What is the Origin of Reading Tens from Right to Left?

Question

Latin languages, as well as English, speak numbers from left to right, in the same direction in which they are written, e.g. forty-two, quarante-deux, but in German, you write from left to right but speak numbers from right to left, in the opposite direction, e.g. zweiundvierzig "two-and-forty". What is the origin of this way of speaking numbers?

Answer 1

The question, why German numbers are "backwards" is naive in many ways.

Spoken language was in existence before written language. Many numerals existing today were created long before reading was practised, so if there is any direction in a language at all, German does not "read" "backwards", it speaks "backwards".

But then, very likely numerals are not named with regard to direction at all, but for the logic behind counting. In Breton, the number eighteen has the name tri-ouch "three (times) six" – I cannot discern any direction in this numeral. In Finnish, eighteen is called kah-deksan-toista "two (from) ten (in the) second (ten)". The logic seems to be to view the decades and then say how far into which decade we are. Again, there is no reading direction implied in the number name. Similar to this Finnish logic, Old Norse used a counting system not based on tens, but on dozens and multiples of the divisors of twelve (e.g. 60 = "Schock" in German). "364 days" in Old Norse is fiora dagar ens fiortha hundraths "four days into the fourth hundred (= 120)". (Please note that "hundred" once meant 120.) I don't claim to understand the logic behind "einundzwanzig", but the question might be to understand the thinking behind numerals and find out about historic counting systems, not about reading direction.

In Old English, a language descended from Germanic dialects, numerals where "backwards", too: fēowertīene "four-teen", ān and twentiġ "one and twenty" etc., and you can still find remnants of an old vigesimal (base 20) counting system, e.g. "score" for 20.

There are many more languages that speak or read (some of) their numbers "backwards", among them Greek, Latin (both directions possible), Celtic languages etc., and of course languages that actually read right to left like Arabic, where our written numbers come from. The question could be rephrased as: Why does English read their numbers in the wrong direction? Because obviously the "backwards" way is older and may even be more widespread (there are thousands of languages and we don't know how they count; why should English be the norm from which to judge numerals?).

Our current number symbols were brought into Western culture from India, via Arabia. They reached Italy in 1200, Germany in 1500. In the 1500s, when the first books on mathematics appeared in German, there was some argument among scholars, if the number names should be adapted to the direction of writing and reading. Luther, whose Bible translation was the basis for the creation of a common German language (prior to Luther, there was no High German only a number of mutually hard to understand German dialects), decided to retain the traditional number names (i.e. "backwards"), contrary to other authors who proposed "zwanzigeins", in accordance with the writing direction of the new numbers.

^{Reference for the last paragraph: "Warum wir Zahlen von hinten nach vorne lesen und warum das nicht so bleiben muss", in: Gerritzen, Hauenschild, KIimmeskamp, Voigt (Eds.), Zwanzigeins, Bochum: 2008, Brockmeyer, and there the section "Das Stellenwertsystem und Jakob Köbel" on pages 23 and 24. (view on Google Books)}

Answer 2

I'm pretty sure it has something to do with the history of numbers and their use in language.

In older English texts, you'll find a lot of numbers reversed in the same way as German numbers: the best known example being "four and twenty blackbirds". Verein zwanzigeins points out that English switched to using "twenty four" instead of "four and twenty" in the 16th century.

I suspect that when people started using decimal places, it wasn't immediately obvious that the most significant digit should be stated first, in newspaper-article "most important facts first" fashion.

It's also worth pointing out that we write numbers "backwards" with respect to Arabic: that is, in Arabic, numbers are written (right to left) with the least significant digit first: so 152 was originally written right-to-left as "two and five tens and one hundred".

I suspect Arabic numbers were not reversed for left-to-right languages more to avoid confusion as to which direction a number was written in, rather than any particular logic, so the fact that left-to-right languages put the most significant digit first is more of an accident than something that happened by design.

Of course, English speakers eventually decided that in speech, we should consistently put the most significant digit first (and this is also done in modern spoken Arabic with no strange reversals as in German).

If I were to venture a guess myself as to why German hasn't made the same transition, I'd guess it's because numbers like 25 are compound nouns in German: one writes "fünfundzwanzig" and says "fünfunzwanzig", not "fünf und zwanzig", so they're in a sense similar to the numbers 13-19, it's better to think of each of them as a single entity, not a sequence of two numbers.

That said, as someone who for several years frequently reversed the last two digits of telephone numbers as a result of studying German, I certainly wouldn't mind if Verein zwanzigeins succeeded in their crusade to modernize German numbers. It should be possible, given that Norwegian underwent a similar reform in the 1950s.

Answer 3

English used to have the "ones" number come first; "four and twenty blackbirds baked in a pie." Not to mention in 13, 14, 15, etc.

