Logarithmic Scales

Date: 12/13/98 at 23:03:29
From: Purvi Patel
Subject: Honors Math Analysis

Dr. Math,

I have a paper to write for math analysis on "logarithmic scales." I 
have found things on logarithmic functions, but not quite what I need 
for this paper. Some of the things I would like to find out about 
logarithmic scales for my paper are, how a log scale is used to 
measure some quantity, what physical characteristics underlie the 
quantity, how the quantity is measured, how it is changed to the log 
scale, and why the logrithimic scale is useful.  

I would really appreciate your help on this question.

Date: 12/14/98 at 18:52:01
From: Doctor Schwa
Subject: Re: Honors Math Analysis

Try searching for things relating math to music (the scale on the piano 
is a logarithmic sort of scale, if you use both white and black keys). 
Also look for Richter scale (for earthquakes) and deciBel scale (for 
sounds)

Materials on the psychology of perception (how humans see brightness of 
light, hear intensity of sound, and so on) also would have lots of
references to log scales.

Or, do your own experiment. Have people look at a 50 watt bulb, 100, 
150, 200 without telling them which is which. Ask them to rate the 
brightness on a scale of 1 to 10. You'll probably see that the space 
between 100 and 200 watts is closer to the space between 50 and 100, 
showing that we see brightness logarithmically.

Log scales are generally useful for things of human perception like 
this (it's how we're wired!), for things with a huge range (like 
earthquakes, where strong ones are a million times bigger than weak 
ones), or for things where the ratio is more important than the 
difference (musical notes sound good together if their ratio is a nice 
number).

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/