Problem Management — principles

Chaos or Order?
Theory A, Theory B, Theory C, and Theory D

Ray Butterworth     Based on an essay submitted for RS 390B, Fall 1999.

1. Introduction

Every aspect of our lives and our environment appears to be continually affected by seemingly insignificant events. At any instant, any number of things can influence our thoughts and actions, changing our future to something completely different from what it would have been. But do these diverging paths that our individual lives might follow really affect the greater scheme of things, or are they merely minor perturbations in the flow of time, or do they not really exist at all?

2. Theory C

If God is capable of knowing everything, then surely it follows that God does know everything, or at least that was the thinking of the protestant reformer John Calvin in the early 16th century. He promoted the belief that everything, in particular each individual's salvation, is predetermined; that if God already knows what we are going to do there is nothing any of us can do to change our futures, for the better, or for the worse.

More than a century later, in the secular world, Newton et al. developed theories of physics that made this view more and more believable. Everything that happened in the physical world was simply the result of the events leading up to it. If one knew enough about a situation, one could reliably predict what would happen next.

By the 19th century, the work of Darwin and others made it seem that man himself was simply a result of random processes.

To Calvin, and those that followed, the universe was simply a mechanical thing. It might have been created by God, but even if it had, God had simply wound up the mechanism and left it to run its inevitable course, every detail predetermined, with nothing left to chance or free will.

3. Theory D

In the 20th century, physicists realized that the universe operates at a quantum level where nothing is certain. Objects can exist in multiple states at the same time, with none of them assuming reality until someone actually measures or observes them.

One view of this, first proposed by Hugh Everett, and later named and popularized by Bryce DeWitt, was the Many Worlds interpretation, in which the universe is continually splitting into multiple instances of itself every time some alternative is possible.

Flip a coin, and there are now two universes, one in which it turns up heads, and one in which it turns up tails. Both are equally real, yet neither can interact with the other. Decide to turn left rather than right, and the universe splits again, one in which you turn left and one in which you turn right.

There isn't one universe, but an infinite number, covering all possible events that could ever happen.

4. Theory B

In 1952, Ray Bradbury published a short story, A Sound Of Thunder (Copyright © The Crowell-Collier Publishing Company), that considered the expanding nature of causality in time.

In this story, which takes place in 2055, a man travels 60 million years into the past to visit the age of dinosaurs. He is told that he must stay on a special path that has been constructed for visitors, and is warned of the consequences:

We don't want to change the Future. We don't belong here in the Past. […] Not knowing it, we might kill an important animal, a small bird, a roach, a flower even, thus destroying an important link in a growing species.

That's not clear, said Eckels.

All right, Travis continued, say we accidentally kill one mouse here. That means all the future families of this one particular mouse are destroyed, right?


And all the families of the families of the families of that one mouse! With a stamp of your foot, you annihilate first one, then a dozen, then a thousand, a million, a billion possible mice!

So they're dead, said Eckels. So what?

So what? Travis snorted quietly. Well, what about the foxes that'll need those mice to survive? For want of ten mice, a fox dies. For want of ten foxes, a lion starves. For want of a lion, all manner of insects, vultures, infinite billions of life forms are thrown into chaos and destruction. Eventually it all boils down to this: fifty-nine million years later, a cave man, one of a dozen on the entire world, goes hunting wild boar or saber-tooth tiger for food. But you, friend, have stepped on all the tigers in that region. By stepping on one single mouse. So the cave man starves. And the cave man, please note, is not just any expendable man, no! He is an entire future nation. From his loins would have sprung ten sons. From their loins one hundred sons, and thus onward to a civilization. Destroy this one man, and you destroy a race, a people, an entire history of life. It is comparable to slaying some of Adam's grandchildren. The stomp of your foot, on one mouse, could start an earthquake, the effects of which could shake our earth and destinies down through Time to their very foundations. With the death of that one cave man, a billion others yet unborn are throttled in the womb. Perhaps Rome never rises on its seven hills. Perhaps Europe is forever a dark forest, and only Asia waxes healthy and teeming. Step on a mouse an you crush the Pyramids. Step on a mouse and you leave your print, like a Grand Canyon, across Eternity. Queen Elizabeth might never be born, Washington might not cross the Delaware, there might never be a United States at all. So be careful. Stay on the Path. Never step off!

