A guide to an enigma
The following pages (via the links below) have been submitted to ACARA (Australian Curriculum, Assessment and Reporting Authority) with the intent to have the information added to the secondary school syllabus. Understanding nonlinearity can be achieved without higher maths and helps immeasurably throughout life.
Nature presents us with many enigmas. Only recently in our history have we begun to unravel some of them, and there is a long way to go yet.
A major part of the challenge comes from the fact that most of the events we are witnessing (and many we don't see, yet are influenced by them anyway) are folded into a black box with layers upon layers of detail and just about all of it hidden.
Why is it hidden, how does something so proliferous camouflage itself? It's because there is so much of it, and altogether that multitude functions in a way that makes the whole tremendously difficult to understand. It becomes a case of not seeing the wood for the trees.
We are dealing with nonlinearity. A phenomenon where each element is interconnected with all the rest to such an extent that the overall result hardly bears any semblance to the detail without which the whole would not be what it is in the first place.
This is a guide into that mysterious world. We neglect it at our own risk. One way to look at it is shown in the introduction to the CauseF program. For some examples of how disastrous a lack of understanding can be, see Why should you care? below.
Nonlinearity is about complex, dynamic systems; it is about chaos. To understand its nature it is necessary to grasp the principles, the laws that govern such systems. It may seem difficult at first, but that's because for most of our history (indeed, for most of our personal history) we have become used to seeing things in a linear fashion.
The math behind chaotic behaviour can be challenging. But relax: this guide explains the behaviour in a functional sense, which allows us to understand its principles on an intuitive level.
It is a matter of shifting one's perspective. Once that has been accomplished (and it won't take long at all) anything performing in front of our eyes will be just as obvious as seeing a cyclist pushing the pedals and recognising the turning wheels as a consequence.
Nevertheless, the mind needs to be prepared to deal with the wider picture before the new perspective can be employed.
Hence the guide comes in four parts. The first is a test to ensure the newcomer is mentally prepared for what is to come. Part 2 is a general introduction to chaos, leaving aside the math. Part 3 and 4 each contain a link to a page on this website which in turn connects to interactive computer programs that allow the user to observe the principles at work. After a short while (which hopefully should be lots of fun!) the newly-gained perspective falls into place and the world will be seen with new eyes. It is a skill shared by only a few on this planet. They are mainly meteorologists, aero- and hydrodynamic engineers, and some biologists. The way events are described in those areas point to the understanding behind them, but outside of those the expressions lack the references one would expect.
Part 1
The mind test may seem utterly trivial, but is it?
Part 2:
The mechanics of chaos: a primer for the human mind. What is chaos; what is meant by complexity; how does it relate to the human mind; how to apply it in practice.
Part 3:
CauseF program. Interact with the squares in a grid, with spheres zipping around on a plane, with virtual planets as they orbit a virtual sun, or have force vectors acting on a cylinder and modifying its
appearance. Observe how impossible it is to foresee their behaviour when changing the input from the outside.
Part 4:
OCTAM, an artificial mind model. Constructed along the lines of nonlinearity the user interacts with the program via web cam and microphone, and its output are visuals on the screen and sound from the speakers.
Nonlinearity is everywhere. Enjoy!
So what, one might say. When it comes to our daily lives, what does all this matter? A lot actually - here are some examples of the kind of disaster that can be avoided if only nonlinearity had been taken into account.
The weather
With temperatures rising around the globe our weather is ever more likely to approach boundary - that is, extreme - conditions. Exactly the kind of situation where nonlinearity makes itself felt for all to see. Although the weather bureau does provide
warnings of approaching severe storms or floods, those warnings need to be understood and interpreted by the general public. Sadly, often they are not. And so it happens that people are caught unawares and homes, businesses and especially lives are lost.
Collapsing bridges
High winds can induce mutually enhancing forces and bridges need to be designed with this in mind. A dramatic example of what happens when wind buffeting is not addressed was the bridge spanning the Tacoma Narrows Strait in the United States. It disintegrated
in a spectacular fashion in 1940. See the video: The Collapse of "Galloping Gertie" (The Tacoma Narrows Bridge).
Aircraft design
There was a time when test pilots of new aircraft literally took their own lives into their hands. Extreme conditions across the wings are easily reached during a stall for example, or in heavy air turbulence. Now, with aerodynamic profiles being able to
handle nonlinear behaviour, test pilots are so much safer.
Political decisions
Usually decisions made by politicians are well-meant, but can achieve a result sometimes directly opposite to what had been intended. That's because society is a nonlinear human activity system, and what one group does affects many others who in turn react
in their own manner, which in turn impacts on yet others ... and so on and so on. Examples can be tax laws, immigration rules, the so-called 'war on drugs'. (Or quite simply the law. Judicial perambulations more suitable to a psychiatrist's couch than
legal chambers can be found in P F Campos' Jurismania: The Madness of American Law, Oxford University Press, 1998)
Biodiversity
Usually meant in a positive sense and thereby neglecting any potential negatives that arise due to the very same characteristics. A case of where the negatives had not been recognised is the cane toad. Introduced into Queensland, Australia, in 1935 the
species quickly spread because its erstwhile natural predators no longer existed. From the perspective of the cane toad the biodiversity in its new home meant it could avail itself of a plethora of food sources, but those sources had no protection
against the newcomer. From the perspective of the locals biodiversity now included the cane toad as well, but to their detriment. How much of a problem it has become can be seen on the NSW Environment and Heritage web
site, Cane toads (https://www.environment.nsw.gov.au/publications/eradicating-cane-toads-nsw-outside-their-current-range-distribution-best-practice-guidelines). Biosystems
are nonlinear per se, regardless of what humans make of it.
Feedback
Feedback is very much invited. Was the guide helpful, are there any further questions (at least within this summary context - this is just an introduction, there are so many more specifics), perhaps relating some discussions that eventuated. Please see the contact page for emails and more.
© Martin Wurzinger - see Terms of Use