On 05/03/12 11:59, Invisible wrote:
> Required XKCD reference: http://xkcd.com/558/
> 
> To most people, "million", "billion" and "trillion" are almost
> interchangeable terms. 

In Finnish we have "miljoona" (equals "million"), "miljardi" (equals
"billion") and "biljoona" (equals "trillion", not "billion"). Now when
someone translates a news article from some USA news service that
contains billion, it gets sometimes translated as "biljoona", which is
actually 1000 times more.

Actually, checking Wikipedia, it's not just us:
http://en.wikipedia.org/wiki/Names_of_large_numbers .

-- Arttu Voutilainen

Post a reply to this message

On 05/03/2012 03:07 PM, Arttu Voutilainen wrote:
> On 05/03/12 11:59, Invisible wrote:
>> Required XKCD reference: http://xkcd.com/558/
>>
>> To most people, "million", "billion" and "trillion" are almost
>> interchangeable terms.
>
> In Finnish we have "miljoona" (equals "million"), "miljardi" (equals
> "billion") and "biljoona" (equals "trillion", not "billion"). Now when
> someone translates a news article from some USA news service that
> contains billion, it gets sometimes translated as "biljoona", which is
> actually 1000 times more.
>
> Actually, checking Wikipedia, it's not just us:

No wonder MS Word has been advising people to just avoid the word 
"billion" altogether. It's too ambiguous...

Post a reply to this message

On Mon, 05 Mar 2012 09:59:40 +0000, Invisible wrote:

> To most people, "million", "billion" and "trillion" are almost
> interchangeable terms.

I think I'd want a cite specifically for non-hyperbolic usages (some 
people 'interchange' the terms when used as hyperbole, that doesn't 
really count as interchanging them.

Jim

Post a reply to this message

Invisible <voi### [at] devnull> wrote:
> To most people, "million", "billion" and "trillion" are almost 
> interchangeable terms.

> But you know what? As far as I can tell, almost nobody mixes up a 
> kilowatt and a megawatt.

  In the same way as nobody mixes up a thousand and a million.

> Nobody confuses centimetres with millimetres. 

  In the same way as nobody confuses a hundred with a thousand.

> No one has trouble with a gram and a kilogram being very different 
> quantities.

  In the same way as no one having trouble distinguishing between 1 and
a thousand.

-- 
                                                          - Warp

Post a reply to this message

> Required XKCD reference: http://xkcd.com/558/
>
> To most people, "million", "billion" and "trillion" are almost
> interchangeable terms. Which is worrying, because those are /very
> different/ quantities. They're not even remotely similar. But it seems
> that when talking about large numbers, people get a kind of "numbness"
> where the quantities are so vast that they seemingly might as well be
> non-finite.
>
> But you know what? As far as I can tell, almost nobody mixes up a
> kilowatt and a megawatt. Nobody confuses centimetres with millimetres.
> No one has trouble with a gram and a kilogram being very different
> quantities. And when was the last time you saw somebody [who has a clue]
> mix up a gigabyte and a terabyte?
>
> So, perhaps what we need to do is start measuring money using SI
> prefixes. For surely 165 megadollars is clearly smaller than 170
> gigadollars.
>
> Sadly, I fear that for some, 20 millicents /will/ equal 20 millidollars.

It's even worst when you speak French. We have an additional step 
between million, billion, trillion...

million = 1000000 = 10^6
milliard = 1000000000 or 1000 millions = 10^9
billion = 1000000000000 or 1 millions millions = 10^12
billiard = 10^15
trillion = 1 million billions = 10^18
trilliard = 10^21
quatrillion = 1 millions trillions = 10^24
quatrilliard = 10^27
quintillion = 10^30
quintilliard = 10^33
...

Alain

Post a reply to this message

On 3/5/2012 10:12 AM, Warp wrote:
> Invisible<voi### [at] devnull>  wrote:
>> To most people, "million", "billion" and "trillion" are almost
>> interchangeable terms.
>
>> But you know what? As far as I can tell, almost nobody mixes up a
>> kilowatt and a megawatt.
>
>    In the same way as nobody mixes up a thousand and a million.

Echoes my thoughts exactly; a thousand-fold difference "mentally" 
matters much more for smaller numbers.  I'd imagine that mix-ups 
between, say,  megabytes, gigabytes, and terabytes are as common as 
those between million, billion, and trillion.  It's also a bit rare that 
I see either of these errors, so I don't know where Invisible got the 
"to most people" aspect, although surveys testing the general public's 
math knowledge tend to be scary enough that I suppose it's possible.