Of course (or this wouldn't have been much of a story), he does step off the path, and upon his return notices that the world is not the same one he left.

Eckels felt himself fall into a chair. He fumbled crazily at the thick slime on his boots. He held up a clod of dirt, trembling. No, it can't be. Not a little thing like that. No!

Embedded in the mud, glistening green and gold and black, was a butterfly, very beautiful, and very dead.

Not a little thing like that! Not a butterfly! cried Eckels.

It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time. Eckels's mind whirled. It couldn't change things. Killing one butterfly couldn't be that important! Could it?

To Bradbury, cause and effect are like ripples spreading out in concentric circles in a still pool of water. No matter how distant something is, it is eventually touched by, and affected by, those ripples. True, the effect might be very small, but there is always some effect, and the effect will spread out forever, affecting everything in its path.

5. Theory A

Starting in 1941, Isaac Asimov published a series of stories that were eventually merged to form three novels published in 1951, 1952, and 1953: Foundation, Foundation And Empire, and Second Foundation.

The central premise of this series is the development of a branch of mathematics for sociology, known as psychohistory, capable of analyzing and predicting the expected behaviour of large numbers of people.

Psychohistory: That branch of mathematics that deals with the overall reactions of large groups of human beings to given stimuli under given conditions. In other words, it is supposed to predict social and historical changes.

Hari Seldon modeled his science of psychohistory on the kinetic theory of gases. Each atom or molecule in a gas moves randomly so that the position or velocity of any one of them cannot be known. Nevertheless, using statistics, the rules governing their overall behaviour can be worked out with great precision. In the same way, Seldon intended to work out the overall behaviour of human societies even though the solutions would not apply to the behaviour of individual human beings. — Galactic Encyclopedia

It's interesting to note that the word gas is likely derived, via Dutch, from the Greek word chaos.

Asimov wrote an article about psychohistory, published in Asimov's, July 1998.

[…] I suggested we add the fact that a mathematical treatment existed whereby the future could be predicted in a statistical fashion, and I called it psychohistory. Actually, it was a poor word and did not represent what I truly meant. I should have called it psychosociology (a word which the O.E.D. lists as having first been used in 1928). However, I was so intent on history, thanks to Gibbon, that I could think of nothing but psychohistory. […]

I modeled my concept of psychohistory on the kinetic theory of gases, which I had been beat over the head with in my physical chemistry classes. The molecules making up gases moved in an absolutely random fashion in any direction in three dimensions and in a wide range of speeds. Nevertheless, one could fairly describe what those motions would be on the average and work out the gas laws from those average motions with an enormous degree of precision.

In other words, although one couldn't possibly predict what a single molecule would do, one could accurately predict what umptillions of them would do.

So I applied that notion to human beings. Each individual human being might have free will but a huge mob of them should behave with some sort of predictability, and the analysis of mob behaviour was my psychohistory. …

[…] a clipping from the April 23, 1987, issue of Machine Design. It reads as follows:

A computer model originally intended to simulate liquid turbulence has been used to model group behaviour. Researchers at Los Alamos National Laboratories have found that there is a similarity between group behaviour and certain physical phenomena. […] Although the analysis cannot predict exactly what a group will do, it reportedly does help determine the most probably consequence of a given event.

Then too, Roger N. Shepard, a professor of psychology at Stanford University, has published an article in the 11 September 1987 issue of Science entitled Toward a Universal Law of Generalization for Psychological Science.

Unfortunately, although I made a valiant effort to read it, the mathematics was too tough for me and even the non-mathematical portions produced only a rather dim and hazy understanding within me. However, here is the summary of the article as given at the beginning:

A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along with[sic - which?] the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, thorough evolutionary internalization, tend to govern the behaviors of all sentient organisms.

