2091: "Million, Billion, Trillion"

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loehnertz
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Million Billion etc.

Postby loehnertz » Fri Dec 28, 2018 8:49 am UTC

In Germany it actually goes like this;

(english)->(german)
Million -> Million
Billion -> Milliarde
Trillion -> Billion
Quadrillion -> Billiarde

So we are compatible to your old system with aditional "-arde" steps inbetween.
Always fun to watch german politicans translating the spending statatements of others into absurd amounts.

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2091: "Million, Billion, Trillion"

Postby Sly » Fri Dec 28, 2018 1:34 pm UTC

Image

Title Text: You can tell most people don’t really assign an absolute meaning to these numbers because in some places and time periods, “billion” has meant 1,000x what it's meant in others, and a lot of us never even noticed.

Thankyou for addressing this issue and assuaging my pain. Here, (Germany) The Exponents of Thousand progress Million, Milliard, Billion, Billiard...
and I can only guess that this pattern continues.

Anyhow, I hope this "First Post" was done correctly.

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Re: 2091: "Million, Billion, Trillion"

Postby Soupspoon » Fri Dec 28, 2018 1:41 pm UTC

Sly wrote:Anyhow, I hope this "First Post" was done correctly.

(Looks good to me!)

I'm also a long-scale person, myself, by instinct.

Although I'm convinced that as Thousand*Thousand is Million and Million*Million is (Long) Billion that it should continue to Billion*Billion being a Trillion, Trillion*Trillion being Quadrillion, etc. We'll get so many more numbers to play with, and the above graph of perception vs actuality of value would be interesting.

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Re: 2091: "Million, Billion, Trillion"

Postby jc » Fri Dec 28, 2018 2:54 pm UTC

Soupspoon wrote:
Sly wrote:Anyhow, I hope this "First Post" was done correctly.

(Looks good to me!)

I'm also a long-scale person, myself, by instinct.

Although I'm convinced that as Thousand*Thousand is Million and Million*Million is (Long) Billion that it should continue to Billion*Billion being a Trillion, Trillion*Trillion being Quadrillion, etc. We'll get so many more numbers to play with, and the above graph of perception vs actuality of value would be interesting.


Of course, the mathematically inclined among us will treat it as a bit of a silly language issue, and continue to prefer the simpler exponential notation as the easiest to understand and meaning the same thing everywhere.

But there is the ongoing problem that the software developers still haven't come up with a reliable way to trick our screens into showing the correct representation of exponentials. Yeah, sometimes you can type things that work in a single app on your screen, but touching the same keys don't produce the same result in other windows, and when you hit Return or Send or Submit or the little winged widget or whatever to send it, it doesn't look the same on other readers' screens. Sometimes you can use TeX formatting, but again it often fails in many readers' windows. You can't even use the HTML (or BBcode) SUP tag and expect it to work in others' browser windows.

You'd think that software developers would understand mathematical notation better than the general population, and make sure simple expressions work widely and consistently, but this seems not to be true.

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Re: 2091: "Million, Billion, Trillion"

Postby MythSearcher » Fri Dec 28, 2018 3:10 pm UTC

That is why you get the cardinal -iards terms in the long scale.
So you go Million (10^6), Milliard (1000 Million or 10^9), Billion (10^12), Billiard (1000 Billion or 10^15), Trillion (10^18), Trilliard (10^21), etc.

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Re: 2091: "Million, Billion, Trillion"

Postby Duffman77 » Fri Dec 28, 2018 3:12 pm UTC

I find it amusing that the average American doesn't know anything above trillion. If you google search "how much water does the Earth have", they tell us the Earth has 326 Million Trillion gallons... this sounds like an 8 yr old saying "million billion gazillion bajillion". So this would be written as 326,000,000,000,000,000,000. Last I checked, a number with 18 zeros after it is called a quintillion-- not a "million trillion"

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Re: 2091: "Million, Billion, Trillion"

Postby Pfhorrest » Fri Dec 28, 2018 5:31 pm UTC

Do billiards as in thousand-billions have anything to do with the game played with hard balls on a felt-covered table?
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Re: 2091: "Million, Billion, Trillion"

Postby cellocgw » Fri Dec 28, 2018 5:51 pm UTC

This my first solid, genuine GOOMHR moment.

