The problem with how we say and write numbers

[Bohandas]

Am I the only one who thinks that numbers ought to be written and pronounced the other way around?


The way we use now it's harder to figure out how to say a large multi-digit number's name from reading it than it is to say anything else you might read.

For example, take the number 20598695 (which I've just pulled up from a random number generator). To figure out how to say this as an actual number and not just a string of digits I first have to count how many digits are in the number, figure out the place value of the leftmost digit (in this case tens-of-millions) and count down from there: "Twenty million five hundred and ninty-eight thousand, six hundred and ninty-five"

However if we said and wrote numbers starting wih the ones column the entire number would come naturally from how it would be written with no unnecessary counting of digits (the same number would be written 59689502 and expressed as "five ninty six-hundred, eight and ninty and five-hundred thousand, and [zero and] twenty million")

On a tangentially related note, spoken numbers would also be easier to understand if we switched to what I like to call a "Very short count" system in which the word "thousand" was dispensed with, and all the other words for large numbers were moved down three places to fill the gap. Thus "million" would now refer to 1000 (which makes more sense anyway from a linguistic standpoint because it's derived from the Latin "mille" meaning 1000, although I must stress that this is NOT my rarionale for proposing this system), "billion" would refer to 1000000, "trillion" woukd refer to "1000000000" and so on. The upshot of this is that the prefix in the large number names would now directly tell you what power of 1000 they were.

EDIT:
Dang, just realized that "million" itself presents a problem in the second proposal. It could naively be seen as meaning 1000^1000 if a reader went by Latin or naively misread as the 1000th root of 1000 (which in this system would be the similarly spelled millillion [sic]) if one went by SI. Maybe change it to "Mollion" (for "mono")

[factotum]

There is very rarely any situation where you actually have to say a really big number with that level of precision. In 99% of situations you could say "Around 20 million" for your example and that would be sufficient. I can say the speed of light is 300,000 kilometres per second and be accurate to within a tenth of a percent. If you needed to accurately read out a number over the phone (for example) then you would be better off just reading it as a series of digits than using the words million, thousand etc. So, I don't think the effort required to make this change is worth it.

[Khedrac]

There are several partial answers to this, and some guesses:

First off, I would not write the number as "20598695" but as "20,598,695" (I'm British, and I believe the European format is "20.598.695") which makes is far far easier to parse - you can instantly see that the number is twenty million, five hundred and ninety eight thousand and six hundred and ninety five.
Yes, working out which of the three digit blocks you are looking at becomes tricker with more digits, but as factotum said, you rarely need that sort of precision.

Next a brief digression - and I blame typewriters and computers!
As you can see there is a problem with the difference between the "British" and "European" formats - which number is 123.456? For me this is simple in hand-written numbers - because I don't use a full stop/period character as a decimal point - it should be · (Alt+0183 on my keyboard - should show as a dot half-way up the letter eight - same height as the cross bars of a minus sign "-", plus sign "+" and a division sign "÷").
{And let's not go into the issue where a keyboard's dash character isn't correct for a minus sign.}
I don't know whether European notation prefers the comma or a true decimal point, but if a period isn't used as decimal point then half the problem goes away "123,456" may remain confusing.

I think the loss in many texts of the thousands seperators is also due to computers - computers like numbers as numbers, not as formatted text and people are adjusting to what the computers display. If you look at an old basic calculator you will see the thousands seperators - because the precision was fixed so the seperators could be.

Also, I believe that the naming of the numbers pre-dates arabic numerals and place-based notation. So MMMDCXCIV is still three thousand, six hundred and ninety four - and it reads left to right correctly.
The way we name numbers came first, arabic numerals and positional notation came second and really helps maths.

As for your proposed renaming system, we then hit the difference between British and German and the United States of America (though 99% of British people use the US system).
In the German/British system:
One billion is 1,000,000,000,000 not 1,000,000,000 (which is correctly called "one milliard").
One trillion is one million cubed - oh look, save for the fact that it based on a million, we have your proposed higher number naming system - it's just a shame that no-one uses it.

