Chance & Necessity: Another Look

In everyday experience, we think of chance as what governs gambling, barring schemes to harness probability in their favor. Necessity, on the other hand, brings to mind the air we breathe, food and/or water. Previously, we discussed Jacques Monod as an early explorer of the collision of probability and chance in biology. In Laws of the Game: How the Principles of Nature Govern Chance (German: Das Spiel: Naturgesetze steuern den Zufall), Manfred Eigen & Ruthild Winkler critique Jacques Monod, stating that his innovation was that the substrate of all biology is chance and accident. You may note that the subtitle of Laws of the Game states the opposite.

This gets even more subtle if you consider Johan Huizinga’s Homo Ludens: A Study of the Play Element in Culture. He emphasizes the role of playful behavior as the university that educates us in the connection between chance and necessity.

Foreword

The lay reader interested in the natural sciences is exposed to a constantly rising flood of information. He may often feel himself cast in the role of a judge before whom different authors appear like competing litigants, each of whom hopes to be found in the right. If these authors are sufficiently clever in presenting their cases, the reader may be swayed by each in turn. But then a reviewer appears on the scene and objects that each cannot be as right as the other, particularly when one author’s claims are the exact opposite of another’s. The reader has no choice but to find the reviewer right, too.

This familiar anecdote, which we have slightly adapted to suit our purposes, contains a moral: Everyone could in fact be right if each one did not insist on being the only one to be right.

Everything that happens in our world resembles a vast game in which nothing is determined in advance but the rules, and only the rules are open to objective understanding. The game itself is not identical with either its rules or with the sequence of chance happenings that determine the course of play. It is neither the one nor the other because it is both at once. It has as many aspects as we project onto it in the form of questions.

We see this game as a natural phenomenon that, in its dichotomy of chance and necessity, underlies all events. Our interpretation of games and play thus goes far beyond Huizinga’s, which considers play only in its relation to human behavior. In applying the concept of play to art, we come much closer to Adorno’s views, which clearly disagree with Huizinga‘s identification of play and art.

The considerations that gave rise to this book go back to the molecular theory of evolution worked out a few years ago. It also draws on the models developed in connection with that theory, models for simulating phenomena like equilibrium, selection, and growth, all of which are based on natural laws. Although this book makes frequent use of examples drawn from the field of biology, its scope is much broader and includes general scientific, philosophical, sociological, and aesthetic perspectives. Our main purpose is to show play in its symbolic nature and in all its metamorphoses. We also make use of its different aspects to illuminate both our scientific understanding of the world and various philosophical positions. We are aware that this brings us into conflict with those who attribute validity to one and only one aspect.

The actual writing of the book was preceded by innumerable talks and discussions with friends and colleagues during our Engadin winter seminars, on hikes and ski tours in the mountains, and, occasionally, over a bottle of wine. We first thought a dialogue would be the appropriate form for our exchange of ideas, but we soon abandoned this concept. The classical dialogues are without exception artificially constructed. Simplicio and Salviati, for example, are both mouthpieces for Galileo. We finally decided that we would both take turns going over all the material point by point. We have, of course, ventured into areas in which we are only dilettantes. We hope the reader will forgive us this in the light of our efforts to uncover parallels and so to emphasize the unity of nature and mind.

We do not want to go any further into the substance of the book here than is necessary to make clear why we chose the title we did. Similarly, the introductions to the individual chapters are meant to lead the reader into the material treated, not to summarize it.

Chance and law (or principles) are the basic elements of games. The subtitle of the book suggests the interaction between them. And here we should add that it is the consequences of chance that are subject to regulation. Only if there is a large number of individual events does the element of chance come under the control of statistical law. This law is at work, for instance, when chance fluctuations undergo self-regulation in equilibrium or when they are amplified in the evolutionary process. The origin of the genetic code, the development of languages by which we transmit our thoughts, the intellectual play of artistic imagination are all based on the same fundamental principles of evolution, even though the results of individual games are determined by the caprice and variability of chance.

