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Posts Tagged ‘Uncertainty’

Jul 30 2010

Wheat fields near Châteauroux

Surrounded by yellow wheat fields I feel a rush of exhilaration, I find myself singing and laughing inside the helmet. I am filled with a bubbly joy as I have spent the day driving at random, wherever I felt, following tiny country roads, through forests and past lakes, more or less heading north. It’s always good not to loose your sense of north. A guide book told me Montrésor, une des plus belles villages de France, should be somewhere around here, and I was lucky to come across it. It is a stunning village with a castle belonging to the late Polish comte Xavier Branicki, in which his descendants are still living. From a fountain in the garden of Xavier Bendickis castle I would like to have a bash at convincing you why philosophy is good, not only the individual but for society at large.

With inner freedom you can be free in a jail.

So what is philosophy? For me it is not primarily about a quest for truth, or love for truth. It is about freedom. Freedom of mind. Without inner freedom there is no freedom, and with inner freedom you can be free in a jail. What is a free mind? It is a mind that does not depend on crutches of certainty. A mind willing to follow through to the logical conclusion and prepared change opinion in light of new insights. A mind that can look at things from different angles, and never assumes that there is only one right answer. A mind that knows there are good arguments for and against everything. A mind that does not mistake familiarity for understanding. Philosophy is one of many  roads that can lead you there.

New thoughts appear in cracks.

Philosophy is not about intelligence. Many very intelligent people have been unphilosophical and done some horrible things based on their certainties. Obviously it helps to have a natural ability to see things in perspective, but even the brightest minds need inspiration. Impressions are the food for thought. A society where people mostly consume the same impressions will have like-minded people. It is very hard to have a free mind there. New thoughts appear in cracks, when bits don’t fit together, where the story doesn’t make sense. If everything is the same there are few cracks. If there is no contrast it is very hard to think as you have nothing to compare with. This may seem trivial but it is actually what makes it all possible. In a society where most people share the same beliefs and values it is very hard to think. It is no coincidence that multiplicity and innovation coincide.

Château de Montrésor

People are not expected too think.

In the way the world is organised today people are not expected too think to much. They are not meant to feel responsible for what happens in or with the world. Even in the most democratic societies the extent of ordinary citizens’ participation in the decision making process is a nod left or right every fourth year.

Comte Xavier Branicki's weapons

The alternative ways of looking at things have been limited to a manageable two. People are expected to work and consume and leave the big decisions to those in charge. Seen that way it is amazing we have made it this far since we have been riding on the brain power of a few privileged families. (Maybe the lack of human control over nature has been our saving grace?) In so far as history has been orchestrated by humans it has been possible because the world has been, for most of its history, fairly predictable. I am not talking about famine and the black plague, but people’s positions and possibilities in society. If you were born into a potter’s family you would end up a potter. The rich could make deals between themselves and make sure the wealth stayed within the right famililies.

...sumptuous feasts with Napoléon

Take this Château de Montrésor. During the 17th and 18th centuries, leading families such as the Bourdeilles and the Beauvilliers lived in the castle. “In 1849, Xavier Branicki, a rich Polish count and friend of emperor Napoleon III, arrived to give new life to Montrésor…the house was the setting for sumptuous feasts with Napoléon.” I somehow doubt I would have been invited to those feasts.

In a predictable world it has been possible for a few to control much of what has happened (although I would not underestimate the skill, knowledge and courage it would take to do so). Now however, the world is too complex for anyone to fully grasp.

The world is fundamentally out of control.

Even if old models have worked to reduce suffering and increase the standard of living for the world, we no longer know where things are going. The world economy is not run by a small elite. It is run by millions of people moving their money at a whim, and in a blind stampede capital can move from one side of the globe to the other in a matter of seconds. Consumerism will not slow down, and hence neither will global warming. People refuse to become more rational, and in a century the population this planet needs to support will have quadrupled. Do you think we are headed for less wars? Do you think religion will help diplomatic negotiations? Would you leave the future of this planet in the hands of a few leading men?

Enter the castle

If our world was hanging in a rope over an abyss it would all depend on the strength of that one rope.

If the world was hanging in a gazillion threads it would not matter much if one snapped.

The only successful way of dealing with the unpredictable is to be prepared for anything. The wealth of a society could be defined by its multiplicity. A society rich in multiplicity is likely to find solutions among some of its members. A healthy, future-proof society is  one with a great many free thinking people exploring many different ways of living. For the first time in history collective thinking is possible. For the first time ever, truly innovative ideas can flourish and spread without any financial obstacles. In essence philosophy is good for a changing world because it inspires free thinking.

