Chapter 4: Planetary Development

Occurrence of Traditional Aesthetic Values on Earth (Geology, Biology,
?Neurology, Architecture).Maldek.Venus.Life on a Sulfate Planet.Life on a Cubic
(or Higher) World

				Conclusion:

	Nature prefers to approximate everything. This allows for multiple
versions of the same goal: variation of form---one of the cornerstones of
Darwin's work. She would much rather not have rational values as the blueprint,
but would rather have irrational values to approximate by way of exact rational
variations. Thus, something like table salt is not a substitute for the tradi-
tional golden ratio, but an approximation of it; chemistry and biology only
indirectly reflect abstact aesthetics.
	At the quadratic level of biological systems, the primary inorganic salt
forming the basis for life on that planet must be a single binary salt. The
polynomial's sets of elements forming approximate ratios of the two roots will
also be just sets of two. Thus there can only be two ions of the same valence:
one charged positive and one charged negative. Also, the x^0 coefficient of the
polynomial blueprint must be a one so that the inorganic binary salt will be
electrically reciprocal, as ions in an aqueous medium, without the need for
outside intervention (multiplication by the x^0 coefficient). This means that
binary salt planets must be restricted to quadratic hybrid polynomials of the
form: 1x^2 +- bx - 1, where b is a whole number. This results in some simple
relationships:
both roots will always be irrational making their chemical approximation an art;
root1 = 1 / (-root2); root1 = b + some decimal fraction, while root2 = the nega-
tive
decimal fraction; b is the relative magnitude value, while the decimal fraction
is the quadratic root-system's identity (the unchanging decimal fraction gives a
sense of stable identity in a system devoted to change and activity); in geome-
try these
roots are found in polygons of b sides. If we retained both roots while making
them both positive or negative, then

	On the other hand, on planets whose biologic systems are derived using
polynomials of degree greater than two, the types of ions will still be just two
(positive and negative), but each of the several primary ions must be able to
form salts with only two other ions by changing both their charge and their
valence. In a cubic system for example,
	ion 'a' must have either a valence of +2, or -3; while
	ion 'b' must have either a valence of +3, or -1; while
	ion 'c' must have either a valence of +1, or -2.
This will result in three salts of: 'ac', 'ba', and 'cb'. All three salts will
then be adjusted in their approximation of their respective blueprint values
by forming three salts with one buffering ion, possibly: 'ad', 'bd', and 'cd'.
Such a buffer would need to vary its valence three different ways: -2 for 'a',
-3 for 'b', and -1 for 'c'. Or the charge of 'd' could be positive. The buf-
fering ion would tend to be a poor conductor of electricity helping to negli-
gibly dampen such flow in solution.
	Whatever the degree polynomial of that system, its x^0 coefficient will
always be a one (unless there is a convenient way to multiply the atomic weight
of a salt whenever the flow of electricity between ions is considered in only one form).

For example, in a cubic system,
there might be an ion of hydrogen forming an
acid with one ion as well as forming a hydride with another. There will
also be silicon or some other ? type of element acting as either a cation
or as an anion. Such a planet would be a triple binary salt system.