When I say "a billion" I usually mean "lots", e.g. "There were a billion errors in this week's edition of the Reporter (http://www.admin.cam.ac.uk/reporter/)".
(When I read it in newspapers, to be honest, reading it as "lots" is generally sufficient for my understanding of the article.)
I can't remember how much a googolplex is, and I can't envisage many situations in which I'd need to know. I'll probably go and look it up after this though out of curiosity.
A googleplex is the number of websites indexed by the world's best web search engine (http://www.google.com/).
Is there anything that anyone would want to use a googolplex for? Big combinatorials, presumably, since there's not that many countable things in themselves.
Does anyone else know Douglas Hofstadter's essay on big numbers? I've lost my copy of Metamagical Themas so I can't refer to it, but I think he talks about how people perceive millions and billions.
The original use was as a counterexample. AIUI even a googol is enough larger than the estimated number of particles in the universe that even astronomers probably bother to draw a distinction.
The American billion system is, of course, stupid. Where million, billion and trillion should have qualities of 1-ness, 2-ness and 3-ness about them respectively, the American ones have 2-ness, 3-ness and 4-ness. The traditional British billion and friends are much more sensible.
Unfortunately, the American billion has shown itself to be the VHS to the British billion's Betamax, by convincingly winning the issue in spite of its technical inferiority. These days I don't expect to see the traditional British billion used in any major publication, and I'd probably use the American one myself if I needed to (although a lingering discomfort might encourage me to make it clear which billion I meant, or to move to scientific notation if that was sensible).
It annoys me, but it's a lost battle as far as I'm concerned...
"Another mathematician (http://www.fpx.de/fp/Fun/Googolplex/) then shot back with Googolplex, and defined it to be 10 to the power of Googol, proving poor old Edward wrong in an instance."
Whilst I agree in principle, there is a need for "milliard" or similar - "thousand million" is talked about way way more frequently than "million million", and as such needs a short way to be expressed.
I tend to avoid using "billion" myself because of the scope for confusion. I will use it if I'm reporting speech or print, or if it's clear from context that the other parties to the conversation have a firm meaning, and it's appropriate for me to use that meaning.
It's a confusing life, meaning one million million when I use the word but understanding one thousand million when I read it. I much prefer 'milliard' for one thousand million but convincing the meeja to use the word is probably a lost cause.
I use "billion" to mean 109, "trillion" to mean 1012, "quadrillion" to mean 1015, and so on.
In doing so, I am conceding defeat and acknowledging that, yet again, boneheaded Americans have broken what was previously a sensible aspect of the language. Unfortunately, pressing the point is just too risky — misunderstandings by many orders of magnitude are at stake.
There is perfectly good English word for 109: "milliard". Why they ever screwed with the meaning of "billion" is beyond me.
I offer an idea I had last time such a discussion arose: We should let the S.I. magnitude prefices stand as words in their own right. Then a giga would be 109, a tera 1012 and so on. "Two peta watts" and "two petawatts" would mean the same thing. You could say "five hundred and thirty-two tera, two hundred and nine giga, nine hundred and sixty-seven million, seven hundred and twelve thousand, six hundred and twenty-six" to mean 532,209,967,712,626. This scheme has the virtue that most scientists and engineers would understand what you meant without needing it explained; many wouldn't even notice you'd done it.
While I know what a googolplex is, I've never regarded it as a useful term. When I get to that stage I normally resort to expressions like 2264.
(To be honest I fail to see why one system is any more logical than the other. They both seem sensible enough from their own equally arbitrary starting positions.)
Kibibyte is a mildly silly word; mebibyte and gibibyte are positively stupid…
Nevertheless, `KiB'/`MiB' does appear to be catching on very slowly. (I was surprised to find it in the man page of a relatively well-known utility the other week, but I now can't remember what that utility was. The new release of Lynx apparently gives you a choice between kB and KiB to appear in the progress report as you download something.)
(Is that statement about first floors, or billions? I can certainly see your point when it comes to first floors - either is as sensible as the other and it's a question of what you're used to. But I instinctively recoil from any word derived from the prefix "bi" which doesn't obviously contain two of something...)