So it was ENGLISH that reversed the order and put the 10s number before the ones number, probably because England was a more commercially sophisticated country, earlier.

German is not "backward" in this regard.

Answer 4

Language is a living beast. It changes over time. It's not always logical. It's not always consistent. Sometimes historical concepts hang on, although they no longer seem to make sense now. Take English spelling and pronunciation, for example. Tough stuff.

Conventions about reading out numbers aloud are along the same lines. The numerical concepts are in your head. The language just gives voice to them, but does not change the maths.

two-and-forty or forty-two are exactly the same.

Just speculating now, but maybe the concept or "zwei-und-vierzig" evolved when people were not very veered with numbers and maths and had to use their fingers to keep track of where they were. Tens in one hand and ones in the other (yes, you can do 10 numbers with just one hand. It's easy. Ping me for details). So, in one region it got common to say "fourty-(and)-two" and in another region it got common to say "two-and-forty". Same difference.

Language is not an exact science.

Answer 5

Another point I'd like to add is: Where do numbers come from?

I think it can be argued that the first usage of numbers in languages in general (before the time of German or even Germanic) would be counting, for example counting your children, your sheep, how many apples you picked and so on.

In counting, the obvious increment is 1, and the most important part of the number you're currently at is not the 10, but the 1, because the 10 is staying the same for quite a while. Then you can count like:

ein(undzwanzig), zwei(undzwanzig), drei(undzwanzig),...

putting the stress on the first syllable and mumbling the rest. That is maybe also why these systems seem to change from top to bottom, i.e. starting at the large numbers and still not being complete for the small ones (one-and-twenty still being in use in the 18th century, and sixteen up until today).

From this it is also clear why this system never made it into the larger numbers: Who seriously wants to count to 238?

Answer 6

Why a new answer to an eight years old question which has already received excellent answers? One point has not really been addressed so far. Quote from the question:

Latin languages, as well as English, speak numbers from left to right, in the same direction in which they are written, e.g. forty-two, quarante-deux, but in German, you write from left to right but speak numbers from right to left, in the opposite direction.

Expressed pointedly, this suggest that spoken German reverses the correct order of digits. The accepted answer rightly says that

Spoken language was in existence before written language. Many numerals existing today were created long before reading was practised, so if there is any direction in a language at all, German does not "read" "backwards", it speaks "backwards".

My point is to discuss the tacit assumption that there is a natural (or if you want: correct) order of digits. In fact, writing numbers as we do it has become a global standard, but is has nothing to do with the (European) way of writing from left to right:

1. Latin is written from left to right, but Roman numbers have a fairly weird structure (I, II, III, IV, V, VI, .., XCII, ..., CXXI, ...). Nevertheless they have succesfully been in use for centuries, although it is annoying to perform elementary algebraic operations like addition and multiplication. This shows that written and spoken numbers may significantly differ.

2. Arabic script is written from right to left. Numbers are nevertheless written exactly as we do (of course with Arabic numeral symbols), for example 13 = ١٣, 19 = ١٩. From 11 - 99 they are spoken in the form 11 = one and ten, 56 = six and fifty etc. Thus, for two digit numbers, this corresponds to the Arabic reading direction. Bigger numbers are spoken in the form 382 = three hundred and two and thirty. See here. This is very similar to German.

Our modern numeral system (the Hindu–Arabic system) is a positional numeral system in which the contribution of the digit at position n from the right to the value of the number is the product of the value of the digit by the (n-1)-st power of 10. For example, 2614 means 4 x 1 + 1 x 10 + 6 x 100 + 2 x 1000. This is just a convention, but writing numbers with this system means that we must arrange the digits in the "correct order" which has mathematical, not linguistic, reasons. But there is no compelling necessity to use a positional numeral system for writing, as the Romans have proved. Anyway, each numeral system must have clear conventions and once people know them, numbers will be correctly understood in written and spoken form. These conventions may differ in writing and speaking, and German has certainly other rules for speaking than English, French etc. But native speakers do not have a problem with that, communication works.

The introduction of the Hindu–Arabic system has of course been a success story. However, they reached Europe fairly late which in my opinion proves that speaking and writing are decoupled. Quote from Wikipedia:

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976. From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe.

The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396, in England, a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral. In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456. By the mid-16th century, they were in common use in most of Europe. Roman numerals remained in use mostly for the notation of anno Domini years, and for numbers on clockfaces.

Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.