If the world was hanging in a gazillion threads it would not matter much if one snapped.

What's in it for me?

-”I catch your drift, but apart from saving the world, what’s in it for me?” I am surprised to hear a voice in the garden, and even more so one that replies to my thoughts. I turn my head and stare at the fountain sculpture of a little boy.

-”Philosophy makes my head hurt. Why should I bother?” he continues. It takes me a moment to regroup.

-”Well, for starters you would never feel lonely again. Or bored for that matter.”

-”How is that?”, he asks.

-”You would be entertained by your own company as you would always have something interesting to think about.”

-”What is interesting about what old men thought about questions without answers? Where are the special effects dude? If I am bored I choose Mad Men over Nietzsche anytime.”

-”Interesting choice of entertainment”, I reply, “because that is exactly where the creative intellectual elite has ended up – in the info- or entertainment industry. They work as speech writers for politicians or copy writers for soap adverts or some such. Whatever the profession they are likely to be engaged in selling you some stuff. It is safe to say they do not have your best interests at heart. You are surrounded by the best poets, orators, artists and musicians, and, adhering to the rules of our liberal consumerist society, they excel at seducing and persuading you. They are not evil. They just don’t care about you. They are paid to make you care about what they want you to care about. And they are good at it. They are better than you. They are the best. Those that don’t succeed are fired. Thus, the most obvious reason why a critical mind is good is to look after your own well-being.”

Philosophy good stuffed

-”Oooooooooooooohhh dear! Poor me! Are you suggesting philosophy is good for my own well-being? If I am not mistaken Herr Nietzsche turned quite a mad man himself. The list of intellectuals who have been killed, committed suicide, gone mad or spent time in prison is quite off the charts. Socrates, Jesus, Galilei, Rousseau, Lorca, Russell, Cantor, Boltzmann, Gödel, TuringKoestler, Nash…”

-”These were all highly sensitive people, so they got more affected by what they saw and realized. They lived in times where dissent was punished by death, imprisonment or excommunication. But is philosophy to blame for that? Is it not the fact that the society surrounding these people was not philosophical enough that caused their misfortunes? After the aristocracy had eliminated them they turned them into martyrs and named streets after them. I am sure there are thousands of other great thinkers whose ideas were eliminated in time.  Today it is not like that. Because of the achievements of dissenters there is a free world where you can think for yourself and express your opinions without risking punishment. ”

-”Exactly! I am living in the free world. I am not manipulated. Things have changed. We are living the dream.”

-”Yes, you are living a dream, like Carlin says, because you got to be asleep to believe you are free.”

Aug 30 2009

I am driving my motorcycle in the south of Spain, and have left the beaches of Cadiz to to stay the night in Zahara de la Sierra, a mountain village with a Moorish castle ruin and a turquoise damn below. As I reach the top I enjoy a view of 30 km in every direction. I check in to a wonderful hotel perched just below the castle.

To kick off my philosophical journey I will make and defend the following ideas.

  1. There are rules independent of our minds that govern the whole of existence.
  2. Any actualised potential in one moment defines what is and what is not possible in the next.
  3. The rules determine what is possible in any given moment, but not what is actualised.
  4. Uncertainty and unpredictability are built into the very fabric of the universe.
  5. There are domains of reality causally independent of our minds.
  6. There are domains of reality causally dependent on our minds.
  7. In the mind dependent domains of reality our beliefs about what is possible can influence what is in fact possible.
  8. It is not the truth of the beliefs per se that gives us the most beneficial possibilities.
  9. A belief is healthy if in the moment it is believed it has beneficial consequences.

These assumptions or axioms seem to me to be true, and from them we can draw some very significant conclusions. I am no expert in any field and if someone can show me where I go wrong I believe I shall be equally happy. I do however believe the world is in one way or another, and in this post I will try to see if I can understand and communicate anything significant about how modern science says it is. At the same time I find myself in the uncomfortable position of believing that knowing the truth about how things are may not prove to be the thing that will help us realize the best possible future. In spite that general reservation in this post I will focus on what I think is true about the word (points 1 to 5). In the next how I think we work (points 6 & 7). And in the following why I think truth and health can be in a highly strained marriage (points 8 & 9).

The Castle at the Top of the Mountain

Art by Front

To make my case let me first set the scene using the mountain village as it strikes me a perfect metaphor for how the world is and the human situation within it. Perhaps you will sense my unease between the lines. There is a castle on top of the mountain. It was built sometime towards the end of 13th century by Alfonso X El Sabio. Imagine for a second that Alfonso was born in the castle and as a young prince is not so wise (sabio) but rather spoilt and credulous. He has servants that cook and take care of him and has never left the castle. He believes that the outside world is a hostile place and that he would be killed should he ever venture outside. He throws stones out through the window at anyone that may have the misfortune of passing below. As the otherwise peaceful villagers get stones on their heads they gradually turn hostile.

