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The Limits of Predictability

Stephen L. Talbott

This chapter is part of a work in progress and is subject to continual revision. Date of last revision: January 6, 2004. The chapter was originally published in NetFuture #153. Copyright 2004 The Nature Institute. All rights reserved. You may freely redistribute this chapter for noncommercial purposes only.

Predictability is comforting, and we humans seem to crave it. This is why superstition, with its promise of predictable control, has long bedeviled our race. Moreover, our desire for control has, in the mechanical sphere, borne fruit. The digital machines of our own era seem a genuine fulfillment of the superstitious hope, designed as they are to accomplish well-defined tasks with high reliability.

When I throw a rock at a tree trunk, I may or may not hit it; but when I dial the number of a friend, I don't waste much energy worrying that an incorrect phone will ring. Instead of crossing myself three times before dialing, I place well-justified trust in the predictable performance of the technology. (Users of Microsoft Windows software, however, may be forgiven the occasional act of crossing themselves.) It seems the nature of a properly constructed machine always to do, at some level, precisely what it was designed to do — although, as I pointed out in NF #151, perfect predictability is a feature of the machine's disincarnate algorithm, not of the material device itself. In any case, to build machines with ever more sophisticated functions and ever greater reliability remains a defining concern of our culture.

This machinery in turn shapes our thinking, encouraging us to view the natural world as if it, too, were, in its ultimate workings, a predictable mechanism. From this preoccupation with mechanistic predictability the whole problem of determinism versus freedom has arisen in its modern guise.

The preoccupation, unfortunately, is no less ridden with delusion than are the superstitions of the gullible. We can recognize the delusion in the failure to acknowledge a simple distinction. I mean, roughly, the distinction between predicting some precise aspect of an event or phenomenon, and predicting the event or phenomenon itself. It's one thing to say that, whatever a series of events may be, it will respect certain laws, and quite another to predict the actual course of the events.

If I walk through a city obeying every traffic light and observing all the other city ordinances, then you could say I am acting wholly in accord with law. Nothing in me is violating the law. Yet the laws, while qualifying my trip, neither cause it nor explain it nor predict it.

Something similar holds for physical laws. In fact, every material domain we think of as in any way lawful presents us consistently with this truth: an event may without exception conform to law, so that nothing in it is a violation of law, yet this lawfulness fails to give us unqualified powers of explanation or prediction.

You may, of course, choose to believe that, if only we knew all the different varieties of law bearing on a phenomenon, and if only we knew all the initial conditions circumscribing it, then the laws would fully explain and predict what happens subsequently. This, we will eventually see, is a gross misunderstanding of the world's lawful order — and the misunderstanding goes far beyond such issues as quantum indeterminacy and chaotic unpredictability. But for the moment my intention is more modest: I wish only to illustrate some of the ways we continually overestimate the explanatory and predictive powers of our current knowledge of law.

Knowledge in a Vacuum

It is easy to forget how hard it is, practically speaking, to impose rigorous predictability upon the world. Predictability is something we achieve, not something that is "just there". When we need things to happen in a more or less precisely choreographed way, we expend a great deal of effort in order to attain the desired approximation within a carefully restricted context. In the case of sophisticated facilities such as a particle accelerator — or a chip fabrication plant, with its purification systems, clean-room suits, and all the rest — the effort to secure repeatable results may cost many millions of dollars.

The idea in general is to construct a carefully designed, closed system that will enable us reliably to produce particular results with the least possible interference from outside. But, of course, there are no truly closed systems, either in nature or among our artifacts. Moreover, insofar as we are successful in this exercise, the whole point of the closed system is to narrow down what we mean by "event", greatly impoverishing the reality we put on predictable display. That is, our increased predictive powers may come at the expense of our broader knowledge of the phenomenon we are predicting.

A simple illustration may help to explain the trade-off.

If I pick a broad leaf from a tree and hold it in one hand, and grasp a rock in the other hand, I can drop them at the same instant and watch them fall to the ground. The rock will descend faster and strike the ground first. Both fall under the influence of gravity, but the leaf's behavior within the earthly field of gravity is radically different from the rock's — a profound fact that lived much more vividly in the imagination of the ancients than in our own scientific imaginations today.

