Talk:Names of large numbers

"It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance." WTF? Is it just me or is this completely weird? --Dyss 19:45, 4 Sep 2004 (UTC)

• I think it's true. It is a fact that the terms "googol" and "googolplex" were invented by a nine-year-old, and I'm pretty sure this anecdote comes from the writings of his mathematician uncle. (Independent verification would be nice, though, just in case.) --Ardonik.talk() 19:50, Sep 4, 2004 (UTC)

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Comment. I'm now actively tinkering with this page, but there's a lot of work to be done, including fact-checking, since a lot of loose statements found in various place on the Web and in Wikipedia about Nicolas Chuquet, etc. don't seem to be exactly right. I've moved Very large numbers to Names of large numbers, which I think is where it should go.

I think it's time to draw a distinction between large numbers themselves and the art/science/game/history of naming them. The list I added to Large number I have now copied to Names of large numbers#Dictionary numbers, and improved (but I have not yet removed it from Large number).

It turns out that Chuquet did not exactly invent billion, trillion, quadrillion and friends. First of all, he spelled them with a y, byllion, tryllion, quadryllion etc, so Knuth collides with Chuquet's namespace. Second, one Jehan Adam used them before Chuquet did. Third, neither Adam nor Chuquet claimed authorship, and apparently the context of their references to the names suggests they were in use earlier. Fourth, Chuquet's work remained unpublished for a very long time, so he didn't directly influence anyone. In other words, the whole topic is a maze of twisty little trivia, all of them hard to pin down.

I'm going to keep nibbling away at it but I could certainly use help.

Meanwhile, anyone who want to add names to this page by all means do so but please document who coined them, where, and when and whether they've received any acceptance. Dpbsmith 02:30, 31 May 2004 (UTC)

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Old VfD discussion can be found here. The listing was removed early because the proposal was withdrawn and there was a strong consensus to keep the page. Guanaco 23:56, 30 May 2004 (UTC)

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Contents

1 Work in progress 2 How silly do these names look?? 3 Google searches 3.1 Think about this system:should it be added?...or other stuff dropped? 4 What did Chuquet really propose? 5 Are billiards, trilliards, quadrilliards, etc. real? 6 Really large numbers 6.1 Layers of exponentiation are problematic 7 Table from List of numbers 8 Billiard, trilliard, quadrilliard are not "standard dictionary numbers" 9 For fanciful extensions, use Other names of large numbers 10 The system behind the madness 11 Authorities in the table

Work in progress

This page is a work in progress. I think the column headings in the section on "extensions of the dictionary numbers" are wrong. The three columns probably reflect American, British, and European usage circa 1950, but I'm not so sure they reflect current usage. And I don't think the names "Chuquet," "Modified Chuquet" and "Pelletier" are quite right. I doubt that Chuquet has any association whatever with the thousands-based system. Oddly enough, it does as if the British millions-based names and the American thousands-based names were both adopted from French usage, but at different times.

"Milliard" is certainly a real word, but does anyone have good authority for actual usage -iard endings of higher powers? What do modern French dictionaries have to say?

I don't really know what to make of the "Chuquet-ized numbering" table. I don't have any problem with documenting coinages, but we have to say where the coinages came from. Dpbsmith 20:20, 31 May 2004 (UTC)

How silly do these names look??

Do the names of these extremely gigantic numbers look silly at all to any of you?? 66.32.93.148 20:24, 1 Jun 2004 (UTC)

Yes. They do. If in a month or so there aren't some decent notes about where those names came from and why they are any more encyclopedic than "bajillion kabillion skillion," I'll probably delete the later sections. There's even worse online at http://michaelhalm.tripod.com/mathematics_beyond_the_googol.htm Dpbsmith 20:39, 1 Jun 2004 (UTC)

Google searches

The smallest name that Google shows fewer than 1000 hits for is undecillion. 66.32.147.233 23:48, 3 Jun 2004 (UTC)

Think about this system:should it be added?...or other stuff dropped?

Whooo...this article has changed since I last looked at it,I'm familiar with a number of large-number webpages (Susan Stepney's,Robert Munafo's,etc.) but not some of the stuff here.

I have a system of large-number nomenclature I've been working on myself since the 1980s,and it seems likely to have as much provenance as some of the stuff in the last section...which confusingly uses some of the same names I use for different numbers.I'm not sure my system belongs in here OR that some of the curio stuff does...I'm open to discussion.

