Thursday, May 10, 2012

5: Growth and Renewal

The Tree of Life, by Gustav Klimt

It's time for the fifth installment of the number series based on The Beginner's Guide to Constructing the Universe by Michael Schneider. 

With the number five comes the pentagon and pentagram. Many natural structures, from leaves to hands, follow a pentagram structure, and so the pentagram often symbolizes creativity and fecundity. Check out the link above to discover more naturally occurring five-ness. 

The pentagram also holds within it various phi relationships, so Schneider uses this chapter as an opportunity to introduce the golden mean and golden spiral. This page has a pretty good explanation of how you get there. I won't dwell on the details, but do try to make your own spiral for the fun of it! (Klimt's painting above is a display of Archimedian spirals. The golden spiral is the spiral of shells and galaxies, but because the distance between its swirls expands with each round, it's harder to find in artwork.) 

Have you ever felt like you were on a spiral path? Jackob Bernoulli created a motto for the golden spiral: Eadem mutato reurgo (Although changed, I arise again the same). There's something beautiful about imagining myself journeying on a spiral labyrinth. Many authors and artists have described the spiral's magical qualities, including the great Nabokov:

"The spiral is a spiritualized circle. In the spiral form, the circle, uncoiled, unwound, has ceased to be vicious; it has been set free. I thought this up when I was a schoolboy, and I also discovered that Hegel's triadic series (so popular in old Russia) expressed merely the essential spirality of all things in relation to time. Twirl follows twirl, and every synthesis is the thesis of the next series. If we consider the simplest spiral, three series may be distinguished in it, corresponding to those of the triad: We can call "thetic" the small curve or arc that initiates the convolution centrally; "antithetic" the larger arc that faces the first in the process of continuing it; and "synthetic" the still ampler arc that continues the second while following the first along the outer side. And so on."
    —Speak Memory, by Vladmir Nabokov

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