Analogy to the purpose of Taylor series I want to know an analogy to the purpose of Taylor series. I did a google search for web and videos : all talks about what Taylor series and examples of it. But no analogies. I am not a math geek and this is my attempt to re-learn Calculus in a better way, to understand Physics and Linear Algebra. 
Having an analogy will indeed help to view its use in real life. Learning seems lacking, if  the concept can't be applied. Appreciate a more laymen term explanation at this challenging point (for me).
Have read this post as of now: What are the practical applications of Taylor series?. That post (the answers, comments) indeed increases the bar of my expectation for a satisfying answer to my question.

I can't think of any good analogies. 
Perhaps the best way to get comfortable with Taylor Series is to look at some interactive examples:
http://demonstrations.wolfram.com/GraphsOfTaylorPolynomials/
Starting with $f(x) = e^x$, step up the highest number of terms from 1 to 10 to see how higher polynomials do an increasingly better job of approximating the function around the point of expansion.

Dare I say it one of the reasons to learn mathematics is it gives you new ways of thinking about things. Taylor series and the idea of an $n$-th degree approximation is itself an analogy or metaphor used many places in the sciences: physical, biological and social.