However, we know something today that they did not. We can build a special chamber, evacuate almost all the air from it, and then arrange for the leaf and rock to be dropped inside the chamber. The two now appear to fall at the same rate. In this way we can discover a law of gravity that, as far as we can determine, is universal. With the right sort of analysis we can recognize this law unchanged even in the whirling, floating, oscillating leaf that slowly descends from the tree on an autumn day.

It's a remarkable achievement, but it comes at a cost. What appeals about the evacuated chamber is that it makes the entire event appear to be almost nothing but a predictable manifestation of the law of gravity. This is what the apparatus has been designed to do. But it achieves this by putting the leaf largely out of sight. It removes the leaf from its natural context and excludes from view most of what we would normally expect to see as leafy behavior. The leaf, you could say, must be prevented from leafing in order to show off just a single aspect of the lawfulness it always respects. We highlight the single aspect by training ourselves to ignore what it is an aspect of.

So in this case we get a phenomenon as the more or less pure exemplification of a law by narrowing down, through artifice, what we mean by "phenomenon". We no longer have the leaf in its own habitat, doing any of the things that leaves do. As far as possible we allow expression only to that aspect of the thing that embodies what we are looking for. Taken as a whole, the phenomenon in the evacuated chamber is actually false to the reality of leaves, which never behave that way in nature. We discover something valid in the experiment by obscuring the larger reality we originally set out to understand.

Our experiment, then, gives us both a penetrating truth and a powerful invitation to false thinking. The scientific method, as usually articulated, systematizes and perfects our drive toward this abstract and partial truth, but offers little guidance for countering the systematic potentials of the falsehood. Scientists themselves have been so enamored of the truth that they have ignored the toxic effects of the falsehood. Many no longer even ask how they might recover an understanding of the phenomenon they began with, as opposed to identifying various laws implicit in it. We may reasonably wonder to what degree the poison has infiltrated and subtly altered the main body of scientific understanding today.

Digital Reductions

We have learned with consummate skill to construct activities that we can assess by reducing complex qualitative realities to simple numerical terms. In a basketball game we give paramount attention to a single consideration: does the ball pass through the hoop or not? Never mind that shots of wildly differing accuracy and grace, resulting from beautiful teamwork in some cases and brute selfishness in others, superbly defended or else sloppily conceded, all count the same when, perhaps after several caroms, the ball drops through the metal ring.

We would be hard put if we had to evaluate the full reality of the game. But there is no need. The scoring, both individual and collective, is what goes down in the record books. However much we may appreciate the artistry of the game, the scoring is the "hard truth" that remains to history, giving us all we need to "explain" why one team is the champion and another is an also-ran1. It is perfectly reasonable to cultivate such an abstract representation of the game (or of the world); what is not reasonable is to lose sight of the reality behind the representation, or to assume that nothing beside the numbers is required in order for us to understand the actual events.

I am not suggesting that laws of nature are like the scoring of basketball. I am only pointing out that, just as we may let the reductive numbers substitute for and explain the events of the game they were abstracted from, forgetting that the game is what explains the numbers, so also we may let the mathematically formulated laws of physics explain reality, forgetting that the reality — an immeasurably richer reality than is captured in the selected mathematical relationships — is what explains the laws.

Whether dealing with subatomic particles or planets, the student of physics quickly learns to reconceive a group of objects as idealized, dimensionless point-masses, isolated from all outside influences in a perfectly closed system — never mind that there are no point-masses in the world, and there are no objects bereft of relationship to all the rest of the universe. The resulting equations, when graphed, give the student a concrete picture he is bound to start conceiving as a little piece of the world. The world begins to appear as nothing more than a reification of its "governing" equations, with the purely imaginal point-mass standing in for real objects.

The deception here is both subtle and earth-shaking — and it receives no attention whatever in the student's education. But the fact remains that his theoretical concepts do not present him with a little piece of the observable world. When he looks at a real mass, his equation describes one element of lawfulness implicit in that little (and somewhat falsely isolated) piece of the world. This mathematical lawfulness no more gives him a tiny event or phenomenon than a player's score of two points gives us one small part of the the player's drive or the flight of the ball — as opposed to a highly abstract condition that must be met by whatever the observable phenomenon may have been. In other words, there is something about the occurrence — the approach to the basket, the muscular leap, the graceful contortion, the ball in flight, the rattling of the hoop, the final descent — truly captured in the score of two points, but it's a long way from this abstract something to any actual event.

