The Quantum Nietszche

©Copyright 1998 William G. Plank. All rights reserved

Part I Part II Part III Part IV


1. The Glass Bead Games of Manfred Eigen

Everything that happens in the 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 many aspects as we project onto it in the form of questions.

Eigen, 1981

Eigen and Winkler's glass bead games interest us greatly because they demonstrate the workings of the recombination of particles (energy centers, unities, etc) in the clearest, starkest way, moraline free and free from judgment and from metaphysics; yet the patterns of chance and necessity they demonstrate may be applied to physics and chemistry, biology and sociology. We shall later investigate how and if they relate to the moral and the aesthetic.

In order to understand these game models, we must understand how they are set up. (The most rewarding way for you to do this would be to read Eigen and Winkler's book.) They are played on square boards with rows of squares which may be chosen randomly by casting dice. For example, a board which contains sixteen squares has four rows of four squares. By casting two tetrahedral (pyramidal) dice, one of which has numbered facets to identify the horizontal row and the other having numbered facets to identify the vertical row, it is possible to choose at random one of the sixteen squares.

If you play on a board with eight rows of eight squares (64 squares) then you will have to have two octahedral dice, one to identify the vertical row of eight squares, and one to identify the horizontal row of eight squares, each facet of which is appropriately numbered to identify either the vertical or horizontal square. If you are playing a game with four colors of beads in order, for example, to observe the variation in numbers of different colors of beads and their differential equilibrium and patterns, you may on occasion have to cast a third tetrahedral die with each facet marked for one of the four colors of beads you want to choose.

You would have great difficulty finding the right kind of dice if you played on a board with a thousand or a million rows of squares and a lifetime would not be long enough to play the game; but some clever fellow could program a computer to identify rapidly and randomly the squares and to tabulate the patterns and populations of the beads. (Nature plays on yet a much larger board, with squares for galaxies and supernovae, but She has all the time in the world, a sleepless eye and a tireless hand at the cast, and as we shall see She makes up the rules as well.) The advantage of such a large playing board is that the statistical deviation from equilibrium or distribution of relative colors of beads would be so small that you could more adequately demonstrate the existence of the patterns and populations of beads (entities, particles, molecules, organisms) as they varied according to the parameters (rules) of the enviroment, and that you could find some comforting and possibly non-metaphysical demonstration of order apparently lodged in the generous bosom of Chance.

Eigen points out (p. 34, ff) that if two dogs share one flea, the percentage of difference in the population of fleas on the two dogs will always be very large, one having all the fleas, the other having none. We can see, however, that if the two dogs share a hundred fleas, there is more likely to be an equilibrium of fleas on the two. The greater the number of fleas, a million for example, the smaller the percentage deviation in the number of fleas on the two. This dog-flea story demonstrates how the law of large numbers works; we must remember that nature plays with gigantic numbers. The law of large numbers makes chance look orderly. "Those iron hands of necessity which shake the dice-box of chance play their game for an infinite length of timeso that there have to be throws which exactly resemble purposiveness and rationality of every degree" and perhaps "we ourselves [who] shake the dice-box with iron hands, ...we ourselves in our most intentional actions do no more than play the game of necessity" (D II 130).

The very number of beads (organisms, molecules, etc.) creates an environment which affects the number of beads (organisms, molecules). The number of beads affects the number of beads. Thus we have the possibility of a self-regulating, autocatalytic population, which may derive the rules for its existence from the nature of its own existence. Nietzsche’s vocabulary fits in precisely"Laws are absolutely lacking...every power draws its ultimate consequences at every moment" (BGE 22). This population may achieve stability in equilibrium, but the "world is not striving toward a stable condition...not a condition of equilibrium" (WP 639). We also have the possibility of a non-selfregulating system which may end in catastrophe for the system. Systems which create their own catastrophes do not survive to replicate themselves. For Nietzsche, Christianity as the institutionalization of sickenss, pity and weakness would be one of these catastrophic systems"If the world had a goal, it must have been reached" (WP 1062). But, "there is no final state" (WP 1064).

The appearance and disappearance (birth and death) of individuals in a population (of organisms, beads, etc.) take place according to three strategies, the conforming strategy, the contrary strategy and the indifferent strategy (v. Eigen, p. 26). These strategies appear as internal controlling mechanisms which arise as a result of the requirements and restrictions of the environment (the rules of the game) and have varying stabilizing or destabilizing effects.

