The Chapter on Symmetry and Resonance is concerned with the human tendency towards symmetry that (I argue) is a result of us being part of the world in which symmetry is ever present in space and time – having high impact-low noticability.
In this post I mention how science, specifically modern neuroscience, has caught up with, and given significant weight to intuitive knowledge about behaviour that is as old as humankind itself.
Also, earlier, I spent some time describing how traditionally, mathematics (generally) ignored chaos (and unpredictability), as the primary applications of mathematics were seen to be the fields of engineering and science, where predictability and the ability to measure accurately were of vital importance.
After all, we, the ordinary citizens, (the consumers of the items that are manufactured by the advances in engineering based on mathematical equations and formulas), won’t buy an engine that is unpredictable, nor will we be enthusiastic in crossing a bridge if we are in doubt as to whether or not it will hold our weight as we walk over!
This has some relevance in this Chapter, because the world of mathematics has been making strides in our understanding of natural phenomena that have been observed as long as humans have had an awareness of the natural world, in particular those phenomena that are chaotic or unpredictable.
In the 20th Century, particularly the latter half, mathematicians began looking again at chaos and its usefulness and/or applications in mathematics, (and vice versa) and, over time, developed theories which proposed that underneath the chaos [1] (or unpredictability) that we experience in our day to day lives there is an underlying order, that is, a predictable pattern that is not immediately obvious. Originally this was applied to phenomena such as the weather, but further developments have reached into psychology and society.
In the remainder of this Chapter I attempt to explore the continual to-and-fro between inevitability, (that which we expect will happen, i.e. our plans) and uncertainty (not knowing what will happen, i.e. our surprises [2]). That is, chaos.
This to-and-fro is a constant reality in our lives which we do not usually have in our conscious awareness.
[1]. The chaos that we are familiar with could be a weather event, the course of a forest fire, the spread of an epidemic, a battle in a war, how a field is taken over by weeds/shrubs etc. if left untended, or, relevant to our area of interest, the day-to-day activities of a family affected by alcoholism and drug addiction.
[2]. When I was younger an older man said to me, by way of cautionary advice: One way to give God a good laugh is to tell him your plans for tomorrow!