Have you Noticed...

Your physics textbook probably has both of these statements.  We need to identify and resolve this contradiction. 

Mankind's notion of "energy" changed radically during the 19th century.  Before that, energy was of the world of poets, a metaphor for our experiences with hunger and food, with toil and rest, with drowsiness and sleep, and eventually with empty gas tanks and long gas lines.  By the start of the 20th century, science had discerned something new, a kind of something which before had been mystery and magic.  The energy of science  become refined into a deep abstraction about which we know almost nothing.  We determined how to calculate a value for it in countless situations, and we discovered that it is conserved.  That's about all there is to it; it's very, very simple and very, very abstract.  But in this new "energy," science had discovered a powerful concept and learned how to use it to great advantage.

The old metaphor is a kind of "capacity for doing work," identified by Aristotle over two millennia ago.  It is not conserved; that is, we "use it up" and must keep searching for new "sources" of it.  It is closely identified with vivid, everyday experiences, which means it's not very abstract.  And science discovered that this "energy" of Aristotle (and of the poets) is very complex.

Science's modern, abstract and powerful concept is very simple...and very subtle.  It is necessary for doing work, but it is not sufficient.  It can be "unavailable for doing work."  It is understood--which means "seen" well enought to be used--only after much hard mental work.  It is, in the poetic words of Indian physicist, Vandana Shiva, "magic found when we have looked in places we had never before thought to look." 

Metaphor and mathematics are two kinds of abstract knowledge which human beings are capable of knowing and using.  They are not wholly different . . . and understanding the difference is part of understanding science.

What is energy? -- Answered by Richard Feynman.