deconstructing mother goose

There was a little girl and she had a little curl
Right in the middle of her forehead
And when she was good, she was very, very good
But when she was bad, she was horrid.

Because I had blonde ringlets and was prone to tantrums, this nursery rhyme struck uncomfortably close to home. That is, until I managed to reinterpret it in a way that I found much more palatable. Analyzing the poem logically, I came to the realization that the last line was clearly completely wrong. My reasoning went something like this:

We can visualize children's behavior as existing along a continuum, with HORRID and VERY VERY GOOD at the extremes and BAD and GOOD somewhere between them. See diagram 1 below.



Based on the third line of the poem, we know that, as applied to the little girl with the curl (LGWC):

GOOD = VERY VERY GOOD

This must mean that, vis a vis regular children, the behavior of LGWC is shifted to the right along our behavior line, so that if regular children's behavior ranges from BAD to GOOD, the behavior of LGWC ranges from GOOD to VERY VERY GOOD. In other words, the high end of a regular child's behavior range is equivalent to the low end of LGWC's behavior range . Therefore, as applied to LGWC:

BAD = GOOD

See diagram 2 below.



Which proved that the final line of the poem should actually be:

But when she was bad, she was good.

I explained this to my mother and after that she recited only the new, corrected version. And from then on, if anyone happened to see a resemblance between me and the little girl with the little curl, it didn't bother me at all.