Would his belief about the world be true or false? There is no simple answer to that question, and it could be argued that the belief is both false and true. What makes it complicated is that the fact the belief refers to is dependent on the belief itself. The fact is a consequence of the belief. The poor prince acts in a way so as to make his belief come true.

A lot in human life works this way. Through our behaviour our beliefs actualise some potentials rather than others, which in their turn bring about a different set of consequences and possibilities, about which we may or may not have a clear idea, based on which we act again, to which the world reacts, and so on, round it goes.

(Legend has it this is that the Moors actually threw stones to check for Christian intruders at night. Normally that would provoke pigeons into the air, and if there were none they would concluce the Christians below had scared them off and they got ready to be attacked. Realizing this trick Christians brought pigeons in cages to let out when the stones fell so as to be able to take the castle by surprise in 1483).

For the prince, does it matter greatly for his survival what he thinks about the world? Is it not true that as long as he has food on his table he can believe anything about the outside world. He could deny the existence of the mountain. He could claim the castle had always been there, that he was the king of the entire universe. He could even deny the very existence of the food in front of him. As long as he keeps on eating he can live out his days in a state of complete delusion as regards the true state of things. And he would enjoy his life all the more for it.

The universe in itself however doesn’t pay special homage to royalties. It just follows its own rules.

The Rules of the Game

Some things are possible, others are not. I do not think I can make an argument about the existence of this distinction that itself does not presuppose it. The entire rational art of deduction is based on it. If anything is possible it must also be possible that not everything is possible, and then we are already in logical difficulties. Let me instead make a symbolic take on the scene I have created. Let the mountain represent that which separates the possible from the impossible. These are the external limitations that we try to capture in the laws of physics, biology and neurology, that underpin our economies, infrastructures, languages, thought patterns and so on. Call them what you wish. I call them the rules of the game. Whether these are immutable and eternal laws, or just acquired habits of the universe I believe is irrelevant because their timespan will vastly exceed that of life on earth. Our knowledge of them has increased, but is inevitably limited especially as regards ourselves.

Further, let the castle, full of symbols and royal crests, represent culture. We build culture on top of nature. One rule is that nature set the limitations and possibilities of culture. The higher depends on the lower. Destroy the mountain and the village goes too. But the opposite is not true. There was a mountain long before there was a castle, and the mountain does not need or care for the castle.

The servants could be our instincts, all the subconscious processes that keep us alive and well. They normally keep making us looking for food and eat even if we wanted to deny the need for and the existence of food. (Only yesterday did I hear a girl proclaim she believed Indian yogis could learn to live off nothing but sunlight).

The prince then, who would that be? It would be our conscious mind. He is a prince and not a slave because he is both spoilt and free. No matter our factual circumstances we are free to interpret them in wildly different ways, some truer than others, some healthier than others. The rules are so permissive that they can enable us to completely deny their existence, much the same way democracy can allow anti-democratic voices free expression or law and order protect the rights of anarchists.

In theory we have an infinite (but not unlimited) creative scope to interpret what happens to us, what we choose to pay attention to, and how we choose to behave. In practice however we cannot think further than the reach of our imagination. We breath meaning into the rules, and our expectations about how the game will play out informs our actions and therefore modifies the outcome.

The lower sets the possibilities of the higher. The higher gives meaning to the lower.

(For sake of clarification, I am in no way referring to human norms. Conventional laws can be broken, but they have no more to do with the rules I am referring to than that they, like everything else, are limited by them.)

Admittedly, neither the claim that there are rules, nor that they are independent of our minds, are scientific claims. They are axiomatic, and cannot be falsified.

A swallow just swept into the open window. On the way out it did not see the crystal pane. People that don´t believe in an external world that sets the limitations better walk around with crash helmets.

Patterns in Nature

Generative art by Jared Tarbell

Generative art by Jared Tarbell

There are many bogus claims about regularities in the universe, invoked to explain (and justify) everything from people´s names to the holocaust (!). On the one hand there are many patterns, and our brain is made up of patterns, why it is only natural for us to find them. On the other hand we can be mistaken, and often fail to find subtle patterns (more on that below ) or believe we have found a pattern that at closer examination is not there (apophenia). Many paranoid schizophrenics are convinced of hidden meaningful connections between random events and that their lives are run by secret conspiracies. Likewise religiously inclined often look for, and find, meaning and purpose in every twist and turn of their lives. Understandably orthodox scientists would like to steer clear of both those threats of apparent irrationality but in so doing may prove to be throwing out some genuine patterns with the proverbial bath water. Findings in the area of quantum physics, complexity and self-organisation have many spooky and apparently irrational aspects to them. The difference however, between scientific hypothesis about some regularity and superstitious claims is that the scientific ones are open to be tested and found false. As far as truth is concerned a rule whose implications are always right no matter what happens is quite useless (eg. if you pray hard enough you will get what you dreamt of). As for mental health it may be quite appropriate.