It's based on powers of a million,allied with SI prefixes in some cases.As in Chuquet-Pelletier,the intervening thousand-multiples are -iard rather than -ion. The thousandth power of a million is a kilillion (Ondrejka's "millillion",he used Latin rather than mixing Greek),the millionth power of a million a megillion (Ondrejka's milli-millillion),and a million raised to a milliard is a gigillion (Ondrejka called this a "milli-millimillillion" and this name is listed in the Guinness Book of World Records editions of the 1970s as the highest name for a number found in linguistic literature).

I proceed to the terillion (million raised to a million million) and so to the petillion,exillion,zettillion,and yottillion (a million raised to a million million million million).At this point the SI prefixes give out and I resort to hyphenating the power of a million using its name under this system.As 10^24 is a quadrillion under this system,a million raised to 10^25 is a decaquadrillio-illion.By contrast,a thousand times this is a decaquadrillio-illiard,a million million million million decaquadrillio-illions is a decaquadrillio-quadrillion (a million raised to ((10^25)+4)),and a decaquadrillia-illion is a million raised to 10^28 (aka ten quadrilliards).The letter before the hyphen,and what side of the hyphen a letter is on,makes an enormous difference.Hyphens are NEVER used up to this level,though names of intervening numbers recapitulate the power of a million working backward from the last digit.(The 1048576th power of a million is a sexseptaginquinhectooctoquatriginkilmegillion).

This iteration goes on to the yottillio-illion (a million raised to a yottillion) before we reach the decaquadrillio-illio-illion which starts the next iteration (and is a millionth of a decaquadrillio-illio-million which is very very much smaller than a decaquadrillio-millio-illion).

This iteration proceeds to the yottillio-illio-illion and its ilk (things like the yottillia-exillia-trilliard follow,obviously) and then the hyphens start again in another generation.I have pondered introducing apostrophes in some context (the only other characters routinely encountered in words) but haven't.Obviously,all these numbers are finite,and these names most effective when used to describe the number of sides in a Moser polygon describing the number of Knuth arrows needed to express a number of Conway chained arrows,or some such permutation.But I like naming gigantic numbers too,and I don't see that my system is any less deserving of publication that that of other experimenters in this.(What of "The One Man Infinity Fears",a Mr. Candelaria who got written up in Guinness with his milli-decilli-fiveillion,I think you have to buy a book to see what it means)? Thoughts?--Louis Epstein/12.144.5.2/le@put.com

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My thoughts. Wikipedia has a policy against personal essays and primary research; see What Wikipedia is not. It is not a publication vehicle. So if your material hasn't been published and is still a personal work in progress, well, then, no, I don't think it belongs in the article. (You're welcome to leave it here on the Talk page, of course!) But if you have it on a web page, a link to that web page would be fine. On the present page, I'd suggest perhaps a section entitled "Various proposals," with a list of references, including yours. The URLs for those other "large-number web pages" ought to be in the article, too.

As for your comment that your proposal is at least as good as some of those in the article... my thinking is that we should move toward dividing the current article into two articles. The first one would include

1 The "standard dictionary numbers" 2 Usage of names of large numbers 3 Chuquet and the origins of the "standard dictionary numbers" 4 The Googol family

and possibly

5 Extensions of the standard dictionary numbers

The other would have a title like "Proposed naming systems for very large numbers," since none of the humongous names are actually used. This new article would include the material in the current section 6, "Other systematic names of large numbers."

But, frankly, if the names in that section can't be better sourced, I think they should go. However, I'd much rather have them sourced and keep them, and I'm not in any hurry to remove them.

Any idea in what article or book Knuth proposed his myllions and byllions? And was he unaware that they conflict with the original Chuquet names, most of which also used "y?" Dpbsmith 01:03, 5 Jun 2004 (UTC)

Munafo might know,his webpage is where I saw the myllion etc. mentioned.The "Googol family"...I believe only the Googol and Googolplex are "real",the Googolplexplex and Googolbangplex and others are more individual proposal-schemes.Thus more suited to the second article.--L.E./12.144.5.2/le@put.com<p>

What did Chuquet really propose?

Several Web pages make a reference to a passage in Chuquet's book in which he shows a large number marked off into groups of six digits and comments:

Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers poit tryllion Le quart quadrillion Le cinqe quyllion Le sixe sixlion Le sept.e septyllion Le huyte ottyllion Le neufe nonyllion et ainsi des ault's se plus oultre on vouloit preceder

(Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go).

