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Million Times Million

susam.net

111 pointssusam95 comments

As a kid I stressed our Olivetti divisumma 24 ( https://www.ithistory.org/sites/default/files/hardware/Olive... ) with a million times a million. It entered a perpetual mechanical cycle that even unplugging it could not break. Finally Dad had to attack its innards and tug and twiddle until he pulled out a spring loaded gear and it caught a cog on the next go-round. It lifted its digit arms and printed out a 'partial answer' that was a series of random numbers as wide as the whole mechanism.

He said "please don't do that again." I moved on to torture computers.

Spanish uses the long scale, but lately I've been noticing people mistakenly using the short scale in Spanish more and more, likely due to the influence of English and the internet, sometimes even in news articles and other "professional" publications. You may see someone speaking of "un trillón de dólares" (a trillion dollars), which while it makes sense in English when speaking of federal budgets or the market cap of FAANG, in long scale that's more than the world's entire money supply.

It's especially annoying because it creates ambiguity and renders the *illón-words fairly useless.

It's only "mistakenly" until it becomes the norm, which as another Spanish speaking person, I bet that will be the case no long in the future.

Yeah, I too think that's likely the direction we're heading, and I'd be fine with either option as long as it was consistently used, this transitional phase is just painful.

In the meanwhile you can say one thousand millions (for what Americans call a billion), like the local tv news does, and for the bigger one say just say millions of millions (what Americans call a trillion), that should be unambiguous enough.

In Dutch the word "miljard" for 10^9 is too well known and deeply ingrained to change I think, but with "triljoen" which could either mean 10^18 or a direct conversion from the American English trillion, all bets are off

If you want to be unambiguously understood, especially in international context, it seems it's better to avoid words beyond "million" altogether.

"million of millions of dollars" or "ten to the twelfth dollars" or "one tera dollar" or even "one EEE twelve" (for programmers) will always be understood correctly, no matter which part of world listeners are from.

The only everyday context where numbers on that scale are commonly used is money/finance, and it's pretty universal in that context that 1e9=B=billion, 1e12=T=trillion. This long scale/short scale distinction gets posted a lot but it's one of those cases where in practice it seems to matter very little.

In science and engineering you'd rather use scientific notation anyway, and in math and CS notoriously only 3 numbers exist: 0, 1 and n.

You don't seem to get the point. That is only universal in current day English. In e.g. Finnish: miljoona = 1e6, miljardi = 1e9, biljoona = 1e12, triljoona = 1e18.

According to Wikipedia the two variants exist because the digits of large numbers used to be grouped into groups of six digits but in order to improve readability this was eventually changed to groups of three digits and some insisted that with that also the naming should be adjusted. A long scale trillion has three digit groups when using groups of six digits (1,000000,000000,000000) and six after the switch to groups of three (1,000,000,000,000,000,000) which then should be a short scale sextillion but somehow it ended up as a quintillion.

So basically

  2 commas = "Millions"
  3 commas = "Billions"
  4 commas = ...

N-illion = 1000^(n-1)

The original long scale makes more sense, billion, bi million, twice six digits.

Yet, mille and milli- mean thousand.

But the suffix -one in Italian is used to indicate something big - spaghetti vs spaghettoni - so a milione is a big thousand, a million.

Isn't it more like:

  N-illion = (Size_of_Digit_Grouping)^(n-1)

Since the OP was saying groupings use to be by 6-digits, not 3-digits (i.e. "1,000") as seen today.

I'm sorry it had to be done https://www.youtube.com/watch?v=rIB5HEcZBs8

Thanks!

This is the key piece of information for making sense of it. Ultimately the OP's insight is that the number-naming system used in the west is thousands based instead of millions based, but came to that by observing the number-naming outcomes instead of the source notation that led to it.

TIL about one more thing US misunderstood and now we have to deal with it. Another one is command key on mac, "borrowed" from road sign indicating "sight seeing place" :)

https://brndstudio.medium.com/how-a-swedish-road-sign-inspir...

What was misunderstood in the command key? The link mentions nothing of the sorts

Don't know anything about misunderstandings, but the symbol in question is https://en.m.wikipedia.org/wiki/Looped_square

I don't see how borrowing the Swedish "point of interest" symbol for the command key is "misunderstanding" something - as I understand the story, they just liked the symbol and decided to use it.

Also, I'm certainly not a US apologist, but I also don't see how the US using the short scale is a case of misunderstanding - it sounds like they just decided that it makes more sense that way (and I would agree, although maybe that's just because I'm used to it).

It makes no sense I’d say. In many European languages it’s milliard, etc.

