2.4.2 - Origin of the -illion Series
2.4.2
Origin & Development of the -illion Series
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Introduction
While humans have undoubtably always been both awed and terrified by large numbers, it seems rarely did it find such speculations practical. Most early notation systems for numbers involved using symbols to represent specific quantities rather than using a place valued system ( the one interesting exception is the sumerians, one of the earliest known civilizations existing some 7000 years ago who were the first to use a place valued notational system). Usually the symbols would represent various powers of 10. Common examples would include the egyptians who used a set of glyphs , and the roman numerals. However there was never symbols used for groups larger than a million.
The Egyptians had unique glyphs for ones , tens , hundreds , thousands, ten thousands , hundred thousands, and millions, but nothing higher. The Roman numerials for example use I,V,X,L,C,D,M to represent 1,5,10,50,100,500, and 1000 respectively. After this however there are no official numerials, although I've heard that they used a bar over the numerials to multiply them a thousand fold ( for for example V with a bar would be 5x1000 = 5000). So the largest numeral would then be M with a bar representing a million.
It may not be too surprising that very large numbers didn't serve much purpose to early civilizations, but it turns out that terminology for large numbers met with some resistence even in later times.
The Million
The modern word "Thousand" actually is a middle english word. Middle English as a spoken language dates from 1066 to 1470 AD. One could therefore reason that the word "Thousand" could not have been spoken before 1066. The word , not surprisingly, has roots in older words however. It is an altered version of the old english "Thusend". In any case, there has probably been a word for "Thousand" in almost every culture and language for the last few millenia.
A word for "million" is far less common. People in the 11th through 15th century were perfectly content to use the term "Thousand thousand" in place of million. It was not as if this term would pop up that often anyway.
The term "million" doesn't seem to exist at any time before the 13th century (1200's). Apparently it is an augmented form of the latin word "mille" meaning thousand. By dropping the e and adding the -ion as a suffix one could translate "million" as literally "Great thousand". It is not known who first coined this term. It was used sparingly in the centuries to follow and was sometimes regarded as a kind of slang and not legimate language ( perhaps much the same way neolisms today are regarded as unofficial ), and writers more often than not prefered the non-ambiguous "thousand thousand".
It's usage, if not mainstream, might have at least been fairly well known by the 15th century. It is in this century that the first -illion series was born.
Byllion , Tryllion , Quadrillion ...
Around 1484 a french mathematician named Nicolas Chuquet (1445-1488) coined a series of extensions of the "million" nomenclature. By using the latin prefixes he coined ,
byllion , tryllion , quadrillion , quyillion , sixillion , septyllion , ottyllion, and nonyllion
Originally these were intended to be powers of a million. For example a byllion, would be a "million million", a Tryllion would be a "million million million" and so on.
In retrospect this does seem quite sensible. Chuquet would have then used these terms to represent these powers of 10 ...
Nicolas Chuquet's Original -illion Series
Chuquet originally used a notation where he seperated groups of 6 digits using apostrophes.
Thus he would write a million as 1'000000, a byllion as 1'000000'000000, a tryllion as 1'000000'000000'000000, a quadrillion as 1'000000'000000'000000'000000, and so on.
Although he coined them in 1484 he did not publish them at the time. They first appeared in print in 1520 in a book by Emile de la Roche. At the time however they were little more than a curiousity and of little practical use. Meanwhile the term "million" began to catch on throughout the european territories with only a few countries reluctant to adopt it. Ironically the new terms faced a similiar road block; rather than say billion people were content to speak of a "million million".
During the 16th Century (1500's) another enhancement was made to this system. Jacques Pelletier du Mans proposed filling the odd powers of a thousand with his own series of terms. Note that Chuquet's system does not provide unique names for a "thousand million" (10^9), a "thousand byllion" (10^15), a "thousand tryllion" (10^21), etc. Pelletier suggested using "milliard" for "thousand million", "billiard" for "thousand billion",etc. In general he suggested using "X-illiard" in place of "thousand X-illion".
Pelletier's system using modern terms would then be as follows...
Jacques Pelletier du Mans -illion/-illiard series
Great! We now have a convientient system to name numbers up to nonilliards.Things get alittle messy at this point however. In the middle of the 17th century (1600's) some french scientists started to use Chuquets terms to signify successive powers of a thousand instead of a million. Thus a billion was a "thousand million", a trillion was a "thousand billion" and so on. Pelletier's terms were consequently dropped in this system.
17th Century Usage
Oddly this system spread and would eventually be inherited by the United states. If you were raised in the US than this is the system you would have been taught. This system didn't slip by without critism though. Many critized the "french version" as
"an entire perversion of the original nomenclature of Chuquet and de la Roche" -- Murray
Ironically this "perversion" would also become fairly prevalent do in part to the influence of the United States in world politics. The original nomenclature still exists however in a number of european countries most notably britian, and spain.