Are fractals the fingerprint of God?

Are fractals the fingerprints of God?

If we have thousands of people chipping away at a claim of some natural regularity, probing, testing and debating, what remains will be vastly more reliable than that of any preacher, no matter how many followers he may have. For all its shortcomings – incompleteness, Eurocentrism, self-forgetfulness, politics etc. – natural science remains the most reliable source we have to identify the rules of the game. To deny the authority of science over superstition is equal to deny that the earth is round. It is science that puts us into perspective and teaches us that life is but a fragile spark.

Many claim that the three milestone achievements in natural science over the last century are: quantum mechanics (QM), the theory of relativity and nonlinear dynamics, popularly known as science of complexity or chaos theory. Generally they focus on the very small, the very large and the scale of life. I will only dip my toe in the very small and the life size as I believe the rules we live under are determined predominantly by them.

Quantum Indeterminacy

Classically the idea that the world is governed by universal laws implied that the world a) is necessarily deterministic, and b) (at least in theory) predictable. I believe quantum mechanics is teaching us that neither is true. If time could be turned back history could unfold differently, therefore knowing the rules not even Laplace’s infinite intelligence would be able to predict the future. This is so not because of our limited knowledge but because the world in itself seems to be indeterministic. Quantum mechanics got its name from Max Planck’s initial insight around year 1900 that electromagnetic energy could be emitted only in quantized form. This insight was only the beginning of a story of 100 years of quantum mysteries such as Bohr’s model (1913) in which a subatomic particle such as an electron could make quantum leaps from one orbit to another without passing the space in between, or John Achibald Wheeler’s (1978) delayed choice experiments where a choice made by an observer determines what must already have happened at an earlier stage. Wheeler writes in 2001 that “today an estimated 30 percent of the U.S. gross national product is based on inventions made possible by quantum mechanics, from semiconductors in computer chips to lasers in compact-disc players, magnetic resonance imaging in hospitals, and much more. “ Yet even if we know how to use the theories we still do not know what they mean.

The observer does not create the observed. The rules are independent of our minds.

One aspect of reality that has been brought into question by QM is the independence between the world and the observer. In the classical Copenhagen interpretation (1920) a subatomic particle – a quanton – is a wave-particle described perfectly by the Schroedinger wave equation yet it could not be measured with exactness in both speed and location at the same time. If speed was measured the position would not be known. The limits of our knowledge are thus set by Heisenberg’s Uncertainty Principle. The question was, and still is, whether this uncertainty is something that is provoked by our equipment, or whether it is the quanton in itself that is uncertain. The classic debate between Bohr and Einstein hinged on this subject and Einstein’s position was succinctly summed up in his metaphor “God does not play dice” by which he meant that there was a world out there, independent of our minds, with precisely determined properties. In his famous EPR paper (1935) he claimed that quantum physics was an incomplete description of reality, and that there were some hidden variables, although unknown to us, that still determined all properties of reality. The EPR paradox pivots on the notion of entanglement between twin quantons, which means wave-particles that appear as each others opposites, such as an electron and a positron. By measuring some property such as spin on the electron one automatically knows the corresponding value for the positron. This is a bit like you do not need to go up to the second floor in a two story building to see if the elevator is there. It is enough to know if it is on the first floor. Experiments show this to be true. If the electron’s spin was undecided before the measurement how come the positron would be determined exactly in the same moment when no measurement has interacted with it? According to Einstein either the twins send information to each other faster than the speed of light, or there are some hidden variables that keep them synchronised. Because it seemed more unlikely that information could travel faster than light (nonlocality) one assumed reality was determined and QM was incomplete. In 1964 however John Bell produced a paper called Bell’s theorem that showed that even if we could not know the variable, we could experimentally test some of the implications if they existed. According to mainstream interpretations these experiments show the Einstein was wrong and that reality is undecided prior to measurement (indeterminacy) and that information can travel instantaneously (action-at-a-distance).