This clearly refers to names in steps of powers of six. But *Robert Munafo's article (http://home.earthlink.net/~mrob/pub/math/largenum.html) quotes a different passage,

Au lieu de dire mille milliers, on dira million, au lieu de dire mille millions, on dira byllion, etc..., et tryllion, quadrilion ... octylion, nonyllion, et ainsi des autres si plus oultre on voulait proceder. French: "Instead of saying one thousand thousand, one may say million; instead of saying one thousand million, one may say billion, and trillion, quadrillion, ... octillion, nonillion, and others as well, as far as you wish to go."

and comments

These number names were adopted throughout Europe during the next century (with minor spelling changes for each language). Chuquet intended the names to represent powers of 1000 as the quote above clearly shows.

So, it's not at all clear to me what the Chuquet system really was.

Are billiards, trilliards, quadrilliards, etc. real?

I asked Anthere, who is a native French-speaker, about this. The discussion is shown below. I suspect that that the information on all of the -illiard may be out-of-date information that has been propagated from book to book for decades and no longer reflects reality.

I'm working on Names of large numbers and would appreciate some input as to what current usage is in French. I'm just looking for what you know off the top of your head, not any deep research.

Have you ever heard of Pelletier, the 1550 mathematician who supposedly created the names ending in -illiard? That is, is the system that was adopted in 1948 referred to as "the Pelletier system?"

Wellll.... no. I checked with a few french. Noone knew

Which of the -illiard words are really used?

mostly milliard.

Are quadrilliards/quintilliards/sextilliards, etc. found in standard French dictionaries and textbooks?

It reminded me of nothing...so I looked in my Larousse. And the answer is no. No billiards, no quintilliards. However, I found a quintillion (10exp30). No sextilliards. However, I found a sextillion (10exp36).

Do I understand correctly that a billion in French was 1 000 000 000 up to 1948 and was then changed to 1 000 000 000 000?

I think that is true. 1 000 000 is a million. 1 000 000 000 is "un milliard", 1 000 000 000 000 is "mille milliard". Un "billion" is a million of million. But we never use the billion because of the confusion with english people.

As of 2004 today, what word do people use for 1 000 000 000 000?

Mille milliard

I'm no expert in French, but in Danish, using the long scale, the words are all real. They are rare because reference to so large numbers "by name" are rare - they mostly show up in science, where SI or scientific notation is used, avoiding naming them. But if they must be named, that is truly what they are called; they have no other names. Believe it or not! Arguably, the long scale (million=1E6, billion=1E12, trillion=1E18, ..., and -iard=times 1000) is more regular and logical than the short scale. It's a bit like driving in the right or the left side of the road...--Niels Ø 21:58, Mar 15, 2005 (UTC)

Really large numbers

10 to the power of 10 to the power of 10 to the power of 10 to the power of...

Those sorts of the numbers in the table are really hard to understand. Is there any simpler system?

Brianjd 08:44, 2004 Jun 17 (UTC)

when you get into layers of exponentiation like that other forms of notation (Knuth and Conway arrows,power towers,etc) become more useful and they have their own articles.The numbers don't get named as in the article here.--L.E./12.144.5.2/le@put.com

Layers of exponentiation are problematic

On my Firefox 0.9.3, even-numbered nested exponents are rendered at the same level as the base, and odd-numbered nested exponents are rendered at the same level as the first exponent — i.e., nested <sup> tags display completely incorrectly to me. I'm sure I'm not the only one with that problem.

• 1 googleplexplexplexplexplex = 10^{1010101010100}
• 1 googleplexplexplexplexplex = 10¹⁰10¹⁰10¹⁰100

On my browser, these both look exactly like the obviously incorrect second expression. Because of this, I replaced the exponents in the huge table with TeX expressions. It looks good, but there are twelve expressions that are not rendered at all. Still, better 12 that don't display than hundreds that look bad. I've marked the expressions that refuse to render as PNGs with <!-- not rendering? --> so that a future champion will be able to tame them. --Ardonik 03:22, 2004 Aug 6 (UTC)

Table from List of numbers

After reviewing this well-researched page, it seems pretty clear to me that the biggest table in List of numbers ought to be merged with the list here and deleted from the other page. The tables are big, so it'll take a little while. --Ardonik 20:12, 2004 Aug 5 (UTC)

Billiard, trilliard, quadrilliard are not "standard dictionary numbers"

The table of "standard dictionary numbers" is intended to be exactly what it says. My purpose is to draw a permanent, stable, neutral, verifiable bright line between these numbers and various other numbers that are proposed, tabulated, occasionally used, etc. If you can find a dictionary that includes the word "billiard" in the sense of 10¹⁵, put it in the table and cite the dictionary in which you found it. With respect to billiard, trilliard, quadrlliard I am not even clear as to whether these words a) are really used in France or other European countries, b) appear in French or other foreign-language dictionaries. If you find them in a foreign-language dictionary I think it would be interesting and legitimate to include them in the table.

