A few years ago Gerald Minnee of the Reformed Church of Wellington asked me if I knew anything about chaos. Hav­ing been out of circulation mathemati­cally for some years, I responded with a puzzled look and another question, "What do you mean by 'chaos'?" He indicated that he had seen references in educa­tional journals to a new field of study called chaos theory.

It took a while, but about two years ago I also ran across references to this new theory. The name sounded oxymoronic: 'chaos theory'. The two terms sounded quite contradictory. How can chaos have any theory describing it? Wouldn't a theory imply, in the nature of the case, that the subject is not after all chaotic?

So I read a bit, became intrigued, and began to recognise a new way of under­standing our world that fitted the Chris­tian world view much better than any­thing I had learned in science and math's classes during my 18 years of public schooling. Furthermore, it answered a few questions I had asked of my theology profs during my seminary training which they could not answer.

Perhaps I can share some of this with the readers of Faith in Focus with the intention of opening up a new under­standing of God's world and majesty and perhaps also stimulating some of our youth to go into their tertiary studies with a new perspective and a greater appre­ciation of the value of further education.

Implications of Chaos Theory⤒🔗

Chaos theory has implications for every field of endeavour. The reason for this is that it deals with the basic underlying structure of change — any kind of change: economic change (and who isn't inter­ested in the ups and downs of the economy?); biological change (which in­volves everyone of us!); quantum effects in particle physics; water flow in rivers or pipes; drips from a leaking tap; motion of the planets and the stars; populations of birds, people, and trees; and of course the changing weather!

Order and Randomness←⤒🔗

We believe and confess that God is a God of order. We also believe and con­fess that God is infinite, i.e. without any limitations in any aspect of His being. Christian scientists three centuries ago, believing that an orderly God had created an orderly universe, searched for and discovered some simple 'laws of nature' that described the order they saw. New­ton, for example, discovered a very sim­ple mathematical formula that describes the force between two bodies. This for­mula we commonly call the law of grav­ity.¹ With this law men have been able to predict the motion of the planets years in advance. Now we are able to send men to the moon and to send space craft to Mars, Jupiter, and beyond because of this simple formula.

And yet it is quite apparent to every­one that most of the change we see all around us does not have the regularity of clockwork as the planets appear to have in their motion around the sun. Rivers meander all over the place. Wind blows with ever-changing speed and direction. Clouds boil and roll in seemingly random patterns that have inspired poets and artists for centuries.

Is there chance after all in the uni­verse? Does God rule some things in an orderly way and allow other things to occur by chance? This is what many people believe. But such a view contra­dicts Scripture and our confession. We confess that God rules in such a way that 'all things, in fact, come to us not by chance but from His fatherly hand' (Heidelberg Catechism, Q. 27).

Is God behind all this apparent randomness? We must say that He is. And how does apparent randomness in our universe relate to the order which we believe God has placed there? Or are order and apparent randomness unre­lated?

A Possible Resolution←⤒🔗

For most of my life I have believed that God directs the universe in orderly ways which he expects us to discover — that is what Christians have thought science is all about: discovering the ways in which God orders this universe. I have also believed that, as an infinite God, He directs many things in random ways with no apparent order which we can dis­cover. After all, an infinite God has no trouble keeping precise track of the zillions of electrons zipping around their respective atomic nuclei even though Mr. Heisenberg has shown us that we are not able to determine exactly where one is and what speed it is going at any particular moment in time.

I have always believed that chance is not ultimate. But I also had to admit that God directs things in a way that appears random to us. I had to admit to my unbelieving university associates during my post graduate studies that their de­nial of God's providence because of the apparently random nature of physical events in our ever-changing universe was understandable. And yet I was not willing to give up my belief that God controlled all things — because the Bible teaches this.

However, this belief (that God directs things in a way that appears random to us), while not theologically wrong, did not satisfy me. God created us to rule the universe and in His grace He will one day restore us to Adam's original perfection so that we may exercise that rule as we ought forever. To rule we must under­stand and be able to describe. Because we are finite we have to simplify in order to describe. The artist simplifies by using large brush strokes to bring out the overall order and beauty he sees. The scientist simplifies by reducing complex motions to simple formulae.

But most of the changes we see around us haven't succumbed to current meth­ods of analysis. The changes seem to be too complex. Until recently scientists have held some basic beliefs about complexity which implied that we won't get far dealing with complex systems (there are too many molecules in the air to predict the weather or even to predict the shape of a snowflake). So we might as well treat changes in complex systems as random changes. Thus the really in­teresting changes occurring all around us were put in the too-hard basket. "Acts of God" they were called by a former generation which still believed in a God of providence. Now they are viewed as the essentially random events by which our universe has evolved from the 'big bang'.

These basic beliefs can be described as follows:

1. Simple systems behave in simple ways which can be predicted by using simple formulae (e.g. a pendulum with one moving part behaves very sim­ply and a simple formula will tell, will give its position even after hundreds of swings).

2. Complex behaviour implies complex descriptions (so, for example, impossibly complex formulae are needed to describe the complex changes in the flow of the swirling water going down the bath tub drain).