When I say "a billion" I usually mean "lots", e.g. "There were a billion errors in this week's edition of the Reporter (http://www.admin.cam.ac.uk/reporter/)".
(When I read it in newspapers, to be honest, reading it as "lots" is generally sufficient for my understanding of the article.)
I can't remember how much a googolplex is, and I can't envisage many situations in which I'd need to know. I'll probably go and look it up after this though out of curiosity.
A googleplex is the number of websites indexed by the world's best web search engine (http://www.google.com/).
England existed before (white) america, so obviously our system is right. Million=10^6, Billion=10^12. There wouldn't be such a word as milliard, otherwise! Using the SI prefixes would do for me. Or use n.nnnnnnEnn and really annoy non-scientists.
I don't think "mi" is a prefix; it was just a bit of the word "million" which could be conveniently discarded to make way for prefixes...
I can never quite remember how "million" came about in the first place. Common sense suggests there must be a link with Latin "mille" = "thousand", but declines to suggest how it managed to square itself along the way :-)
I tend to avoid it for the same reasons. My filling in polls carelessly and thinking "no, I meant those the other way around" seconds after clicking the button doesn't help. Ah - filling it in again (keeping my wrong guess for googleplex) does change my answers.
Million comes from French (around the 14th century), which borrowed it from Italian, where it was formed from mille "1000" + -one (augmentative suffix) and used to mean a thousand thousands.
My COED says of billion: From French billion, purposely formed in the 16th century to denote the second power of a million (by substituting bi- (prefix) for the initial letters), trillion and quadrillion being similarly formed to denote the third and fourth powers. The name appears not to have been adopted in English before the end of the 17th century [first quote is from Locke 1690]. Subsequently the application of the word was changed by French arithmeticians, figures being divided in numeration into groups of threes, instead of sixes, so that French billion, trillion denoted not the second and third powers of a million, but a thousand millions and a thousand thousand millions. In the 19th century, the US adopted the French convention, but Britain retained the original and etymological use (to which France reverted in 1948). Since 1951 the US value, a thousand millions, has been increasingly used in Britain, especially in technical writing and, more recently, in journalism...
So, it was the French who came up with the "unetymological" meaning, a very long time ago. The Americans and British simply selected different options from an existing variation, rather like aluminium and herb and -ize etc.
It's my understanding that "a billion" has been defined in England as 10^9 to match the American usage since the 1970s or so, which is how I tend to use it. More information in the alt.usage.english FAQ.
I guess the usage has migrated firmly to the American because it's much more useful in everyday life to have a term which applies to a thousand million than a million million, simply because things in quantities of thousand millions are discussed more often.
If we can develop a sense for the number of chairs in a room, why not as good a sense for the number of zeros in a numeral? That is the basic premise of this article.
Just as Hofstadter handles indices well, he provides excellent (back-of-the-book) indexes.
I got the impression I was already regarded as pedantic and nerdy using it to mean 1012 as a teenager in the mid-eighties. Books still used it that way (though I'm not sure in retrospect how many of them were recently published), but in common parlance, it had already become 109.
I think this was the first instance of British English succumbing before Vespuccian in my lifetime I observed. (The "ae" in "mediaeval" is another lost cause; I still use it myself, but when such authorities as Oxfnord University don't, you know it's on the way out.)
when i read a billion in a paper, what i read it as depends on what i'm reading. so, in the sun, i'd read it as lots, where as in something more sane, i'd read it as 1,000,000,000,000. unless it was american, in which case i'd read it as 1,000,000,000.
as to what i am, i suppose, technically british, and in practise continental (spanish) when it comes to upbringing.
I use "billion" very rarely in either sense, as I have little occasion to talk about numbers of that magnitude. I'd probably use it to mean 10^9 though due to seeing it in that use in financial contexts.
I'm British by nationality but probably mostly German culturally. In German, I'd say "Milliarde" for 10^9 and "Billion" for 10^12, though, since even newspapers use that format (well, "Milliarde", at any rate; "Billion" doesn't get used often).