See "Are billiards, trilliards, quadrilliards, etc. real?" above.

If you can find it in a dictionary (as the name of a number!) it goes in this table. Otherwise, it does not. [[User:Dpbsmith|Dpbsmith (talk)]] 16:11, 9 Oct 2004 (UTC)

Since you are using dictionary definitions (as opposed to Google webpage usage) as the criterion for their existence, then there is some work to be done on Wikipedia, where articles on these words have existed for some time without any queries having been raised (no, I did not create these) - see billiard, trilliard. The term Quadrilliard is mentioned in List of numbers and Order of magnitude (numbers). I was simply trying to ensure coherence between one part of Wikipedia and another.

Billiarde, for example, does exist in German, see Oxford-Duden English-German dictionary (revised 1997). Ian Cairns 16:52, 9 Oct 2004 (UTC)

Yes, there's a lot of inconsistency in Wikipedia. Furthermore, there are people that enjoy creating very short articles about names of numbers and so forth and they are constantly being created and re-created. For example, it took a lot of energy to get rid of the entries about the non-words nonabyte and doggabyte which appear on various websites but not in any dictionary or document promulgated by and standards authority.

The fact about Billiarde is interesting. I'd like to see it in the "standard dictionary number section." I think perhaps the best way to do it is to just put it in baldly as a statement, following the table. If enough of them get accumulated, there could be another table about foreign languages, or integrated into the main table, dropping the phrase "English dictionaries."

But I really want to draw a bright line between words that are in some dictionary, any dictionary, cite the dictionary.

Yes, the article on Trilliard makes me cranky. Probably what should be done with it is to add a line to it and all the others saying "This word is not found in standard English dictionaries." One of the things I hate about people creating many of short, related articles is that if there's a problem with them, the correction needs to be made many separate times... [[User:Dpbsmith|Dpbsmith (talk)]] 17:13, 9 Oct 2004 (UTC)

Well, there were only two of them and I've added that note to them both.

By the way, apologies for my cranky tone. Out of line. I probably should take these number articles off my watchlist and chill. [[User:Dpbsmith|Dpbsmith (talk)]] 17:18, 9 Oct 2004 (UTC)

No problem. Well done for editing those articles. Did you spot the German links? I have spent much time in the last few months correcting the prevalence of long scale as current UK usage. I hold no torch for the above terms - I was simply looking to be complete / consistent. Thanks, Ian Cairns 18:09, 9 Oct 2004 (UTC)

For fanciful extensions, use Other names of large numbers

84.66.195.243, please stop adding dubious entries to the section on extensions of the standard dictionary numbers. This article tries to limit itself to names that have some degree of authority to them. Many people have produced fanciful and creative extensions to the systems of number names, but none of them are more than proposals or curiosities or imaginative exercises.

1) Please make your edits to Other names of large numbers, not here. 2) Please accompany your edits with some kind of reference, citation, or authority (the book or website from which the name was taken). Dpbsmith (talk) 21:52, 15 Mar 2005 (UTC)

The system behind the madness

I came to this article because I was aware of the fact that there's a naming system for very large numbers, and I wanted to know the -system- that is used. This page is great for giving the list of names, and if I ever feel the need to speak a word meaning 10³⁶ I'll know where to look, but it seems to me that all these names have a very clear METHOD to how the names were generated, though I'm not 100% certain of how it works.

I mean, at the lower end, it's pretty obvious. billion is bi (meaning two) illion (meaning uhh... big number?)... so it's the "2nd big number". Likewise, trillion would be the 3rd big number, and so on. But I don't quite get the naming convention once you get past nine. Unedecillion? I'm assuming that's the first of the tens? But duodecillion seems to refer to the 11th big number, while the name suggests the 12th? Or am I misreading something? Or do I just not get it?

Could someone more knowledgable than me put up a section describing the system? Fieari 03:06, 16 Mar 2005 (UTC)

deci: n=10; undeci: n=11; duodeci: n=12. On the short scale, n-illion = 1000^(n+1) = 10^(3n+3), so e.g. duodecillion = 1000^13 = 10^39. On the long scale, n-illion = 1000000^n = 10^(6n) and n-iard = 1000*1000000^n = 10^(6n+3), so duodecillion = 1000000^12 = 10^72, and duodecilliard = 10^75 (a.k.a. "one thousand duodecillions"). That explains everything... except the greek/latin system naming the numbers. I agree with you that a clear neat explanation of the system would be good - and probably more relevant in an encyclopedia than a list of numbers that are so rarely used.