The Inertia of Thought

To mistake laws for the phenomena embodying them is to be forever overreaching with our "explanations". It is to mistake the predictability of inherent laws for the predictability and understandability of the events in which they inhere. We are then beguiled into the conviction that we have a solid grip on the nature of things, when in fact we have in many respects retreated from the things, refusing to see them for what they are. Take, for example, Newton's first law of motion:

Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it.

The formulation itself already suggests that it is somehow in the nature of bodies to move in straight lines. The factors that compel them out of this course are impressed upon them from the outside, as if these factors were foreign to the nature of the things themselves. But if we bother to observe real things — things not isolated in carefully designed closed systems, things which are, at least in part, their relatedness — we discover that the nature of just about everything in the universe, from the arms of the vastest galaxies to the smallest trickles of water, is to find a center they can spiral around.

It is, after all, not merely accidental that in the world from which Newton abstracted his laws, "external" and "compelling" forces always just happen to be there. Nor is it an accident that the very meaning of "external" has been blurred by modern physics, so that no particle can, even in principle, be isolated and defined apart from its interactions with every other particle in existence. And it is no accident that even those archetypically straight shafts of light we occasionally see streaming through the clouds — if only we can achieve their vantage point, their scale of action, their natural habitat — are found to be pursuing great and sinuous circles touching the rim of the known universe.

How easy it is to mistake the laws we tease out of things for an adequate declaration of their nature! And how easy it is to overlook the truth that what we abstract from a phenomenon may tell us very little about the nature of the phenomenon. An object moving in a circle, as the student of calculus learns, may be said to traverse an infinite set of infinitesimal straight lines — an assumption that wonderfully serves the purposes of calculation. But we had better not tell the dancer (who will in any case not believe us) that movement in a circle has the character of movement in straight lines.

Truth and Calculation

When we say (as Newton's severe abstraction has tempted us to say) that the nature of material objects "left to themselves" is to move in straight lines, we forget that, left to itself, the object is no longer there as that particular object. On the other hand, what we do find there, in all its insistence upon existing through relatedness, clearly prefers movement along curved paths. Only when actual phenomena have fallen from view, leaving us to contemplate the disincarnate and partial motions we have abstracted from them, can we accept the change of viewpoint hailed by philosopher Daniel Dennett:

Central to Newton's great perspective shift was the idea that ... rectilinear motion did not require explanation; only deviations from it did. (Dennett 1995, p. 364)

But if we're trying to understand the actual world rather than the detached logic of our equations, then surely any object in strict, rectilinear motion would require explanation, just as a leaf falling like a stone requires the explanation of our evacuated chamber. After all, strict, rectilinear motion in nature is all but impossible. Rather than saying it does not require explanation, Dennett should have said it does not require special calculation. In wholeheartedly accepting Newton's "great perspective shift", he has mistaken the abstracted, idealized quantities of scientific calculation for things themselves.

It is a great and useful feat to achieve the calculation and the implicit truths it points to. We really do recognize mathematical regularities in phenomena, and these regularities can be correlated with various forces. But it is wrong to think of forces as pure causes operating externally on, and thereby explaining and predicting, the behavior of passively receptive "things". We think this way only when we imagine forces in relation to matter much as we imagine equations in relation to graphs conceived as the paths of idealized point-masses. The graphs give us beautifully exact pictures of cause and effect, except for the minor problem that there is neither cause nor effect in the mathematics or the graph. And when we do consider real things, we can hardly believe that forces make them do what they do in any simplistic sense — if only because the forces are themselves being done by the things.2

Heavenly Order

The entire phenomenal universe is gloriously ordered and patterned. But we will scarcely grasp its order if we bring to it a mentality that says, "laws make things happen" — a mentality that imagines a law to govern events in the way an equation governs its graphical representation.

We can get a healthier grip upon the world's order by considering what we learn from our own possibilities of action. Meaningful activity, originating from ourselves, would not be possible in a universe lacking lawful order. How could we act coherently and meaningfully if there were no ordered relations between act and consequence — if we could say nothing predictable at all about the results of our actions?

