4.2 Chaos, Critical Mass, and Fractals

We exist due to the unpredictability of our parents meeting.  Our personality and physical appearance (and some might say our destiny) emerge from the unpredictability of conception when one of millions of our father’s sperm reaches our mother’s fertilised egg.

We begin, and live out our entire lives in a world that is on the one hand beautifully ordered and symmetrical (as we described in the previous Chapter) and at the same time utterly chaotic.

Chaos is a reality in our lives, and affects us profoundly whether we like it or not.

This Chapter is about chaos and topics which I feel are related, such as critical mass, and finishes with a description of the relevance of fractals and self-similarity (all of which will be described below) in working with people in distress.

It is divided into seven Sub-Chapters.

4.2.1                CHAOS, CRITICAL MASS AND FRACTALS – INTRODUCTION

4.2.2                CHAOS

4.2.3                CRITICAL MASS

4.2.4                STRESS AND STRAIN

4.2.5                APPLICATIONS OF CHAOS THEORY, FRACTAL GEOMETRY AND SELF-SIMILARITY

4.2.6                IMPLICATIONS OF CHAOS THEORY FOR HEALING

4.2.7                CHAOS, CRITICAL MASS AND FRACTALS, CONCLUSION

This website is concerned with human growth.

It is the continual dance between predictability and unpredictability that allows nature to form its own unique patterns and structures when it comes to growth.

As we know from systems theory, if every living thing was precisely identical, and its behaviour, like a machine, was absolutely predictable, it could never adapt to its environment, so it would die if the environment changed.

I mentioned a murmuration of a flock of birds earlier.  To our eyes it is entirely unpredictable, yet it has order, as all the birds turn in unison, at high speed, without (seemingly) getting instructions from a lead bird.  Something similar is observed when we look at a shoal of fish. And the same goes for the colony of termites also mentioned earlier.  Like the murmuration, it looks chaotic at first glance, but of course it has a very well structured and ordered pattern of behaviour that is necessary for the colony to survive and thrive.

All these examples have an element of unpredictability, but they also have some predictability, which is called self-similarity (which I will be describing in a following post) in their patterns of behaviour.  That is, the patterns are similar, and to some extent predictable, but they are never identical.

This has been known by police for approx. 150 years in police and detective work, when it was established that even though all our fingerprints are very alike – they are unique.

In many phenomena in nature, wise, experienced observers will see patterns where others see chaos – or, (in respect of human behaviour), will see order where others see anarchy.

And isn’t it interesting that we use the expression sure that’s human nature to describe the way we typically behave!  Human nature is, of course, as unpredictable as nature itself and yet has a kind of order woven into it that the interested onlooker will spot. 

For example, a mother will almost always see an order and pattern in the chaotic behaviour of her child.  This is because she is so familiar with her that she almost feels part of her, as she was once part of her.

Chaos is often mentioned in the context of families in our Focus Group.  For example in this website (and in many others) children may be described as growing up in the chaos of addiction.  Such chaos is deemed to be very unhelpful to children’s healthy development, whereas predictability, consistency, and order are all considered to be very important.

(This is true not only in respect of children but in human development and growth in general).

When people come together to form a group, (whether it be a political party, a commercial company, a sports club, a class, a group sharing the same hobbies, a community council, even a therapy group), the first thing that is done is that rules are written – so that as much chaos as possible can be eliminated and something can be achieved, as we all know that nothing will be achieved if chaos prevails.

Even in very loose groups where there are no set rules, unwritten rules and courtesies are adhered to so that the familiar order which we all yearn for can be present.  And at a personal level, this applies too.  Think of the amount of time we spend tidying up, sorting, classifying things etc.

It is through the continual dance between order and chaos, or certainty and uncertainty that we evolved to what we are today.

In the Chapter on the Family Support Shamrock we mentioned how a picture is more attractive when it is framed, or a game is more attractive when there are rules. These examples reflect our conscious and unconscious need to eliminate chaos.  With the addition of the boundary (the frame, or the rules) it is complete and our expectation is that it will not change again.

Or think about gardening. Even though we humans are part of nature, every time we pull a weed out of our garden we are imposing our desire for order on nature’s chaos. But, non-human nature is not really chaotic – in fact, as I stated above, it is beautifully ordered. It’s only chaotic when it is viewed from the perspective of desire for order as defined by us!