Why is million special when the numbers are grouped in 3s (thousands)? That makes no sense. Why flip flop suffixes between ion and iard?

this is so funny because i always envied english for it being so clear: million, billion, trillion. in german we have these "awkward" names in between: million, milliarden, billionen, billiarden. but now hearing about this long scale it actually does make quite a lot more sense when thinking about it in multiples of millions

same in polish milion, miliard, bilion, biliard, trylion, tryliard, kwadrylion, kwadryliard...

I think they forgot "thousandard" = 1,000,000. And million is a thousandard of those.

Swedish does that as well. miljon, miljard, biljon, biljard.

This is sufficiently confusing to people that every time I see a newspaper article mention something is a biljon of something they have to mention how much it is and remind readers to not confuse it with an American billion (that is only a miljard).

In most contexts when big numbers like those show up though the metric-system comes to the rescue, since things will be referred to as being a mega-something or giga-something etc anyway. That works great until Americans attempt to do it and get the letters wrong or use K instead of k or M instead of m that causes new confusion and then we're back at having to guess what something means depending on what side of the Atlantic it was written.

same in Italian: milione (1E6), miliardo (1E9), bilione (1E12) etc.. the long scale a "one" is 1E6 bigger than the previous one, example: bilione is 1E6 bigger than milione.

I am British and the old scale (million, milliard, etc) makes more sense to me as it allows you to describe much larger numbers with fewer words.

And in East Asia, we use a system based on exponents of 10000. I kind of like it, except when I have to think about it and the short/long scales at the same time.

10000^1 = 万 10000^2 = 億 10000^3 = 兆 10000^4 = 京

Ah the Myriad system. Curious how the sinosphere adopted this alongside the Greeks.

These do converge I think at

10^12 = Short Trillion/Long Billion

Which makes for some non-frictionless translating since 10^6 and 10^9 are all in-between words, and 10^12 is not a commonly used number to count anything in everyday life.

It is used in all European countries (I don't know any European country that doesn't use it). I know the long scale under the name "European" and the short scale as "American".

UK used to do it the European way, but has adopted American way since (IIRC) about 50 years ago. As a Brit I wish we still used the traditional way.

(And despite Brexit, UK still is a European country!)

It may take fifty years, but I think that you will eventually rejoin the EU.

Or whatever the thing is then.

I definitely hope so! (And hope it won't take that long, but it wouldn't surprise me.)

>I don't know any European country that doesn't use it

With the exception of people over 70, the UK has pretty uniformly moved to the American system. All of our govt statistics, corporate finances info, day-to-day conversations involving billions refer to "one thousand million"

Same in Ireland, the long scale was already an elderly person thing when I was a child

Same in Australia. I vaguely remember learning the old scale at school and being confused by American usage. Now everyone uses short scale, and most young people probably don't even know the old scale existed.

I guess US could change to Long scale and that would make their debt sound way less, it is no longer in trillion dollar range!

I just seamlessly switch scales and units with the language.

When I talk Swedish I think in terms of long scale, 24 h clock, SI units.

When I talk English I think in terms of short scale, 12 h clock, imperial units.

It's like different cultural basis vectors.

Numberphile did a video on this many years ago: https://www.youtube.com/watch?v=C-52AI_ojyQ

Long scale seems to be much better because you have to remember fewer prefixes, so with fewer easier to remember rules you get wider coverage

Why didn't this principle win?

On the other hand, I think short-scale millions and billions are used far more often than the larger numbers, and the starts of words tend to be more salient than the ends, so it's useful to have them distinguished by the first letter instead of the last syllable.

(Plus, "milliard, with an 'ard'" doesn't have the same ring to it.)

Well who wants to be a milliardaire? Or even worse, a billiardaire, sounds like you just play pool.

A theory that's been brewing in my mind is the success of the US can largely be attributed to having a single common language.

Even in England itself people use different words to describe the same thing, causing confusion. In many other countries they speak completely different languages!

In the US it's all the same. As an Englishman it's remarkable to me that people in Boston and people in California are really not that different at all. Some may say it's boring, but it can't be denied how easy it makes business etc. So many of the problems I have at work are due to language. It's doubly difficult when you're talking with people with a different native tongue. Some things just don't translate and even if they do it adds overhead.

So, ultimately, it doesn't matter what Americans say or how much they've "misunderstood" English etc, what matters is that every single one of them understands the same billion, the same units of measurement, the same idioms etc.

I'm kinda wondering are there any countries that still use the long scale nowadays? For me the biggest thing I've had to learn is that in Russian we use a short scale, except we don't have "billion" and instead it's "milliard". So it's just that you need to be careful with translating that one word. Are there other countries where the scale "shifts"?

In Italian, "billion" is still normally called "miliardo".

edit: can't spell

Small typo, but it's "Miliardo" (one "l").