But neither could we act meaningfully if there were an iron, spirit- crushing necessity in this order. The world supports us by offering a certain resistance to mere arbitrariness, but in doing so presents us with coherent possibilities for acting — that is, for creating new realities. These realities do not violate the lawful structure of their context, but neither are they determined by this structure. To fail to take either side of this truth seriously is to abandon the truth of our own existence.

By analogy: grammar imposes a certain order upon our speech. But even if I speak in perfect "obedience" to the rules of grammar, I do not thereby foreclose my possibilities for free expression. We cannot imagine meaningful speech without some grammatical ordering principles, but neither can we imagine meaningful speech if those ordering principles fully explain and predict what I will say. Very clearly they don't.

Historically, the serene and regular motions of the heavens have tutored us in the apprehension of lawful order. But it's a long way from the personal, contextual, fate-driven order of the Egyptians, Babylonians, and Greeks to the isolated Newtonian object whose supposed "nature" is to move in a straight line. As brilliant and necessary as the latter abstraction was, it all too easily invites us to lose sight of truths those earlier civilizations effortlessly apprehended.

Unexpected Discoveries

This loss of sight may help to account for some of the miscalculations of modern astronomers. Seduced by the timeless verities of their clean formulas of motion, they could not help projecting a certain timelessness upon the various bodies of the solar system. So they imagined these to have been pursuing their largely undisturbed motions for millions of years.

It came, then, as an unwelcome shock when one after another of our billion-year-old, "cold, inert, and dead" neighbors, from Venus to the moons of Jupiter, were revealed during the age of space exploration to have warm cores and to be geologically active. It requires powerful interactions to warm a planet, and apparently a lot more has been going on in relatively recent times throughout the vast, "desert"-reaches of space than we moderns ever dreamed of.

The second half of the twentieth century brought countless other surprises, ranging from the solar wind to the violently carved canyons of Mars, from the Van Allen radiation belt to the unforeseen break-up, in the year 2000, of Comet Linear. And, as astronomers now turn to the investigation of other solar systems, the jolts to expectation have already been extreme, with orbits turning up at baffling distances from suns, and with planets of the "wrong" size occupying those orbits.

All this points to a broad truth of science: when we extend our observational reach to embrace new phenomena, we typically find the phenomena quite unexpected, even though they may only rarely require revision of previously formulated laws. Those distant planets may have been found in districts of ill repute, but we can be quite sure that, in their gravitational and other relations, they remain respectable citizens of a lawful cosmos.

Someone reading this text in the future, perhaps the near future, will probably reply, "What do you mean, planets in the 'wrong' orbits? We now have a theory that perfectly accounts for those orbits". Yes, and this theory probably will not require any revision of fundamental laws. This illustrates my point, which is only that the new observations came initially as a surprise, and the laws now "predicting" them had to be orchestrated in such a way as to save the observations and achieve the prediction. That's the way an observation-based science is supposed to work: even assuming that the currently formulated laws need no revision, we are continually forced to fit them to unique phenomena — and the phenomenal surprises we encounter along the way show no sign of lessening with our growing knowledge of the various domains of scientific law.

Martian Puzzle

If anything has clinched our errant conviction that mathematically formulated laws "make" things happen, or at least explain why things happen, it is the astronomer's success in predicting eclipses with the aid of Newton's equations. In this we recognize one manifestation of that celestial order we depend upon to define the rhythms — the days, months, and seasons — that still regulate much of life on earth.

As I said above, without regularity our existence would be chaos. But we are not justified in interpreting such regularity as the unalloyed, mathematical necessity of events, as opposed to the necessity of a lawfulness implicit in those events. When we predict and verify an eclipse, we are not only acting as mathematicians; we are also acting as observers discovering what is actually happening, and we can never discount the possibility for new and unexpected observations. This is why, for example, there are serious preparations afoot within the scientific community for dealing with the possible approach of an earth-destroying asteroid.

But I fear this kind of possibility is too remote to underscore my point in any vivid way. Allow me to pick an item out of the current news for brief comment.