So an enormous amount of our time, energy and effort is spent trying to eliminate, or at least minimise the effect(s) of chaos (and unexpected change) in our lives, and make everything certain and predictable.

Yet; chaos and uncertainty are things that we know both intuitively and from our lived experience, will always be with us.

I believe that in our efforts to be relevant in the lives of people whose day-to-day experiences include regular chaotic events, acceptance and admittance of a manageable amount of chaos can give people courage to be themselves, take a risk and/or show a part of themselves that would remain forever hidden in a more ordered and structured environment.

Here is a nice poem by a colleague of mine, the redoubtable Mick Lacey, about the human desire to put order on chaos.

So, after all that, has chaos any positive attributes – or is it helpful in any way to humanity?

In a previous post I explored how darkness – which we all dislike and want to avoid, can have beauty and attractiveness. Our abhorrence of chaos reminds me of our attitude to darkness.

And, like trauma (as I described in the Chapter on Trauma and Related Topics), chaos in respect of designing initiatives to assist families in the Focus Group probably deserves a book in itself.

Here I will attempt to describe practices that may be developed to continually refine the response to the chaos that will inevitably occur, and how they can be used in a positive way to enhance our work. An awareness of this and development of skills to do it is far preferable than using vast amounts of energy and time trying to eliminate it. (Again, think of the enormous amounts of energy used all over the world trying to eliminate darkness)!

Rolling out initiatives that encourage agencies to accept the reality of chaos and work with it may be very challenging.  Once again, it’s a question of balance.

As a general rule, I would like to propose that if chaos rules, nothing is ever achieved, but if rigidity rules, people who matter most are often left out.

One of the reasons why accepting (or indeed embracing) chaos and unpredictability may be very challenging is that uncertainty holds such fear for us.

For example one of the techniques of torture is to not tell people what is going to happen to them.  While this is an extreme example of the terror that can be brought about by uncertainty, it can also be used by unscrupulous people in authority in our day-to-day lives to keep employees on their toes so to speak.

In encouraging organisations to accept the realities of chaos, I’d like if people get what I mean – I do not in any circumstance promote the use of uncertainty as some sort of control tool.

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 20^th 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!

Later (in Sub-Chapters 4.2.5 and 4.2.6) I will propose further applications or uses of chaos in some detail – and link it to systems theory (that I described in a previous Section) but prior to that I will briefly explore critical mass.

This term was originally coined by physicists experimenting with nuclear fission to describe the point at which a nuclear device will be self-sustaining, there being no way of stopping it after that point.

In addition to its relevance in the world of nuclear fission, you might have heard of critical mass as it applies in a phenomenon popularly known as the butterfly effect. That is, the flap of a butterfly’s wings in one part of the world setting off a tornado in another part.  (A butterfly’s flapping wing represents a small, virtually imperceptible change in an initial condition of a climatic system, which causes a chain of climatic events leading to a tornado).  Had the butterfly not flapped its wings the tornado might not have occurred! 

More importantly, at some point along the course of events, the process reaches critical mass that is, a tipping point [1] after which there can be no reverting to the original state.

So let us consider critical mass when applied to human behaviour. 

There is a saying among stand-up comedians that if a third of an audience laughs all will laugh.

We are all familiar with the phenomenon of the buzz, that is, we know something is happening and we want to be associated with it.

And why does a team usually play better at home?  And related to that, consider a big crowd in a stadium, how each individual’s identity becomes blurred as everyone behaves as one.

Another example would be a country at war.  Enthusiasm to embark on a campaign to kill others and/or be killed reaches critical mass so that if one is seen to be against the prevailing feeling then one becomes separate from the tribe. On the other hand, I have referenced, in a previous post, people power that reached critical mass in USA in the 1960’s-70’s that was very influential in putting an end to the Vietnam War.

This, of course, also shows the power of relationship – one of our root foundations – in us. That is, our need, or even our necessity to belong.