(1) The indifferent strategy If the rate of appearance and disappearance (birth and death rate) is not influenced by the size of the population, we refer to this mechanism as the indifferent strategy. (2) The conforming strategy If the death and/or birth rate of a population (of beads, organisms, molecules, etc.) increases with the increase in size of the population, this mechanism is said to be a conforming strategy. Likewise, if the birth and/or death rate decreases with the decrease in size of the population the behavior is called a conforming strategy. (3) The contrary strategy If the change in the size of a population causes the inverse in the birth/death rate, e.g., if the birth rate drops as the population increases, this is said to be a contrary strategy. These three strategies are produced by the nature of the environment which provides the parameters of the chance recombination of particles. Eigen and Winkler show how these strategies come about as they vary the environments, i.e., as they vary the "rules of the game," rules which they take to be the manifestation of the unity of nature, a unity which is evident more in the relations between unities and structures, rather than in the unities and structures themselves. We will have occasion to refer to these strategies later when we discuss the Will to Power because they are the mechanisms which contribute to the success or failure of a system without the necessity of talking about morality, justice, decision, consciousness, intention, and which alter even the idea of cause and effect. In order to make these ideas more clear, let us look at five or six of the glass bead games in more detail.

a. The bead game "Random Walk"

Two players, one with 16 black beads, the other with 16 white ones, play on a square board with 16 unnumbered squares. Each player puts 8 beads on his half of the board so that the board is covered. By tossing a coin, they determine whether a white bead with be replaced with a black bead or vice versa. If two angels played this game for eternity it could get pretty boring, but we would see that, as an example of the indifferent strategy, all possible combinations of the white and black beads would randomly and eternally recur with the same probability a configuration where all the beads on the board were white, all the beads on the board were black, half were black and half were white, etc., would all recur with the same probability as 15 black beads and one white bead.

By introducing one rule into the game, one can change the outcome drastically the "cooperative" rule states that one player may remove an opponent's bead if he has surrounded it with his own. Thus, when the configuration happens that all the beads on the board are black, it becomes impossible to introduce a white one without losing it immediately--and the game is over. There is another curious idea Eigen introduces, that of "memory," i.e., a curious definition of memory.

If all the beads on the board are white, this all white and a nearly all white configuration will persist for some time, since 50% of the time the coin will choose a white bead and reinforce the whiteness of the board. Thus the more white beads there are on the board, the more slowly will the black beads replace them. We can see that the rate of replacement of the white beads appears to depend on the number of the white beads. Nevetheless, any other configuration of white and black beads will persist with the same probability. Eigen calls this persistance "memory." All possible patterns will "drift" with the same probability until the game is ended.

b. Bead game "equilibrium"

Although any square board may be used with the appropriate dice for this game, let us use octahedral dice and, consequently, a board with 64 squares. Each player must have 64 beads, 32 of which he puts randomly on the board, so that the board is full at the begining of the game. The dice are rolled and a white bead replaces a black bead, or vice versa, on the square chosen. If we decide to end the game arbitrarily after having rolled the dice a great number of times and if we keep score of the average number of black beads as compared to white beads at the time of each roll, we will find that tabulating the score at the end of the game we will always have an approximately even number of white beads and black beads--that is, an equilibrium of the colors is the rule. As in the "Random Walk," all possible distributions of the beads will occur with the same frequency but we will always have an approximately even distribution of the colors of beads. The larger the board and the greater the number of beads, the smaller is the percentage of deviation from equilibrium.

Considering that nature plays with very large numbers--there are, for example, 1022 water molecules in a cubic centimeter of water (v. Eigen, p. 38), we would not have measuring devices sensitive enough to measure the standard deviation from equilibrium in such a number. We should not be surprised then to realize that what we may call a species of organism, a bird for example, may not be absolutely identifiable, that a species is in fact a consensus or at some point a perceptual illusion, that is, an illusion which is related to the nature of our perceptual apparatus. We will later discuss the nature of the perceptual apparatus and its perceptions when we deal with quantum mechanics.

