A brief digression is necessary before presenting an alternative balance centered around observations where natural forms are neither ordered nor disordered as opposed to the impossible and the extreme duality that entertain mathematicians and their followers concerning geometry.

The non-periodicity of the arithmetic Pi represents the relationship between diameter and circumference where a radius represents a new diameter within this structure. In other words if you can create a circumference from a diameter it holds that there is also a radius. This was covered nearly two decades ago at a time when celebrity physicists would show up in the newsgroups -

(John Baez) wrote in message ...
In article ,
Oriel36 wrote something like:

For those who prize logic, this Planck length is the funniest
thing; seeing that this thread covers a wide range of groups it is
worthwhile posting a simple geometric refutation.

Draw a circumference around a Planck length, the circumference being of
course 3.141 times greater than the length, if you can determine a
circumference you can also determine a radius which is half the
original length and from this discrete length you begin again
constructing a circumference around this half Planck length.

What you get geometrically is a form of the Zeno paradox and you guys
take the Planck length seriously!

[Actually this sort of argument goes back to the "Mutakallimun",
Jewish and Islamic philosopher/theologians of the 10th and 11th centuries
AD. Many of these were very fond of atomism, taking it beyond Democritus
to argue that *everything* was made of discrete units - even space and
time. Others brought forth certain paradoxes to disprove this. John Baez]"


There is no lower limit to length otherwise Pi would possess a periodic arithmetic or geometry would disappear altogether as a discipline. Two decades on from pointing this out and with a much softer overview of how the narrative developed I can't say I feel sorry for mathematicians but I do realise that it was a time when academics were trying to escape the confines of the clockwork solar system by putting experimentation and mathematics at the heart of physical sciences including the celestial arena.

The alternative approach based on a balance between order and random does not reach for extremes nevertheless it has all the properties of complex and intricate relationships that some people are comfortable dealing with.