One of the implications of these basic beliefs was a deep seated conviction that nothing described by a simple for­mula could evidence complex behaviour. As a result when a simple formula was found to describe some system (like Newton's law of gravity) the matter was considered finished and no further inves­tigation was done. Furthermore if a com­plex system 'almost fit' a simple formula, that formula was used as an ap­proximation and it was assumed that the predictions it led to would also 'almost fit'. But in the real world this is similar to a woman making plans for her future based upon a belief that she is 'almost pregnant'.

A New Perspective — Chaos Theory←⤒🔗

In fact the two simple beliefs given above are wrong! Very complex motion, even apparently random motion, may be described by a very simple formula. Per­haps a simple example will illustrate this amazing truth. I won't burden you with any mathematics!

You may have seen in a gift shop one of those little trapeze-like swings with a little man or a little monkey hanging from it. When set in motion the swing goes back and forth but the little man swings wildly, sometimes in the same direction as the swing, sometimes in the opposite direction, sometimes making the full cir­cle around the bar of the swing. There are only two moving parts. That's pretty sim­ple compared to water going down the drain or the weather. Yet the motion is apparently random. The formula for the motion of this contraption is quite simple (so I am told, I'm not a physicist). If you put 10 seconds into the formula, a few calculations will give an answer telling you exactly where the man and the swing will be at the end of 10 seconds.

But there is a great difficulty in actu­ally using the formula to predict where the swing will be after 10 seconds. You have to know exactly where the swing started. This swing isn't like the simple pendulum. If you are a millimetre out in measuring the starting position of the pendulum you will only be a millimetre out after 10 seconds, or 100 seconds. But if you are even a 1000th of a millime­tre out in measuring the starting position of the man on the swing, you will be totally wrong in your prediction after 10 seconds. Scientists have a name for this: sensitive dependence upon initial conditions.

Consider a much more complicated system: the weather. This sensitivity to initial conditions means that a butterfly flitting from the rose bush to the bottle brush tree may set of a sequence of events that lead to a snow storm that drops a metre of snow in New York City.

Now expand your thoughts from a mechanical toy with two moving parts to the weather. If a butterfly flits from the rose bush to the bottle brush tree in your garden, that may set in motion a chain of events that will lead to snows a metre deep in New York City! God alone can completely understand (and direct) this vast complexity giving full attention to every minute detail any one of which may lead to a completely different chain of events.

Think about it. Almost everything in life is like this. Things are generally sensitively dependent on initial condi­tions:

• For want of a nail the shoe was lost.

• For want of a shoe the horse was lost.

• For want of a horse the warrior was lost.

• For want of a warrior the battle was lost.

• For want of a battle the kingdom was lost.

And all because some careless black­smith missed a nail in that shoe two weeks ago!

In the real world (not the artificial world of over-simplified scientific descrip­tion) everything matters! Every action is significant. Nothing can be left out. Surely this is why God says that we will be held accountable for every careless word we speak. Every word we speak has great significance in our world because things in general are complex and also sensi­tive to initial conditions.

And yet it is possible to understand what is happening in the world around us because there are simple patterns in the complex changes we observe around us. The weather is seemingly random and yet summer and winter, springtime and harvest are seen every year. And now chaos theory leads us to suspect that there are patterns that describe the longer changes (of winter temperatures over the centuries, for example).

Scientists are starting to discover quite simple formulae which describe some of the complex changes we observe around us. But we will not be able to use these formulae to predict the future (of the weather or the position of the man on the trapeze)! We can't measure accurately enough for that. We can only use them to describe, to show the boundaries within which things move, to show the patterns generally followed, to show the overall stability of changing systems. Apparently random motion is not random after all. It follows very clear and simple patterns.

We may learn these patterns through careful observation and study and thus be more effective in our ruling of this marvellous creation which God has made as our home. Tertiary students over the next generation will no doubt discover many enormously exciting patterns as they carry this new perspective into every discipline.

God is a God of order. But His order is very complex. So complex that we will never be able to predict the future even for a toy man on a trapeze. But not so complex that it defies all description. There are patterns and simple formulae to be found which will enable us better to understand the mind of God as it is revealed in the creation, and better to serve Him and our fellow man through our scientific (and artistic) labours.

Man Humbled, God Magnified←⤒🔗

Through the development of chaos theory over the last 20 years proud man has once again been humbled. The arro­gant dream of total control through scien­tific prediction held by scientists in the past has now been shown to be vain. Weather prediction more than a few days ahead is now seen to be totally beyond man's reach. (One wonders if weather prediction more than two seconds ahead might not be beyond man's reach!)

God has ordained that we should learn and understand (though we will never completely understand) His marvellous creation. But He has reserved for Him­self the providential supervision and di­rection of all that he has made. He is infinite and all that such supervision entails is well within His reach.

The patterns we are learning to recog­nise are already increasing our under­standing of heart irregularities, popula­tion fluctuation, turbulence in fluids, and how chaotic tissue growth may suddenly become stable again.

This new perspective has even brought the artist and the scientist together. A thing formerly unthinkable! Scientists have learned the simple formula that describes the appearance of clouds. And they have found another formula that describes the appearance of mountains and another for ferns. Picturing such things was formerly the exclusive do­main of artists. On the other side artists have begun to see beauty in the calcula­tions of mathematical formulae (can you believe that some artists even have por­tions of the Mandelbrot Set hanging on their studio walls?)²

There is much to learn. All of it ena­bles us to magnify our great and glorious God.