Until recently, scientists assumed that what we find on Mars today must be essentially the same (barring a crater or two here and there) as what we would have found a thousand, a hundred thousand, or even millions of years ago. The uniformitarian conviction that things don't change much — that we can safely project known processes forward and backward in time, rather as we extrapolate the graph of an equation — reigned in astronomy just as it did in many other scientific disciplines. Unfortunately, the history of space exploration has tended to explode this conviction on one front after another.

In the case of Mars, an article in the New Scientist (Chandler 2003) reviews a series of "profoundly mysterious landforms that have left geologists scratching their heads .... All point to amazingly fast processes taking place on the surface. Mars has changed considerably in the past few thousand years — in some places even the past two years. Yet nobody knows why. Unraveling the mystery will require a radical leap in theoretical thinking...."

At the planet's south pole the alternate layers of ice and dust are "vanishing before our eyes", with three meters or more being eroded each year between 1999 and 2001. At the current rate, one entire layer will disappear in twenty years, increasing the Martian atmosphere's thickness by one percent. "The magnitude of the changes implies an enormous amount of energy is being pumped into the ice to melt and vaporize it".

Clearly this process cannot be projected forward or backward for very long! Expressing "shock" at the data, one researcher notes that "all the visible ice, all the carbon dioxide that we see in this 'permanent' ice cap, could be eroded in less than a century".

Other recently discovered features are equally startling.

For example, huge fields of granular dunes preserve detailed features that show that they once marched across the landscape like sand dunes on Earth, blown by the wind. Yet these dunes are frozen in place, without a trace of motion over a two-year interval.

The only plausible explanation is, again, climate change. If the atmosphere was much thicker in the recent past, its winds may have been able to push along dunes that today's winds can no longer even ruffle.

And, again, the pattern of crater impacts on the floor of a 3.5 kilometer- deep canyon indicates that it is less than a million years old. "But if it is that young, [one researcher] asks, 'how did it get exposed from under three and a half kilometers of material'. So far, there is no answer".

Well, there are some proposed answers, and they include the previously unthinkable suggestion that Mars has participated in major celestial catastrophes within the span of recorded history. Nor is Mars our only companion in the solar system to provoke such speculation.3

Ancient Fears

I am not suggesting anything at all about the likely outcome of the current Martian investigations. I am merely using these to point out the obvious: if we encounter a certain uniformity in a particular field of phenomena for a given period of time, this is in part a discovery of observation, not something we could have predicted with any absolute certainty. As a doctrine, uniformitarianism is either the simple statement that we have found observational evidence for such-and-such limited uniformities over specific time spans, or else a silly declaration of universal faith. If lunar and solar eclipses have been wonderfully regular in recent historical times, we can be thankful for the stability, but we cannot know, on the basis of current evidences, that they were equally regular as recently as a few thousand years ago or that they will be regular over the next decade.

Actually, if we were to attend seriously to the fearful preoccupation of the ancients with the sky, we might raise serious questions in this regard. More and more astronomers are in fact asking such questions, and over the past several decades catastrophist thinking has progressively, if slowly and against great resistance, invaded the various astronomical disciplines.

It was, of course, easiest to accept the idea of a celestial "invader" when we could locate the event many millions of years ago, with dinosaurs as the victims. But once the irrational prejudice against heaven-sent disruptions was (at least partially) overcome, our earthly "closed system" came to seem increasingly vulnerable to outside influences. Astronomer Mark Bailey suggests that "human societies may have been witness to a somewhat more active celestial environment during past millennia". In fact, he sees evidence for "a once powerful extraterrestrial source with the capacity to cause both local and global destruction and trigger a common social response".4

Similarly, the astronomer, Bill Napier, reminds us that "modern astronomical evidence does not support the common supposition that the night sky has been unchanging for 5000 years". And another astronomer, Duncan Steel, refers to the "limitation" of previous work in archaeoastronomy, which was "the assumption that the phenomena seen in the sky by the ancients were the same as those which we now see". He goes on to state more explicitly that "the celestial phenomena which ancient man would have been most concerned with — objects which moved around the sky relative to the background of stars — may have been quite different to those observed now".