Personally, for the higher powers of numbers, I am all in favour of using 10^9, 10^12 etc. rather than trying to work out what something like "one octillion" means.

Speaking of working out the names, I recently came cross a depressing example of ignorance pushing through an incorrect word into acceptance.
The word is "septagon" which apparantly means a seven-sided shape - which it should not (latin root vs. greek root), a seven-sided figure is a "heptagon", but that term has been so little used and taught that the other is usurping its place!
(The latin prefixes: quin-, sex-, sept-, oct- etc. are used for groups of musicians, i.e. quintet, sextet, septet, octet etc.; the greek prefixes: pent-, hex-, hept-, oct- etc. are used for shapes, i.e. pentagon, hexagon, heptagon, octagon etc.)
What made me check a dictionary and discover the septagon was a reasonably tough TV quiz asking the question "how many sides has a septagon?" and the professional quizzer saying "7" not "a heptagon has 7 but a septagon isn't a shape"...

[Radar]

Or... just use scientific notation? It is universal, easy to read and does not require any major overhaul of how we read things.

[snowblizz]

Am I the only one who thinks that numbers ought to be written and pronounced the other way around?

No. And the day I can get a number of European languages to stop doing it will be a happy one.

Have you got any idea how difficult it is to parse five-twentyfifts. I never understand if they are going for 25 or 55 or something entirely different. And the less said about the inanity of the four-twenty-seventeen the better.

In reality though we never speak such large numbers that it tends to be a problem. So it is unlikely to be an issue, ever. Also it will be going agaisnt most human logic. The reason being I believe that the biggest number is the important one. It's critical to know if we are in tens, thousands or millions rather than if it ends in a two or three. Since we read left to right and as posted above used (Roman) numerals that strictly followed that order it'll stick. I'd call it a personal context focused approach. Compare to the date system I mention below. A "scientific", I think, way to look at it is year-month-date. Of all the potential years ever existing we talk about 2019. Of all the limited months in that year we talk about August. Of all the possible days in August we are talking about the 29th. It's a general to specific logic. However, a human doen't work that way. A human mind goes from itself outwards. If I say a date I start with the most contextually relevant information, the 29th. And since am talking to another intelligent being they know I mean this month this year because that is the one most relevant to us. If I don't mean this month I'll then add the month to the explanation. On the off chance I am talking about something further removed from context I add the year.

Effectively everyone's cognitive load has to be increased (everything we read is left to right, but numnbers are right to left) to solve a problem that does not really exist and which in context largely is irrelevant. If 20.598.695 is "five-ninty-sixhundred-eightthousand-ninetythousand-fivehundredthousand-twentymillion.....(long pause... oh you done talking number now) it's much harder to parse than "twentymillion (ok I know the upper bound, I know whether it's relevant to me or not already now) fivehundredninetyeightthousand (I stopped caring now already) sixhundredninetyfive. That said, am sure some cultures do numbers as suggested. I want to say Japanese and it somehow made multiplicating or adding them together superfast.

All this ignoring that we don't generally say large numbers. I compare to Swedish where the "rule" IIRC about writing out numbers as text is that below 20 you write it out with letters and above that you use numerals. Basically the larger the number the harder it is to grasp it anyway.





As in understand it the "European" way uses comma (,) as a decimal point (comma) and the point (.) as a thousands separator. And the UK does it the opposite way. Yes it gets confusing and yes I think the UK needs to get with the program. But that's just one of a number of issues with the 3 date systems and the insanity of refusing the "metric system".

I wouldn't blame computers I learned the use of comma and point way before any computers got involved.

[Grey_Wolf_c]

First off, I would not write the number as "20598695" but as "20,598,695" (I'm British, and I believe the European format is "20.598.695") which makes is far far easier to parse - you can instantly see that the number is twenty million, five hundred and ninety eight thousand and six hundred and ninety five.