Let me close with a remark concerning the "correct direction" of writing and speaking Arabic numbers. We do it from left to right, and this seems to be natural because we write anything from left to right. But if you think about it, it appears not that logical: The contribution of a digit (value of the digit times a power of 10) is determined by its position read from right to left, i.e. in the opposite direction. This is nothing else than a convention. I think one could very well argue that writing numbers in the opposite direction (for example 314 instead of our familiar 413) would be more favorable because the power of 10 which gives the value of a digit agrees with its position in the "new" writing direction. One could of course believe that the reason for writing numbers as we do is that the digit at position 1 from the left makes the biggest contribution, i.e. is most important in a sense. However, the simple reason is that they have been imported from Arabic script without changing the order of digits. For example, the number ١٣٢٩ got the form 1329. See 2. above. By the way, a punch line is that Arabic numbers have been imported from India to Arabia - and in Sanskrit the writing and reading direction is from left to right as in European languages. It seems that the import of numbers twice happened without changing the order of the digits in the foreign source - although the writing direction as such is the opposite.

Our way of writing and reading numbers causes a problem: You must first determine how many digits your number has before you can begin to speak. If the number has only a few digits, you see that at first glance as e.g. for 1045, but if it is a big number, this is not easy as e.g. for 473078977440658967, even if digit grouping like 473,078,977,440,658,967 is used. By the way, digit grouping is used when speaking - for example 96,102,239 is 96 million, 102 thousand, 239. The "big number problem" indicates that speaking numbers in the other direction from right to left would in a sense be easier, for example 58967 = "seven - sixty - nine houndred - eight thousand - fifty thousand" or perhaps using digit grouping from right to left. Morever, it would be consistent with the ascending values of the powers of 10 from right to left.

Conclusion:

Do not believe that there is a perfect logical approach to writing and speaking numbers. But admittedly the English way of speaking is more compelling than the German (if we put aside the numbers 11 - 19).

Answer 7

Indeed, good question ;) As long we only switched the spelling of the 10 and 1 series (zweiundvierzig) but not the hundred and thousands (2100 => zweitausend einhundert) I expect it is related to the Arabic and somewhere in the past, it was adapted the wrong way?!

Unless you are really familiar with the way words and numbers are written in the Arabic language, it is very likely you would read the numbers backwards because when writing in this language you write from right to left.

…

In addition to reversing the numbers to form numbers from 21 - 99, when you read these numbers you inset the word "wa" between the numbers. Wa means and in Arabic to when reading 53, which actually looks like 35, you would say three and fifty.

http://www.articlesbase.com/languages-articles/the-difference-between-english-and-arabic-numbers-599461.html

Answer 8

Well for sure, language is a quite terrible mixture of history, logic, and custom. As a native English speaker living in German for over 10 years, I can express my constant issues with the Germanic approach. Clearly this is not 'wrong' but I can tell you that the technique adopted by your own mother tongue is incredibly deeply ingrained. I have lost count (please excuse the pun) of how many times I counted out coins to pay, and reversed the digits I hear spoken, counting out the wrong amount. It makes you look and feel stupid and it is almost impossible to overcome. I'm quite sure that two very different parts of the brain are involved in language interpretation and mathematical manipulation. So it would seem, from a historical perspective, English has a mixture of 3 different mechanisms in our phonology. The first, (11 & 12) are very old, coming from old norse, meaning 'left over'. (11) 1 left over after taking away 10, and (12) 2 'left over' after taking away 10. Then secondly, from 13-19 we have a more typical germanic root, with the least significant digit expressed first. eg (13) 'thir' from three, and 'teen' from ten and so on until 19. Third and finally, from 20 onwards English has adopted a more modern and clearly logical expressive style that reflects how we write the numerical form mathematically. Indeed this continues past 100 and onwards across the entire scale of numbers. I would advocate that this was influenced by the need to integrate the interpretation of numerical writing with phonological compounds. Having said this and because of my own first hand experience of speaking German daily, I can understand why any such accepted structure contrary to the logical approach is so difficult to remove from a language. If English where to be truly logical we would replace (11-19) with a similar structure to the higher numbers for example, we might say, "tenone, tentwo, tenthree, tenfour" etc. But as we all know English is also not prefect. Maybe I will try it and see what happens :) "From little acorns great oaks grow"

Answer 9

Note that this different order between German and English pertains only to the last two digits:

One thousand three hundred and twenty four
1   000      3     00       +  4      20

Ein tausend  drei  Hundert     vier und zwanzig.
1   000      3     00          4    +   20

Roman numeric digits are also not always ordered from largest to smallest:

XI  = 11 = 10+1
XV  = 15 = 10+5 but
XIV = 14 = 10 + (5 - 1).

Answer 10

There's a nice German TV episode about that question: https://youtube.com/watch?v=L5YZSZTO2tk

Answer 11

Quite simply, if you calculate a small number while speaking, you come up with the least significant digit first, if you are using the now common place system addition (whatever it is called). I don't know if this had been known in ancient times, but it is implied.

Given the coincidence with the Arabic system, the question must correctly be, why do they write the least significant cypher first, and the logic behind counting (as per the top answer), would be the most logical explanation. The exact method that was used to calculate the numbers is probably besides the point.