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Postfix Notation & Good & Evil

I've been teaching stacks in my data structures class lately, and no lesson on stacks is complete without a discussion of how they are used to evaluate expressions in postfix notation. (You don't really need to know postfix notation to get the point of this posting. If you are curious, you can click the link.)

I showed them an example of an expression in infix notation


and the equivalent in postfix notation

5 2 + 3 6 *

Some of you may not be familiar with the term "infix", even though  you have almost certainly used infix notation before. I said the same thing to my class. I told them we have the unfamiliar word "infix" for a familiar thing because in the absence of other notations, no word for it was necessary. Only the introduction of postfix notation required us to introduce a new term to the vocabulary.

It works the other way, too. Some terms fall into disuse because they are names for things that have become ubiquitous since they were named. "WYSIWYG editor" comes to mind.

I thought about it later, and realized what I said could be applied to good and evil. I've often heard the argument that evil is necessary, because without it there would be no goodness.  We wouldn't have the *concept* of good without evil, because there would be no need for it.  And there would be no need for a word to describe it. But good would still exist. Just as infix notation would exist, albeit without a distinguishing name, if there were no postfix (or prefix) notation.

This example is probably too nerdy to use in a counter argument. The old metaphor of good as light and evil as darkness is a little clearer. It makes a stronger statement as well. Darkness is defined as something that does not exist in and of itself...it is mere absence of light. Postfix notation does exist in it's own right, and if the history of mathematics had progressed a little differently, I might be making an argument for why the term "postfix" is necessary rather than infix.

Once something other than good (i.e. evil)  is introduced into the world we need a distinguishing term for the good, because it is no longer the only thing there is. In the same way, we need a term for infix notation once postfix notation is introduced.