For sufficiently large numbers, it even uses subscript to help identify which grouping of numbers it is:

2059869520598695 would be 2.059₂869.520₁598.695. It also makes it a lot easier to look at that number and see it is 2000 billion and change.

Grey Wolf

[Khedrac]

For sufficiently large numbers, it even uses subscript to help identify which grouping of numbers it is:

2059869520598695 would be 2.059₂869.520₁598.695. It also makes it a lot easier to look at that number and see it is 2000 billion and change.

Grey Wolf

I have never seen this notation before - but I like it - it does make it much easier to parse. Also I note that it divides the number up into what I called the German and British way of naming numbers - one billion = a million million.

[Grey_Wolf_c]

I have never seen this notation before - but I like it - it does make it much easier to parse. Also I note that it divides the number up into what I called the German and British way of naming numbers - one billion = a million million.

I don't think I've ever seen it in the real world - it was taught to me in Spanish class. I suspect it might be in decline, in part because computers don't make it easy to use.

Grey Wolf

[Lvl 2 Expert]

I'm of pretty much the opposite opinion of Bohandas. I think in general the most important information, the information the reader or listener is most likely to be interested in, should come first. If someone tells me there are 20598695 possible different games of checkers the important thing is that it's roughly 20 million, which is why I would write it as 20,598,695, 20.6 million or 20.6*10^6 (in American English or scientific literature, in Dutch the dots and comma's are the other way around). I don't want to read past 5 numbers of absolute irrelevance to get to anything even mildly interesting.

Similarly, I think both English and Dutch have their adjectives and nouns the wrong way around. If someone is yelling to me about how there's a big scary dangerous hairy angry spider in the kitchen I'm half a sprint and two broken vases into a rescue operation before I hear it's a false alarm. The word spider should come before big, scary etc.

I am in favor, at least theoretically, of Bohandas' mod of the millions system. I have made this argument ones or twice in the past. The American system doesn't make sense because a billion is not in any way a bi-million. The link between the counting parts, bi-, tri- etc and the amount of zeroes is more complicated than it needs to be. The European system does make sense in that aspect. A million has six zeroes, a billion has 12. But a billiard doesn't have twice the zeroes of a milliard. It's also less intuitive to count in, there's more steps involved in deciding which term comes next or how many zeroes any used term has. It might just be too much English language Wikipedia, but I find myself working with the American numbers more easy than with the European ones. So million for 10^3, billion for 10^6, trillion for 10^9 etc would be an improvement over both. There is the little issue that it sounds stupid in any language that uses some form of "mille' for a thousand, and it would be super confusing if part of the world would adopt this system tomorrow because now there's 3 competing standards, so it might be better to just make up new words for the powers of one thousand altogether (thousand, bisand, trisand?), but neither of the current systems is really the best it could be.

[Grey_Wolf_c]

I don't want to read past 5 numbers of absolute irrelevance to get to anything even mildly interesting.

From which I can deduce you are not in banking, finance, or fraud detection. To people in those, and similar, professions, the significant digits are "all", because quite a lot of money can be misplaced or worse down the line, even if it is a vanishingly small percentage of the full figure.

Grey Wolf

[Lvl 2 Expert]

From which I can deduce you are not in banking, finance, or fraud detection. To people in those, and similar, professions, the significant digits are "all", because quite a lot of money can be misplaced or worse down the line, even if it is a vanishingly small percentage of the full figure.

Grey Wolf

Yet even to them the big numbers are more interesting.

Unless you'd want your accountant to notice a 2 cent discrepancy before finding out someone just stole 20 million from your account in the Bahama's.

[Grey_Wolf_c]

Yet even to them the big numbers are more interesting.

Unless you'd want your accountant to notice a 2 cent discrepancy before finding out someone just stole 20 million from your account in the Bahama's.

In the number I gave above, the accountant would not spot either, if they "don't want to read past 5 numbers". As it turns out, finance departments don't make a distinction between a discrepancy of 20 million and one of 2 cents - they consider them both important, and want to know about both, and usually will bring them up at the same time. Because they, as Roy, are capable of multitasking.

