Talk:Names of large numbers

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Articles for deletion This article was nominated for deletion on July 14, 2006. The result of the discussion was Keep.

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[edit] 2006 comments

does the section about the sand reckoner make no sense to anyone else? Apart from anything else it talks about the number of grains of sand needed to fill the universe, and then states that the volume would fill our galaxy or whatnot. eh? —The preceding unsigned comment was added by 202.63.45.194 (talk • contribs).

  • I think the purpose of the passage is to elucidate on ancient concepts of big numbers. Archimedes attempted to estimate how many grains of sand would be required to fill the universe. He had to do so without recourse to our relatively modern terms like "billion" and "trillion", or scientific notation. it seems his estimate wasn't that far off, only a few orders of magnitude. — MSchmahl 16:39, 5 April 2006 (UTC)

Does it make sense to refer to "Traditional British values"? Since British tradition has changed, and we now universally use the short scale (for at least 20 years), the old system is now better referred to as "Obsolete British...". This would help clarify the widespread myth among die-hards, expatriates and foreigners that anyone in Britain still uses the long scale. Bobcousins 14:47, 15 December 2006 (UTC)

[edit] Usage of names of large numbers

2nd Paragraph: "For example, the first hit on "quintillion" is about a man who is trying to preserve the Etsako language by codifying it..." The first hit on Google is this article with that sentence. --WildKard84 01:49, 16 August 2006 (UTC)

[edit] 2004 comments

"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)
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)

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)

[edit] 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)

[edit] 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)
They're Francais/ Chemistry like, my child: Million as Mon-oxide, billion as in 2, trillion as in 3, Quadrillion as in Quatre which means 4 in French, Quintrillion which i don't know, sexcillion which is related to 6 in English and French, Septillion which means 7 in french, and the obvious octliion comes from the octopus' 8 legs. etc. Hope that helps ;) Sum1else 10:28, 21 September 2006 (UTC)

[edit] 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)


[edit] 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

My thoughts. Wikipedia has a policy against personal essays and primary research; see Wikipedia: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

[edit] 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 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.

[edit] 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)


In swedish we use (swedish - eng translation):

  • miljon - million - E6
  • miljard - milliard - E9
  • biljon - billion - E12
  • biljard - billiard - E15
  • triljon - trillion - E18
  • triljard - trilliard - E21

..etc

A thought on the rarity of these words and their absense from dictionnaries, even in the languages where they are used: In Danish, 463284 is called firehundredetreogtrestusindetohundredefireogfirs. (You may insert a few blanks or hyphens, but that is the name of the number.) You will not find it in a dictionnary, because it is rare to spell it out, and anyway it follows the same pattern as zillions of other numbers. The situation for e.g. quintilliard is pretty much the same: Correct, following a pattern, and rare.--Niels Ø 11:58, 1 June 2006 (UTC)

[edit] 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

[edit] 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 = 101010101010100
  • 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)

[edit] 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)

[edit] 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, quadrilliard 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)
Billiard/biljard is sometimes used in Swedish (for 10^12) (the alternative way of saying the same thing is 1000 billioner/biljoner; 1 biljon/billion=10^9). Not that you talk about numbers that high very often, and when you do, for example in physics, it's much, much more common to just say 10^12 (or just add "tera" if that's possible). 02:21, 18 December 2005 (UTC)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] Usage in science

Shouldn't this article have a bit of text about the fact that none of these words are used in science because of their ambiguous nature?

