Tuesday, November 23, 2010

The Sacred Spiral

too proud to submit we commit to complicity
in our existential angst until free to rant
upon a new attitude of voluntary simplicity
when it be a gift to bow and bend we shan't
be ashamed to turn turn will be our delight
'til by turning turning we come round right
to see the shaker song at center and recant

A couple of weeks ago this video on Sacred Spiral crossed my path. It is narrated by Kiesha Crowther the Little Grandmother, who seems too young to be a grandmother, but very ancient in wisdom. Last week she gave this talk in Zurich where she talks about the changes that are to be coming upon us in the next few months and how important it is to navigate these changes by thinking through the heart rather than the head. Spirals are back in the news again with this piece posted on Nov 11th, 2010 on spiral Aurora Borealis which have never been seen before, and we know these have nothing to do with Russian rockets, but since we have no clue what they are about it is mystery.

I have some really interesting things to say about spirals and their relationship to the transcendental numbers of pi, phi and the golden mean. It was a couple of decades ago that I had a short affair with these numbers (more so with the pythagorean theorem BTABP). Pi was rather simple, being a ratio of minimum and maximum between adjacent dimensions; for the circle the minimum length (a first dimension) for the maximum area (a second dimension), or the minimum area (a second dimension) for the maximum volume (a third dimension). Plus the fact that these numbers never ended and never repeated. and you could never define exactly what they were, but that's what makes them transcendental numbers. To me the big question was whether these numbers existed before matter, and thereby defined the spatial component of our universe, or if they only came after and the universe defined what they were.

Phi was a lot more interesting. Phi has a value of 1.6180339..., another transcendental number without end and it creates a number series similar to the Fibonacci series. In both of these the last two numbers add together to create the next number in the series. The phi series works like this but it also has the property that multiplying the last last number by phi gives the next number in the series. So it is the only number that is both additive and multiplicative, which also gives subtraction and division, and hence defines the basic elements of mathematics.

The phi ratio is know as the Golden Mean and is most esthetically pleasing proportions in architecture since first noticed by the Greeks way back when, and prehistoric carvings before that. It is also a pleasing proportion in other aspects as can be seen here.

Fibonacci and the Phi sequences also map out into spirals and here is slide show that shows how this is done. This basic shape is found throughout nature. Another area where this shape occurs is in relation to a math graphing problem. The four color map problem says that you only need four colors to color a map such that no two adjacent countries have the same color; there is an exception to this law which is if the map is drawn on a torus (i.e. doughnut) there is one configuration that would require seven colors, and if you were to lay the map out flat it turns out to have the shape of a series of phi spirals. There are no doubt more curiosities about this fascinating number. Why just today at coffee I was introduced to a phiona though I suspect she spells her name with an F.


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