If, from the start, researchers had been as attuned to the possibilities of historical evidence as to the "causal" neatness of their lawful formulations, they might have addressed these issues much earlier. And they might even have asked whether they themselves, with their modern civilization and uniformitarian convictions, are the products of a period of uncommon celestial stability following upon more fearsome times. The ancients, with their insistence that civilization was a gift of the heavens, may not have been all that far from the mark. When we casually reject the ancient views wholesale as nothing but superstition, our much- too-easy and observationally untested judgment reflects only our own arrogance.

Knowledge of mathematically precise law becomes an illicit faith whenever it tempts us to forget how much fuller every phenomenon is than the lawfulness it respects, and how much we depend upon historical and observational evidence to know what actually happened.

I am not here arguing for or against recently unsettled heavens, and nothing in my discussion hinges on the outcome of the question. But I am saying that the question cannot be answered solely through an appeal to physical law and the predictability of phenomena — as far too many astronomers wanted to conclude a few decades ago. While the final answer must certainly cohere with physical law, the essential investigation will be the historical one. It is remarkable how long astronomers have managed to ignore this truth by letting their minds contemplate phenomena in the same way they are in the habit of contemplating the comforting and predictable clarity of quantitatively formulated law.

At Home in the Universe

One final note. The temptation to mistake our understanding of mathematical law for an adequate understanding of phenomena is born of our desire to find ourselves at home in a universe warmly receptive to our existence. Reassurance on this score, I'm convinced, is a primary function of mechanistic thinking. It may seem otherwise when someone like the astronomer Allan Sandage says,

What's it like out there? I don't know what it's like out there. It's cold, it's impersonal. It is the machine, if you like to put it that way, that has created you. (Quoted in Ferris undated.)

This hardly sounds like reassurance! But the matter appears very differently when you look beyond the barren content of such mechanistic thinking and consider its function. You can get a hint of the function by noting the evident smugness with which pronouncements like Sandage's are often spoken. The smugness reflects, among other, less savory things, the satisfaction of "getting it" — which is not in itself a bad sort of satisfaction to feel.

Perhaps nothing more poignantly expresses our need for belonging to the universe, or our conviction that we must belong, than our legitimate and deep-felt urge to comprehend things — to bring about a faithful "marriage of sense and thought" within the intimacy and universality of our own consciousness. In comprehending the objective world, we assimilate its existence to our own in a unity of truth, thereby proving our kinship with it. We shape our minds to things themselves, which is only possible because the things themselves are mind-shaped.

The problem with the mechanistic thinker is not that he is driven by this urge to find himself at home in the universe (which is at the same time to find a home for the universe within himself), but rather that he yields to a simplistic understanding of the material universe based on our limited human experience in building machines from pre-existing matter. Little thought is given to the differences between the predictable algorithmic lawfulness we try our best to impose upon our constructions, and the dark, unplumbed, material depths of reality from which they are constructed. The mirage of perfect, mechanical predictability, while it seems to make the world knowable, does so by projecting a single domain of (partly wishful) human experience upon the world. Another word for such projection is "superstition". It would be far better to discover what the world, in all its fullness, is prepared to reveal of itself.

We require neither superstition nor the reassuring predictabilities of mechanistic thinking in order to know ourselves at home in the universe. If we were willing to withhold our projections and open ourselves to the Eternal Surprise of the universe, its biggest surprise might be the knowledge that we truly do belong — and that our belonging doesn't depend on simplistic, machine-influenced thinking.


1. Here we see the central principle of the digital machine, which is to take all qualitative differences and, at one level, re-present them in terms of simple, binary differences. Either the basketball goes through the hoop or it doesn't. Did it or didn't it? Yes or no? One or zero?

2. I will have much more to say about this in a subsequent article.

3. For some highly unconventional views by a plasma physicist, see

4. The quotations from Bailey and the following quotations from Napier and Steel are among many gathered by Marinus Anthony van der Sluijs at a web site entitled "Myth and Celestial Catastrophe": Apart from the convenience of the collected quotations, however, there is not much I can recommend about this web site.


Chandler, David L. (2003). "All Eyes on Mars", New Scientist 179, no. 2409 (Aug. 23), p. 40.

Dennett, Daniel C. (1995). Darwin's Dangerous Idea: Evolution and the Meanings of Life. New York: Simon & Schuster.

Ferris, Timothy (undated). "The Creation of the Universe", a PBS television special.

Steve Talbott :: The Limits of Predictability

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