Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I often find two numbers roughly "in the same ballpark" if they are within a factor of about $e$ of each other. For example, if I know computers generally cost upward of $\$1000$, then $\$2700$ would probably be the most I would a priori feel is a reasonable upper limit for computer prices.

Is this just a coincidence, or is there some mathematical deep reason why $e$ is inherently the "best" order-of-magnitude exponent?

share|improve this question

closed as off-topic by Antonio Vargas, Daniel Rust, Norbert, Dominic Michaelis, T. Bongers Nov 7 '13 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – Antonio Vargas, Daniel Rust, Norbert, Dominic Michaelis, Community
If this question can be reworded to fit the rules in the help center, please edit the question.

    
Interesting observation. –  Lord Soth Nov 7 '13 at 17:48
4  
That is a subjective assessment. Different people have different notions of close or not close. It is easier in certain math operations though. –  Eupraxis1981 Nov 7 '13 at 17:49
    
$e$ is an amazing number and pops up a lot of places. –  MasterOfBinary Nov 7 '13 at 17:58

1 Answer 1

up vote 3 down vote accepted

I think that we subconsciously think in a logarithmic way and since the root of 10 is around 3.162, we think of 3 as half way the order of magnitude. So anything under 3,000 we perceive in the order of magnitude of 1,000 and anything over that we perceive as being in the 10,000 order of magnitude.

In other words if 1,000 is 3 in 10 based logarithm and 10,000 is 4 in 10 based logarithm then 3,162 is the 3.5 on this scale and anything under 3,000 is closer to 3 and almost everything over 3,000 is closer to 4.

share|improve this answer
    
Umm, what does the root of 10 have to do with logarithms? –  user54609 Nov 7 '13 at 18:08
    
@user54609 The second paragraph explains it –  DannyDan Nov 7 '13 at 18:12
1  
@user54609 Because $\log_{10} \sqrt{10} = 0.5$, i.e., half way on the logarithmic scale. –  Danikar Nov 7 '13 at 18:27

Not the answer you're looking for? Browse other questions tagged or ask your own question.