One error I *do* see all the time though, is a misuse of the term 
"exponential" to mean anything superlinear (or just "a lot").  In 
informal conversation it's a little grating, but sort of ok since it's a 
relatively standard use of the word.  When grading physics labs, 
however, I saw parabolas called "exponential" more often than I saw them 
called anything correct, and it drove my absolutely bonkers.

Post a reply to this message

>> In the same way as nobody mixes up a thousand and a million.
>
> Echoes my thoughts exactly; a thousand-fold difference "mentally"
> matters much more for smaller numbers.

I read a book recently which suggests that the human sense of numbers is 
inherently logarithmic, and that humans instinctively use ratios to 
assess things. Because, think about it, if you're going to climb tree A 
or tree B, it doesn't actually matter precisely how many applies are in 
each tree. What matters is what the /ratio/ between them is.

...which would explain why, for really large numbers, people develop 
this strange sense of numbness, as if all really big numbers are somehow 
"equally huge". (A similar thing happens with really tiny numbers, by 
the way.)

> It's also a bit rare that I see either
> of these errors, so I don't know where Invisible got the "to most
> people" aspect, although surveys testing the general public's math
> knowledge tend to be scary enough that I suppose it's possible.

The guy who does XKCD clearly sees this too. Maybe you only meet smart 
people? Because where I live, there are many, many dumb people.

> One error I *do* see all the time though, is a misuse of the term
> "exponential" to mean anything superlinear (or just "a lot").

This.

Did you know that an exponential curve actually starts out /quite 
shallow/? Saying that something is increasing "exponentially" does /not/ 
just mean it's increasing quite quickly. It means a very specific 
mathematical relationship.

Post a reply to this message

On 3/5/2012 11:43 AM, Orchid Win7 v1 wrote:
>>> In the same way as nobody mixes up a thousand and a million.
>>
>> Echoes my thoughts exactly; a thousand-fold difference "mentally"
>> matters much more for smaller numbers.
>
> I read a book recently which suggests that the human sense of numbers is
> inherently logarithmic, and that humans instinctively use ratios to
> assess things. Because, think about it, if you're going to climb tree A
> or tree B, it doesn't actually matter precisely how many applies are in
> each tree. What matters is what the /ratio/ between them is.
>
> ...which would explain why, for really large numbers, people develop
> this strange sense of numbness, as if all really big numbers are somehow
> "equally huge". (A similar thing happens with really tiny numbers, by
> the way.)

I don't see how a logarithmic sense of numbers explains this, since 
under this hypothesis a "thousand-fold difference" should be judged 
equally whether between one and a thousand or a billion and a trillion. 
  I was actually implicitly pointing out that this "logarithmic 
representation" hypothesis fails for very large (or small) numbers 
(incidentally, I actually think if fails much more than just then). 
It's pretty easy to construct examples where this is the case.


>> It's also a bit rare that I see either
>> of these errors, so I don't know where Invisible got the "to most
>> people" aspect, although surveys testing the general public's math
>> knowledge tend to be scary enough that I suppose it's possible.
>
> The guy who does XKCD clearly sees this too. Maybe you only meet smart
> people? Because where I live, there are many, many dumb people.

I think he was referring to a slightly different phenomenon where people 
tend to assume that the units match when two values are being compared. 
  I think the comic would apply equally if the units were meters and 
kilometers, and it's not like your average metric-using person people 
don't know the difference between the units themselves in that case.

Post a reply to this message

On 3/5/2012 5:32 AM, Stephen wrote:
> On 05/03/2012 9:59 AM, Invisible wrote:
>> To most people, "million", "billion" and "trillion" are almost
>> interchangeable terms.
>
> Names and addresses of at least three people who use them
> interchangeably? (Your mother does not count.)

How about Congressmen?

Regards,
John

Post a reply to this message

>> The guy who does XKCD clearly sees this too. Maybe you only meet smart
>> people? Because where I live, there are many, many dumb people.
>
> I think he was referring to a slightly different phenomenon where people
> tend to assume that the units match when two values are being compared.

I think actually the comic was referring to the phenomenon where news 
producers like to distort reality to make it sound more interesting, but 
hey...

Post a reply to this message