I have a very detailed numbers path in my mind that probably started when I first learned 1 thru 10. Then my curve takes a hard left from 11 thru 20, and then straight upwards to 100. And lots more strange but consistent bends.

On top of that, at times I just drop a few triplets of exponent, so what was the 1000 point on my curve is treated as the 1000 * 10^9 , and so the one million point is now 1 000 000 *10^9, and so on.

BTW, complex numbers get no respect -- they're all in an X-Y plane. Go figure.
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Re: 2091: "Million, Billion, Trillion"

Postby Heimhenge » Fri Dec 28, 2018 5:55 pm UTC

Pfhorrest wrote:Do billiards as in thousand-billions have anything to do with the game played with hard balls on a felt-covered table?


Only if you're playing the game with a billiard balls.

https://www.etymonline.com/word/billiards

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Re: 2091: "Million, Billion, Trillion"

Postby da Doctah » Fri Dec 28, 2018 6:15 pm UTC

For years now I've been trying to get people to accept Thousiard as another name for 10^6.

Here's one I foisted upon a trivia contest a few years back: what's the next number in the series 3, 9, 27, 2, 0, ...? When everyone announced they were stuck, I offered the first hint that I would accept an approximate answer correct to five decimal places.

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Re: 2091: "Million, Billion, Trillion"

Postby Justin Lardinois » Fri Dec 28, 2018 6:56 pm UTC

Duffman77 wrote:I find it amusing that the average American doesn't know anything above trillion. If you google search "how much water does the Earth have", they tell us the Earth has 326 Million Trillion gallons... this sounds like an 8 yr old saying "million billion gazillion bajillion". So this would be written as 326,000,000,000,000,000,000. Last I checked, a number with 18 zeros after it is called a quintillion-- not a "million trillion"

Colin


I think it’s a useful way to explain the number. I’m aware of what a quintillion is, and could write it out numerically, but I don’t really have a mental concept of how much a quintillion is. I can sort of conceptualize a million, less so with a billion, and even less so with a trillion. It drops off entirely after that.

da Doctah wrote:For years now I've been trying to get people to accept Thousiard as another name for 10^6.

Here's one I foisted upon a trivia contest a few years back: what's the next number in the series 3, 9, 27, 2, 0, ...? When everyone announced they were stuck, I offered the first hint that I would accept an approximate answer correct to five decimal places.


I’m gonna need another hint.

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Re: 2091: "Million, Billion, Trillion"

Postby yakkoTDI » Fri Dec 28, 2018 7:39 pm UTC

I explain it to people like so.

If you spend $1.00 per second $1,000,000.00 (that's million with an illion) will last about 11.574 days.

If you spend $1.00 per second $1,000,000,000.00 (that's billion with an illion) will last about 31.709791 years.

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Re: 2091: "Million, Billion, Trillion"

Postby Showsni » Fri Dec 28, 2018 7:51 pm UTC

Also chiming in my support for the long scale. I don't care if we've officially decided to move to the short one since 1974, I'm not changing!

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Re: 2091: "Million, Billion, Trillion"

Postby da Doctah » Fri Dec 28, 2018 9:55 pm UTC

Justin Lardinois wrote:
da Doctah wrote:Here's one I foisted upon a trivia contest a few years back: what's the next number in the series 3, 9, 27, 2, 0, ...? When everyone announced they were stuck, I offered the first hint that I would accept an approximate answer correct to five decimal places.


I’m gonna need another hint.


Okay. The part of the sequence already supplied relies in two different ways on using the American names for numbers rather than the British.

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Re: 2091: "Million, Billion, Trillion"

Postby jeanrenaud » Fri Dec 28, 2018 11:52 pm UTC

This is why we begin to see "M$, G$" in some publications. With the computer era, most people will understand these terms and their signification is the same in every language. Mega/Giga/Tera/Peta/Exa (i don't think an ExaDollar will come to life soon)...

... even if there is a confusion between base 2 and base 10 depending on the context (MegaByte = 2^20 <> MegaDollar = 10^6) - Computer guys know that a Mega is in base 2 in computers, and in base 10 everywhere.

In french, we also use "Milliard, Billiard" terms.

