## Tuesday, May 29, 2012

### "Exponentially Better"

Dear residents in my little area of the country,

I keep hearing you use the word exponential in reference to a drastic change from one examined point in time to another.  For example, "I slept exponentially better last night than I did the night before."  Or, "My coffee tastes exponentially worse at this Starbucks as opposed to the one on Main Street."

I usually just smile and nod.  As if I understand what you're saying.

But, I really don't.

How do you know the change is exponential when you're only comparing two points?  How do you know it's not linear, perhaps with a steep slope?

To illustrate my point, let's say on Day 1 you rate your sleep as a 2.  On day 2, you rate your sleep as a 4. (I have no idea what these numbers indicate, but you must be able to rate your sleep on some kind of scale if you can make a statement like the aforementioned one.)  Well, then, maybe your sleep pattern, indeed, is following an exponential trend line:

 An exponential function:  y=2^x

Or...you could have trend lines such as:

 A linear function:  y=2x
 A logarithmic function:  y=2+2.88539ln(x)

And these only represent a few of the possibilities.

So, residents of the great Midwest:  I urge you--be more creative in your comparisons.  Don't assume you need to use the phrase "exponentially better."  Nay.  Why not try something like, "quadratically better," or "logarithmically better"?

Sincerely,

The Picky One

1. This is also one of my pet peeves. On a few occasions I've tried to explain that the word "exponential" only makes sense when used to describe a rate of change, but this inevitably leads to me being called a pedant and "besides, everyone knows what I mean." (Actually no, they don't.)

2. in the life of a high school math student, anything increasing and concave up is "exponential"

3. I remember when I was in college, right after I do my math homework, I make it a point that I read some quotes about sleep to relax my mind before I go to sleep.

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