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Forum » SpaceEngine » Off-topic Discussions » Number Scales (Short scale vs. Long scale, etc.)
Number Scales
midtskogenDate: Wednesday, 12.06.2013, 09:34 | Message # 16
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Continued from the Off-topic thread. --Watsisname

I don't think 1Gm³ is ambiguous at all (just appearing like sloppy typography like 1km for 1 km). Writing things like "1k m³", "1 k m³", "1G m³" etc could be useful, but isn't since it's begging for confusion.

And if only English could decide whether one billion is 109 or 1012... British English seems to migrate to the former in agreement with the US but disagreement with much of the world. And Indian English still seems to prefer counting in lakh, crore and lakh crore just to add to the confusion.





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Edited by Watsisname - Wednesday, 12.06.2013, 13:34
 
HarbingerDawnDate: Wednesday, 12.06.2013, 09:42 | Message # 17
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Quote (midtskogen)
I don't think 1Gm³ is ambiguous at all

It obviously is since we just encountered a scenario in which it caused confusion. The problem is that in most cases billions of meters and gigameters are interchangeable. But when you throw exponents in there that changes. So it goes from being unambiguous to ambiguous. However, most of the time Gm will mean gigameter, and some other notation used to denote billions of meters, for instance 1e+9 m3 rather than 1Gm3. If that standard is adhered to then ambiguity can be avoided.

Quote (midtskogen)
And if only English could decide whether one billion is 109 or 1012

It's 109 and I don't care what anyone else says.

Also, it's not a linguistic issue. Short scale and long scale numbering is independent of language and is used differently in different nations and cultures. There are several differences between usage of units, numbers, and even spellings and stylings of words between those in the USA and those in the UK, even though both speak English. However, short scale is the predominant scale used in science today, thus I think that even debating which is being used in a particular case is meaningless. It should be assumed to be short scale unless there is cause to think otherwise.





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Edited by HarbingerDawn - Wednesday, 12.06.2013, 09:46
 
apenpaapDate: Wednesday, 12.06.2013, 10:43 | Message # 18
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Quote (HarbingerDawn)
It's 10^9 and I don't care what anyone else says.


It's 10^12 and I don't care what anyone else says. tongue





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WatsisnameDate: Wednesday, 12.06.2013, 10:58 | Message # 19
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Yeah, I wrote it that way since it was the format werdnaforever used in his post, with him specifying that he meant it as billion meters cubed. It didn't occur to me how ambiguous it was since I use the G for giga prefix frequently but I use Gm for gigameters... almost never, so I naturally read it that way. But it is indeed horribly ambiguous. Using a space (1G m3 vs. 1 Gm3) would have been slightly better, and 1x109 m3 is perfect.

Quote (HarbingerDawn)
It's 109 and I don't care what anyone else says.


Agreed.

Thousand - 103
Million - 106
Billion - 109
Trillion - 1012
Quadrillion - 1015
Quintillion - 1018
etc.

This system makes perfect sense to me. Starting at thousand you go through the standard numerical prefixes for each additional 3 powers of ten. I don't understand the logic for swapping any of them.





 
apenpaapDate: Wednesday, 12.06.2013, 11:04 | Message # 20
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Well, the thing is you're starting at a thousand, rather than at zero. If you start at 0 and go with a factor of 10^6 every time, you get a more sensible system.
Million - 10^6 (6=1*6)
Billion - 10^12 (12=2*6)
Trillion - 10^18 (18=3*6)
Quadrillion - 10^24 (24=4*6)
Quintillion - 10^30 (30=5*6)





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WatsisnameDate: Wednesday, 12.06.2013, 11:13 | Message # 21
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Yes, but we don't count by 6 powers of ten here. :P

I would actually not mind going by
Million - 10^3
Billion - 10^6
Trillion - 10^9
etc.

But 'thousand' is pretty deeply entrenched. smile





 
HarbingerDawnDate: Wednesday, 12.06.2013, 11:28 | Message # 22
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Quote (Watsisname)
I would actually not mind going by

Yes, that would remove the only existing flaw in the short scale system. Apenpaap and I discussed this in another thread a long time ago. But even with thousand I still think that the short scale is more sensible.

If we're going to continue this discussion then we should do so here: http://en.spaceengine.org/forum/23-688-1





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Edited by HarbingerDawn - Wednesday, 12.06.2013, 11:30
 
midtskogenDate: Wednesday, 12.06.2013, 11:41 | Message # 23
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Quote (Watsisname)
This system makes perfect sense to me. Starting at thousand you go through the standard numerical prefixes for each additional 3 powers of ten. I don't understand the logic for swapping any of them.

Perfect sense: One step up and add 6 to the power, but then some American redneck got confused by the big numbers and messed it up. smile Well, actually, both systems arose in Europe, but northern America happened to import the system that lost in Europe.

So in Europe, southern America etc:
million - 106
milliard - 109
billion - 1012
billiard - 1015
trillion - 1018
trilliard - 1021
etc.

It may sound alien to you, but this is the system that I grew up with (from age 5 I loved numbers and I quickly memorised this), so a quadrillion will always have 24 zeros in my mind. smile

The long scale has the advantage that you don't have to learn so much Latin counting to express big numbers (decillion is more likeable than undevigintillion for 1060). Beside, the short scale has an awkward offset:
decillion = 1033 (short) or 1060 (long)
centillion = 10303 (short) or 10600 (long)

The south asian system:
lakh - 105 - 1,00,000
crore - 107 - 1,00,00,000
lakh crore - 1012 - 10,00,00,00,00,000

Edit: I'm slow to refresh. Apenpaap already pointed out the offset problem with the short scale.

