Stephen Few on Logarithms

Data viz expert Stephen Few on Logarithms.   I recall very early in my experience in the enterprise,  having to work with execs on this concept and how it could improve their understanding of visual measures, but also confuse them.  Here a considerable and interesting view.  'Sensemaking' is a good term here.

Logarithms Unmuddled  by Stephen Few

I often write about topics that I myself have struggled to understand. If I’ve struggled, I assume that many others have struggled as well. Over the years, I’ve found several mathematical concepts confusing, not because I’m mathematically disinclined or disinterested, but because my formal training in mathematics was rather limited and, in some cases, poorly taught. My formal training consisted solely of basic arithmetic in elementary school, basic algebra in middle school, basic geometry in high school, and an introductory statistics course in undergraduate school. When I was in school, I didn’t recognize the value of mathematics—at least not for my life. Later, once I became a data professional, a career that I stumbled into without much planning or preparation, I learned mathematical concepts on my own and on the run whenever the need arose. That wasn’t always easy, and it occasionally led to confusion. Like many mathematical topics, logarithms can be confusing, and they’re rarely explained in clear and accessible terms. How logarithms relate to logarithmic scales and logarithmic growth isn’t at all obvious. In this article, I’ll do my best to cut through the confusion.

Until recently, my understanding (and misunderstanding) of logarithms stemmed from limited encounters with the concept in my work. As a data professional who specialized in data visualization, my knowledge of logarithms consisted primarily of three facts:

Along logarithmic scales, each labeled value that typically appears along the scale is a consistent multiple of the previous value (e.g., multiples of 10 resulting in a scale such as 1, 10, 100, 1,000, 10,000, etc.).

Logarithmic scales make it easy to compare rates of change in line graphs because equal slopes represent equal rates of change.

Logarithmic growth exhibits a pattern that goes up by a constantly decreasing amount.
If you, like me, became involved in data sensemaking (a.k.a., data analysis, business intelligence, 
analytics, data science, so-called Big Data, etc.) with a meagre foundation in mathematics, your understanding of logarithms might be similar to mine—similarly limited and confused. For example, if you think that the sequence of values 1, 10, 100, 1,000, 10,000, and so on is a sequence of logarithms, you’re mistaken, and should definitely read on.

Before reading on, however, I invite you to take a few minutes to write a definition for each of the following concepts:   ... "