###### 1 October 2019

Traditionally Chaos Theory is associated with Sensitive Dependence on Initial Conditions (SDIC) aka The Butterfly Effect (BE) – the idea that a small change can have a large and disproportional effect at some point in the future. But this is a naive understanding of Chaos.

Chaos is much more than the butterfly effect, but the very concept of the BE is demonstrative of how intellectual progress is often hindered by locked-in thinking.

To describe something as being SDIC is to be locked into linear thinking, more specifically locked into the ubiquitousness of linear mathematics in physics

Up until about 350 years ago mathematics was a subject primarily about, geometry, trigonometry, and algebra was just beginning to emerge, and then out of the blue Newton and Leibniz introduced some dynamism into mathematics, in the form of “Calculus” – *The Mathematics of Change…*

The introduction of calculus changed everything, suddenly mathematics could be used to describe behaviour, but more than that, mathematics could now be used to predict behaviour.

Over the following decades and centuries Differential and Integral Calculus found their way into virtually every field of science. However something that has been generally overlooked about these powerful mathematical tools is that they rely on a fundamental assumption that is build into calculus; and that assumption is that all change fundamentally occurs in a smooth continuous fashion.

In the latter part of the 20^{th} Century Chaos Theory came along and seemed to upset the apple cart somewhat…

Chaos Theory shows us that not all change occurs in a smooth and continuous way, some types of change are distinctly nonlinear.

Chaos Theory shows us that nonlinear dynamics are essentially unpredictable, but given the widespread allegiance to the belief in a predictable clockwork-like universe, physicists have described this chaotic lack of prediction in the language of linear dynamics, and hence equated chaos with the concept of SDIC (aka the BE)…

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**So where do we stand today?**

Well, all the excitement about Chaos Theory more or less came and went and this locked in thinking still exists. Science is pretty much still wedded-to linear dynamics predicting smooth continuous change…

Unfortunately such locked-in thinking can blind one to the truth. And the truth in this case is that much of mathematical physics is devoid-of any form of abrupt change.

With continuous change things are easier to predict, but with abrupt change, prediction becomes a tad more difficult; and the more abrupt the change, the more unpredictable the behaviour becomes…

Such abrupt change is, of course, ubiquitous in all types of systems, and so Chaos/BE seems to imply that there is little that we can ever know about the future behaviour of these systems…

But we have been looking at Chaos the wrong way around. Too often is the focus on the BE. The BE is of a lack of order (and equilibrium), but what chaos mathematics is really trying to tell us is that, in reality, there is an invisible hand at play in all things in the universe (even if it looks like there isn’t)…

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Some 300 years ago Adam Smith used the idea of an invisible hand to illustrate how economies self-organize themselves to an optimal economic equilibrium.

Chaos Theory is about how some very simple mathematics can act as an “invisible hand” not just in economic systems, but in every conceivable type of system.

Chaos Theory suggests that Smith’s invisible hand is not limited to economics, and shows us that there is a mathematical hand at play in all things in our universe; even to the point that this hand ultimately helps order and complexity emerge from the emptiness of space…

So forget the BE, it is virtually irrelevant! Chaos Theory is more than the BE. **Chaos Theory explains the mathematics of “Dynamic Equilibrium”…**

Chaos Theory reveals 4 things about all forms of dynamics

- An Invisible Mathematical Hand is at play in all system behaviour…
- The existence of mathematical “Attractors” (both orderly and chaotic) means that some things are more likely than others…
- The type of attractor we see is determined by the amount of energy in the system…
- These attractors exist at all levels of scale (including the quantum scale)…