German does.

Portugal uses it, but probably due to foreign influence there’s more and more people that use the short scale, which makes everything a mess

Yep it's a mess. Most newspapers and official channels just avoid the word billion altogether, just writing "mil milhões" (a thousand million).

AFAIK the exception is the finance world, where I believe B stands for the short scale for a long time, and $1B has been used in newspapers for a long time too due to globalisation of the economy.

Isn’t “mil milhões” the proper term in the long scale? “Bilião” would be equivalent to the short-scale trillion, e.g., “NVidia vale $4 biliões”, which is equivalent to “NVidia is worth $4 trillion”.

I’m

Germany and France do. It can be a PITA when dealing with English texts... But then again when dealing with things in an international context you'll also encounter Chinese and Indian systems for large numbers.

Chinese:

  1 yi
  10 shi
  100 bai
  1000 qian
  10000 wan
  10 x 10000 shi wan (hundred thousand)
  100 x 10000 bai wan (one million)
  1000 x 10000 qian wan (ten million)
  1 x 100.000.000 yì (hundred million)
  10 x 100.000.000 shi yi (one billion)

Indian: no idea how it works in practice but it involves crore and lakh...

China seems to have even more scales..

  myriad scale - based on 10.000
  mid-scale    - based on 10⁸
  long scale   - based on doubling of exponent (4, 8, 16, 32, ..)

The Indian system is coincidentally being discussed right now at https://news.ycombinator.com/item?id=44492175 .

> Indian: no idea how it works in practice but it involves crore and lakh...

They write thousands just like in the U.S. system, with the same commas: 20,000. But beyond that, the "lakh" is 100k, the "crore" is 10M, and commas in written figures go in twos:

The population of Australia is about 2.8 crores: 2,80,00,000. The Delhi metro area is over 3.4 crores: 3,40,00,000.

They have more unique words for every 100-multiple unit after crore, to go along with the commas, but in everyday practice they don't use those terms. Instead, they go "long" on the crores. Thus, India's population is about 146 crores; the new Mumbai underground Colaba-Bandra-SEEPZ line will cost ₹21,000 crore.

When reporting foreign money, they use the U.S. system with millions and billions as usual: ₹21,000 crore is parenthesized (US$2.5 billion).

Czech does as well, milion, miliarda, bilion, biliarda...

Pretty much all of continental Europe is on long scale. In computing it's masked by SI prefixes. Nobody talks about billion bytes whatever it means.

https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/ES...

Would be cool to use "ten giga-euros" to express "10 billion €". A bit like giga-gram in ... astronomy?

I'd prefer if US tech went with giga parameters instead of billion.

Same in Turkey. We say Milliard instead of Billion. In my childhood I can swear it was like Million->Milliard->Trillion->Trilliard. They were in daily language because 1 Million Turkish Lira was like a few dollars. At some point they decided Trilliard does not exist and it became something like a Mandela Effect for me. We never used Billion though.

I still don't know which is which. Just give me the power to the 10, Is it 10^9 or 10^12? Who know?

So you skip billion? What comes after, Quadrillion or Quintillion? (Sure they are not common, but in theory.)

Sweden still does (and I believe the other Scandinavians as well).

Spain.

But more and more people use "billions" (not billardo, which is our own term for it). The same people that say "diez kas" (for 10k) instead of "diez mil" like they're saving words for doing that (hint: no).

>The same people that say "diez kas" (for 10k) instead of "diez mil" like they're saving words for doing that (hint: no).

I sometimes say (in Portuguese) "dez kapa".

It's just slang. Language changes a lot faster than you realise, and a lot of words that are "normal" to you would illicit the same response before you were born.

The same thing happened to me, except I was younger and could adapt more easily.

I'm bilingual, I watch and read content in both Spanish (my native language) and English. Back in 2021, I heard that Rick Astley's "Never Gonna Give You Up" had hit 1 billion views on YouTube. I loved that song back then.

I was really amazed, so I decided to check it out for myself. But to my surprise, the video said “1000 millones de vistas” (millón = million). Confused, I asked myself, “Why do they say the video hit one billion views if it only says one thousand million here?”

That’s when I figured out that billón doesn’t mean the same as billion.

And now, years later, I’m reading your blog post about your experience, and commenting on it in a language that’s not even my native one.

I'm from Denmark were we use the long scale. I didn't know a long scale form existed in English! It happens quite often that a billion, in English, gets translated to a billion in Danish, which is off by 999 billion and, of course, should have been a milliard. ;-)

If it happens in Spanish, it probably happens in most of Europe. https://news.ycombinator.com/item?id=44509534

The bit about the name “billion” still literally meaning “million million” in long scale really shows how old language shapes modern confusion.