If we play this game with four players and four colors of beads, with an extra tetrahedral die in order to choose the color of the bead to be replaced, the tendency to equilibrium of the four is still preserved. However, if we begin to mess around with the environment of these beads (organisms, energy centers) by introducing a "cooperative" rule (e.g., you may replace a bead on the board only if four beads of a different color are next to it), you interere with the equilibrium (will to equilibrium?) to such a point that one of the colors may end up replacing all the other colors on the board.

c. Glass bead game "Once and for all," or catastrophe

This is also what Eigen calls a "cooperative" game, i.e., extra rules (environmental parameters) have been added to keep the game from ending up in eternally repeated statistical equilibrium. Rolling two octahedral dice in order to choose one of 64 positions on the board, one does not merely replace the bead selected with one of the opposing color. If chance identifies a white bead, one removes a black bead and adds yet another white bead. The play speeds up. The more white beads there are, the greater the chance of selecting a white bead, until a point of no return is reached. There arrives a point at which there is no more system of black-white because there are only white beads. We commonly refer to such a model when we say, "The rich get richer and the poor get poorer."

d. The glass bead game "Selection"

The games described so far show how, according to the rules imposed by the environment, equilibrium is maintained or catastrophe results. But such conditions (i.e., equilibrium or catastrophe) do not explain how one can get a functional order out of a complex system. If molecular or biological evolution had had only such models to work with, viable species would have had much less probability of appearance, i.e., on the one hand such stability retards change and on the other, the results of catastrophe are obvious. The game Eigen and Winkler call "Selection" shows us a model that deals "productively" with instability. Instability "forces a clear selection from available aternatives and prevents the return to an already tested state" (Eigen, p. 51). In this context, and to remind the reader that this is supposed to be a book about Nietzsche, we should recall that Nietzsche rejected the idea of substance. We must conclude that he did so because he considered the idea of substance to be of such an absolute nature that it would have precluded the functioning of the Will to Power. Substance as a substratum is of such an absolute reality that it would have supported a rigid metaphysic. The Will to Power incorporates instability. The concept of substance would increase stability and arrest the flux. Nietzsche's view of Christianity in the terms we are using here would be that of a model which preserved the stability of non-evolutionary patterns, i.e., of the weakest, arrested the creativity of the Will to Power and created an organism which was, in Nietzsche's terms, "sick." Christianity arrests moral and spiritual evolution by making decadent selections, and contributes thus to the survival of the least fit. Christian perfectibility is based on stasis and conservative strategies which make the Will to Power and its concomitant concept, the Eternal Recurrence, unthinkable. We must understand the Eternal Recurrence in terms of the Will to Power if the Eternal Recurrence is to make sense. The perfectability and stability of Newton's mechanics likewise reflect the static Christian view of a universe divinely constructed.

In the bead game, Selection, two octahedral dice are used to identify one of the 64 positions on a square board. Equal numbers of red, blue, green and yellow beads are placed randomly on the board; there are enough beads of each color to fill the entire board. There are two rules which are applied in alternationFirst, the bead selected by the first throw of the dice is removed; a second roll of the dice selects a bead which is then doubled by placing a bead of the same color in the space that was vacated by the first roll. The game ends when one color occupies the whole board.

An alternate version of this game introduces the idea of mutation. After the second roll, i.e., the even-numbered roll which identifies the bead to be doubled, a third roll is made. If, for example, a six (determined by fiat) turns up on the dice, then a bead from the color with the fewest beads may be placed in the square. At any rate, one can see that rather than mere reproduction of a bead, as in the first version, the idea of mutation is introduced. Occasionally such a mutation may give a great advantage to one of the colors. A third version of the game would use yet a third die. This "value die" would choose a color which has been arbitrarily assigned a greater removal value or a greater doubling value than the other colors. Such a rule, "enforced" by the value die, puts some of the colors at great advantage, and assures their selection, their survival, and their victory, even if one tries to even the odds at the beginning of the game by increasing the number of "disadvantaged" beads. The next bead game we want to consider here is "Struggle" because it introduces a kind of game we have not yet seen, namely, the dissipative pattern.

e. The bead game "Struggle"

This is a very commonsensical game which may be simply summarized as follows Grass (green beads) is eaten by rabbits (yellow beads), which are then eaten by foxes (red beads), which are then removed from the board as the fox-skins (blue beads) are taken as trophies by hunters. When the red beads are identified, they are removed from the board and exchanged for blue beads which are counted as points at the end of the game. Octahedral dice identify one of the 64 squares; there are 30 beads in each of the four colors. When the green beads are placed on the board, then 16 yellow and 4 red beads are placed in such a strategic way that the beads may profit from proximity of the diagonal or orthogonal squares. This proximity reflects the nature of an ecological model the yellow beads may replace green beads only in areas where there are other yellow beads, and red beads may replace yellow beads only where there are other red beads.