The manifestations of the game that matter plays in time and space and the effects this game has on human beings are the themes of the central chapters in the book. Much as we may agree with Jacques Monod in his view of molecular biology, we differ from him greatly in the conclusions he draws from it for mankind and society. We see Monod’s demand for an “existential attitude toward life and society” as an animistic inflation of the role of “chance.” Such a demand neglects the complementary role played by natural law. Criticism of the dialectical overemphasis on “necessity”—a criticism we find fully justified—should not move us to deny completely its obvious infiuence.

We are in complete agreement with Monod’s statement that ethics and knowledge cannot be divorced from each other. For us, however, this view does not condemn the great religions but rather sets them a new task. As we have occasion to point out in the present work, the natural sciences yield no proof of God’s existence, but neither do they claim that men “can do without faith in God.”

The unity of nature is expressed more in the laws governing the relationships between structures than in the structures themselves. Taking this “motto” as a point of departure for Part IV, we examine a number of problems that have recently come more and more under the purview of the natural sciences and that are still far from being solved. In these considerations, we are mainly concerned with the mechanisms of cognizance. In terms of the elementary processes involved, these mechanisms always amount to a falsification in Karl Popper’s sense. Still, we cannot fully accept the views of this great epistemological logician, particularly when he claims: “There is no induction.” Good enough! But there are different mechanisms of falsification that vary in their degree of inductive adaptation.

One of our main concerns in this book lies at the heart of Part III. There we raise the still unsolved question of the hubris of human knowledge. Friedrich Dürrenmatt’s categorical imperative “What concerns all can only be worked out by all” is as relevant for the physicist whose knowledge can unleash the forces of nature as it is for the biologist who is now in a position to manipulate genetic material and influence psychic behavior with drugs. And our appeal here is also directed at the economist and the politician, who have the task of creating, maintaining, and protecting the conditions necessary for a worthwhile human existence.

Pessimistic predictions based on simple extrapolation are widespread today. We will not be able to solve the problem of limited resources by frugality alone. A raw material that will be used up in about fifty years at present rates of consumption might last a hundred years if we cut down on its use. (Such a reduction might, of course, threaten the stability of our economy.) In other words, the catastrophe could be delayed for another fifty years. Would it not be more sensible to concentrate on ensuring unlimited resources, perhaps by reusing our raw materials in a recycling economy and by developing sufficiently productive sources of energy? However we solve this problem, the practicability of our solution will depend on stopping population growth, perhaps even on reducing the world’s population.

We must be clear about one thing: The human being is not a fluke of nature, nor does nature automatically guarantee his survival. The human being is one player in a huge game, the outcome of which is, for him, uncertain. He has to make full use of his capabilities to hold his own as a player and not become a plaything of chance.

Manfred Eigen / Ruthild Winkler-Oswatitsch
Göttingen, September 1975

ONE

The Taming of Chance

Research in physics has shown beyond the shadow of a doubt that in the overwhelming majority of phenomena whose regularity and invariability have led to the formulation of the postulate of causality, the common element underlying the consistency observed is chance.

Erwin Schrödinger, “What Is a Natural Law?” (Inaugural Address delivered at the University of Zurich, December 1922)

1

The Origin of Play

Play is a natural phenomenon that has guided the course of the world from its beginnings. It is evident in the shaping of matter, in the organization of matter into living structures, and in the social behavior of human beings.

The history of play goes back to the beginnings of time. The energy released in the “big bang” set everything in motion, set matter whirling in a maelstrom of activity that would never cease. The forces of order sought to bring this process under control, to tame chance. The result was not the rigid order of a crystal but the order of life. From the outset, chance has been the essential counterpart of the ordering forces.

Chance and rules are the elements that underlie games and play. Play began among the elementary particles, atoms, and molecules, and now our brain cells carry it on. Human beings did not invent play, but it is “play and only play that makes man complete.”1

All our capabilities arise from play. First, there is the play of limbs and muscles. The aimless grasping and kicking of an infant develop into carefully coordinated movements. Then there is the play of our senses. Playful curiosity sends us in search of profound knowledge. From play with colors, shapes, and sounds emerge immortal works of art. The first expressions of love take the form of play: the secret exchange of glances, dancing, the interplay of thoughts and emotions, the yielding of partners to each other. In Sanskrit, the union of lovers is called kridaratnam, “the jewel of games.”2

Every game has its rules that set it apart from the surrounding world of reality and establish its own standards of value. Anyone who wants to “play” has to follow those rules. In parlor games, rules established before the game begins determine the course the game will take and define the scale of values by which it is played. But the effects of a chance occurrence can change the constellation of the game and set it running in a totally new direction. This is how life initiated its first games, and this is how our thoughts and ideas continue to play those games.