Grey Wolf

[Lvl 2 Expert]

In the number I gave above, the accountant would not spot either, if they "don't want to read past 5 numbers".

If I had that number on my bank account, I wouldn't really mind either of those amounts missing, I'd pretty much own the world.

As it turns out, finance departments don't make a distinction between a discrepancy of 20 million and one of 2 cents - they consider them both important, and want to know about both, and usually will bring them up at the same time.

So you're saying the number 20598695 should be pronounced as twfisievehunxhuntyndrdredmiledninlinineetyeightoth ousnandtyfive? Because, you know, I don't really see another way to get people to read all numbers at the same time. One of the numbers needs to come first, and in most circumstances the bigger number is going to be the most important one.

[Grey_Wolf_c]

So you're saying

No I'm not, and since we've progressed to the point in the conversation in which you put words in my mouth to try to make a point, I'm no longer interested in trying to talk to you.

Grey Wolf

[Fyraltari]

First off, I would not write the number as "20598695" but as "20,598,695" (I'm British, and I believe the European format is "20.598.695")

I can't speak for the "European" format, but in France, that would be "20 598 695"

As for your proposed renaming system, we then hit the difference between British and German and the United States of America (though 99% of British people use the US system).
In the German/British system:
One billion is 1,000,000,000,000 not 1,000,000,000 (which is correctly called "one milliard").
One trillion is one million cubed - oh look, save for the fact that it based on a million, we have your proposed higher number naming system - it's just a shame that no-one uses it.[/QUOTE]
Hey!

Personally, for the higher powers of numbers, I am all in favour of using 10^9, 10^12 etc. rather than trying to work out what something like "one octillion" means.[/QUOTE]
I am not sure "ten to the power of forty-eight" is necessarily clearer than "a million to the power of eight" and "an octillion" is just easier to say than either.

And the less said about the inanity of the four-twenty-seventeen the better.

I have to admit that we could learn from our Belgian brethern. And we could all agree to say "octante/huitante" for 80 as well.

[Dexam]

No. And the day I can get a number of European languages to stop doing it will be a happy one.

Have you got any idea how difficult it is to parse five-twentyfifts. I never understand if they are going for 25 or 55 or something entirely different. And the less said about the inanity of the four-twenty-seventeen the better.

Relevant:

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[Khedrac]

Relevant:

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And what comes after that image is English perking up and going - ah - this makes sense again - four score, four score and one, fore score and two...

If you want a really messy way of counting, I think some of the ancient numbering systems that used different bases at the different levels?
Or take the Babylonian system - sort of base 60, positional notation but no concept of zero. Even after they invented a placeholder for missing digits they only used it between digits - so the actual value had to be inferred from context.

[Fyraltari]

And what comes after that image is English perking up and going - ah - this makes sense again - four score, four score and one, fore score and two...

If you want a really messy way of counting, I think some of the ancient numbering systems that used different bases at the different levels?

This is what is happening there. These are remnants of a base twenty system.

Or take the Babylonian system - sort of base 60, positional notation but no concept of zero. Even after they invented a placeholder for missing digits they only used it between digits - so the actual value had to be inferred from context.

The idea of a symbol for a null value is much less intuitive than we think. Every single numbering system started without zero. Which only makes sense, counting was invented by piling stones (calculus is latin for pebbles by the way) and you cannot pile ‘no stone’.

[farothel]

Relevant:

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And it get's worse, because in French you go four-twenty-nine and then four-twenty-ten, four-twenty-eleven,...

In Dutch and in German (and probably in others as well) it's flipped around, but only for numbers below 100 (otherwise it would be too simple, now wouldn't it ).
25 for instance is vijfentwintig (five and twenty) in Dutch. It's something non-native speakers have difficulties wrapping their heads around at times and it makes it more difficult to for native speakers to learn another language where it's the other way around.

