THE PARADOX PRINCIPLE
By Red Rachtagáin
What do the cycle of the seasons, population fluctuations, traffic flows in Manhattan and the throw of a set of dice have in common? In recent years, the study of such patterns has increasingly perplexed both mathematicians and philosophers. However, I think that there is a great deal of evidence to suggest that these seemingly disconnected phenomena are all governed by a single underlying law, and that there is a 'hidden controller' which lies at the heart of everything. But first, let me start with a small 'thought experiment'.
Imagine that I am standing alone on a deserted beach, looking out to sea. The Sun is rising, and it is the beginning of a new day.
As I listen to the waves, I am aware of the rhythms of nature around me. The daily cycle follows a clear symmetrical pattern: dawn, day, dusk and night. Dawn and dusk are opposites, as are day and night. These pairs of opposites stand on opposing sides of the cycle.
The seasonal cycle of spring, summer, autumn and winter follows this same symmetrical pattern. Spring and autumn are opposites; so, too, are summer and winter. A similar pattern also finds its expression in the phases of the Moon.
It is clear that polarity is a feature which is common to the cycles of nature: the ebb and flow of the tides, the Moon's wax and wane, and nature's growth and inevitable decay. Tomorrow is the summer solstice, the point at which the Sun reaches its zenith. Having crossed over this tipping-point it, too, starts its decline, towards the long, cold winter.
Polarity, I conclude, is nature's hidden controller.
Consider a fox that goes hunting for rabbits. If it is skilful, the fox will catch enough rabbits to sustain itself and its litter. But if a particular breed of fox is too skilful as a predator, the rabbit population will reduce significantly and the foxes will be left with very little to eat. In other words, a predator's effectiveness will increase until it reaches a 'critical point', beyond which this skill becomes a liability. With only a few rabbits left, the foxes start dying out. When most of the foxes have gone, the rabbit population begins to pick up and it continues to grow until the opposite critical point is reached. There are now enough rabbits to sustain a predator, and the diminished fox population once again increases.
We may observe that this pattern follows precisely the same pattern as the cycles of nature. When the population cycle reaches a critical point, the process 'polarises'; that is, having rotated upwards, it then rotates downwards. Once the opposite critical point is reached, it polarises again. (When the rabbit population falls below a certain point, the fox population decreases; once the rabbit population has increased,the fox population revives).
Social systems too have two conflicting and seemingly irreconcilable tendencies. On the one hand, they tend towards chaos. A large part of a social organisation's energy is devoted to overcoming entropy and maintaining structure. Paradoxically, social systems also have a propensity to return to their original order when they are disturbed. Change in a social element is frequently followed by corresponding changes in related elements, which work towards diminishing the original disturbance.
The term given by sociologists to this latter process is social equilibrium. There are many examples of this polar-cycle finding expression in human history. The Counter-Reformation, for example, clearly came about as a response to the Reformation, just as Romanticism finds its origins in the Enlightenment. Two hundred years ago, the philosopher Georg Hegel saw history in terms of such a process. The clearest example he gives is that of the supposed origin of all things: when 'Being' and 'Nothingness' combine, the result is what he calls 'Becoming'. Another less clear example he gives is of the French Revolution. Here the first stage is the revolution, and the second stage is the so-called Reign of Terror. The synthesis of the two is the emergence of the constitutional state. Thus, the same polar process which controls the cycles of nature also has a bearing on the patterns of history.
According to Karl Marx, an economic cycles follow this same model. When an economy contracts, Marx observed, wages also drop and labour becomes increasingly cheap. As the unemployed workers lower their wage demands beneath a certain level, it becomes possible for employers to employ them again and to expand their businesses. This expansion helps the economy to gather strength. Thus recession turns to regeneration, and the economy revives. Marx also observed the polar-cycle controlling boom phases: an economic boom increases workers' wages which reduces profitability. Expansion, like recession, provides its own limits.
But whereas Marx observed a precise pattern underlying the processes of economic recession and regeneration, economics will never be a precise science. The factors which control economic markets include the elaborate and subtle forces of human nature, and there are a great many conflicting influences at play.
Consider the economic state of the UK back in 1988. At this time, indicators such as the levels of inflation and unemployment were looking lacklustre. The Chancellor decided that they needed a boost, so he dropped taxes and interest rates. What he did not know was that a natural resurgence was on its way. The combination of this natural resurgence and the Chancellor's added boost pushed the economy over a critical point, and there followed a sharp downturn in the economy.
This unhappy outcome would not have surprised Adam Smith, the advocate of laissez-faire economics. In Smith's view, the economy is a self-regulating system which maintains equilibrium by means of a series of polarities. This 'hidden hand', as he called it, keeps order in the marketplace.
Smith identified a pattern to the process of demand-and-supply. If a retailer charges too little for their merchandise, they will not be able to meet their overheads. If they charge too much, however, they will be undercut by other suppliers. So they must find what Smith termed the 'fair' value, which lies midway between these polarities. This process is polar-cyclical: once the optimum price has been reached, any further increase in the price of goods will lead to a decrease in profits.