It is not necessary to explain all of Eigen's rules in order to see the possibilities as the game evolves. In situations where there are neighborhoods of green-yellow and yellow-red, we will see a chain reaction to yellow-yellow and red-red, i.e., the foxes will multiply as the rabbits multiply, both of them at the expense of the grass. When a player gets a transformation of yellow-red to red-red, he gets an extra two rolls, on which he can act however only if chance identifies a red bead, which is then traded for a blue bead counting as a point. But the interest of this game lies especially in its dissipative, open-ended, out-of-equilibrium nature and its potential to produce a cyclical, periodic population of the species involved.

The growing grass does vary depending on the number of grazing rabbits, but it is a renewable resource, so to speak, and provides a steady input. On the other end of the process, the number of fox pelts taken depends on the number of foxes, not on the number of hunters. But steps two and three of this process (rabbits and foxes) are autocatalytic (self-regulating) in naturerabbits must be present to produce rabbits, likewise for the foxes. But grass production and the shooting of foxes are not autocatalytic. To put it simply, when grass meets rabbit, it is changed into rabbits. If the rabbits find a lot of grass, the amount of grass will be reduced but the growth rate of the rabbits will increase because of autocatalytic reproduction (remember our definition of conforming strategy earlier). This growth rate will lower when the grass becomes scarce; but meanwhile the foxes have been transforming rabbits into foxes, so the population of rabbits rapidly decreases as the foxes increase. The population of foxes will then follow the same cycle of increase and decrease as the rabbits and the high and low periods of grass, rabbits and foxes, given the regular input into the system will describe rather regular oscillations on a graph (v. Eigen, p. 94-95).

In the earlier games, we saw order preserved in the shifting equilibria by conservative forces. But the game "Struggle" demonstrates that dissipative processes (structures) likewise produce form in nature. "There are no limits to the complexity of structures occurring in nature" (Eigen, p. 96). The production of form in nature (morphogenesis) comes about thus through both conservative and dissipative forces, showing up in the structures of proteins, in wave patterns, in population fluctuations, in inorganic chemical reactions, in genetic material, etc. The dissipative system is a metabolic and a dynamic system. Surviving by being fed, it organizes the conservative forces of morphogenesis, dissipating energy or creating a product. "The cooperative interplay of forces in conservative patterns corresponds to autocatalytic reactivity in dissipative models" (Eigen, p. 99). When we come to the discussion of Nietzsche and the Will to Power, we want to remember this context of the self-organization of inorganic matter in crystals, in the glass bead games, in living organisms, and in the evolution and constitution of our ideas. That is why we will later consider Michael Ruse's ideas on Darwinian epistemology and ethics.

Games may likewise be constructed showing that symmetry in nature comes about when symmetry is useful. Some proteins, for example, do not find symmetry useful as they cut and splice with their enzymes in the manner of a tiny self-regulating machine. Regular or irregular patterns may occur as chains of molecules arrange themselves to connect to appropriate bonding points. Neveretheless, regular structures have an evolutionary, selective advantage because each regular sub-unit is more spatially efficient in fitting into an overall pattern. Consequently, such regular structures evolve more rapidly. Symmetry need not be perfect but only functional, i.e., approximate symmetry may allow an organism to function quite well. After all, "a living thing seeks above all to discharge its strength" (BGE 13). The glass bead game is the model of a living organism, without the telos of self-preservation except in the "memory" of a pattern of mostly one color of beads, in the relative slowness of this configuration to change.

f. Hypercycles

Although Eigen and Winkler have set up a game showing how the hypercycle functions (p. 230 ff.) it is not necessary to describe the game in order to understand its conclusion. A self-reproducing cycle, i.e., an autocatalytic process as we have seen earlier, may produce the environment congenial to another self-reproducing cycle. The two cycles, becoming mutually dependent, become cooperative rather than competitive. When A produces the conditions for B, B produces the conditions for C, C produces the conditions for D, and D produces the conditions for A, the nature of the game is the reinforcement of cooperation and survival, even though occasionally catastrophe will result when one of the units disappears. That is to say, these four colors of beads (cycles, organisms, etc) are given the following order of precedence red-yellow-green-blue-red, etc., ad infinitum. The four different colors of beads placed on the board are chosen randomly by the dice, but the rules for doubling the bead operate depending on whether the bead finds itself in orthogonal proximity to a bead which precedes it in the cyclical order. The success of one color depends on the success of another color and extensive playing of the game will show the oscillation of the colors, even though occasionally there is a catastrophe for the whole system when one color dies out. Eigen concludes that the conditions for hypercycles "were obviously present in the prebiotic phase of evolution" (p. 233), and that the successful hypercycle was based on a non-linear rate of self-reproduction in order to account for the interaction between legislative and executive which gave rise to the genetic code.