There are however several alternative interpretations that avoids indeterminacy by accepting some even more absurd idea, such that the world would split at each moment of choice and each history would unfold in its own version of the universe. The most respected realist interpretation of QM, and the only one apparently equally compatibly with test results was formulated by David Bohm in 1952. It is very “ironic” that mainstream physicists reject determinism and realism based on Bell’s theorem while Bell himself is defending Bohm’s interpretation (Bell 1987):

But in 1952 I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how parameters could indeed be introduced, into nonrelativistic wave mechanics, with the help of which the indeterministic description could be transformed into a deterministic one. More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the ‘observer,’ could be eliminated. …

Hence there are many ways of interpreting the equations, their predictions and the experimental results, and some are consistent with an independently deterministic world, and some (more common) with a world inherently probabilistic and uncertain. In none of these cases however is the world created by the mind. The outcome of the experiments are not determined by the observer. The wave-particle will behave as it will independently of the wishes of the observer, and in every case follow the rules. It may be that matter or energy is not determined in itself, but the rules that govern their possibilities are still independent of our minds. In this way the world is in one way or another and it is not up to us to dream it up. I think this brings home my first point.

Dice play God.

While the jury is still out on what to make of QM and determinacy, theories that try to reintepret the results so as to save a precious principle such as locality (Einstein) or determinism (Bohm) have something ad-hoc and unscientific about them. It is not trying to see what is, but trying to recast it to fit some model. That is an outrageous and heretic thing to say about two of the most profoundly creative and daring minds of last century, and I know of few people, physicist or otherwise, that have spent more time working on keeping their own and others’ minds open. Still it does seem to me that it is rather dice that play God than the other way around. What I take away from quantum physics is that freedom and indeterminacy are built into the very fabric of the universe, and choices creating new choices are being made constantly. The future is thus open and there can be no final Omega point for our existence. Whatever possibilities there are they keep on changing and none is predestined.

The Nonlinearity of Everyday Life

Nonlinearity is not the exception, it is the rule.

The belief in a final destination of human existence is an idea common to both Christianity, Islam, neoconservative and communicst ideology. This teleological idea has had a firm grip on popular imagination in spite the fact that in nature there are no straight lines, and the only final destination we know for sure is the grave. While the old science was based on an idealised special case of nature where processes were seen as linear, we now know that most, if not all, natural and social processes are nonlinear. In nonlinear systems changes over time are not proportional, i.e. they do not follow straight paths, instead they can be erratic, haphazard, showing booms and bust cycles, have negative and positive feedback loops, sometimes momentarily predictable then utterly random. The real world is full of nonlinear processes, such as weather systems, population growth, traffic, financial markets and the spread of ideas, and not only are they individually unpredictable, they all interact and influence each other in dramatic ways. Nonlinearity is not the exception, it is the rule. It describes the very real processes that determine and shape our individual lives. How many influential men were born because a rainy day their parents decided to stay in bed? How many are not born to potentially loving couples since they are busy getting divorced due to stress caused by the current financial crisis?

Every time a choice is made in the universe one out of several possibilities is actualised. Each choice leads to new choices. What was possible in one moment is gone once a choice is made and may never return again. Each choice – irreversible. The collective interaction between all processes – unpredictable. If the world is a field of vibrating dominos, the arrow of time is determined by those already fallen and those yet to fall. The present is the point where the choice is made between those that will fall and those that will remain standing forever. Not even the tile itself knows how it will fall until it has fallen.

The Impossible and the Impossible

There is more than one type of impossibility.

One implication of the axiom that the rules determine everything that is possible is that there is not only one type of impossibility. There is the impossible that could never come into existence because the rules do not permit it. For instance, there could not be a Divine Dictator ruling all in a rule based universe like ours since everything depends on everything else and you cannot bend some rules without bending all rules. For it to be possible for some processes to follow rules, all processes must follow rules, or else arbitrary disorder would spread like cracks travel in the ice of a lake. If a god answered one prayer complete disorder would ensue. Nothing external can control a web of rule based processes with creative choice built in. Whatever order there is will have to emerge from within the system itself. The Austrian philosopher Alexius Meinong called the outer region of the impossible absistence and it is made up by all those ontological freaks that could never, and will never, be.

Knowing the rules however we can imagine various scenarios that could play out, but may not. You remember those books where you could choose how the story continued by jumping to another page? Similarly those alternative endings reside somewhere between absistence and actuality. Each potential is a viable candidate for existence that adheres to the rules but by the fall of the dice may or may not pass the frontier into actuality. Missed opportunities are impossible now but not in the same way as an omnipotent being is impossible. In my Meinongian parlour missed opportunities and existential crossroads not yet reached neither exist, nor absist, they subsist. Subsistence plays a greater part in the life of our souls then existence. We regret past mistakes and dream of a future still in the making.