The ability to predict patterns of consumer behaviour is an essential tool in retailing. Most retailers have limited space and they can therefore stock just a few brands of an item, whereas superstores are able to provide a wider selection. Studies have shown, however, that too many options leads to a sort of analysis paralysis. The process is polar-cyclical: whilst consumers prefer to have a variety of different brands to choose from, they find too much choice off-putting.
Polarity may be defined as 'the presence or manifestation of two equal but opposite principles or tendencies'. How does this differ from balance? On a set of weighing scales, the scales counterpoise. Without this opposition there is a complete fusion of contraries, or nothing. Balance brings to mind static equilibrium, and polarity dynamic opposition, but the principle behind them is the same. There can be no balance without both equality and opposition. The simultaneous co-existence of order and chaos is the feature of the world that gave rise to 'Chaos Theory'. It has been well described by the weatherman and mathematician, Edward Lorenz, in his water-wheel example.
The surf breaking on the sand is composed of a multitude of bubbles. Each bubble takes the three-dimensional form of balance, a sphere, which has the smallest surface area for a given volume: left-hand balances right-hand, top balances base. But such is the tumult of bubbles merging and bursting that the impression given is one of random chaos.
Complex effects such as this arise out of a multitude of conflicting forces, but all elements in the process counterpoise perfectly. Any self-regulating system maintains equilibrium by means of symmetry. Left-hand balances right-hand, and spin is met by counter-spin. Each action is equal but opposite to a preceding action. Even where the overall pattern appears random, every movement, every wave, every current balances.
Nature likes simplicity. But the contradictory structure of balance - the simultaneous coexistence of harmony and opposition - means that it is anything but simplistic.
Our understanding of the universe is based upon two different theories. On the one hand we have Einstein's general relativity theory, which explains to us the large-scale universe of planets and galaxies. On the other hand we have a completely different set of rules, quantum mechanics, which tells us about the small-scale, subatomic universe. Whereas general relativity theory presents us with a rational model of space and time in which things behave harmoniously, the rules that govern quantum mechanics are contradictory.
Which brings me back to watching the waves on the beach. As I stand barefoot there, I can feel the sand beneath my feet. Each of these grains of sand contains a world of paradox. Physicists have discovered that under certain experimental conditions, subatomic matter may be seen either as particle (which is confined to a very small volume) or wave (which is spread out over a large area). Some observers may see matter in particle form, whereas others will see it as a wave. Neither of these descriptions gives a full picture of reality; both need to be taken into account, simultaneously, if we wish to understand the true nature of subatomic matter. Often it is believed by scientists that a paradox is merely someone misinterpreting what they are seeing, but quantum physics demonstrates that paradoxes are a key feature of the world. Reality, at its deepest level, is more paradoxical than science ever thought possible.
A thick, dark cloud forms on the horizon, further emphasising the intensity of the seascape. The contrast between the light and the dark is so acute now that it has taken on a new dimension. It is as if the stage is set for a battle. On one flank stands the Sun, whilst to the north-west there looms the storm cloud.
Clouds are formed by means of a hydrological process. Sea water evaporates and accumulates in the atmosphere. Once a critical point has been reached and sufficient water has gathered in a cloud, the upward movement reverses and it rains. The process of evaporation and precipitation follows a polar-cyclic pattern.
As moisture rises, it collides with ice or sleet which is to be found in the lower portion of the cloud. This process gives rise to an electric charge which creates a storm. Electromagnetic force is controlled by polarity: like charges repel each other, and opposite charges attract. The universe achieves electromagnetic equilibrium, every positive charge being met by a corresponding negative one.
Explosions of thunder are governed by polarity, for they are created by electromagnetic force. All sound travels by means of periodic wave oscillation between opposite poles. Whenever the process reaches an extreme, it polarises. Light is carried on the wings of polarity for it, too, travels by means of the oscillation of its electro-magnetic wave.
Each falling raindrop disperses as it hits the ground. Forces always occur in equal and opposite pairs, the action and the reaction. If one object exerts force on another object, then the latter will polarise this and exert an equal but opposite force on the first. This is known as the law of reciprocal actions, and it is one of the most fundamental laws of physics.
Polarity is central to the laws of physics, controlling everything from the cycles of nature to light waves, storm patterns and electricity. It 'controls' them inasmuch that it guides the patterns of their behaviour.
How far does the influence of polarity extend beyond physics? Let us take a selection of completely disconnected fields - sport, health, safety, human society and the roll of a die - and see what bearing, if any, polarity has on them.
It is generally accepted that regular exercise is good for you, increasing energy levels and improving physical and emotional well-being. If you train beyond your body's natural limits, however, the process will polarise and it will have the opposite effect.
Professional athletes also have another, more subtle, polar-cycle to contend with. Suppose Joe is a basketball player and about to play an important game. He is nervous as he always is before a fixture, but today is different. It is the series final, the biggest match of the season.
Joe's nerves generally help his athletic performance, pumping his body full of adrenaline and heightening his awareness. With just seconds to go before the game ends, one of Joe's team- mates passes him the ball. Joe jumps up at the basket. It's an easy shot, but he fluffs it.