Edit2: Did you by the way know that the word "hundred" at some point changed from 120 to 100 and for some time both meanings were in use?





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Edited by midtskogen - Wednesday, 12.06.2013, 11:54
 
HarbingerDawnDate: Wednesday, 12.06.2013, 12:09 | Message # 24
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Quote (midtskogen)
Beside, the short scale has an awkward offset:

Which would be easily fixed by simply removing the word "thousand" and starting million at 10^3. This would make much more sense than the long scale. You should have new names for each power of three. "Milliard" and "thousand million" are absurd abominations that need to be done away with.

Also, this REALLY should be continued in the thread I linked. I can't move these posts there due to my internet being way too slow to load this ENTIRE thread to do so, so you'll have to pick up and move on your own.





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midtskogenDate: Wednesday, 12.06.2013, 12:37 | Message # 25
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Quote (HarbingerDawn)
Which would be easily fixed by simply removing the word "thousand" and starting million at 10^3.

Or removing the word "million" and starting billion at 106, or have thousand and million mean the same (perhaps confusing since "million" comes from "mille" in the sense "a big thousand"). Or to invent a whole new system: mille (10³), bille (106), trille (109) etc.

I'm tired of Norwegian journalists using English material where a billion is 109 who then write "billion" in Norwegian in which it cannot mean anything but 1012.

Seriously, the solution is to use powers of 10 for anything from 109.





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Edited by midtskogen - Wednesday, 12.06.2013, 13:35
 
apenpaapDate: Wednesday, 12.06.2013, 13:49 | Message # 26
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Quote (HarbingerDawn)
"Milliard" and "thousand million" are absurd abominations that need to be done away with.


I disagree about a milliard. Sure, a thousand million sounds clunky and unhandy, I fully agree with that, but that's why the quite nice word milliard exists.





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midtskogenDate: Wednesday, 12.06.2013, 14:38 | Message # 27
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Diverting somewhat from the topic, Latin had a different way of expressing large numbers aided by a fairly rich numeral system. In addition to cardinals and ordinals, Latin also have a complete set of distributive numbers (how many each) and adverbs (as English once, twice, thrice, but for any number). So 2×2 is bis bina (lit. "twice two each"). This was used to express big numbers. The basic unit was 100,000 (like lakh): centena milia (using the distributive), often omitted. For larger numbers simply add an adverb. 200,000 becomes bis centena milia (bis = twice).

1,000,000 = deciens centena milia (deciens = ten times)
10,000,000 = centiens centena milia (centiens = hundred times)
100,000,000 = miliens centena milia (miliens = thousand times)
1,000,000,000 = deciens miliens centena milia
10,000,000,000 = centiens miliens centena milia

Above that, I don't really know. Miliens miliens centena milia might not be attested. The system eventually breaks down.

Add to this that Latin numerals (except the adverbs) also were inflected in gender and case, things get a bit messy. We might think that the billion/milliard confusion is a problem, but it could be worse.

I wonder how they do big numbers in Japan, where they have many number series, the one used depending on the characteristics of what's being counted (birds, container, pretty arbitrary stuff).





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HarbingerDawnDate: Wednesday, 12.06.2013, 15:16 | Message # 28
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Quote (apenpaap)
the quite nice word milliard

It's not nice. It's terrible. Besides, having a new word for one power of three, and then a derived word for the next power of three, and then a new word for the next power of three, and then a derived word for the next power of three...

It's silly and complicated. Why not just have a new word for each power of three rather than alternating new words with derived ones?





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apenpaapDate: Wednesday, 12.06.2013, 15:28 | Message # 29
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Well, I think it's nice, but I guess we could argue about which words we like and which not until the Sun goes red giant.

And I see it more as a new word for every 6 powers of ten, and between them using lower numbers as modifiers, where milliard is a sleeker form of a thousand million. I find this a far more elegant system than using 1000 as a starting point and then using new -illions every three powers of ten. It's inconsistent too when you think about numbers smaller than one: 10^-6 is a millionth, which works perfectly in the long scale, while in the short scale there's a break between 10^-3 and 10^3. (or you'd have to call it a trillionth, which would be very silly indeed)

There's also the fact that the short scale runs out of gas much earlier than the long scale, going up to only 10^303, rather than 10^603. Sure, not many things require you to use such enormous numbers, but that's a difference of a quinquagintillion times there.





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HarbingerDawnDate: Wednesday, 12.06.2013, 15:47 | Message # 30
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Quote (apenpaap)
I find this a far more elegant system than using 1000 as a starting point and then using new -illions every three powers of ten.

Like I said before, just remove thousand and replace it with million and your argument becomes invalid and the short scale becomes indisputably superior.

Quote (apenpaap)
It's inconsistent too when you think about numbers smaller than one: 10^-6 is a millionth, which works perfectly in the long scale, while in the short scale there's a break between 10^-3 and 10^3. (or you'd have to call it a trillionth, which would be very silly indeed)

Again, simply rename thousand to million and that issue disappears.

Quote (apenpaap)
There's also the fact that the short scale runs out of gas much earlier than the long scale, going up to only 10^303, rather than 10^603.

That's irrelevant since nobody even knows how to say numbers above octillion anyway, aside from centillion obviously. And I don't see how that's "running out of gas". Why is centillion arbitrarily defined as the end point? Surely you could simply continue on with new names derived in the same way as those from 1-100? It seems a hollow argument to me.

Quote (apenpaap)
a quinquagintillion

Short scale or long scale tongue





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