Next iteration: But what if you want to count up non-fiction and fiction? There's just a slightly different "reduce" step, because people have to add up both of them. You could also break it down by subject, or author, or pretty much anything else.
Next iteration: Of course, you don't have to just add. You can do anything that has mathematical properties similar to addition (my mom teaches math at high-school). You could add up the set of all the offense words found, since addition and set addition have similar mathematical properties. You couldn't take the average number of pages, because some people will find more books than others, and you wouldn't get a fair average. But you might be able to keep track of a couple of attributes that can be summed up, and use that to calculate the average after the job is done (for example, total number of pages, and total number of books).
Now if only everyone's mom understood the concept of a linear set operation... :)
A good example that would also help someone appreciate the power of map/reduce might be something like "how many times does each letter of the alphabet appear in the library?" For the map step I take shelf 1 and you take shelf 2, but now for each book we'll have to write down something like "a:300,b:50,c:90,..." and so on. But now there are more things to "reduce" than there are books (since we now have a value for the number of occurrences of each letter in the alphabet for every book). Well, there's nothing stopping us from splitting up the reduce step as well - we could split it up by shelf again (where you add the totals for each letter on your shelf and I'll do mine, then we'll do one final reduce of at the end), or you can add up letters a-m and I'll do n-z.
I remember a Stanford lecture video that said "well, if we called it Map, Sort, Group-reduce then no-one would use it :P" but that's a minor naming issue to describe just the subtly you are exactly describing, which is to just not be entirely random in the specifics of how the MapReduce is executed.
Oh, I see. I was struck by the direct phrasing of "You couldn't take the average number of pages", which made me parse the rest of the comment incorrectly.
Next iteration: But what if you want to count up non-fiction and fiction? There's just a slightly different "reduce" step, because people have to add up both of them. You could also break it down by subject, or author, or pretty much anything else.
Next iteration: Of course, you don't have to just add. You can do anything that has mathematical properties similar to addition (my mom teaches math at high-school). You could add up the set of all the offense words found, since addition and set addition have similar mathematical properties. You couldn't take the average number of pages, because some people will find more books than others, and you wouldn't get a fair average. But you might be able to keep track of a couple of attributes that can be summed up, and use that to calculate the average after the job is done (for example, total number of pages, and total number of books).