Sunday, August 19, 2007

Beauty, Structure, and Space

I have a theory that Beauty is a function of 2 and 3.

1. Suppose we have an unlimited set of 2's and 3's. 2 and 3 are Fibonacci numbers. Add them together (2 of them) and it makes 5. Add the previous to the two (three of them - 1 2 and 2 3's) and you have 8. 8:5 (or 5:8) is a good approximation of the golden mean as seen by our eyes.

Pleasing proportion is in the ratio of two consecutive Fibonacci numbers (1:1, 1:2, 2:3, 3:5, 5:8, converging on the Golden Mean).

2. And take 3 2's as in 2 to the third power 2x2x2 - again you have 8, one more than the conventional comfort zone for short term memory of simple things (7 being 2 2s added to a 3), the point +/- 2 of our tolerance for breadth - things that have to be seen all at once.

Comfortable reading requires space - a maximum list length without a break is 2**3 +/- 2. If the list is complex, limit to 5, if simple, stretch to 9.

3. Consider 3 alone. This is the comfortable maximum nesting level. Your reader will forget the top of the argument by the time you reach the 4th subdivision of your paragraph structure. We can go visually and intellectually much deeper than 3, but our concurrent consciousness of more than 3 complex things seems limited. (This is why the structure of Romans is difficult for us. It has a length of 10 at depth level 4, a depth of 5, and a sustained sequence of 55 questions essentially without a break.)

Beauty is a function of proportion and complexity (breadth and depth) - so when writing, what should we do with our words and images to enable understanding? Chunk them, group them, and place them in recognizable relationship to each other in 2s and 3s. Curious that John Hobbin's theory of ancient prosodic structure conforms to these guidelines in his choice of 2 and 3 when measuring verse and if we stay above the syllable level. Qinah meter conforms most closely at the syllable level.

These principles have emerged for me from long experience in software engineering. They are not limits to complexity but guides to effective communication. They have wide application. It is one reason why software cannot be complete as a one-person effort. (That's for zhubert.) Yet do not despair, though we must have 2 or 3, we are also made safe even in solitude -
Psalm 4 - לְבָדָד לָבֶטַח תּוֹשִׁיבֵנִי
in separation, in safety, you make me live
(per Fokkelman's interpretation).

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