[1]. In terms of human violence the most destructive tipping point in human history could be thought to be the assassination of Archduke Ferdinand of Serbia in Sarajevo in 1914, which resulted in the start of the First World War, the perceived unjust consequences of which (many would argue) led to the rise of Nazism and thereafter the Second World War.  Between 1914 and 1945 it is estimated that over 70 million people died because of the rivalries, power struggles and expansionist ambitions of the Great Powers (including the USA) that had been going on for a hundred years that had reached critical mass prior to the assassination of the Archduke.  This I covered in more detail in the Chapter on Power and Control in Society.

Very often – in respect of critical mass in human behaviour – a tipping point is reached along a timeline where there is a substantial element of predictability.

For example, in a sports championship, over a season, a team might be improving match-by-match and a sense, or feeling, comes over the team that they are going to win the championship outright. An away victory, three-quarter’s way through, against particularly challenging opposition might be considered to be the tipping point. Thereafter, little things begin to go their way and their belief reaches critical mass as the weeks turn into months and eventually they win the championship.

Another example might be a political party on the campaign trail, as week by week they gain more and more support to the point where the party’s belief in winning the election reaches critical mass. As momentum builds, there may be an event that people can point to that is significant in swaying public opinion. (In US Politics, this is called ‘The Big Mo‘)!

In the present day, many scientists are speculating that global temperature increase will reach a tipping point sometime soon, and that no matter what we do after that we will be unable to stop the temperature rising to catastrophic levels. It is tragic that we appear to be so helpless in this very predictable sequence of events.

However, an unpredictable event can also spark a tipping point!

Sometimes there are hidden forces that have been building up unnoticed by the vast majority, and an unpredictable event reveals, to everyone’s surprise, just how powerful those forces are, or were. (I gave an example of such an event in footnote [1] in the previous post when I mentioned the murder of the Archduke Ferdinand in Sarajevo in 1914).

Unpredictability is in everything we experience, starting with our own existence, but also in the world in which we live; e.g. the weather, the ups and downs of the stock market, political life, economics, religion – everything.

For example, in the late 1970’s, when Pope John Paul II visited Ireland, very few would have predicted the downward spiral in the status, esteem and power of that most certain and predictable entity when I was growing up, the Catholic Church in Ireland.

The Bishop Casey affair in the early 1990’s (which, from the perspective of the third decade of the 21st Century might be deemed to be relatively innocent) was the unexpected event – the tipping point – that, like a dam bursting, unleashed an unstoppable torrent of negativity not only about the Church itself but about how the Pillars of Irish society were perceived – with, of course – hindsight, to have lived a lie through many decades.

The speed at which anger, cynicism, suspicion and apathy replaced reverence, obedience and respect astounded everyone.  Reaching a tipping point implies the point of no return and it is very unlikely that there will be a return to the unassailable status that the Catholic Church held in decades past in Irish society.

Currently the amount of concern about protecting the environment is probably greater than it has ever been.

Take one example – the dangers that plastics pose to our oceans.  In this, we can do all the small things we want like recycling plastic but until legislators face down the corporate world and actually force them to do something radical about plastic nothing substantial will be achieved.

And the legislators are people who spring from our communities and are elected by us, the ordinary people.  So until a critical mass of society want things to be different – they won’t be – really!

At a different level, and once again, more relevant to our subject matter, all adult males will be familiar with, and will probably have been affected by, the gang or pack mentality, in teenage years, that demands loyalty and can be very destructive and harmful.

Much late night street violence results from this pack phenomenon where a group of young men’s willingness to be violent reaches critical mass, seemingly due to the influence of each other, (that is, it becomes self-sustaining) and one or more or all of them do things that they most probably would not have done had they been on their own.

The butterfly effect is observed here also, as the result (output) of the incident (serious injury or possibly even death) is highly disproportionate to the input, (possibly an innocent remark, a look, or a mistimed joke).  The event takes on a life of its own and proceeds with little relevance to the input.

More importantly, somewhere along the timeline a tipping point is reached where there is no going back to rational thought or reasonable behaviour. (Remember the example that I gave describing how a tipping point in such a situation was avoided by compassion, and compassion alone)?

Fashion is not something that we immediately associate with crime, child protection or responsibility!  Yet fashion is very influential in human behaviour.  This is known to anyone involved in sales and marketing and the word fashion sometimes suggests ostentation or showiness, as if it is only applicable in the world of clothes, advertising, music, etc.