As I said, I don't really understand this but I have the feeling that Hari Seldon would understand it without trouble. I am also concerned, suddenly, that psychohistory may be developed within the next century. I placed its development 20,000 years in the future. Is this going to be another case of my science fictional imagination falling ludicrously short?

The mathematics was as useless for predicting the behaviour of individuals as probability theory is for predicting the behaviour of the physical world. But just as statistics can be extremely reliable in predicting the average behaviour of a large number of events, so too was psychohistory a reliable predictor of history over hundreds or even thousands of years.

Psycho-history dealt not with man, but with man-masses. It was the science of mobs; mobs in their billions. It could forecast reactions to stimuli with something of the accuracy that a lesser science could bring to the forecast of a rebound of a billiard ball. The reaction of one man could be forecast by no known mathematics; the reaction of a billion is something else again. — Foundation and Empire, Copyright © 1952, Isaac Asimov

Consider an ant colony in your driveway. Kick the sand mound away, stomp on a few dozen ants, and watch the chaos that results. There's no question that the lives of the colony have been severely affected, particularly for the few dozen chosen ones, but by the next day everything will have returned to normal, and no one will be able to tell the difference between that colony and any of the others nearby. It is as if the incident never happened.

Of course this concept doesn't apply only to social behaviour in humans or insects, and Asimov later extended it to the rest of the world in his non-fiction writing.

To Asimov, cause and effect are like splashes in a river. No matter how great the splash, a few seconds later all traces of it are gone. Even something huge enough to totally block the flow will have only a temporary effect; soon the river will find a way around the blockage and resume its course. True, it is possible to divert the river to a completely new course, but such events are extremely rare, certainly not the common case.

6. Theory C In The Real World

The late 19th century revealed problems with Newton's physics, and the resulting development of Quantum Theory showed that at the subatomic level, not only were things not perfectly predictable, but events actually depend upon whether or not someone is observing them.

Why question the existence of Man's free will when even subatomic particles behave as if they have it.

Even more destructive of this theory is perhaps its inherent boringness. If it were true, then the only reason one would ever study it is simply because one has no choice but to study it.

7. Theory D In The Real World

This might seem to be the extreme opposite of Calvin's predestination, but from the perspective of human participants, it is effectively the same.

Suppose we spend significant time deciding whether to turn right or left. If we decide right, the universe forks into two, one in which we turn right and one in which we turn left. If we decide left, the universe forks into two, one in which we turn right and one in which we turn left. It really didn't matter which we chose, the result was identical.

Under either theory, when we think we have decided something, we have actually wasted our time. Calvin says we would have done it no matter what, and DeWitt says we would have taken both choices anyway. Whether there is no free will, or there is free will but what we choose has no effect, we end up with the same uninteresting conclusion.

8. Theory B In The Real World

We can of course ignore the use of Bradbury's fictional time-machine, and consider how predictable things are in the present time of the real world.

Think of any important or significant event in our lives and then consider how many tiny insignificant events contributed to its ever happening. Things such as how we met our spouses, got our jobs, chose our homes, or had our children, were all highly dependent upon a long series of improbable events. Perhaps if we had been a few seconds later or earlier, we would never have met our future spouses; if we hadn't blown the job interview with company X, even now we might still be stuck in a dull job producing Brand X Widgets, if someone hadn't decided to hold their open house that weekend or it hadn't happened to have been located near where we were visiting, we would have ended up living somewhere else; and trying to consider the timing and number of possible genetic combinations that could have produced our children is staggering.

And the effects are cumulative: if we hadn't met our future spouses, we might not have blown the job interview, not needed that house, and certainly not had the same, or even any, children.

And of course all the possible changes in our lives have an effect on the lives of everyone else that we meet, or fail to meet. Attempting to predict the effect of the slightest change is next to impossible.

Similarly, in the physical world, cause and effect is equally random and unpredictable. As has been said in a much more recent butterfly theory, even something as seemingly insignificant as a butterfly can, many months later, affect the weather half way around the world.

It's very difficult to argue that Theory B doesn't apply every moment to every aspect of our lives.