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Re: 2091: "Million, Billion, Trillion"

Postby GlassHouses » Sat Dec 29, 2018 3:00 am UTC

jeanrenaud wrote:This is why we begin to see "M$, G$" in some publications. With the computer era, most people will understand these terms and their signification is the same in every language.

Except in financial jargon, M means thousand and MM means million...

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Re: 2091: "Million, Billion, Trillion"

Postby djn » Sat Dec 29, 2018 12:43 pm UTC

I kind of have the opposite problem - I have to remind myself that a milliard/billion is just a thousand millions, not more.

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Re: 2091: "Million, Billion, Trillion"

Postby MrT2 » Sat Dec 29, 2018 5:04 pm UTC

GlassHouses wrote:
jeanrenaud wrote:This is why we begin to see "M$, G$" in some publications. With the computer era, most people will understand these terms and their signification is the same in every language.

Except in financial jargon, M means thousand and MM means million...

I've seen people writing G as in (a) grand, rather than using k for thousand... shades of xkcd 927 (Standards).

I remember as I grew up, the UK flipped from the old approach to billions to the US version, so for clarity, news reports etc. would either write/say billion (1000 million), or just plain said "thousand million" "million million" as needed. Either I'm too young for milliard/billiard, or it wasn't common usage in the UK, and thousand million was used instead.

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Re: 2091: "Million, Billion, Trillion"

Postby da Doctah » Sat Dec 29, 2018 9:38 pm UTC

MrT2 wrote:I remember as I grew up, the UK flipped from the old approach to billions to the US version, so for clarity, news reports etc. would either write/say billion (1000 million), or just plain said "thousand million" "million million" as needed. Either I'm too young for milliard/billiard, or it wasn't common usage in the UK, and thousand million was used instead.


Back in college when I was doing some songwriting, my lyricist chose "thousand million" because he needed the extra syllables for the meter.

Even then, it made me picture a beturtlenecked Carl Sagan standing there repeating "beelion, beelion, beelion....

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Re: 2091: "Million, Billion, Trillion"

Postby kdb » Sun Dec 30, 2018 11:39 am UTC

da Doctah wrote:For years now I've been trying to get people to accept Thousiard as another name for 10^6.

Here's one I foisted upon a trivia contest a few years back: what's the next number in the series 3, 9, 27, 2, 0, ...? When everyone announced they were stuck, I offered the first hint that I would accept an approximate answer correct to five decimal places.


Thousiard for million would not make sense though. I mean, originally million was basically a fix for "hey, mille is thousand, and millemille sounds stupid" (it went that way, right?). German and other languages with the "-iarde" steps are pretty consistent, as it results in "-illion" always being "10⁶ⁿ" where n is the numeric prefix (bi-, tri-, ...), but becoming fully regular only beginning with Billion (10¹²). The english way currently is "10³ⁿ⁻³" and regular starting with billion (10⁹), which may count as advantage. Thousiard would result in "10⁶ⁿ⁺³", also only becoming regular at billion (10¹⁵), thus being the worst of the three.

But all of them neglect the weird irregularity! So I suggest to go through consistently, and derive the lesser numbers from latin numeric prefices too! I thus suggest to to 1=nihillion, 10³=nihilliard, 10⁶=unillion, 10⁹=unilliard, 10¹²=billion, ... !!!!

Code: Select all

       EN           Yours        My Suggestion  GER

 1e0   one          one          nihillion      Eins
 1e3   thousand     thousand     nihilliard     Tausend

 1e6   million      thousiard    unillion       Million
 1e9   billion      million      unilliard      Milliarde

 1e12  trillion     milliard     billion        Billion
 1e15  quadrillion  billion      billiarde      Billiarde

 1e18  quintillion  billiard     trillion       Trillion
 1e21  sextillion   trillion     trilliard      Trilliarde

 1e24  septillion   trilliard    quadrillion    Quadrillion
 1e27  octillion    quadrillion  quadrilliard   Quadrilliarde

       EN           Yours        My Suggestion  GER



Can someone suggest this to a standards comittee? It would make budget discussions so much more fun, if politicians can speak about nihillion coins!
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Re: 2091: "Million, Billion, Trillion"

Postby Soupspoon » Sun Dec 30, 2018 3:10 pm UTC

My version: Slightly irregular powers for tens (1) and hundreds (2) being exclusive to each other. Treat everything else as the power that is a given binary exponential times 3. Thousand as 20.3, Million as 21.3, the rest (Bi-, Tri-, etc) are 2prefix.3

A "hundred thousand million billion trillion" is ten to the power of (2)+(20.3)+(21.3)+(22.3)+(23.3) or 2+3+6+12+24, or 1047. (In short form that's maybe quadecilion (or quattuordecillion, or others like that). In normal long form that'd be a hundred septilliard or a hundred thousand septillion).

