 25, 2017

In many countries people write numbers using Arabic numerals, though these are poorly named as they come from India, and in the Middle East today very few of their numerals look the same; e.g. 2, 3, and 4 appear as ٢,٣, and ٤ respectively. There are many more systems of writing numbers out there, but in the West there tend to only be two used commonly, including the Arabic numerals of course, and Roman numerals. The latter use letters—I, V, X, L, C, D, and M—to express numbers, similar to many other systems. The Greek numerals, though less common than their Roman counterpart today, also use alphabetical letters to represent numbers. Some on the Roman system was somewhat arbitrary, such as V and L for fifty when the Latin word for both starts with a Q, but Greek numerals represented 1-10 with the first ten letters of their alphabet, and 20-90 (going up by tens) is represented by the 11th through 18th letter, and hundreds are represented by the 19th through 27th letter (including the archaic sampi).

878: Anumberic languages May 4, 2017

People who are brought up in cultures that use numberless languages such as the Manduruku in Amazonia have a comparatively more difficult time observing and recalling quantities greater than even three. According to the Sapir-Whorf hypothesis, which in its strong form tries to explain that one's native language determines the way one thinks and is able to interpret the world, these anumeric languages would merely be an example that not having numbers such as 'one' 'two' 'three', and instead using words equivalent to 'some' or 'many' results in that speaker's inability to comprehend these concepts. While it may seem reasonable on the surface, the issue is not simply linguistic in its nature. For anyone, regardless of one's first language, learning to count numbers requires a great deal of time and energy and aside from recognizing two quantities as different in size, almost nothing is innate about numbers which can take years to comprehend. Anyone has the ability to learn these same skills irrespective of mother-tongue. Historically too, the precise numbers in which people in industrialized cultures may often interpret the world were far less important, and were comparatively little-used.

For more on how aspects of Amazonian languages can seem completely different from more familiar ones, click here.

845: Long Hundred Apr 1, 2017

Not all cultures use a base-10 system for mathematics. Some peoples have used 20 as their base for counting, and some have used 12, which is not too hard to believe considering there are separate words for eleven and twelve before getting into the -teens, not to mention that there are twelve inches in a foot and twelve sections on a clock. While that same distinction for 'eleven' and 'twelve' exists in Romance languages, the Romans counted in base-10, as can be seen with Roman numerals, and the word 'digit'. Therefore, when they encountered northern Germanic tribes, they translated what is now 'hundred' as 'centum' (100) without taking into account that the Germanic 'hundred' was equivalent to 120. To avoid this confusion between these hundreds, people now use the term 'long hundred' for the Germanic one. Therefore, when the Icelandic historian, Snorri Sturluson wrote about the size of the peasant army that fought King Olaf II in AD 1030 as 'one hundred hundred', this would be 14,400 and not 10,000.

It should be noted that while a 'long hundred' equals 120, a UK 'long hundredweight' is equivalent to 112 lb avoirdupois.

838: digit Mar 25, 2017

It is not clear necessarily whether when someone says, 'digit' if that refers to fingers or numbers, unless maybe you are having a conversation with a mathematician or a surgeon. This similarity is not coincidental, though the connection to numbers specifically occurred later. This term comes from the Latin noun, 'digitus' meaning either ‘finger' or 'toe’. The sense of the word as a number from 0 to 9 (or 10) came about due to the practice of counting on the fingers. Not all cultures use a base-ten system of counting, but those that did relied on the number of digits making the association very strong. Fingers also are, among many other things, used for pointing; indeed another term for forefinger or index finger is 'pointer finger'. Unsurprisingly then, the term 'diction' in the sense of telling or showing is related to 'digit'.

678: second Oct 16, 2016

For most words, there is a reason that people use them, especially if the word can mean more than one idea. A second is called such because it is the third division of periods of time within a day...sort of. The first is a division of the day into two sets of twelve hours, which was devised at least a few thousand years ago. The Greeks took this originally Egyptian model, defined the hours more precisely, and then divided that further into minutes and seconds, more or less as we know them today. The term 'second' comes in because it is the second sexagesimal division: a sixtieth of a sixtieth of an hour. 'Minute' also comes from the concept of division, as it comes from the Latin for 'lessen'. For more on 'minute', see this post.