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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