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(no subject)
Date: 2004-02-25 05:10 am (UTC)(no subject)
Date: 2004-02-25 05:13 am (UTC)(When I read it in newspapers, to be honest, reading it as "lots" is generally sufficient for my understanding of the article.)
I can't remember how much a googolplex is, and I can't envisage many situations in which I'd need to know. I'll probably go and look it up after this though out of curiosity.
A googleplex is the number of websites indexed by the world's best web search engine (http://www.google.com/).
(no subject)
Date: 2004-02-25 05:14 am (UTC)How do you describe lions with partners of both sexes, then?
(no subject)
Date: 2004-02-25 05:15 am (UTC)(no subject)
Date: 2004-02-25 05:17 am (UTC)(no subject)
Date: 2004-02-25 05:18 am (UTC)Surely that comment should read: I don't use the word "".?
(no subject)
Date: 2004-02-25 05:20 am (UTC)(no subject)
Date: 2004-02-25 05:21 am (UTC)(no subject)
Date: 2004-02-25 05:21 am (UTC)(no subject)
Date: 2004-02-25 05:23 am (UTC)"A googleplex and thirty eight, a googleplex and thirty nine..."
*DING DONG*
Oh no!
(no subject)
Date: 2004-02-25 05:27 am (UTC)What's the counterexample? Something along the lines of Levinthal's paradox (http://www.sdsc.edu/~nair/levinthal.html)?
(no subject)
Date: 2004-02-25 05:28 am (UTC)(no subject)
Date: 2004-02-25 05:31 am (UTC)(no subject)
Date: 2004-02-25 05:31 am (UTC)Whatever seems right in context.
(no subject)
Date: 2004-02-25 05:33 am (UTC)(no subject)
Date: 2004-02-25 05:44 am (UTC)Unfortunately, the American billion has shown itself to be the VHS to the British billion's Betamax, by convincingly winning the issue in spite of its technical inferiority. These days I don't expect to see the traditional British billion used in any major publication, and I'd probably use the American one myself if I needed to (although a lingering discomfort might encourage me to make it clear which billion I meant, or to move to scientific notation if that was sensible).
It annoys me, but it's a lost battle as far as I'm concerned...
(no subject)
Date: 2004-02-25 05:44 am (UTC)(no subject)
Date: 2004-02-25 05:48 am (UTC)(no subject)
Date: 2004-02-25 05:49 am (UTC)(no subject)
Date: 2004-02-25 05:52 am (UTC)(no subject)
Date: 2004-02-25 05:59 am (UTC)In doing so, I am conceding defeat and acknowledging that, yet again, boneheaded Americans have broken what was previously a sensible aspect of the language. Unfortunately, pressing the point is just too risky — misunderstandings by many orders of magnitude are at stake.
There is perfectly good English word for 109: "milliard". Why they ever screwed with the meaning of "billion" is beyond me.
I offer an idea I had last time such a discussion arose: We should let the S.I. magnitude prefices stand as words in their own right. Then a giga would be 109, a tera 1012 and so on. "Two peta watts" and "two petawatts" would mean the same thing. You could say "five hundred and thirty-two tera, two hundred and nine giga, nine hundred and sixty-seven million, seven hundred and twelve thousand, six hundred and twenty-six" to mean 532,209,967,712,626. This scheme has the virtue that most scientists and engineers would understand what you meant without needing it explained; many wouldn't even notice you'd done it.
While I know what a googolplex is, I've never regarded it as a useful term. When I get to that stage I normally resort to expressions like 2264.
I offer an idea I had
Date: 2004-02-25 06:17 am (UTC)(no subject)
Date: 2004-02-25 07:30 am (UTC)(To be honest I fail to see why one system is any more logical than the other. They both seem sensible enough from their own equally arbitrary starting positions.)
