It's All in the Numbers...!

Today's post looks at some cool math that forms the structure of some very important books in the English language. I was recently reading parts of The Divine Comedy by Dante Alighieri. As you know, this is the Italian medieval epic poem that famously describes the descending and concentric circles of hell. If you have an X-box, you may have even played the game called Dante's Inferno, based on this work written nearly 700 years ago! At any rate, although there are many cool things about Alighieri's original spiritual allegory you might find the math behind the story especially interesting.

First, keep in mind that 10 was considered the perfect number (perhaps it still is). It then follows that 10-squared (or, 100) is also significant; as are the numbers 3 (representing the Trinity, for example, but also a significant number in other religious traditions) and subsequently the number 3-squared (or, 9).





The Divine Comedy itself consists of 3 parts:



1. Inferno (or Hell)

2. Purgatorio (Purgatory)

3. Paradiso (Heaven).

Each part is divided by cantos (the epic poem's equivalent of a chapter in a novel).

1. Inferno=34 cantos

2. Purgatorio=33 cantos

3. Paradiso=33 cantos

Total= 100

(and should you feel the extra canto in the first part feels less than symmetrical, note that this section includes an introduction to the entire poem itself, 
 thus accounting for the extra canto).




ONE MAN'S HELL...



Within each section, the 3/9 structure abounds. 
For example, in Inferno, the lost souls are arranged in 3 main groups and occupy 9 circles of hell. As you can see from the illustration to the right, the nine circles of hell are contained within this funnel-shaped geometric opening (extending from the surface of the earth downward toward an icy center....note: this is written before our modern concept of a molten earth's core.)


Purgatory, depicted as a mountain rising up from a solitary island, has 9 divisions as well.

1. Ante-Purgatory (the base of the mountain)

2. 7 divisions of Purgatory (the middle of the mountain)

3. The Garden of Eden, or an earthly paradise (at the summit)
















And finally there is the True Paradise (aka, Heaven)!












NOW LET'S TURN TO THE BOOK OF LUKE...



Since we're dealing with a text about a spiritual journey, let me suggest another math-based group of allegorical stories that you may know--the parables of Jesus.

Huh? Jesus as a math whiz?

Check this out (from the Book of Luke):

When asked by a group of religious leaders who were suspicious of Jesus and concerned that Jesus was hanging out with the wrong crowd (generally referred to as tax collectors and sinners), Jesus responds with three stories--or parables--to illustrate his answer. They each follow one another to make a triptych response...(and remember, the number 3 is a special number in many spiritual practices!).



At any rate, in these stories it's interesting to look at ratios. In the first story, the shepherd has 100 sheep, but 1 has wandered. The shepherd rejoices that the 1 is found. The ratio is 1:100.









In the second story, a woman has 10 coins, but loses 1. She searches all over the house and eventually finds it. The 1:10.

In the final story, a man has 2 sons. One becomes lost--the prodigal son--but then returns to the overjoyed father. The ratio is now 1:2.













Cool, huh? By shortening the ratios from 1:100 to 1:2 these stories not only hold together in structural unity and mathematical unity, but also thematic unity--Jesus can in this way respond that God is overjoyed at the return of ANY of his lost lambs, valuable souls, and beloved children (including "tax collectors and sinners"). Rather elegant, isn't it?



Now, both of these examples were spiritual allegories, where you might say numbers hold a unique significance. You can also draw an obvious line of influence from the biblical text to the medieval one written centuries later.

Perhaps you have examples of your own? Do you know of a novel or poem supported by a mathematical structure--or in which math concepts play a major role in theme or plot? Do tell!

Fun with Words

"Emil asleep, Allen yodelled "Oy."

Nella peels a lime."

If you don't understand this sentence, read it backward.

Okay, it's the same thing!

This sentence is a palindrome.

Definition according to Wikipedia:

A palindrome is a word, phrase, number or other sequence of units that can be read the same way in either direction (the adjustment of punctuation and spaces between words is generally permitted). Composing literature in palindromes is an example of constrained writing. The word "palindrome" was coined from Greek roots pálin (πάλιν; "again") and drómos(δρóμος; "way, direction") by English writer Ben Jonson in the 1600s. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (καρκινική επιγραφή; crabinscription), or simply karkiniêoi (καρκινιήοι; crabs), alluding to the backward movement of crabs, like an inscription which can be read backwards.

Today's posting is just for fun. For more palindrome sentences, check out Ralph Griswold's collection at www.cs.arizona.edu/icon/oddsends/palinsen.

Stick and Elastic Book

Since it's summertime, here is a little project to do with younger children. I'll post this tutorial by Susan Kapuscinski Gaylord and then let you know how we did with our project. For more information on making a variety of books you might visit her website at www.makingbooks.com.

Enjoy!