Spontaneous Emergent Order out of Disorder

The notorious second law of thermodynamics states that left to itself a closed system will increase disorder. The simplest sign of order is differentiation, differentiation between two substances, hot and cold, light and dark, inside and outside, positive and negative etc. Disorder is the same as homogeneousness, everything the same. A battery left to itself will eventually go flat on its own. If there is an Omega point for the universe it is when all the energy is used up and it has reach maximum disorder. In thermodynamics that state is called heat death. It is not an uplifting idea, but an extension of something well all know to be true from our daily lives. Eventually the fire goes out.

But if the universe as a whole is producing more and more disorder, how come life would appear? Life is going in exactly the opposite direction. It is producing more and more order all the time, more complexity and more differentiation. If the universe at large is not evolving how can goal oriented forms suddenly appear? How can life and purpose emerge from a bunch of randomly bouncing particles? Life and human civilisation seems to be a blatant contradiction of the second law of thermodynamics.

Life obviously exists and hence under some conditions a spontaneous increase in order must be possible. What are those conditions? Ilya Prigogine got the Nobel Prize in chemistry 1977 for his work on irreversible thermodynamics where he showed the spontaneous order can appear out of disorder in dissipative structures far from equilibrium. A dissipative structure is an open system that receives, processes and dissipates energy to its surroundings. To be far from equilibrium means there is a big difference in temperature, pressure or concentration, and thus a lot of energy exchange.

Bénard cell

Bénard cell

A simple example of this is a shallow pan of water or some other liquid that is heated evenly from the bottom. To start with the molecules in the liquid are moving around at random with the same kind of arbitrary motion no matter where you look. As the temperature increases a sharp contrast between the bottom and the top produces a far-from-eqiulibrium state and all of a sudden the microscopic randomly moving molecules organise themselves into hexagonal convection cells. This phenomena is called a Bénard cell. One of the most fascinating aspect of this jump is that the exact direction of the hexagonal pattern is determined by the tiniest initial changes such as the force of gravity which in normal stable conditions would have only negligible effects on a liquid a few millimeter thick. (Prigogine, 1985)

The fact that in ordinary water disconnected and non-communicating molecules in an instant can go, correction must go, from macroscopic disorder to a beautiful ordered pattern by simply adding heat proves that locally increased order is neither an absisting freak nor an improbable subsisting potential but a natural necessity. According to the rules under these special conditions nature must jump from a state of complete disorder to a state of perfect order, as if that was the most energy efficient solution to a specific thermodynamic challenge. But does this spontaneous emergence of order not contradict the second law of thermodynamic? Not at all as the local increase of order happens at the cost of increased disorder in the surrounding. Islands of order appear in an ocean of disorder by stealing negative entropy (aka syntropy) from the environment, thus making the sum total of disorder increase. These local exceptions, however tiny on a cosmic scale, are enough to bring about the basis of our entire civilisation. Given the rules and the contrasts created in the Big Bang, spontaneously emerging order – the very basis of life – must appear from within the system itself without fail.
Every star in the universe is one such source of far-from-equilibrium conditions.
For an extensive list of examples of order emerging spontaneously check out the entry on self-organisation in scholarpedia .

Unpredictability and Butterfly Moments

According to Prigogine a complex system passes through stages where they behave in a classical and deterministic way. Only at certain crucial moments, so called bifurcation points, does a system have a choice, and tiny random fluctuations can dramatically influence its future. “The ‘historical’ path along which the system evolves /…/ is characterized by a succession of stable regions, where deterministic laws dominate, and of instable ones, near the bifurcation points, where the system can ‘choose’ between or among more than one possible future./…/This mixture of necessity and chance constitutes the history of the system.” (Prigogine, 1985, p. 169) Think of a leaf floating in a river. When the river is flowing calmly it is fairly easy to predict where the leaf will be a second down the line, but the moment the river reaches some obstacles the flow changes radically from laminar to turbulent, and becomes in effect chaotic. Suddenly the smallest change in the leaf’s position will throw it one way or the other and it is impossible to predict at what side of the river it will end up. A bifurcation is a choice, a fork in the road, and it is often at these moments chaos emerges.

Popularly and historically chaos is virtually synonymous with randomness, but over the last 60 years scientists have come to find subtle order behind many seemingly erratic processes.Thus the history of science has taken another ironic twist. The world is more chaotic than we thought, while chaos is, well, less chaotic. With the help of computers and enough empirical data never before available scientists are finding that the behaviour of the leaf in the swirling river may be controlled by surprisingly simple rules. The branch of science dealing with such simplicity in complexity is called nonlinear dynamics, or more popularly, chaos theory. The chaos that chaos theory is concerned with is not the kind of chaos we normally think of. In fact quite the opposite, and is often called deterministic chaos as it is a collection of many orderly behaviours.