Joe's 'flunk-dunk' is encapsulated in the phenomenon known in sports science as the Yerkes- Dawson law: whereas a limited amount of nervous energy has a positive effect upon an athlete's performance, too much is counter-productive. Psychologists have observed this same polar-cycle conditioning patterns of human behaviour in a wide variety of skill-based tasks.
Picture a modern school playground. The tree has been cut down so no child can climb on it, the grass beneath the swings has been replaced with rubber, and the spikes on the periphery fence have been removed. Playtimes are carefully monitored by CRB-checked adults, and every conceivable risk has been identified and eliminated. This is a super-safe environment.
Or is it? Studies clearly demonstrate that people living in risk-free environments tend to be less careful, because less aware of danger. How will children brought up in this way adapt once they are free of adult supervision? Are we teaching them effective life skills? The answer, of course, is no. A generation is being brought up devoid of personal responsibility. By comparison, when health and safety initiatives were first introduced in the nineteenth century, there was a culture of negligence, cost-cutting and exploitation in the workplace which would be unacceptable by today's standards. In those early pioneering days, health and safety measures were seen in terms of of a balanced model in which both sides were expected to play their part. The polar-cycle underlying this situation is easy to identify. By over-protecting our children, paradoxically, we are putting them at risk.
Of course, it is not just children who adapt their behaviour according to the perceived level of risk. The phenomenon has its own name - the Peltzman effect. Another example is that motorists seem to respond to safety regulation by behaving less safely. For example, it has been observed that compulsory seat belt use has had the effect of increasing the number of road accidents, because motorists tended to drive less cautiously. And if drivers themselves sustained less serious injuries from these accidents due to their wearing seat belts, it seems that the risk was at the same time being transferred from vehicle users to pedestrians and cyclists.
By contrast, initiatives in which urban planners and traffic engineers have tried to blur the distinction between the road and its surroundings, building upon an inverse Peltzman effect, can improve safety. Road markings, barriers and signs are removed, and traffic lights are dismantled. The scheme is built, regulation by the state (in the form of safety features installed by urban planners) is reduced, and individual responsibility for avoiding accidents correspondingly increases. The higher the perceived risk of a situation, the more cautious road users are.
Perhaps a small fire breaks out at a night-club. People start by walking briskly towards the exits, moving in an orderly manner. Then the fire intensifies. People move more quickly now, but still in an orderly manner. However, due to their greater speed, the volume of people leaving the club has increased, creating a sense of urgency. As the fire and smoke further intensify, people begin to panic. Some start pushing and hurrying towards the exits. Two things then happen: people trip over one another, and the doorways become congested.
We are already familiar with the pattern which is central to this process. Whereas the number of clubbers vacating the building in any given minute increased as people headed for the exits more quickly, two factors - speed and volume - have passed a critical point, and the process has polarised.
One of the most intriguing examples of polarity in everyday life is to be found in random variables. A random variable is a quantity to which a probability distribution is assigned, such as the possible outcomes of a throw of a die. A theoretical model known as Central Limit Theorem tells us that no matter how chaotic a large set of random variables appear to be, the normal distribution of these variables has a tendency to cluster around a central point of equilibrium. The greater the quantity of random variables, the more evenly counterpoised they are. If we take a cross-section of a large number of throws of a die, for example, the average number of times a particular face falls upwards will approximate the total number of throws divided by the number of faces on the die. Some numbers will fall upwards more often than the average, and some less often, but the normal distribution of numbers will polarise around the centre.
Central Limit Theorem takes us nearer to the paradox which lies at the heart of polarity. Nothing could be more random than the throw of a die, yet it is subject to an underlying order. In a letter to physicist Max Born, Albert Einstein wrote, 'You believe in a God who plays dice (with the universe), and I in complete law and order.' Central Limit Theorem indicates that neither man's position was wholly correct. Order and chaos both need to be taken into account, simultaneously, if we wish to come closer to an understanding of reality.
Few philosophical or scientific theories are entirely new. Early Taoist philosophers observed that all processes, from human activity to the patterns of nature, follow a cyclical polar pattern. They illustrated this by means of the tajitu symbol (below). As the cycle rotates, each side of the polarity increases in volume before reaching a critical point and giving way to its opposite. Taoism finds its origins in eastern central China in the seventh century BCE. The word tao roughly translates as 'the flow of the universe', or the natural law.
Every epoch believes its collective attitude to be superior to that of every age which has gone before, and we in the contemporary West are no exception. We dismiss the philosophical and theological systems of most ancient societies as being simplistic and naïve, but for all our scientific achievements, we do not hold the monopoly on wisdom.
There is no doubt that the polar-cycle is a highly significant process which finds expression in a wide variety of different fields, yet it is a function which we ignore. Polarity is life's hidden controller. The logic behind this is entirely sound. All movement is caused by polarity: as soon as a state of equilibrium is achieved, movement stops. Even where we see random behaviour, there is order beneath the surface. In a stormy sea, every reaction has a preceding action, and each current is met by a countercurrent. Complex effects arise out of a multitude of conflicting forces, but every constituent element in the process balances perfectly.
Address for correspondence:Red Rachtagáin <redrat11@gmail.com>
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