[edit] Merge with Power numbers

I think that the power numbers page should be merged into this one, or possibly deleted. It's only a few people that are updating that page, and it seems to simply duplicate information found here and in other names of large numbers. I didn't want to go ahead and do anything yet, because I'm not sure, though. Quentin mcalmott 21:36, 21 August 2005 (UTC)

I concur. Clay Barnes 12:35, 24 August 2005 (PST)

"Power numbers" is a low-quality article with no source citations at all. It is a miscellaneous collection of word with no indication of where they came from and whether they are in any real use. The phrase "Power numbers" is not a term in real use, as far as I know. The article is a miscellaneous collection of numbercruft. I would hate to see it merged with this page. This page was once similar to "power numbers" and I've put a lot of work into trying to make sure that it only deals with "real" number names, that is names some degree of actual acceptance, as opposed to being mental exercises in creating names. Anyone can create "vanity" names like "googolminex." I think Power numbers should simply be nominated for deletion. Dpbsmith (talk) 00:12, 29 September 2005 (UTC)

P. S. It would make more sense to merge it with Other names of large numbers, since that too is a catchall, miscellaneous list. Dpbsmith (talk) 00:13, 29 September 2005 (UTC)

  • I would agree with the merge, but this page is already quite large. How about renaming "Power numbers" to something like "Table of numbers by power"? -- Reinyday, 16:00, 2 October 2005 (UTC)
Power numbers should not, IMHO, be merged at all, because the information in it is much poorer than the information in the other related articles.
It could redirect to List of numbers#English names for powers of 10.
Actually, I believe I'm going to be bold and do it now.
I'm not going to merge the words that are in Power numbers but not presently in List of numbers#English names for powers of 10. I take strong exception to non-words like "Millitricentihexagintiquadrillion" being merged anywhere, unless someone can come up with a source citation showing actual use, and the burden of proof should be on the person who wants to put this in.WP:NOT says, "Articles about words formed on a predictable numeric system (such as "septenquinquagintillion") are not encyclopedic unless they are defined on good authority, or genuinely in use." If someone wanted to write a paragraph describing some well recognized system for assigning names like Millitricentihexagintiquadrillion, and wanted to use that as an example of how the system works, fine, but we can't just have it in an article based on our own authority that there is such a word and that that is what it means is. People that want those words in List of numbers#English names for powers of 10 can add them one by one citing sources. Dpbsmith (talk) 17:02, 2 October 2005 (UTC)

[edit] Usage of Commas

Commenting on:

>> Throughout this article, exponential or scientific notation is used. 10^6 could also be written as the number 1 followed by six 0s, 1,000,000; 10^9 could be written as 1,000,000,000, and so on. <<

In ISO 31-0#Numbers it is stated:

Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.

At no point (pun not intended) is the comma designated as a thousands separator, and should not be used as such here.

ISO 31-0 applies to science and technology, not necessarily wikipedia; is there any kind of Wikipedia:policy out there we can reference in this regard? I imagine it has been discussed before. Peyna 14:42, 14 September 2005 (UTC)

[edit] Google hits

Is the information on how many google hits each particular number receives really worth keeping? It just makes the article real cluttered and might even amount to original research. Peyna 22:37, 13 September 2005 (UTC)

I understand your point. Yes, it's somewhere in the hazy border of between original research. But it is also somewhere on the hazy border of citing sources.
Let me explain why this material is there. This page was and is subject to constant problems from people adding various invented names for large numbers, names that are basically neologisms created for the purpose of illustrating various creative ways in which one could devise names for unimaginably large numbers which have no practical use. These run the gamut from print-published material from the likes of Donald Knuth to conlang-like curiosities posted on individual websites.
The purpose of the table and the section, which has been fairly successful, is to draw a clear, convincing bright line between what might be called "real" names and "concocted" names. The purpose of the Google hit counts is to provide some objective indication of the frequency of usage of the various words. I know some people who hate Google hit counts on principle, but they are much better than no evidence at all, and they show very clearly how even the dictionary numbers fall into three categories: those up to quintillion, which are really used; the ones from the ones from undeceillion to novemdecillion, which are really obscure; and the ones from sextillion to decillion, which are in between.
I'm not sure what the difference between the page counts and article counts is supposed to be, or who put it there or why.
It would probably make more sense to change this column to something like "Relative frequency of use," with, say, "trillion" being set to 100, and then put a note at the bottom saying that the source of the relative frequency is Google hits. What do you think? Dpbsmith (talk) 15:43, 14 September 2005 (UTC)
Yeah, I think the Google hits make a convenient way to check for some kind of legitimacy; but to see it on the main page is a bit out of place. Something like that is better suited for the talk page, as a way to determine whether or not it is worth of mention on the page.
That said, your suggestion is probably the best way of dealing with this presently; or even just list them in order of frequency of use from high to low without assigning a number, especially since the number of Google hits provides at best a somewhat accurate relative ranking of frequency of use, but it's absolute frequency numbers could be subject to a lot more problems. (In other words, it probably gets them in the right "order" but the "strength" assigned to each could wildly fluctuate). Peyna 16:28, 14 September 2005 (UTC)