For the sake of argument: There is nothing in Wikipedia on the number 371074 (randomly chosen), though that number gives 1480 hits in Google. The number name ("three hundred and seventyone thousand seventyfour" with some variants) gives no hits anywhere. The word "duodecillion" gives 548 Google hits; the vast majority of these are from dictionaries and the like, and very few "in the wild" (if any at all). But various other notations for that number (1000000000000000000000000000000000000000, 1E39 etc.) gives thousands of hits. My point is that for 371074 as well as for the very large numbers on the Names of large numbers page, the following is true:

• The numbers exist in a mathematical sense - you can't count forever without needing them eventually.
• Their names hardly exist in the sense that they are commonly used.
• Their names do exist in the sense that, if you come across the number "in the wild", you can construct the name on demand (knowing the system), and it is unambiguous (apart for some annoying details).
• In most situations where those numbers could come up, they would not be named; instead, they would be expressed in some convenient notation.

--Niels Ø 07:47, Mar 16, 2005 (UTC)

By the way... I don't know if it's an invented explanation, but the comment in Fowler's 1926 comment in Modern English Usage at least gives some explanation of the "off-by-one-in-the-short-scale" issue:

"It should be remembered that this word ["billion"] does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform."

I think the question, "what is the system," is meaningless. I don't think anyone, anywhere has "officially" promulgated such a system. There's no practical need for one. It's all an abstract mathematical or computer science game. Chuquet proposed names for specific numbers up to a decillion centuries ago, and with small variations they've made it into the dictionaries. Even on the short scale, names for numbers above a quintillion are simply not needed in ordinary discourse. Mathematicians and scientists use exponential notation and SI prefixes. And numeric notation suffices in print.

Since the early days of computer programming, there has sometimes been a real practical need to generate the English representation of a number, and I'm sure many individual programmers have tried to make the algorithm general enough to handle the highest values their computer can represent. But of course even the standard dictionary numbers handle everything up to 2⁶⁴ or even 2¹²⁸. Somebody could formally propose an system, defined with algorithmic precision, capable of indefinitely high extension, and probably someone has, but it would still be just a curiosity because no body of authority is going to take the trouble to adopt it.

Another argument for the meaninglessness of the question is that it is all but impossible for a person to retain more than (you choose) nine, twelve, whatever digits in short-term memory. For anything where only an approximate value is needed, you'd use an SI prefix; 12.34 terameters or whatever. For anything where a precise-to-the-unit value is needed, you need to write the number down, because if you say (using long scale here) "three hundred sixty-eight thousand one hundred ninety quintillion, nine hundred sixteen thousand five hundred fifty-six quadrillion, two hundred forty-three thousand seven hundred thirty-nine trillion, eight hundred ninety-six thousand twenty-one billion, eight hundred seventy-three thousand six hundred fourteen million, one hundred one thousand, six hundred twenty-five," by the time you get to the end you've forgotten the beginning. And if you're going to write it down there's no good reason to use words instead of numerals.

It's sort of like asking "is there a system for naming every possible placement of pieces on a checkerboard?" You can construct one if you want to, but apart from showing that you can, nobody cares about it and nobody is going to adopt it.

If someone wanted to research a list of published algorithms for generating names of numbers and include the list or a representative algorithm in the article—but not as original research, i.e. not your own algorithm—that would be a valid addition to the article. Dpbsmith (talk) 13:51, 16 Mar 2005 (UTC)

"That explains everything... except the greek/latin system naming the numbers." So... where can I go about finding THIS information? Perhaps such an explanation would be good for its own page, as it's pretty clear that the system is also used for naming other things, like shapes (septagon, octagon, duodecahedron, etc). Seems like it would be a pretty useful article to have. Because while no one in their right minds would really use the huge number names outside of trying to impress someone with thier trivia knowledge, if you do encounter a 63 faced regular solid, you'll want to know its name and you probably will actually use it. Not that encountering such shapes is common, but it isn't outside the realm of possibility. Fieari 19:56, 17 Mar 2005 (UTC)

Authorities in the table

I think that instead of the current system of ticks and crosses in a variable length list, it would be better to have a narrow column for each source (number them and put a key where the abbreviation list is currently, so the column only has to be 1 or 2 character wide) and put a mark (x perhaps) for each source that sites a particular word and leave blank the ones that don't. I would do this now but don't have time. Thryduulf 10:38, 5 Apr 2005 (UTC)

I've now reworked the table as I proposed above, and added the entries for dictionary.com. Thryduulf 11:48, 22 Apr 2005 (UTC)