From the terrifying realm of elemental forces and the holy realm of laws arises the aesthetic impulse, which creates a third, carefree realm. This is the realm of play and appearance. In it, man is freed from the bonds of all circumstance and liberated from compulsion, moral as well as physical.1

It is our intention in this book to trace the interplay of chance and law that has come down to us from the farthest reaches of time and found its most perfect expression in the inexhaustible creativity of our ideas. We hope to translate Hermann Hesse’s symbol of the glass bead game back into reality. Hesse described this game as one that incorporated all the values of our culture.

All the insights, noble thoughts, and works of art that the human race has produced in its creative eras, all that subsequent periods of scholarly study have reduced to concepts and converted into intellectual property—on all this immense body of intellectual values the Glass Bead Game player plays like the organist on an organ. And this organ has attained an almost unimaginable perfection; its manuals and pedals range over the entire intellectual cosmos; its stops are almost beyond number. Theoretically this instrument is capable of reproducing in the Game the entire intellectual content of the universe.3

There is something mysterious about glass beads. The reflection and refraction of light make them glow, and as we explore the idea of play in this book, Hesse’s glass beads will take on a new life. Part of their symbolic significance derives from the fact that they can exemplify the constant transformations and metamorphoses we observe all around us: atoms evolve into crystals, molecules into genes, living cells into cognitive beings, letters into words, notes into harmonies. The course the bead game takes is determined by the roll of the dice, yet at the same time it is also influenced by the rules of the game, just as chance in nature is subject to the laws of physics. The dice and the rules of the game these are our symbols for chance and natural law.

List of References

  1. Schiller, Friedrich von, “Über die ästhetische Erziehung des Menschen (On the Aesthetic Education of Mankind),” in a series of letters from the years 1793-94, printed in his Philosophical and Critical Writings (many eds.).
  2. Huizinga, Johan, Homo Ludens: A Study of the Play Element in Culture. Boston: Beacon Press, 1955.
  3. Hesse, Hermann, The Glass Bead Game: Magister Ludi. New York: Holt, Rinehart & Winston, 1969.
Manfred Eigen & Ruthild Winkler. Laws of the Game: How the Principles of Nature Govern Chance. Translated by Rita & Robert Kimber, Princeton University Press, 1993, pp. xi-5.

Theodor Adorno, a Marxist theoretician, believed the filter before any interpretation of the world was ever-present advertising and, by extension, capitalism. While Adorno thinks of capitalism as destiny, Yeats came to realize that “accident is destiny” (as we previously discussed). Amid these infinitely debatable opinions, the world is often a perplexity machine that may not be described by a single view.

Existence and the Problem of Separability

In contracts and legal documents, there is a concept of “separability” which means that clause A is connected to clause B in a way that cannot be undone.

The great twentieth century French philosopher, Gabriel Marcel, has a profound non-separability analysis of existence itself. Marcel wrote:

…We cannot really separate:—

  1. Existence
  2. Consciousness of self as existing
  3. Consciousness of self as bound to a body, as incarnate.
Gabriel Marcel, Being and Having: An Existentialist Diary, Harper Torchbooks, 1965, page 10.

This leads to saying things that are very deep aspects of existential thinking governed by the points above. For example, Marcel wrote, “As I have said elsewhere, the moment I treat my body as an object of scientific knowledge, I banish myself to infinity.” Consider the end of the previous phrase. The very notion that someone, within themselves could go down a route to “banish themselves” in this way, shows you a door into very deep psychological problems. In other words, Marcel is telling you that some psychological problems could have a philosophical or existential root cause and are a type of blunder.

This is not to say that one should avoid scientific thought. Taking a drop of your blood and viewing it under a microscope is not a blunder. However, if you take this to the extreme of trying to analyze everything scientifically, to the exclusion of philosophy in daily life, this is Marcel’s warning.