[edit] Googleplex

Isn't a googleplex a google to the power of a google? -Jawr256

  • Nope. First, it's spelled "googolplex." Second, Kasner and Newman's Mathematics and the Imagination defined it as "one followed by a googol zeroes," i.e. ten to the power of a googol. Dpbsmith (talk) 13:28, 9 December 2005 (UTC)

[edit] Links, and something else

I removed the statement immediately under the table which stated that undecillion, duodecillion, etc. are not included in dictionaries. They're in my Merriam-Webster's dictionary and listed (and checked as appearing in some of the dictionaries cited) in the chart. Also, why are many of the numbers (such as undecillion) linked to an article for "undecillion" then redirected back to the same article? I'm going to remove these links.Rt66lt 05:20, 10 December 2005 (UTC)

[edit] Whole possible range of names of large numbers in short

Million 1 Billion 2 Trillion 3 Quadrillion 4 Quintillion 5 Sextillion 6 Septillion 7 Octillion 8 Nonillion 9

Decillion 10 Vigintillion 20 Trigintillion 30 Quadragintillion 40 Quinquagintillion 50 Sexagintillion 60 Septuagintillion 70 Octogintillion 80 Nonagintillion 90

Centillion 100 Bicentillion 200 Tercentillion 300 Quadricentillion 400 Quinquacentillion 500 Sexacentillion 600 Septuacentillion 700 Octocentillion 800 Nonacentillion 900

Millillion 1000

[edit] Missing billiard?

In french, 10^15 is called a billard. I am surprised that it is not included in the list. Is there a reason for this or is it just missing?--Powo 08:12, 10 January 2006 (UTC)

I guess that's because this is an English encyclopaedia. Why include the French word (and if we do include it, we should also include the Greek and the Russian and the Chinese etc.) -- Jitse Niesen (talk) 12:29, 10 January 2006 (UTC)
It is, however, of interest with regard to the article on long and short scales.
Can you personally confirm that "billiard" is in real, everyday use in French-speaking countries to mean 1015?
I ask, because English dictionaries and reference sources often say that "milliard" is an English word meaning 109 but in fact it is very, very, very rarely used. I've gotten conflicting answers on the French use of the word "billion;" there's no doubt that 'when it is used it means 1012. But when you ask the question the other way around—what do French-speakers call the quantity 1012?—a native-French-speaking Wikipedian has told me that billion is hardly used at all and the normal locution is "mille milliards."
What word is used in French for the game called Billiards in English? Dpbsmith (talk) 13:12, 10 January 2006 (UTC)
I don't know about French, but in Dutch biljard is used for 10^15 and miljard for 10^9. Miljard is used a lot, biljard not that much but that's just because numbers of that magnitude do not occur very often. Billiards is called biljard. -- Jitse Niesen (talk) 13:37, 10 January 2006 (UTC)
"Mille milliard" or "billion"? I reaccon people who use mille milliards do this either because they forgot the meaning of the word billion, or because it is confusing due to the fact that its got a different meaning in english (typically true in scientific circles...). Billion = 10^12 would therefore be used exclusively by litterate french speakers, probably in non scientific circles... I am tera-times sorry if this is slitely confusing... ;)--Powo 16:55, 10 January 2006 (UTC)

[edit] Si Prefix

Would it be helpful to add the si prefixes in the table? --Salix alba (talk) 17:55, 21 January 2006 (UTC)

[edit] No existence?

