False Slopes


If you zoom in on a curve enough, you can convince yourself the line is straight. Similarly, if you only look at the average value of a sine or cosine curve, you may mistake the functions for constant functions going through the horizontal axis, when they are anything but constant.

The problem lies in what we are observing. When we look at functions the wrong way, we miss information that could be vital to what we are searching for. Since our perspective isn’t optimal, we lose that potential insight.

The key, then, is to actively search to improve our perspective. If we aren’t checking that we are looking at a problem or task at the right angle, how can we possibly know we are getting the best perspective? We can’t, so we need to analyze our situations in various ways to make sure we understand it to the best of our ability.

If we want to be accurate in our assessment of situations, we cannot simply analyze in one way. That is too simplistic, and could result in thinking that a curve is straight when it is actually not.

Don’t fall prey to false slopes. Check your work.

Related Posts

Snapping Into Focus

Escaping the Path

Give Yourself A Gift

Not The Usual Outreach

Chasing The Carrot

Discovering Mathematics

Bag of Examples

Only Numbers and Algebra

Not Necessary

Memorization in Education