When I was a teenager, the tendency of young male teenagers to wear their hair long, reached critical mass around the middle of the 1960’s.  Something that was not at all fashionable became fashionable because one pop group who got very famous (The Beatles) wore their hair long.  In addition to their music, this was a very creative (and original) thing to do.

In the context of this discussion fashion could be a common expression or manifestation of critical mass and as such is interesting to us in our discussions on patterns of behaviour in humans.

I believe that Solution Focused Brief Therapy (SFBT) [1] uses the concept of critical mass even though I cannot recall seeing the term referred to in any of the books that I have read on SFBT.

In focusing on solutions instead of problems, (as the medical diagnosis traditionally does), SFBT ensures that the client’s strengths will be affirmed by the client him/herself on an ongoing basis until they have more power than the problems and the solution becomes more the norm than the problem, so the practice of thinking about solutions becomes self-sustaining.

If I am a young man or woman growing up in a family in the Focus Group, and I am getting involved in at-risk behaviours – on a journey towards a life of chaos, crisis, addiction, crime and ultimately imprisonment – critical mass may be reached at some point where I form the belief, at a deep unconscious level, that self-destructive behaviour has become self-sustaining, and that there is no turning back, no matter how I might coach myself at a cognitive, conscious level to be better behaved to please others and have an easier life.

And – now for some good news – I propose that responsibility can reach critical mass if I am say, recovering from addiction.  I reach a point where I am confident enough, (though not arrogant, which in fact comes from lack of confidence), that I can live a drug-free, life-affirming existence, and that there is no going back.  (I have that feeling myself at this point in time as a former smoker, though it took me some years to get here).

I believe that this can also happen in a family (or any group of people, but more particularly a small group) as responsibility becomes the norm where previously the norm had been irresponsibility. (This belief is very important in the context of the principal aim of this website).

The important term to remember here is self-sustaining.  This implies that a feedback loop of unconscious (or barely conscious) positive reinforcement of behaviour is enough to maintain the behaviour, as it (over time) becomes the norm.  This is further explored below when we discuss uses and applications of chaos in Sub-Chapters 4.2.5 and 4.2.6.

[1]. It is important to note that in SFBT the word brief can refer to the duration of an encounter or the number of sessions offered.

Stress is a term that is commonly used nowadays as we describe children under stress in school, parents under stress when their teens are acting out, relationships under stress when conflict arises, families under stress if a member gets into trouble – i.e. goes to prison etc.

In the physical world of materials science, stress is a force that results from pressure being imposed upon a solid [1]. When humans come under pressure, we may recognise it, or identify it, as stress.  In respect of human emotion, it is first mentioned in the 1920’s.  (Of course, humans were stressed before that – there must have been some other name for it)!

Strain is the result of stress. Getting back to materials science, when pressure is put on an iron bar the bar comes under stress.  The bar will then bend as a result of the stress.  The strain is the amount of bending that takes place, away from the original shape of the bar.  If the bar is too strained, it breaks under the stress.

Now think about the difference between an iron bar and a wooden dowel, of approximately the same thickness.

The iron bar will bend quite a lot, depending on how flexible it is, but as both are put under stress the wood will probably break while the iron bar is still bending.

Obviously, some solids are more resilient [2] than others, and are able to bend a fair amount before they break.  Just like humans!

Stress is a common feature of many areas of helping, and most practitioners will be aware of good stress and bad stress.

We cannot live our lives without good stress – it motivates, inspires, enthuses, entertains, drives us on to achieve, and adds to the enjoyment of life.  The stress of watching our team in an important match, or watching an enjoyable thriller, competing against others for a prize, being challenged by difficulties at home or at work, are all rewarding and life affirming.

This is true even if we lose, as we motivate ourselves to do better next time.

In common usage, however, stress usually refers to bad stress.  That is, the experience of being in seemingly impossible situations which cause us emotional pain and distress.  This, if not dealt with in a healthy manner, is usually experienced as debilitating and negative.  (I’m stressed out)!

In the helping professions in general, practitioners often find themselves in situations of responsibility without power, which is very stressful and ultimately debilitating.

I believe that it is interesting for anyone who works with people in distress (di-stress)? to consider the link between stress and strain.   