The articles says, "It can be argued that a number such as a "trigintillion" has no existence in the physical world. There simply is not a trigintillion of anything, and no practical need for such a name." I don't think this is actually true for trigintillion or any other number, no matter how high. For example, the volume of the universe is 2000 trigintillion cubic micrometers ([1] and [2]). I know that's arbitrary, but is correct and there are other possible meanings for that number. Thus, I feel this line should be removed. Thoughts? Superm401 - Talk 00:56, 27 January 2006 (UTC)

i agree , surely these "monster numbers" have some relevance in the realms of theoretical physics and the like ? t ali 29/01/06

but surely we should measure everything in terms of the Planck's constant, what size would the universe be then? --Salix alba (talk) 10:44, 1 February 2006 (UTC)
Although I think Superm401 is being overliteral, I'm not going to object to the excision of the sentence. My main concern is trying to keep this page reasonably free from neologisms, protologisms and, in general, words that have been invented but not used widely by real people who were trying to use them to describe the actual number of something—as opposed to demonstrating how a hypothetical number could be given.
I certainly would agree that trigintillion is a neologism. However, the sentence as written was simply false; that is all I wanted to demonstrate. I have no intention of adding my statistic to the article or attempting to argue that trigintillion or similar numbers are in common use. Superm401 - Talk 21:46, 3 February 2006 (UTC)
Saying there is "not a trigintillion of anything" is too strong. It also shows my age. That was derived from a talk I heard Philip Morrison give some decades ago. The universe has gotten bigger since then. Dpbsmith (talk) 10:55, 1 February 2006 (UTC)

[edit] Other names of large numbers

I have listed other names of large numbers on AfD (Wikipedia:Articles_for_deletion/Other_names_of_large_numbers), people watching this page might want to comment on it. —The preceding unsigned comment was added by R.Koot (talk • contribs) .

[edit] Conway numbers

What does the "Conway number" system look like?? Georgia guy 16:53, 20 February 2006 (UTC)


To Whom It May Concern:

I saw your Large Number Denominations (LND) beyond Centillion they are not correct since they can not extend themselves far enough to reach even a Googolplex 10^(10^100) or the Googoltriplex 10^(10^(10^100)). Yes, my LND's can easily name numbers beyond these named numbers and beyond. I am John Candelaria the guy that made into the Guinness Record Books in 1985 through 1990 for devising an LND system of self perpetuating number names that made it into the GBR books. Then they decided to change their priorities from educational information to records of physical feats. So they just selved these type of records for the physical type of records. Anyway, if you would like to see how these number names are actually arrange in order to reach the mega numbers please e-mail me at this address <John_Candelaria@dot.ca.gov.>

For example, here are some LND names to taste, the 21st LND period is Viginti-million (10^66 US), not primo-vigintillion or unvigintillion. As for the hundred period LND's they begin with Ducentillion (10^603 US), Trecentillion (10^903 US), ..., Decingentillion (10^3003), not millillion, yet)... Thus,the millillion has been delayed back a thousandfold of LND's to its rightful millionth LND period place. They all work out by the following mathematical formula of if you know the LND period, you just enter it as 3(period)+3 = gives the number of zeros and the reverse by dividing the no. of zeros by 3 - 1 gives the LND period number name... I hope by touching on a few of these LND's it is clearer to see how the rest are formed...

Dear Sir,

One of the reasons why lexicographers of dicionaries have not shown a complete LND listing is because they are not sure themselves how to illustrate LND's between the 20th and the hundredth period LND. As such, I have already shown the Webster's people how to devise the best way to extend-on the LND system. By recycling the number naming analogy from the previous listing of number names. I even showed Donald E. Knuth of Stanford University years ago, and he also agreed that it was the best LND listing he has ever seen. An wholly rational LND system is proven out by its ability to extend itself beyond the googol, googolplex and Googoltriplex, ...Whithout running into any abiguious LND's. Otherwise the only thing one has listed is a short lived scheme of names that are doomed.