Marcel’s context for this thinking is given here:

Notes for a Paper to the Philosophical Society

Undated, written in 1927 or 19281

When I affirm that something exists, I always mean that I consider this something as connected with my body, as able to be put in contact with it, however indirect this contact may be. But note must be taken that the priority I thus ascribe to my body depends on the fact that my body is given to me in a way that is not exclusively objective, i.e. on the fact that it is my body. This character, at once mysterious and intimate, of the bond between me and my body (I purposely avoid the word relation) does in fact colour all existential judgments.


What it comes to is this. We cannot really separate:—

  1. Existence
  2. Consciousness of self as existing
  3. Consciousness of self as bound to a body, as incarnate.

From this several important conclusions would seem to follow:

  1. In the first place, the existential point of view about reality cannot, it seems, be other than that of an incarnate personality. In so far as we can imagine a pure understanding, there is, for such an understanding, no possibility of considering things as existent or non-existent.
  2. On the one hand, the problem of the existence of the external world is now changed and perhaps even loses its meaning; I cannot in fact without contradiction think of my body as non-existent, since it is in connection with it (in so far as it is my body) that every existing thing is defined and placed. On the other hand, we ought to ask whether there are valid reasons for giving my body a privileged metaphysical status in comparison with other things.
  3. If this is so, it is permissible to ask whether the union of the soul and body is, in essence, really different from the union between the soul and other existing things. In other words, does not a certain experience of the self, as tied up with the universe, underlie all affirmation of existence?
  4. Inquire whether such an interpretation of the existential leads towards subjectivism.
  5. Shew how idealism tends inevitably to eliminate all existential considerations in view of the fundamental unintelligibility of existence. Idealism versus metaphysics. Values detached from existence: too real to exist.

Existential and personalist interests closely linked. The problem of the immortality of the soul is the pivot of metaphysic.

Every existent is thought of like an obstacle by which we take our bearings—like something we could collide with in certain circumstances—resistent, impenetrable. We think of this impenetrability, no doubt, but we think of it as not completely thinkable.2 Just as my body is thought of in so far as it is a body, but my thought collides with the fact that it is my body.

To say that something exists is not only to say that it belongs to the same system as my body (that it is bound to it by certain connections which reason can define), it is also to say that it is in some way united to me as my body is.

Incarnation—the central ‘given’ of metaphysic. Incarnation is the situation of a being who appears to himself to be, as it were, bound to a body. This ‘given’ is opaque to itself: opposition to the cogito. Of this body, I can neither say that it is I, nor that it is not I, nor that it is for me (object). The opposition of subject and object is found to be transcended from the start. Inversely, if I start from the opposition, treating it as fundamental, I shall find no trick of logical sleight of hand which lets me get back to the original experience, which will inevitably be either eluded or (which comes to the same thing) refused. We are not to object that this experience shews a contingent character: in point of fact, all metaphysical enquiry requires a starting-point of this kind. It can only start from a situation which is mirrored but cannot be understood.

Inquire if incarnation is a fact; it does not seem so to me, it is the ‘given’ starting from which a fact is possible (which is not true of the cogito).

A fundamental predicament which cannot be in a strict sense mastered or analysed. It is exactly this impossibility which is being stated when I declare, confusedly, that I am my body; i.e. I cannot quite treat myself as a term distinct from my body, a term which would be in a definable connection with it. As I have said else-where, the moment I treat my body as an object of scientific know-ledge, I banish myself to infinity.

This is the reason why I cannot think of my death, but only of the standstill of that machine (illam, not banc). It would perhaps be more accurate to say that I cannot anticipate my death, that is, I cannot ask myself what will become of me when the machine is no longer working.3

[1] This paper was never delivered.

[2] It is thought of, but it is never resolved. The opacity of the world is in a certain sense insoluble. The link between opacity and Meinbeit. My idea is opaque to me personally in so far as it is mine. We think of it as an adherence. (Note written Feb. 24th, 1929.)

[3] ‘To be involved.’ (idée d’un engagement) Try to shew in what sense this implies the impossibility (or absolute non-validity of my representing my death. In trying to think of my death I break the rules of the game. But it is radically illegitimate to convert this impossibility into a dogmatic negation. (Note written Feb. 24th, 1929.)

