Subsidiarity and kids' rhymes

One useful idea in explaining to children the idea of subsidiarity - or at least the nested quality of a hierarchy - is the famous "This is the House That Jack Built," which gives the various layers of activity in Jack's farmhouse.

Another one, which is more of a riddle, but sounds so silly, is this:

As I was going to St. Ives,
I met a man with seven wives.
Every wife had seven sacks.
Every sack had seven cats.
Every cat had seven kits.
Kits, cats, sacks, and wives: how many were going to St. Ives?

Of course to solve this we simply consider the powers of seven:
7 to the zeroth power = 1 man
7 to the first power = 7 wives
7 to the second power = 49 sacks
7 to the third power = 343 cats
7 to the fourth power = 2401 kits
so it's a BIG SIGMA running i from 0 to 4 of seven to the i power...

(Ahem!)

but the real answer of course is ____

[Beep, beep. Blogg authority has left this for the reader to determine!]

Of course as GKC would point out, there are some very interesting things to think about here. What kind of man has seven wives? Was he already coming back from St. Ives? Was he to confession, perhaps? Were his wives? Are all those poor felines stuck inside those sacks? Also, this very interesting riddle reminds us of Peter's question about "how many times must I forgive?" It also brings to mind the parallel riddle which starts "There were seven brothers" that the Sadducees tried to trap Jesus with. All of this suggests....

(Ahem!) To return to my initial topic.

I have been sniffing around for other such poems or songs. There is a famous academic article in CACM called "On the Complexity of Songs" by Donald Knuth, so you need not tell me about that one. (There's another, also in CACM called "The Telnet Song" with the chorus "control up-arrow q" but that is of interest only to grad students preparing for prelims.) I have also found the Hebrew "One Only Goat", which I am told has a parabolic meaning, but I don't have that yet. (I have the English, and the Hebrew too, though the Hebrew is, well, Hebrew to me.)

Omitting (for other reasons) the triangular "12 Days of Christmas" song, and the merely decrementational "xx Bottles (Barrels) of Beer on Wall" song, do any of my readers know of other such "nested" songs or poems?

(I also know about the "old lady that swallowed a spider", thanks.)

And yes, I am writing one to describe my former company's work in cable TV - a poem, not a song. Hopefully it will be done soon, though perhaps it will not be singable. Then again, there are all those bottles of beer....