# Order of spoken numbers with respect to powers of the base of the numerical system

I am interested in the history of how numbers were spoken with respect to hundreds, tens, unities... (or more generally powers of a base if the systems is not decimal). To clarify, here is an example: in English, we say twenty one and, accordingly, write it 21, but there seems to be an older structure in numbers like sixteen, which we write 16 for mathematical consistency, but speak in the opposite order: 'six and ten'. Since this happens only for small numbers (less than twenty), I think it may be the way numbers were originally spoken and after the introduction of numerical systems the way bigger numbers were spoken was inverted. Also, since the positional number system as we use today comes from Arabic (an ultimately from Hindu) and they write in the opposite direction, I would also like to know how they speak their numbers, if they say the unities before and tens last, or the other way around, as in English or Portuguese.

• It's not likely there was a single "way numbers were originally spoken" -- the answer will vary from language to language.
– TKR
Commented Jul 30, 2020 at 20:43
• Yes, I guess so, though that's not clear in my question. I am more interested in Latin, in fact, since I speak Portuguese, but also in English. Commented Jul 30, 2020 at 20:57
• Uttering numbers like "539" is fairly uncommon in human experience, and it is very difficult to identify "native" patterns (big-endian vs. little-endian) free of the influence of educational systems and the pattern of the dominant language. Commented Jul 30, 2020 at 20:58
• Some few languages don't have numbers. As to where they come from, "one" usually comes from an article or pronoun of some kind, "two" is a weird word in many ways, and from 3 to 10 there are usually unique names. From 10 to 20 there is a simple system, and from 20 on there is a different system. Considering that 20 is a lot, of anything, the first two decades make up almost all the numbers any human needed often for about a million years. The rest is modern technology by comparison. Commented Jul 30, 2020 at 20:59
• @jlawler that is what I'm interested in, "small" numbers, from 1 to 20 or so. Is there any study of how these were in, say, proto-indo-european or something like that? Commented Jul 30, 2020 at 21:05

An example of how the spoken numerals influenced the way they were written numerically is the Slavic languages and their Cyrillic alphabet. Since Cyrillic is derived from the Greek alphabet, it also inherited the Greek tradition of writing numbers with letters, isopsephy (gematria), which dates back to Euclid, about 300 BC. The first 9 letters were assigned the numeric values of 1 to 9, the next 9 letters meant tens, 10 – 90, the next nine letters meant hundreds, 100 – 900. 9 × 3 = 27, but the Greek alphabet had only 24 letters, so 3 old letters which had already been abandoned for writing words were kept to be used when writing numerals with letters. The principle was simple: the higher orders first, so, for example, 666 was written as χξϛ (600 + 60 + 6). Also, a horizontal line was drawn above the letters used as numbers to tell them from letters used in their usual way to mean sounds. Unfortunately, I cannot reproduce the horizontal line on this site, but in the above link Wiki shows the way it looked like:

The Slavic languages have more phonemes than Greek, the original Cyrillic alphabet had 43 letters, so all the orders had their corresponding letters, 16 letters remained without any numeric value ascribed. The Cyrillic numbers had a special diacritic above them called титло (titlo) which descends from the Greek horizontal line over the numerical letters:

In the Slavic languages of the 9th century AD when Cyrillic appeared and all the way until now the numbers from 11 to 19 are formed according to the model “n + on ten”: modern Russian for 11 is одиннадцать (один-на-дцать) “one on ten”, 13 is тринадцать (три-на-дцать) “three on ten”, etc. As you can see, the principle is practically the same as in English with the numerals 13 to 19, that is, a lower order followed by a higher one, which goes against the Greek tradition of writing the higher orders first. Although in the Greek language numerals 11 to 19 are also formed as n + ten, Greeks wrote the corresponding number according to the numerical logic, 10 + n, e. g. 11 was ια, 10 + 1. The Slavs, however, did not agree with that obvious contradiction of mathematical logic versus natural language, and since the earliest times and all the way until now (in church books and in linguistic research papers) whenever a number from 11 to 19 is written in letters, in Cyrillic it is “n + 10”:

• The Greek use of the letters of the alphabet as numbers is attested from about 450 BC, before the time of Euclid.
– fdb
Commented Jul 31, 2020 at 9:37
• @fdb - Do you mean that the difference between "about 450 BC" and "about 300 BC" is substantial and important for the topic discussed? Commented Jul 31, 2020 at 15:40

I don't know how it was in Latin, but English used to work like German. In German you say the units before the tens. For example 24 is vier-und-zwanzig (four-and-twenty).

• Five and twenty continued in English very recently, at least for some speakers in some contexts. I had a friend thirty years ago who regularly used that form in telling the time. Commented Sep 8, 2021 at 15:47