It is evident that this whole train of thought is at the root of le Gouvernail: the first notes on the theme of le Gouvernail were composed a few days after these. (Note written April 13th, 1934.)

Gabriel Marcel, Being and Having: An Existentialist Diary, pages 10-12

The reader should not be afraid of converting this level of discussion to everyday life and everyday slang. For example, when Marcel uses phrases like, “I banish myself to infinity” that should resonate with phrases like “flipping out.”

Take this example from Kierkegaard. There’s a book-seller in Copenhagen and he greets a customer who has just entered his shop. The book-seller turns to his wife and says, “It is I who am speaking, isn’t it?” Kierkegaard’s book-seller seems to have “banished himself” and cannot return.

Heidegger vs. Marx as World Watchers

Marx (1818-1883) implies that the foundation of human reality is econo-technical, and on that basis society creates thoughts and philosophies, art and poems. This explanation seems appealing when we think of the economic development of China in our time, for example, or the rise of computers and software.

In a way, Heidegger (1889-1976) turns this upside down. At the basis of world history is society producing culture. You can make a simple “cartoon” and say that for Marx, economics shapes everything, and for Heidegger culture replaces economics.

For example, in his book, What Is Called Thinking? (English translation, 1968, Harper & Row), Heidegger argues the foundation of all Western thinking and culture comes from axioms such as logos [Ancient Greek: λόγος] (from which we have logic, cosmology, psychology, epistemology, etc.), as well as legein (the Greek verb λέγειν, “to speak”).

Heidegger states (on page 204), “Without the λέγειν of that logic, modern man would have to make do without his automobile. There would be no airplanes, no turbines, no Atomic Energy Commission.”

Our MI comment on this is that any monocausal explanation of how mankind went from Neanderthal to the Manhattan skyline is completely inadequate. You must create a “double-helix” of Marx and Heidegger, adding the dimensions of surprise and unintended consequences. Without the physics concepts of emergence and complexity, we have no possibility of understanding how we got to now. In the site tagline, we use the word “composite” as a reference to this kind of deeper understanding.

Education and Word and Number Hidden Vagueness

These mini-essays help students of any age to re-understand education in a deeper and more connected way.

They look for “circum-spective” intelligence. (Not in the sense of prudential or cautious but in the sense of “around-looking.”)

One of the things to begin to see is that explaining things in schools is misleading “ab initio” (i.e., from the beginning).

Let’s do an example:

In basic algebra, you’re asked: what happens to (x2 – 1)/(x – 1) as x “goes to” (i.e., becomes) 1.

If you look at the numerator (thing on top), x2 is also 1 (since 1 times 1 is 1) and (1 – 1) is zero. The denominator is also (1 – 1) and zero.

Thus you get 0 divided by 0.

You’re then told that’s a no-no and that’s because zeros and infinities lead to all kinds of arithmetic “bad behavior” or singularities.

You’re then supposed to see that x2 – 1 can be re-written as (x – 1)(x + 1) and since “like cancels like,” you cancel the x – 1 is the numerator and denominator and “get rid” of it.

This leaves simply x + 1. So, as x goes to 1, x + 1 goes to 2 and you have a “legitimate” answer and have bypassed the impasse of 0 acting badly (i.e., zero divided by zero).

If you re-understand all this more slowly you’ll see that there are endless potential confusions:

For example: you cannot say that (x2 – 1)/(x – 1) = x + 1 since looking at the two sides of the equal sign shows different expressions which are not equal.

They’re also not really equivalent.

You could say that coming up with x + 1 is a workaround or a “reduced form” or a “downstream rewrite” of (x2 – 1)/(x – 1).

This reminds us of the endless confusions in high school science: if you combine hydrogen gas (H2) with oxygen gas (O2) you don’t get water (H2O). Water is the result of a chemical reaction giving you a compound.

A mixture is not a compound. Chemistry is based on this distinction.

Math and science for that matter, are based on taking a formula or expression (like the one we saw above) and “de-cluttering” it or “shaking loose” a variant form which is not identical and not the same but functionally equivalent in a restricted way.