Ten times more than that rolls up as follows:
Ten times that hundred is a thousand (…thousand million billion trillion).
That new thousand thousand (…million billion trillion) is a million (…million billion trillion).
That new million million (…billion trillion) is a billion (…billion trillion).
That new billion billion (…trillion) is a trillion (…trillion).
That new trillion trillion (…) is a straight quadrillion.
Quadrillion is ten to the power of 2⁴.3, i.e 1048 (Possibly known as quin(que)decillion, in short form, octillion in long form). 1047x10 = 1048. QED!

For more significant places you use the existing method of "forty three thousand, four hundred and sixty two" (the "and" features in the English format - the American one misses it out, as usual!).where a quadrillion minus 1 is… "((((nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) million, (nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) billion, ((nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) million, (nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) trillion, (((nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) million, (nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) billion, ((nine hundred and ninety-nine) thousand, nine hundred and ninety-nine) million, (nine hundred and ninety-nine) thousand, nine hundred and ninety-nine". With ()s added just in case you somehow get confused by my utterly simple method of lower power being considered a subordinate (i.e extra) part of the multiple w.r.t. higher powers they precede but purely in their final form additive to anything larger that they succeed. Obviously!


If you want to rename million to unillion, then make the thousand (d|h|s)emillion. Hundreds and tens should probably be somewhere along the line of tritillion and hectillion. Because decillion-with-a soft-c (to go with centillion) would be confusing, as would using sextillion at the million1/6 level.

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Re: 2091: "Million, Billion, Trillion"

Postby Flumble » Sun Dec 30, 2018 6:46 pm UTC

Why do we insert magnitude qualifiers into numbers anyway? Like 12,548,207 is pronounced "twelve million five hundred and forty eight thousand two hundred and seven". That's four orders of magnitudes sprinkled throughout the number. Why not say the magnitude followed by the (most significant) digits of the number: "ten million one two five four eight two oh seven"? Or simply start with "seven orders" instead of -illion/-illiard words and give those words back to french/italian/latin/PIE.* Call it blatant plagiarism of scientific notation, but we could use some more granularity (and consistency) in magnitudes while at the same time making numbers easier to process.

I don't know what you'd lose when using this system in practice—I guess it mostly lacks error correction, because if you miss a digit (either in the exponent or the mantissa) you can only find out that you missed something, not where or what. Then again, if something involves more than 4 significant digits, it should involve a computer.
Also, adding numbers of different magnitudes becomes more taxing in your head (just like it does in computers BTW) because what's 5°738+3°611? It definitely starts with 5° and 7, and fortunately the rest is not relevant for a quick estimate. But what about 5°938+4°6318? 5°...+4°... usually comes out to 5°... except if you calculate this one to three digits. Fine, every digit higher than 3 rounds to log(x)≈1 order, so 5°938 and 4°6318 should be mentally rounded to 6° and 5° anyway, so you'd end up with 6°. Which begs the question: can you devise a notation that doesn't have this problem? A purely logarithmic notation 4°6318≈10^4.801 would make the rounding easy, but you lose the integers (except powers of 10). And counting 0°1, 0°2, 0°3, 1°4, 1°5 feels absurd too.


*This also makes a dad joke "Everyone wants a beer? ...that's a whopping 5 orders of beer! But I only have a few crates!" commonplace. It may be an awful joke, but it's still orders of magnitude better than "Why is 6 afraid of 7? Because 7 @ 9.".

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Re: 2091: "Million, Billion, Trillion"

Postby orthogon » Sun Dec 30, 2018 8:14 pm UTC

Soupspoon wrote:If you want to rename million to unillion, then make the thousand (d|h|s)emillion.

