>> 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.

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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.

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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

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>> 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...

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