[factotum]

And what comes after that image is English perking up and going - ah - this makes sense again - four score, four score and one, fore score and two...

For some reason this reminds me of when a character in one of the "Lord of the Rings" books says, when asked how he knows how their force is outnumbered, "You have a score of scores counted ten times and five", which is possibly the silliest way to say 6,000 I've ever seen!

[Wardog]

For some reason this reminds me of when a character in one of the "Lord of the Rings" books says, when asked how he knows how their force is outnumbered, "You have a score of scores counted ten times and five", which is possibly the silliest way to say 6,000 I've ever seen!

Celtic myths and legends also seem to be very fond of factorising numbers ("I gave him thrice nine hounds"; "nine times ten will fall by Cormac in his first onset, and nine times ten will fall by his people"), but I don't think I've seen any that go quite as far as Tolkien did there.

[The Random NPC]

Or take the Babylonian system - sort of base 60, positional notation but no concept of zero. Even after they invented a placeholder for missing digits they only used it between digits - so the actual value had to be inferred from context.

From what I understand, this is a bit mistaken. Nearly everyone understood the concept of zero, they just didn't have a symbol to represent it.

[Lvl 2 Expert]

From what I understand, this is a bit mistaken. Nearly everyone understood the concept of zero, they just didn't have a symbol to represent it.

Didn't always need it either. Calculations were handled differently in different times and places, but some systems used symbols placed in little trays. A zero would just be an empty tray, 100 is a 1 in the third tray, with tray 1 and 2 empty. Other places used an abacus. All beads into the off position is zero. No symbol needed. You start needing a zero when you want to write numbers with a zero in them down. If your easiest method of calculation does not involve writing (paper is everywhere now, but in those times it hadn't been invented yet) having a symbol for zero is an accounting problem, not a math problem. (Okay, it would still not be a math problem today, technically, but it would be a problem for people trying to do math.)

Then again, maybe they had zeroes all along, we just haven't recovered anything on which one was written.

[Jay R]

If I were trying to simplify English, I certainly wouldn't start with the names for very high numbers.

[Beleriphon]

No. And the day I can get a number of European languages to stop doing it will be a happy one.

Have you got any idea how difficult it is to parse five-twentyfifts. I never understand if they are going for 25 or 55 or something entirely different. And the less said about the inanity of the four-twenty-seventeen the better.

Five-twentyfifths would one-fifth of a whole, or five part of twenty-five from my reading. That would be a standard North American reading at least. French is just dumb when it comes to numbers. The joy of living in Canada where I can go to Montreal and order things like such: "vignt-three please. Merci". Or distances: "Dix minutes, nord".

[snowblizz]

Five-twentyfifths would one-fifth of a whole, or five part of twenty-five from my reading. That would be a standard North American reading at least. French is just dumb when it comes to numbers. The joy of living in Canada where I can go to Montreal and order things like such: "vignt-three please. Merci". Or distances: "Dix minutes, nord".

I was being abit facetious. But a number of European languages go 5-and-twenty, 2-and-fifty, and naturally as spoken it's hard to untagle it. For someone not native it is hellishly hard to learn and understand whether they are saying 25 or 52. And I swear I vaguely remember sometimes some languages mess with it too so it's not consequent. As someone who over time does/has know(n)/learnt 6 European languages I've had a lot of opportunity be annoyed by numbers.

Much can be said about English but at least they have the common deceny to start in the big end and go smaller. And it doesn't matter where you go a fter the initial sequences, it follows the same logic.

[HouseRules]

Another Endian Argument?

Many Languages switched from Little Endian number system to Big Endian number system.

In programming, we know that Little Endian is better, except for Network protocols that wants Big Endian.

Given that the number system came from Arabic Numerals, and Arabic is written Right-to-Left, they assume the number system is Little Endian.

Little Endian - easier to find exactness instead of looking for the quantity of digits.

Big Endian - find the "most significant figure" faster, so it is faster in dealing with "major" accounting issues.