Bifurcation diagram of butterfly moments

Although chaos is unpredictable, it is deterministic. If two nearly identical chaotic systems of the appropriate type are impelled, or driven, by the same signal, they will produce the same output, even though no one can say what that output mighty be./…/ The distinguishing feature of chaotic systems is that they exhibit a sensitivity to initial conditions. /…/ if two chaotic systems that are nearly identical are in two slightly different states, they will rapidly evolve to very different states. To the casual observer, chaotic systems appear to behave in a random fashion. Yet close examination shows that they have an underlying order.” (Ditto & Pecora, Scientific American 1993)

Are all complex and apparently random events controlled by some simple rules? I am not aware of any chaos theorist that claims that randomness and chance do not exist. What they have realized though is that under certain conditions what appears to be random is in fact ordered. There is a lot more spontaneously emerging patterns in nature than previously thought. Conditions that can produce deterministic chaos include (adapted from a longer list in Williams, 1997):

  1. The process is nonlinear.
  2. The outcome of a process is fed back into the same process again, the output of an equation in one step is used as input for the next iteration. Today’s events affect tomorrow’s events.
  3. Sensitive dependence on initial conditions. The process unfolds very differently given the tiniest differences in some variable (The Butterfly Effect).
  4. Changes in the variables of the system, when plotted in a diagram called phase space, display fractal shapes. Fractals repeat self-similar shapes no matter the degree of zoom.
Chaotic attractors in neural networks

Chaotic attractors in neural networks

What is unique about chaotic processes as opposed to linear ones is that while they follow rules they are unpredictable. In an linear equation if you wanted to find out how things will be at time t you simply put it into the equation. In chaotic equations you must repeat the calculation over and over again, perhaps millions of times, to actually get to the point you are interested in. Whatever error you have in your initial value it will multiply every time and eventually the accurate data will be cancelled out by noise. Historically it was assumed that while we could not measure anything with complete exactness what ever degree of certainty we started with it would hold for our predictions as well. What the meteorologist Lorenz discovered was that the error will increase rapidly and drastically, and with every repetition of the calculation we will loose one decimal place of exactness. Knowing the rules does not mean being able to predict the outcome. This “sensitive dependence on initial conditions” became known as the Butterfly Effect. A butterfly flaps its wings in the Amazon rainforest that two years later causes a tornado somewhere in China.

In butterfly moments a single idea can change the future course of history.

As you can appreciate I have gone to some trouble to give support for my second (!) initial point that “any actualised potential in one moment defines what is and what is not possible in the next“. In chaos theory it is dramatically illustrated by the Butterfly Effect, which is thus the outcome of a repetitive process where each successive step is dependent on the outcome of the previous one. But of course we all assume this to be the case when we consider any historical evolution, whether a physical system, social or personal history. If it were not for x then y would never have happened. We intuitively believe in cause and effect chains, and maybe my point can be interpreted as such a simple statement of causal determinism. That is not my intention though, and that is why I think the third point is the most contentious, i.e. that the rules only set the limits, they do not define the outcome. This I believe is the sticking point in the debate between Einstein and Bohr, and it comes back in chaos theory, and is of utmost important in bifurcation points. I think that if indeterminacy is found to be impossible in quantum physics it cannot be possible anywhere else in life. The conclusion seems inevitable to me that if Einstein was right there is no freedom, and thus personal responsibility is merely a useful fiction. The question thus is what chance really is, if it exists, and whether the same cause can have different effects given the same conditions. Quantum oddities have often been ignored when dealing with ordinary life processes, as they seemed to concern only the tiniest things in the world. It seems to me that in chaotic bifurcation points, lets call them butterfly moments, we can no longer afford such luxury since normally negligible effect can have dramatic consequences. And this is not just abstract metaphysical speculation any longer but theoretical reflections on empirical results. In butterfly moments individuals can have dramatic consequences for the whole and their behaviour can result in that the system as a whole is favouring one reaction path over a number of equally possible paths. Tiny random fluctuations in the right moment can shape the pattern in a Bénard cell, the crystallisation of frost, the morphogenic process giving stem cells their position and function in the body. Why would this not also be the case for moments of crisis in human history and the chance fluctuations produced by influential individuals, such as prophets, political leaders or revolutionaries? Why should we assume that human history only had one possible subsisting path to follow? Take quantum uncertainty and magnify it with chaotic sensitivity to initial conditions and I cannot see why you would not end up with indeterminate quantum effects on a macro scale. That means that human life is intrinsically indeterminate and unpredictable, not only due to our inexact data and imperfect knowledge, but rather in itself. If we could rewind human history 5000 years it would play out in very different ways. Jesus, in the unlikely event of being born, would probably have been forgotten as 99% of the other paranoid prophets, Columbus would not have discovered America and Latin America would not speak Spanish, Hitler would have been locked up in jail and most of Europe communistic. Large and small events are all dependent on an interplay of chance and necessity and to look for a hidden plan, an invisible hand, divine guidance, astrological patterns or predictable Hegelian-Marxist dialectics is all a fool’s game as inspired as foretelling the future through coffe grounds.