I thought a semillion was half a Chardonnay, or something?
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 2091: "Million, Billion, Trillion"

Postby somitomi » Tue Jan 01, 2019 11:58 am UTC

jc wrote:
Soupspoon wrote:
Sly wrote:Anyhow, I hope this "First Post" was done correctly.

(Looks good to me!)

I'm also a long-scale person, myself, by instinct.

Although I'm convinced that as Thousand*Thousand is Million and Million*Million is (Long) Billion that it should continue to Billion*Billion being a Trillion, Trillion*Trillion being Quadrillion, etc. We'll get so many more numbers to play with, and the above graph of perception vs actuality of value would be interesting.


Of course, the mathematically inclined among us will treat it as a bit of a silly language issue, and continue to prefer the simpler exponential notation as the easiest to understand and meaning the same thing everywhere.

But there is the ongoing problem that the software developers still haven't come up with a reliable way to trick our screens into showing the correct representation of exponentials. Yeah, sometimes you can type things that work in a single app on your screen, but touching the same keys don't produce the same result in other windows, and when you hit Return or Send or Submit or the little winged widget or whatever to send it, it doesn't look the same on other readers' screens. Sometimes you can use TeX formatting, but again it often fails in many readers' windows. You can't even use the HTML (or BBcode) SUP tag and expect it to work in others' browser windows.

You'd think that software developers would understand mathematical notation better than the general population, and make sure simple expressions work widely and consistently, but this seems not to be true.

So just use E-notation, which works even with only ASCII characters or Morse code.
But if metric units are involved, you can just use prefixes properly and say "the Earth is 150 gigameters from the Sun" instead of nonsense like "million kilometers"
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Re: 2091: "Million, Billion, Trillion"

Postby rmsgrey » Tue Jan 01, 2019 3:47 pm UTC

somitomi wrote:But if metric units are involved, you can just use prefixes properly and say "the Earth is 150 gigameters from the Sun" instead of nonsense like "million kilometers"


How would you express the volume of the observable universe in metric units using prefixes properly?

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Re: 2091: "Million, Billion, Trillion"

Postby GlassHouses » Tue Jan 01, 2019 4:50 pm UTC

rmsgrey wrote:
somitomi wrote:But if metric units are involved, you can just use prefixes properly and say "the Earth is 150 gigameters from the Sun" instead of nonsense like "million kilometers"

How would you express the volume of the observable universe in metric units using prefixes properly?

Four hundred million cubic yottameters.

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Re: 2091: "Million, Billion, Trillion"

Postby somitomi » Tue Jan 01, 2019 4:51 pm UTC

rmsgrey wrote:
somitomi wrote:But if metric units are involved, you can just use prefixes properly and say "the Earth is 150 gigameters from the Sun" instead of nonsense like "million kilometers"


How would you express the volume of the observable universe in metric units using prefixes properly?

I'd say "fourhundred million cubic yottameters".
Yes, there are corner cases (very distant ones) where my advice doesn't work, but then this order of magnitude rarely appears in everday life, news or even scientific papers. And you can always try convincing the CGPM to make "hella-" a thing.
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Re: 2091: "Million, Billion, Trillion"

Postby jonhaug » Wed Jan 02, 2019 8:44 am UTC

For you unold (aold, disold, ilold, imold, inold-, irold, nonold?), the MIT professor Douglas Hofstadter's had a Scientific American article worth mentioning: https://www.gwern.net/docs/math/1982-hofstadter.pdf. A random quote:

THErenowned cosmogonist Professor Bignumska, lecturing on the
future ofthe universe, hadjust stated that in about a billion years, according
to her calculations, the earth would fall into the sun in a fiery death. In the
back ofthe auditorium a tremulous voice piped up: "Excuse me, Professor,
but h-h-how long did you say it would be?" Professor Bignumska calmly
replied, "About a billion years." A sigh ofrelief was heard. "Whew! For a
minute there, I thought you'd said a million years."


/Jon

PS Did Carl Sagan really say "Billions and billions"?

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Re: 2091: "Million, Billion, Trillion"

Postby da Doctah » Wed Jan 02, 2019 9:30 am UTC

I'm sure that on many occasions after he became known to the general public, people who met Dr Sagan on the street were able to persuade him to say "billions and billions". I do recall him saying things like "a billion billion stars in a billion billion galaxies" during the course of the original Cosmos series.