Yes, even Isaac Asimov before he died, wrote me back to tell me that my LND system made his head swim endlessly, and before Carl Sagan died my LND system left him speechless, probably because they were beyond his billions and billions and billions...ad infinitums. There's my proof...and then some..."I have saved the best for last by holding back another LND that extends the US/Brit. LND system of number names even further than ever before, which many people know about including the Guinness authorities, etc. It is known as the "MilliONEillion", note how it can be easily extended on and on... By ascending the internal "ONE" from "ONE" to "TWO", "THREE", "FOUR", etc...and so on... What we now have is a self perpetuting LND system of LND's that can extend indefinitely. Of course the LND names will still slowly expand out wider and wider, but not as quickly as before. The US/Brit. system of number names never had this potential before, until I showed the lexicographers how to do it in one of their main periodical reference magazines called "The Journal of Recreational Linguistics, Word Ways". —The preceding unsigned comment was added by 198.31.97.254 (talk • contribs).

  • If you want these in the article, please give some verifiable source citations that show that your names are accepted and in actual reasonably-widespread use. Many people have devised theoretical systems for naming large numbers, but as far as I know, so far, none of them have made it into dictionaries or are used in scientific writing. Dpbsmith (talk) 17:32, 6 March 2006 (UTC)

[edit] Extensions of the standard dictionary numbers--sources requested

I would like to see good, verifiable source references for the numbers above vigintillion, which is, as far as I know, the largest number name to appear in any dictionary.

If none are forthcoming, eventually I intend to remove the portion of the table dealing with numbers larger than a vigintillion, per the verifiability policy. I'm not going to do this instantly, and I will be looking for references myself, but it's about time to start providing sources or removing unsourced material in this article. Dpbsmith (talk) 17:37, 6 March 2006 (UTC)

  • The dictionary of numbers names http://home.comcast.net/~igpl/NWM.html mentions those numbers. I've added that source. TreeFrogz 23:24, 7 March 2006 (UTC)
    • That's just a personal website, and, regrettably, it does not cite its sources. I'm not going to do anything in a hurry, but I don't think I accept that as a reputable source within the meaning of the verifiability policy. Dpbsmith (talk) 02:08, 10 March 2006 (UTC) P. S. With regard to your edit comment, "How is reference to a dictionary unreliable?", obviously R. Koot does not accept that site as a real dictionary, nor do I. Wikipedia:Reliable sources says "A personal website or blog may be used only as a primary source, i.e., when we are writing about the subject or owner of the website," but actually the big problem with that page is not that it's a personal page, but that it says nothing whatsoever about how it was compiled or by whom or where they got their information. If it were, say, a page maintained by a mathematics professor at a university and it cited sources, I'd accept it even if I couldn't (or didn't want to bother to check those sources directly. Dpbsmith (talk) 10:59, 10 March 2006 (UTC)
  • Asimov wrote an article, I believe called "T-Formation", which claimed that a googol could be referred to as "ten duotrigintillion", implying that he was familiar with the system which is there currently (below the centillion level anyway). Ben Standeven 05:46, 16 March 2006 (UTC)

Asimov later saw that the actual number name for a googol is a large compound number name as "10 triginti-billion" (=10^100), not 10 duotrigintillion. Why because the Latin numeral names are arranged backwarks. Translated over to English it is like saying "10 twothirty" and we are are talking about the US system of consistent number names...Otherwise, we are talking about a doomed system of strange names, but not the names of consistent numbers that's for sure.

The existence or non-existence of serious sources for these Long scale or Short scale number words is irrelevant. No ordinary reader will understand them anyway. Readers who do not understand 10100 supplemented by an explanation like "1 followed by 100 zeros" will not be helped by these unusual number names. So why use them at all?--Niels Ø 20:42, 18 March 2006 (UTC)

Extension of this table past decillion seems to me like original research. Admittedly it's kind of fun to do this, but, whether or not there are other such lists (from reliable sources), if these numbers are not used in practice, they're irrelevant. --Ant 14:47, 8 January 2007 (UTC)

[edit] Quadrillion

Just thought I would mention I found this article when I actually needed to use the word for 1015 and did not know it's word[3].