9. Theory A In The Real World

It's true that at the smaller personal level no cause can be considered trivial or inconsequential, nor any effect to be highly predictable, but in the larger scheme of things, how much does any of that really matter?

Perhaps a butterfly in China really can change next year's weather in Africa, but can it change the climate? It might rain on Monday morning instead of Monday afternoon, and the timing of that rain might be a very significant factor in the behaviour of millions of people. But looking back on it years later, it didn't really matter to the vast majority of people and certainly not to the world in general.

Perhaps we can't determine the precise location and momentum of even one unpredictable electron, but in general, why would we want to? Certainly physics would like to have such an ability to describe the theory of the nature of matter and energy, but chemistry gets along quite well without such knowledge. Schrödinger's equations are an extremely reliable predictor of the overall effect and behaviour of electrons without one's ever needing to know the elusive details.

A single molecule of caffeine will move around in a cup of coffee in a totally unpredictable way, as will every individual molecule of water. To someone analyzing the Brownian motion of a speck of dust in that cup, such information may be useful or significant, but to anyone about to drink that coffee it is useless and not worth considering. That all the hot molecules could move to one spot and burn the drinker's tongue is extremely unlikely, and not very believable should anyone ever report such an unreproducible incident.

Even what we may consider highly critical turning points in history can often be seen as inevitable events. Columbus discovered America, but surely European politics and economics were such that had there not been a Columbus then someone else would have done it instead. Edison invented hundreds of things, but do we really think that they wouldn't soon have been invented by others had he not done so? Hitler united Germany and had an extremely significant effect on Europe and the rest of the world, but was it Hitler himself that did it, or was he merely a tool of the historical forces that would have eventually used some other person had he not been there?

10. Religion

Theory C claims that God created the universe in all its details from beginning to end; it simply exists and progresses through time along its predetermined course. Theory D doesn't require God, but it too defines a predetermined universe that progresses through time along all possible courses. In either view, humans play no role in the course of events.

But if there is a God running this universe, would he really want to be concerned with Theory B's fine tuning, directing every little thing to prevent the universe from continually diverging from his great plan? Isn't it much more reasonable that he would have designed a stable, self-correcting universe that operates in a way that tends to redirect deviations back toward the desired direction, and that such diversions would be merely an amusing side show with the vast majority of the universe flowing along its inevitable course according to Theory A?

Certainly some unusual circumstances can occasionally disrupt the flow and cause things to head off course, and certainly some intervention would be required in those cases, but such events would be few and far between, miraculous events one might say.

(Note that this lack of need for intervention does not preclude the possibility for other purposes that do not conflict with the overall great plan (e.g. prayer requests, If it be your will).)

Perhaps one could look at the path of events in time as a flow within channels bounded by long ridges. There is some room to move, but any large movement to either side automatically results in a restoring force pushing back toward the center of the desired path (like Hot Wheels® cars in their track, or a bowling ball in the gutter). This is a very stable system that needs very little tending.

Similarly, within those troughs there could be smaller ridges, and perhaps one could view the life of the elect as a very unstable system, traveling along the crests of those ridges rather than within troughs. Their path is very narrow and requires constant diligence to traverse, and even a slight divergence from the correct path will be amplified into a major change in direction. Once one has fallen off the path, only divine intervention can get one back onto the right track.

11. Summary

There is no question that every aspect of our lives and our environment is continually subject to random changes beyond our control or ability to predict.

But it seems almost equally obvious that if there is a purpose for the universe in general, and for mankind in particular, then there must be an overriding flow of history that makes these variations insignificant within that grand plan.

I will say that he must indeed have a blind soul who cannot see that some great purpose and design is being worked out here below, of which we have the honour to be the faithful servants. — Winston Churchill
— Joint Session of Congress, Washington, 26 December 1941

And it is equally clear that unless we as individuals are offered the chance to be part of the grand plan, and unless we also choose to accept that chance, the universe will continue to flow along its destined course regardless of our existence or behaviour.

[…] it doesn't take much to see that the problems of […] little people don't amount to a hill of beans in this crazy world. Someday you'll understand that. — Richard Blaine