What is Science?
What is the deeper level of abstraction that underlies science?
PERCEPTION

IMAGINATION
........ 
METAPHOR (LANGUAGE)
VEGETABLES                         POTATO

A potato is a vegetable.             That's easy.
A vegetable is a potato.            That's wrong!
(A vegetable might not be a potato.)
next, learn some science
.
"Energy is the capacity to do work."
...so say many textbooks
If "energy" is the energy of Aristotle (the "energy" of everyday language) that's OK.
But it's not going to be much help to you for making things happen the way you want.
It's a bit of learning, but it's not science. 
Science redefined energy in the 19th century.
.
next, begin to see science
"Energy is the capacity to do work."
but
"Energy can be unavailable for doing work."
(Energy might not be capacity to do work)
MATHEMATICS

There is a pattern here.
Seeing such patterns is what science and math is all about.
"Energy is the capacity to do work."     That's wrong!
 
The pattern might be put this way:
VEGETABLE
is to
POTATO
 
as
  
ENERGY
is to
CAPACITY
TO DO WORK

Which combinations are possible?

VEGETABLE  and  POTATO

vegetable  potato                 YES
vegetable   not potato           YES
not vegetable   potato           NO
not vegetable   not potato     YES
ENERGY  and   CAP.  DO WORK

energy          cap do work           YES
energy          not cap do work     YES
not energy    cap do work           NO
not energy    not cap do work     YES
This is the "pattern."
It has a name: implication

Potato implies vegetable.
(But vegetable does not imply potato.)
Capacity to do work implies energy.
(But energy does not imply capacity to do work.)

When you see the deeper pattern you have begun to see the science.
You have also discovered a logical fallacy in a common textbook definition.
You have begun to discover science's answer to the question:
"What is energy?"


Mathmaticians always want to express abstract patterns in symbols.
Here's how this one is done:

potato (or cap do work) = a
not potato (or not cap do work) = a
vegetable (or energy) = b
not vegetable (or not energy) = b

These combinations happen:
 a & b, a & b, a& b
(This one doesn't: a & b)
If you have a, you will have b.  If you don't have a you might, or might not, have b.
(If you have a, you will never not have b.) 

It is written:
a implies b = (a.b)v(a.b)v(a.b)
 (a Boolean equation) 
v is pronounced "vel" and means and/or
See it written.
(in Unsuspected Dimensions)

You're more likely to see not-a and not-b as a and b with little lines over them.
That's not readily done in html.

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