Thanks for the informative article.

[edit] Original research concerns

From the article:

Frequency of usage determined by the number of Google hits on pages in English on the web, as of September, 2005.

That is unacceptable. We can't be performing original research to try and determine the relative frequency of usage of various names for numbers, and even if that were allowed, doing it using a Google Search is an absurd methodology. Unless anyone has any compelling reasons for this original research not to be removed, it needs to be removed. --Cyde↔Weys 20:47, 18 July 2006 (UTC)

I found that field to be doubious too. HighInBC 02:37, 20 July 2006 (UTC)

[edit] Googolduplex vs Googolplexian

When doing a search on Google, "Googolplexian" is far more common than "googolduplex" for 10^googolplex. Which should we mention here on Wikipedia? Andros 1337 18:47, 16 August 2006 (UTC)

  • For which terms can you cite a source meeting reliable source guidelines? I don't believe either term has any real usage but I'm willing to be convinced otherwise. Dpbsmith (talk) 20:29, 16 August 2006 (UTC)

[edit] Confusion - Clarification needed?

I am certainly confused with these names, as these large numbers are quoted, as it is never specified if the user talks of long or short numbers, and a distinction is clearly necessary for disambiguation (if you like the expression) and I wish that an international conference on mathematics or the sort would decide how to make certain we understand what the author talks about.

In a simpleminded way I would say prefix the US & Modern British naming with a B, like BBillion or ABillion (American Billion) for example, or the long system with an E for European. Alternatively s and l could be used, but without either confusion will reign 86.197.31.139 14:01, 14 September 2006 (UTC)

[edit] Hudelson proposal

Matt Hudelson - an assistant professor in the Department of Pure and Applied Mathematics at Washington State University - has proposed the following scheme for names of huge numbers.
The term "k-oogol" is used to indicate 10^(10^k).
So a one-oogol would be 10^(10^1) = 10 10 = somewhere between an American "billion" and "trillion". (André Joyce was the Franco-American mathematician-cum-creative-writer who coined the word "oogol")
A two-oogol would be 10^(10^10) = 10 100 = one googol. (The word "googol" was coined in 1920 by nine-year-old Milton Sirotta, nephew of Jewish American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.)
A five-oogol would be 10^(10^5)=10 100000
Matt Hudelson also proposed that we should use the construction "k-plex" to indicate raising 10 to the k.
So, a oogolplex is 10 oogol and a googolplex is 10 googol and a googolplexplex is 10 googolplex etc. Thus, 100 is also a twoplex, which makes a googol a twoplexplex and a googolplex a twoplexplexplex. Thus, a k-oogol is also a k-plexplex. Finally, he also suggested that we use the Greek and/or Latin prefixes, so instead of writing plexplex, we write duplex, and plexplexplex should be triplex, etc.

No sources are given. Is there is a published source for this? This material should be reinserted in the article only if it is accompanied by a citation of a published source. Dpbsmith (talk) 20:13, 26 January 2007 (UTC)

[edit] Contradiction?

Under the subheading "Usage of names of large numbers" there appears a contradiction:

He concluded that it would take less than "one thousand myriad myriad eighth numbers" (1075) grains of sand to pack the universe solid with sand. This much sand would fill a volume larger than our galaxy, the Milky Way, but smaller than the group of galaxies it is part of, the Local Group (which would take about one million times as many grains of sand to fill).

So, would this much fill the universe, or just a volume larger than the Milky Way? Yahadreas 18:05, 10 February 2007 (UTC)

We think now that the Universe is bigger than Archimedes thought it was. Spacepotato 20:21, 10 February 2007 (UTC)

[edit] Grillion

is it a real number?

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