While we might agree that using powers of millions is more logical from a languistic point of view, it is somewhat impractical for the purposes of measuring. In the modern world millions, billions, and trillions, come up fairly often, but very rarely is there a need in commerce for a quadrillion of anything let alone anything higher. Using the original chuquet nomenclature that means we would only really have use for the terms million and billion (meaning million million here ). Also there would be no denomination for 10^9. It's true that Pelletier mitigated this problem, however alternating between suffixes is not the most efficient way to create a naming system because you then need to take the suffix and prefix into consideration. Perhaps the french use was not a mistake but an attempt to make the terms more useful.
None the less, by the 17th century (1600's) the usage of milliard and the Chuquet/Pelletier system had become prevalent in Holland and many other european countries.
Here is a table with a term by term comparison of the two systems. The Chuquet system is usually refered to as the "Short Scale", and the later one used by the french scientists the "Long Scale".
Comparing the Short and Long Scale Systems.
As you can see the british system supplies about twice as many denominations. One could argue that this system conserves nomenclature, and so in the long run is a more "efficient" use of terms. However as pointed out earlier, this is kind of a moot point, because only the first 3 terms are of any day-to-day use. It's therefore irrelevant to consider the systems range.
Today the "US system" is refered to simply as the "short scale", and the traditionally "British system" is refered to as the "long scale". These labels are less ambiguous because the usage of the two systems changes over time in the various countries across the world.
Historically the "long scale" was more dominant, and only a few countries used the clunky short scale, such as france, and the US. It's sort of like how the US has hung on stubbornly to feet and inches, when most of the world has converted to metric.
But in more recent history the "short scale" is more and more becoming the international nomenclature, so much so that britian now is beginning to use it more than their more traditional "long scale". The role the US plays in world economics probably plays a large part in why this conversion is occuring.
This being said, none the less, the use of two systems world wide still leads to a certain degree of ambiguity in international documents, for example when billion is used, do they mean 10^9 like in the US, or 10^12 ?
As a kid I learned the short scale, and so it is kind of ingrained in me. However I can appreciate the sensibility of the long scale. It would seem logical that the world should have one way to assign number names, yet which system deserves international recognition ?
I will return to this dilemma later, and offer some solutions proposed by others as well as my own solution.
But for now I will continue my story of the development of the -illion system. From here on I will be exclusively using the "short scale" so that a billion is 10^9 , a trillion is 10^12 , etc.
The Modern Canonical -illions
Later others took on the challenge of extending Chuquets nomenclature. Chuquet in fact encouraged such an extension because he suggested that one could use the latin prefixes to continue "as far as one wished". In fact, this is what was actually done. Sometime in the 19th Century ( around 1847) the system under went further extension. Using the latin number names one could resonably follow nonillion (10^30) , with decillion (10^33), since deci- is the latin prefix for 10.
Modern dictionaries consider the following illions canon ...
Modern Canonical -illions
The illions end at vigintillion, but oddly these same dictionaries also coin a Centillion as 10^303, making it the hundredth illion in the series. These are the only "officially" recognized illions. There are NO official -illions between a vigintillion and a centillion. It may seem strange that there is such a wide gap between them, but that's the way it is.
I had first learned of all of these -illions as a kid, because they were listed under the entry "number" in the ninth edition websters dictionary in my home. I was quick to study all of them and memorize them, and probably was the only kid in my class who knew the entire series from a trillion all the way up to a vigintillion. But even as a kid, the huge gap bothered me. In fact the very first thing I did as part of my large numbers project was to fill in this gap with a series of illions of my own invention. We'll be discussing filling in the gap alittle later in this chapter.
Other than the 21 illions mentioned, no other illions are officially recognized. However, a casual search on the web will reveal a wealth of illion numbers. Some of these are legitimate attempts to create an extended and logical illion system, others mascarade as numbers when in fact they are fake, and some are just for fun with no specific magnitude. There are also many erroneous illions which are none the less well defined, if awkward and convoluted.
As we shall see, the numbers that they represent are no less real than numbers represented by the canonical illions. The issue here to me seems to be a matter of usage. Such terms are of such rare and impractical use, that it is difficult for a definitive nomenclature to emerge.
We will be going over many of these systems, and also calling out the counterfeits. As you will see, the gap has more or less been filled in a reasonable way and there is already a regular and widely accepted system which serves to name many hundreds of seemingly legitimate illions.
In the next article we will talk about some of the illegimate -illions that started to crop in the 20th century in response to the ridiculous extension of the -illions up to vigintillion....
Next : Zillions, Bazillions, Gazillions, ...
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