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Re: 2091: "Million, Billion, Trillion"

Postby Archgeek » Thu Jan 03, 2019 1:39 am UTC

Flumble wrote:Why do we insert magnitude qualifiers into numbers anyway? Like 12,548,207 is pronounced "twelve million five hundred and forty eight thousand two hundred and seven". That's four orders of magnitudes sprinkled throughout the number. Why not say the magnitude followed by the (most significant) digits of the number: "ten million one two five four eight two oh seven"? Or simply start with "seven orders" instead of -illion/-illiard words and give those words back to french/italian/latin/PIE.* Call it blatant plagiarism of scientific notation, but we could use some more granularity (and consistency) in magnitudes while at the same time making numbers easier to process.

I don't know what you'd lose when using this system in practice—I guess it mostly lacks error correction, because if you miss a digit (either in the exponent or the mantissa) you can only find out that you missed something, not where or what. Then again, if something involves more than 4 significant digits, it should involve a computer.
Also, adding numbers of different magnitudes becomes more taxing in your head (just like it does in computers BTW) because what's 5°738+3°611? It definitely starts with 5° and 7, and fortunately the rest is not relevant for a quick estimate. But what about 5°938+4°6318? 5°...+4°... usually comes out to 5°... except if you calculate this one to three digits. Fine, every digit higher than 3 rounds to log(x)≈1 order, so 5°938 and 4°6318 should be mentally rounded to 6° and 5° anyway, so you'd end up with 6°. Which begs the question: can you devise a notation that doesn't have this problem? A purely logarithmic notation 4°6318≈10^4.801 would make the rounding easy, but you lose the integers (except powers of 10). And counting 0°1, 0°2, 0°3, 1°4, 1°5 feels absurd too.


*This also makes a dad joke "Everyone wants a beer? ...that's a whopping 5 orders of beer! But I only have a few crates!" commonplace. It may be an awful joke, but it's still orders of magnitude better than "Why is 6 afraid of 7? Because 7 @ 9.".

Keep your hundreds around and you wind up with spoken Engineering Notation, like "twelve point five four eight two oh seven million", which happens to be the way I tend to think (and speak) about such figures.

Adding remains trivial enough when magnitudes are close: 5°738+3°611 = 73.8E+6 + 611E+3 = 73.8E+6 + 0.611E+6 = 74.411E+6 = "seventy four point four one one million" and 5°938+4°6318 = 93.8E+6 + 63.18E+6 = 156.98E+6 = "one (hundred) fifty six point nine eight million".

This of course has the usual scientific/engineering notation bonus of working gleefully with negative exponents for very small quantities, and the engineering notation bonus of dovetailing nicely with the SI prefix festival.

It's also easy enough in this case to prevent making the counting numbers (and the large decimals) weird by explicitly leaving out the exponent when it's within (-4, 3) : (999E-4, .001, .002 ... .999, 1 ... 999, 1E+3), which fits with the pattern of there never being more than three digits in the mantissa on the business end of the radix.

Edit: adjusted that exponent range for leaving it out. Intent was to leave unit and milliunit exponents to be implied by the radix alone. I do not know where I got -6 from.
Last edited by Archgeek on Fri Jan 04, 2019 4:32 pm UTC, edited 1 time in total.
"That big tube down the side was officially called a "systems tunnel", which is aerospace contractor speak for "big tube down the side."

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orthogon
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Re: 2091: "Million, Billion, Trillion"

Postby orthogon » Thu Jan 03, 2019 10:21 am UTC

Archgeek wrote:SI prefix festival
There's an SI prefix festival? Where is it? How do I get tickets? Who's headlining this year?
xtifr wrote:... and orthogon merely sounds undecided.

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YellowYeti
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Re: 2091: "Million, Billion, Trillion"

Postby YellowYeti » Thu Jan 03, 2019 11:22 am UTC

orthogon wrote:
Archgeek wrote:SI prefix festival
There's an SI prefix festival? Where is it? How do I get tickets? Who's headlining this year?


That'll be The Killers.

With Megadeth as the support.


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