One the most baffling and fascinating aspects of how parts and wholes interact – holons as Koestler called them – is that the whole can sometimes behave as a coherent individual. How can individual Uranium atoms decay at the right moment so as to produce a holistic regularity when the individual does not know about the whole? How can a water molecule moving at random jump into hexagonal order in perfect synchronisation with all the others? How can ants organise an anthill in perfect symmetry without any control from above? How do the parts know how to behave so as to produce holistic order without having access to any bird’s eye view? “We believe that models inspired by the concept of “order through fluctuations” will help us with these questions and even permit us in some circumstances to give a more precises formulation to the complex interplay between individual and collective aspects of behaviour. From a physicist’s point of view, this involves a distinction between states of the system in which all individual initiative is doomed to insignificance on the one hand, and on the other, bifurcation regions in which an individual, an idea, or a new behaviour can upset the global state. Even in this regions, amplification obviously does not occur with just any individual, idea, or behaviour, but only with those that are “dangerous”- that is, those that can exploit to their advantage the nonlinear relations guaranteeing the stability of the preceding regime.” (Prigogine, 1985, p. 206 )

Some implications and conclusions

There are many conclusions to be be drawn from these insights. I am just trying to come to grips with them myself and welcome any criticism or suggestions you might have. This is what I make of it though.

  • Life and order does not need an external architect to arise. Once the necessary far-from-equilibrium conditions exist, order will arise. I remain utterly agnostic as regards the origins of the rules of the game but once existing any exogenous force, such as influence by some divine dictator, could do nothing but destroy it. Any programmer will tell you that changing so much as a comma in a working program will most likely grind it to a halt. “If it ain´t broken, don´t try to fix it.”
  • While indeterminacy does not offer any support for the notion of free will and personal responsibility per se, without indeterminacy the concepts are (ontologically) nonsensical as there can be no genuine options to choose between. It seems to me that the most impartial interpretation of quantum physics is supporting the idea that indeterminacy and uncertainty is part of the very fabric of the universe, and that everything could therefore have been radically different from how it happened to turn out.
  • Spontaneously emergent order realizes one out of several possibilities that exist in a given moment, but we have no reason to assume that this particular choice is the “best” of all possible choices. It may be just good enough to survive. In molecules and cells the degrees of freedom are more limited than in more complex systems, and taking our world as a vast complex whole we have no reason to assume we are living in Leibniz’ “the best of all possible worlds“. The way our society is organised for instance may be a short terms solution, a local optimum, that has taken us this far, not a global optimum that will ensure our long term survival.
  • With or without indeterminacy, chaos theory shows that our attempts to make long-term predictions of the future are futile. Anything we pretend to know about the future is only conjectures, better or worse guesses, and never true or false. In one blow this renders belief in religious and ideological prophecies delusional, and as a consequence makes the bulk of Judaism, Christianity, Islam, Marxism and Neo-Conservatism nonsensical.
  • In butterfly moments individual actions can dramatically change which of several possible futures will become reality. While history is paved with times of crisis and relative stability, our times seem to be more chaotic than ever in terms of the far reaching consequences our actions may have. I believe that among the non-random factors that influence our socio-cultural evolution individual ideas that inspire behaviour play the most crucial role. A single idea can change the world, save it or destroy it.

These are some of the conclusions I draw from man’s latest insights into the rules and I think they should have a great impact on the way we think about ourselves, our view of the world, our morality and legal system and so on. Whether they will remains to be seen as just like the prince can deny the food in front of him relativists or a religious fanatic can, in a loud voice, deny an independent reality and rules governing our existence using megaphones and TV sets built using the very understanding of the world whose validity they are trying to undermine. But just like life does not contradict the second law of thermodynamics, human behaviour never contradicts the rules of the game. How our misconceptions of the rules are not only permitted by them but might actually improve how well we play is the subject of the next post.

Further reading

Check out my recommended reading section on complexity.

Inspiring blog on fractal ontology
Is quantum probability really chaotic order?
Introduction to chaos
Introduction to self-organisation