Being under stress is generally thought to be a condition where we may feel that we have to change, and this could be for good or bad.  Eventually if the stress is too much for us we, metaphorically, change our shape to adapt to the new situation.  This change we may denote as strain.

An example might be how parents have to change as they experience stress when they are rising to the challenge of raising teenagers. In this, they change their shape. That is, learn new skills, put them into practice, have a different attitude, be more vigilant, listen more attentively etc. etc. – after which there is no going back to the parents that they were when their child was a relatively compliant pre-teen.

So we might say that strain is the critical mass of stress.

In other words, when it reaches the point of no return – the tipping point – the shape is changed permanently.  And if we are not resilient, when we cannot take any more pressure, or stress, the strain becomes too much and, like the wooden dowel, we break.  Perhaps this is what is popularly known as a nervous breakdown.

And what can we say about good stress?  Can good stress, like bad stress, lead to a breakdown?  I believe that it can.  However what is broken down under the pressure of good stress may be a negative or destructive pattern of behaviour. It can lead to a positive life changing event where someone feels there is no going back – like – as I mentioned in a previous post – recovering from addiction.

Like the long-practiced pattern that I had of smoking!

This is an example of critical mass in changing behaviour in a positive direction.

[1]. Of course, liquids and gases can come under pressure also – but this discussion focuses on solids.

[2]. Resilience in a solid is its ability to spring back to its original shape after it is bent. In the world of humans, it can be defined as the ability to bounce back after a negative event in our lives.

Critical Mass and in particular the butterfly effect interested me because it is connected with, and indeed arose from, studies that the meteorologist Edward Lorentz was doing on the weather, which is one thing in nature that I always feel is as unpredictable as human behaviour.

And it was while doing these studies that the rudiments of chaos theory were formulated, and connections were made by Lorentz with previous studies in physics in particular Heisenberg’s Uncertainty Principle.

It is also interesting to note, in considering systems theory – that is, how everything affects everything else – that the growth of interest in chaos (and indeed, an appreciation of chaos) was not confined to the world of mathematics and physics.

In music, chaos was evident in the growth in popularity of jazz.  It was around this time that it became acceptable to write poetry that didn’t rhyme, and modern art also had a far more chaotic aspect than the works of the old masters of the Renaissance, or even the impressionists.

Of relevance to this website, it was also around this time that Sigmund Freud [1] was formulating his groundbreaking theories on how unhappiness, discontentment and even mental illness in adults were linked to suffering as children – challenging many long-held beliefs about people being mad, or possessed by devils etc.

And perhaps Heisenberg and his colleagues’ unconscious minds were more open to uncertainty than previous generations of scientists.  Systems theory would suggest this. After all, uncertainty had been gathering some momentum in European society from the mid-19^th Century on. 

Looking back today on the late 19th or early 20th Century Western World, it is hard to imagine how different this must have been for people who always knew their place in society – and were virtually certain of it from birth to death.  It can’t be a coincidence that allowing every adult to vote (first all men, but some decades afterwards all men and women) that led to so much uncertainty paralleled the scientific, social and medical upheavals of that period.

(As an aside, it is worth noting that democracy, where the general public vote for candidates that put themselves forward to represent the ordinary citizen’s interest in a secret ballot – that we take for granted nowadays, is only about 140 years old – in the Western World anyway. But in what the Western World regards as primitive societies, the democratic selection of wise elders as leaders is, and always has been commonplace).

The Uncertainty Principle was initially concerned with the behaviour of sub-atomic particles but Lorentz applied the principle to the weather, and from it developed general theories on the incidence of chaos in nature.

Still further developments included applications in the general area of evolution of systems that can be deemed to be complex.  I define complex here to mean a system that has many variables, that is; things that change (vary) over time.

The uncertainty principle suggests that the evolution or the growth over time of a complex system cannot be accurately predicted.

When applied to humans, I suggest that the family is an example of a complex system, as it contains many elements that vary over time.

Uncertainty and chaos have relevance and/or implications in child protection within families affected by imprisonment – and their relevance and implications need to be taken seriously.

[1]. The father of modern psychotherapy, Sigmund Freud, who was a medical doctor, developed theories focused on the importance of healthy emotional development to ongoing mental health.  Much reading on Freud and his theories is available from a wide variety of sources.