What’s interesting is that the long scale actually matches the literal Latin root more closely, so in a way, the “modern” short scale is less intuitive linguistically, but more practical numerically.

Any of those numbers higher than a trillion are a bit useless really — when dealing with large numbers I'm using scientific or engineering notation, or using SI prefixes.

Oh I never got why there was a confusion for the value of billion and co. I always assumed I did not get the proper value, but now it makes much more sense!

A number-to-words in both long and short scale in various languages would be a neat selling point for a calculator program.

I Spanish language we have this dad joke:

¿Que es un millón? Mil miles.

¿Que es un billón? Un millón de millones.

¿Que es un semillón? ???

Una semilla muy grande.

"Mr. President, two Brazilian soldiers were killed yesterday in Iraq." "Oh my god... How many is a Brazilian?"

Is the billiard (10^15) the name sake of the 15-ball game by the same name?

I don't think so: https://www.etymonline.com/word/billiards

The 80's song "One Billion is Big" by the "Fat Boys" seems very relevant here: https://www.youtube.com/watch?v=TdnLhN4SeYY

I know we're not supposed to complain about being voted down, but this is a case where the downvoters are simply wrong and need to be corrected.

This is a fantastic educational song designed to teach children how big a billion is by using examples involving hamburgers. I promise it will be the best 80's educational rap you hear all day.

Oh thanks for completely breaking my numeracy. Gotta relearn maths real quick

>imagine my disappointment when I left home for university, got access to computers and the World Wide Web, and discovered that the names I had learnt were off by several orders of magnitude

imagine discovering mega- giga- tera- then not mentioning them

In the long system how is a billionaire called? A milliardaire? That doesn't sound right.

Milliardaire yes, of course. Why doesn't that sound right to you?

https://fr.wikipedia.org/wiki/Liste_des_milliardaires_du_mon...

It doesn't sound like English, at least in my brain it doesn't register as English, and I may have found a plausible reason: If you look up the amount of English words with the letters "iarda" on them you only find 3 words (at least according to wordmine.info), but French shows 38 words, even just "arda" the difference is huge: 317 vs 2017 words https://www.wordmine.info/french/words-with?minletters=2&max...

Well, it's mostly the -aire ending that is uncommon in English, because it comes from French, as far as I know all -aire words in English are straight French loanwords. It's somewhat equivalent to the English suffix -ar.

That makes millionaire and billionaire about as unenglish as milliardaire, I think it just doesn't sound weird to you because you see them more often.

>It doesn't sound like English [...]

Guess what? Some people (70-80% of the world) speak other languages.

In Czech, which uses the long scale, yes. The equivalent of "milliardaire".

Exactly how it's called in french

Well, Trump and Musk can just get up in front of the UN and say, "to most of the world we're mere milliardaires, not billionaires!"

The Economist (British) changed from million million -> thousand million in (1944) -

"If it is objected that a billion in this country is reserved for the meaning of a million million, then it can be counter-objected that, if so, it is reserved for a use that interests nobody but astronomers and the historians of German inflation"

The US leading the way in a sensible measuring system.

This was flagged. I vouched for it as it has an interesting insight, even if you find the joke unnecessary.

I did however not find the quote via Google search. Can you share the source?

EDIT: I have found the source! https://archive.org/details/sim_economist_1943-11-06_145_522...

The Economist, November 6, 1943:

>The “Billion”

>This week, for the first time, the note circulation is in excess of £1,000 million. There is, of course, very little real difference between £999 million and £1,001 million—apart from a difficulty for the compositor who works within a narrow column. And yet there is a great psychological barrier, and the setting-down of that extra digit, with its comma following, seems to symbolise the breaking of fresh ground. The totals of revenue and expenditure have, of course, been in ten figures almost ever since the beginning of the war, and the total of the national debt—a rather shadowy notion anyhow—is well into eleven. With the line crossed by a third familiar statistic it is natural to ask what this magnitude of 1,000 million is to be called. There is no word native to these islands. The continental word “milliard” was in some use some years ago, but has not been used very much recently. Well over half the English-speaking peoples, however, use “billion” to mean a thousand million, and if it is objected to this usage that a billion in this country is reserved for the meaning of a million million, then it can be counter-objected that, if so, it is reserved for a use that interests nobody but astronomers and the historians of German inflation. For some time past, The Economist has been using “billion” in American contexts with the American meaning—i.e:, one thousand million. It now seems convenient to extend that usage to British and foreign contexts. Henceforward, in these columns, in the absence of specific indication to the contrary, “billion” means 1 and nine 0’s.

> I have found the source

Nice work.

So you know, all your comments are getting auto-flagged (aka. [dead])

Reply on news.ycombinator.com