Longread

Any kind of processes described by classical mathematics implicate the existence of borders within which they are defined. Expansion is limited in life by contact inhibition (not defined or not allowed space). In elementary physics expansion can be understood as limited by the axiomatic Pauli principle not allowing masses to penetrate one another. This kind of expansion can preferably called or meant by growth. However expansion described by fractal mathematics does not assume to respect borders and can thus be considered as genuine unlimited development. Growth thus means spatial expansion, while development is an outcome of following generations. By genuine development however the coming about and eventual disappearing of features is meant, while evolution rather means the showing up of permanent new features.

Thus the terms growth and development are understood as basically different or opposed to one another. They can be seen as a dualism or possibly even be assumed as prototype of all kinds of dualism in Nature. The particle/wave dualism found by de Broglie in 1924 refers to particles of limited space and simultaneously includes the notion of waves not being limited in extension.

Economic growth involves political limits as it became known by the Club of Rome 1972. Growth is understood as short-term outcome of the respect of borders, while various historical invasions illustrate long-term developments despite or by respect-less breaking of borders or taboos. Borders and taboos as seen this way mean to a large extent the same. Sedentary life needs and seeks respect of borders and restricts freedom, while nomadic life tends to do the opposite valuing freedom higher than borders or taboos. More freedom allows for more genuine development as defined above.

Both forms of expansion exist and may be needed. By unilaterally using either space and time or else following generations as reference scheme, conflicts are programmed and hard to avoid. To respect and not to respect logically exclude one another. This could be different when taking a partial non-binary view. Expansions then become at least less dependent on borders and taboos, more follow guidelines of optimization, and can extend beyond spaces and times defined as allowed.

This means modifications of before existing strict static rules of logic, moral, and as shown by the existentialism, also of authenticity. Classical logic strictly decide between true and false, classical morals decide the same way between good and bad, and classical authenticity between either genuine or fake. These three pairs can be considered as maximal or extreme values of basic dimensions of life. Modern view means accepting that variable intermediate and thereby dynamic values occur. Things can be more or less true, more or less good, more or less authentic. In principle these kinds of evaluation are found in sciences, technology and classical mathematics.

It is evident that the actual world cannot be described only by black and white or by left and right. There is always a continuous spectrum between the extremes, thus also between true and false, leading to fuzzy logic, and similarly between good and bad and between genuine and fake. The path of progress has to be found between those extremes by optimization. Extreme positions characterizing static solutions are considered to be equivalent to fundamentalism. Optimizing becomes a typical task of the consequent dynamic view and clearly hints to arts. Any kind of arts in Nature, in life, and as work of an artist, need optimization.

Extreme solutions, a purely static view, or types of fundamentalism therefore are rather not sufficient. Totally true means law and order, while by completely false, neglect of laws and anarchy is to be meant. Exclusively good would be renouncing on competition and relying only on social aspects, while extreme Darwinism excludes any notion of good in the moral sense. Total authenticity would include only egoism and self-realization, while fake is the opposite with complete disguise and lack of own essence.

Any kind of expansion,- growth as well as development and even evolution,- follows guidelines and thus is vectorial. In a spatial system time is a unidirectional guideline (the arrow of time) and could therefore be measured by natural numbers hinting at the counting of steps. In a fractal system this aspect is taken by the fourth "dimension" left over, which is the degree of order or chaos and is not unidirectional, but needs optimization. This is an important issue. Neither complete order nor total chaos, but an intermediate way between them is the guideline. You may think of the Middle Way in traditional Buddhism. Here, however, it leads to the understanding, that real life can not be optimized neither in a monastery nor on a battlefield. Art finds its best expression along the borderlines between order and chaos. Our existence has to be realized between striving for authenticity and assuming role play as required in social life. As a warning should be said that in misleading manner in fractal theories some times the term dimension is also used for describing the degree of order.

Why did we choose just religiousness, art and science as base for optimization? Religiousness refers to good and bad, arts follow rules of authenticity, which can be related to beauty and harmony, and sciences consider the truth as most important, which only in classical mathematics leads to strict logic. In fractal view consistency instead is a quality to be optimized, not an absolute one.

The right balance between order and chaos is getting to be the general guideline. The right path can be optimized between the extremes of arts, being authentic and fake, of religion, being good and bad, and of sciences, being true and false. This view attributes a modern meaning to the Middle Way between the extremes of total order or total chaos. While traditional Buddhism understands the Eightfold Path as eight important aspects for finding insight and fulfillment, the view taken here means a balancing between eight extremes, four on each side of the way.