Wednesday, September 21, 2005

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...


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....


At 21 September, 2005 15:24, Blogger rhapsody said...

Hi Dr. T,
The only thing I think I know is the answer to the riddle- thank goodness it doesn't involve a lot of math! No offense :)
Will let you know if any nesting poems turn up-

At 22 September, 2005 15:44, Blogger rhapsody said...

The children's librarian recommended four cumulative tales: "We're Making Breakfast for Mother," "Our Class Took a Trip to the Zoo,"
"The House I'll Build for the Wrens,"
and "The Jacket I Wear in the Snow," all by Shirley Neitzel.

The reference librarian came up with some songs- which sorry I am not singing even tho tonight is choir practice... "A Gaping Wide-Mouthed Waddling Frog"- sounds yummy- He gave me some others but I'm not sure they're nesting songs- "Children Go Where I Send Thee," & "Green Grow the Rushes, Oh!" There are others- a book called "My Sister Ate One Hair" but we didn't know the author- it might not have come out yet. Sorry I can't do the links- I'm too slow.

Hope it helps,


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