A lot of students who fail to follow high school or college science sense these and other “language and number” problems of hidden vagueness.
School courses punish students who “muse” to themselves about hidden vagueness. This behavior is pre-defined as “bad woolgathering” but we turn this upside down and claim it is potentially “good woolgathering” and might lead to enchantment which then underlies progress in getting past one’s fear of something like math or science or anything else.

One is surrounded by this layer of reality on all sides, what Wittgenstein calls “philosophy problems which are really language games.”

Think of daily life: you say to someone: “you can count one me.” You mean trust, rely on, depend on, where count on is a “set phrase.” (The origin of the phrase and how it became a set phrase is probably unknowable and lost in the mists of time.)

“You can count on me” does not mean you can stand on me and then count something…one, two, three.

In other words in all kinds of language (English, say, or math as a language) one is constantly “skating over” such logic-and-nuance-and-meaning issues.

The genius Kurt Gödel (Einstein’s walk around buddy at Princeton) saw this in a deep way and said that it’s deeply surprising that languages work at all (spoken, written or mathematical) since the bilateral sharing of these ambiguities would seem deadly to any clarity at all and communication itself would seem a rather unlikely outcome.

You could also say that drama giants of the twentieth century like Pinter, Ionesco and Beckett, intuit these difficulties which then underlie their plays.

All of this together gives you a more “composite” “circum-spective” view of what is really happening in knowledge acquisition.

Education and the “Knowability” Problem

There was a wonderful PBS Nature episode in 2006 called “The Queen of Trees” [full video, YouTube] which went into details about the survival strategy and rhythms and interactions with the environment of one tree in Africa and all the complexities this involves:

This Nature episode explores the evolution of a fig tree in Africa and its only pollinator, the fig wasp. This film takes us through a journey of intertwining relationships. It shows how the fig (queen) tree is life sustaining for an entire range of species, from plants, to insects, to other animals and even mammals. These other species are in turn life-sustaining to the fig tree itself. It could not survive without the interaction of all these different creatures and the various functions they perform. This is one of the single greatest documented (on video) examples of the wonders of our natural world; the intricacies involved for survival and ensuring the perpetual existence of species.

It shows us how fragile the balance is between survival and extinction.

One can begin to see that the tree/animal/bacteria/season/roots/climate interaction is highly complex and not quite fully understood to this day.

The fact that one tree yields new information every time we probe into it gives you a “meta” (i.e., meta-intelligent) clue that final theories of the cosmos and fully unified theories of physics will be elusive at best and unreachable at worst. If one can hardly pin down the workings of a single tree, does it sound plausible that “everything that is” from the electron to galaxy clusters to multiverses will be captured by an equation? The objective answer has to be: not particularly.

Think of the quest of the great unifiers like the great philosopher–physicist Hermann Weyl (died in 1955, like Einstein):

Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature–a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars. This work spurred the purely mathematical development of differential geometry.

Hermann Klaus Hugo Weyl (9 November, 1885 – 8 December, 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.

His research has had major significance for theoretical physics as well as purely mathematical disciplines including number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.

Weyl published technical and some general works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. While no mathematician of his generation aspired to the “universalism” of Henri Poincaré or Hilbert, Weyl came as close as anyone.

Weyl is quoted as saying:

“I am bold enough to believe that the whole of physical phenomena may be derived from one single universal world-law of the greatest mathematical simplicity.”

(The Trouble with Physics, Lee Smolin, Houghton Mifflin Co., 2006, page 46)

This reminds one of Stephen Hawking’s credo that he repeated often and without wavering, that the rational human mind would soon understand “the mind of God.”

This Weyl–Hawking–Einstein program of “knowing the mind of God” via a world-equation seems both extremely charming and beautiful, as a human quest, but potentially mono-maniacal à la Captain Ahab in Moby-Dick. The reason that only Ishmael survives the sinking of the ship, the Pequod, is that he has become non-monomaniacal and accepts the variegatedness of the world and thus achieves a more moderate view of human existence and its limits. “The Whiteness of the Whale” chapter in the novel gives you Melville’s sense (from 1851) of the unknowability of some final world-reality or world-theory or world-equation.