KiB
Date: 2004-02-25 07:32 am (UTC)Nevertheless, `KiB'/`MiB' does appear to be catching on very slowly. (I was surprised to find it in the man page of a relatively well-known utility the other week, but I now can't remember what that utility was. The new release of Lynx apparently gives you a choice between kB and KiB to appear in the progress report as you download something.)
(no subject)
Date: 2004-02-25 07:37 am (UTC)They've infested Linux's ifconfig and also at least some bits of the kernel.
...so, uh, how big is my hard disk?
(no subject)
Date: 2004-02-25 07:41 am (UTC)(no subject)
Date: 2004-02-25 07:49 am (UTC)What does the prefix "mi" on "mi-llion mean, then, if a "bi-llion" is two llions (some kind of Welsh big cat, presumably)?
(no subject)
Date: 2004-02-25 07:57 am (UTC)(When I read it in newspapers, to be honest, reading it as "lots" is generally sufficient for my understanding of the article.)
I can't remember how much a googolplex is, and I can't envisage many situations in which I'd need to know. I'll probably go and look it up after this though out of curiosity.
A googleplex is the number of websites indexed by the world's best web search engine (http://www.google.com/).
(no subject)
Date: 2004-02-25 08:19 am (UTC)Using the SI prefixes would do for me. Or use n.nnnnnnEnn and really annoy non-scientists.
(no subject)
Date: 2004-02-25 09:03 am (UTC)I can never quite remember how "million" came about in the first place. Common sense suggests there must be a link with Latin "mille" = "thousand", but declines to suggest how it managed to square itself along the way :-)
(no subject)
Date: 2004-02-25 09:28 am (UTC)(no subject)
Date: 2004-02-25 09:44 am (UTC)My COED says of billion:
From French billion, purposely formed in the 16th century to denote the second power of a million (by substituting bi- (prefix) for the initial letters), trillion and quadrillion being similarly formed to denote the third and fourth powers. The name appears not to have been adopted in English before the end of the 17th century [first quote is from Locke 1690]. Subsequently the application of the word was changed by French arithmeticians, figures being divided in numeration into groups of threes, instead of sixes, so that French billion, trillion denoted not the second and third powers of a million, but a thousand millions and a thousand thousand millions. In the 19th century, the US adopted the French convention, but Britain retained the original and etymological use (to which France reverted in 1948). Since 1951 the US value, a thousand millions, has been increasingly used in Britain, especially in technical writing and, more recently, in journalism...
So, it was the French who came up with the "unetymological" meaning, a very long time ago. The Americans and British simply selected different options from an existing variation, rather like aluminium and herb and -ize etc.
(no subject)
Date: 2004-02-25 09:47 am (UTC)(no subject)
Date: 2004-02-25 09:58 am (UTC)(no subject)
Date: 2004-02-25 09:59 am (UTC)(no subject)
Date: 2004-02-25 10:09 am (UTC)And I ruthlessly remove it from any document that I edit or proof read, becuase it is ambiguous.
(no subject)
Date: 2004-02-25 10:18 am (UTC)1-ness
Date: 2004-02-25 12:44 pm (UTC)(no subject)
Date: 2004-02-25 12:44 pm (UTC)Just as Hofstadter handles indices well, he provides excellent (back-of-the-book) indexes.
(no subject)
Date: 2004-02-25 12:45 pm (UTC)Of lost and losing battles in the arena of English
Date: 2004-02-25 01:35 pm (UTC)I think this was the first instance of British English succumbing before Vespuccian in my lifetime I observed. (The "ae" in "mediaeval" is another lost cause; I still use it myself, but when such authorities as Oxfnord University don't, you know it's on the way out.)
(no subject)
Date: 2004-02-25 04:25 pm (UTC)as to what i am, i suppose, technically british, and in practise continental (spanish) when it comes to upbringing.
(no subject)
Date: 2004-02-26 02:30 am (UTC)I'm British by nationality but probably mostly German culturally. In German, I'd say "Milliarde" for 10^9 and "Billion" for 10^12, though, since even newspapers use that format (well, "Milliarde", at any rate; "Billion" doesn't get used often).
(no subject)
Date: 2004-02-26 04:34 am (UTC)