But this discussion of the glass bead games is sufficient at present to serve the purpose we had in mind and that was to provide a vocabulary different from the post-Kantian vocabulary in which Nietzsche is occasionally trapped and to see Nietzsche and the "modernist" developments of the 19th and 20th centuries from a different perspective, especially a scientific perspective. It is therefore time to stop beating about the bush and state baldly The Nietzschean Will to Power is a term which includes all the possible [glass bead] games that Nature can play, whether She uses the indifferent, the conforming, or the contrary strategy, the random walk, equilibrium, struggle, dissipative metabolism, symmetry, or the hyperycle with linear, exponential or hyperbolic growth rates. Nature and the Will to Power are the sum all these games. Let us appraise how the Will to Power and the concept of games provide a common perspective on some of the major issues which concern us. At some point we must tackle the problem of where Nietzsche comes down with moral, ethical and aesthetic postures in relation to this scientific Will to Power; we may see him as one of the first philosophers to confront starkly and courageously the relation between science and morality. This will come as no surprise to those who have studied The Genealogy of Morals , but the game theory approach should clarify the nature of the project.

2. The Will to Power and the Rules of the Game.

What similarities can we see between Nietzsche's Will to Power and the Nature that Eigen and Winkler describe as the sum of all games? First of all, using the perspective of the game model of the recombination of particles (unities) with its unified view of the universe as a locally maximized autocatalytic recombinatory cyclical-periodic process, we begin to see that Nietzsche's work is a rather tightly thought-out and internally self-consistent whole. He emphasized that in his published work he had carefully read and reread the texts before publication. Yet, critics have been ready to see in the staccato nature of his texts, in the paragraphic style and in the rapturous tone the proof that he was disorganized and unable to carry through a system of thought to its conclusion.

However, the major points in the philosophy of Nietzsche are so closely interrelated that it is difficult to know with which one to begin in making the point that his major intuitions are consistent with modern scientific thinking. If the reader had time to study most of Nietzsche, Eigen and Moles and then to sort out the points of contact, he would see that the following points are interconnected. We will briefly list a few and clarify some of them after.

Both the glass bead games and the Will to Power describe the nature of things without recourse to teleology, without the claim for the ultimate reality of substance, without the supposition of an agent or prime mover behind the scenes, without a self as the necessary location of decision and the motor of change, without the necessity of free will for creation and change. The psyche may be a closed or a dissipative thermodynamic system (as Freud understood) and psychical health could even be defined in such terms. Will and change are animal phenomena; personality may be a selection process; the mind-body problem may be seen as a hypercycle. Inorganic, organic, and human reality are dissipative systems in which survival is not merely an idea of the will to live. Perception itself is a dissipative model (something we must consider later on when we deal with the implications of quantum mechanics). Activity rather than passivity is the nature of change and the nature of things (thus reactivity becomes pathological for Nietzsche). Both the game model and the Will to Power work on a holistic level--on an inorganic, organic, psychological, social and conceptual level. They are both rhythmic discharges of force, active in a state of flux in which equilibrium is considered conservative, even static and negative.

Cause and effect in the game model and in the Will to Power are nonlinear or not necessarily linear relations of events and may be seen as interpretations of a systemic holistic process. Randomness and chance may appear to be at the origin of events, but all events actually take place by a kind of necessity, the same kind of necessity in Eigen and Nietzsche. The nature of these events is such that chance and necessity are subsumed in a holism of natural processes and are made to seem anthropomorphic illusions of an irrelevant and manipulative humanism. Neither the game nor the Will to Power shows chaos in Nature; the course of "chance" events demonstrates a lawfulness where man ought to feel at home Thus Eigen rejects Monod's morose existentialist stiff upper lip, and Nietzsche dances to the rhythm of the Eternal Recurrence.

Nietzsche describes a Will to Power which maximizes itself locally; Eigen shows entities which optimize their position and patterns. For both, something new is created at every moment, something new which is nevertheless a part of the whole and which leaves the future open to change. The statistical recombination of particles (entities, energy centers) is immanent in the system, not transcendent. Events reflect their neighborhoods and the importance of proximity. The universe as totality of glass bead games or as Will to Power does not maximize itself totally; if it did, there would be an end to flux . The holism of the game model and the Will to Power change chance into necessity and "gives meaning to accident," as Moles remarks (p. 219). Each configuration of beads is fully actualized, like the localized Will to Power. Each step is always and fully what it is, "drawing its ultimate consequence" (Moles, p. 234). Each state is discrete, but not isolated. There are no isolated moments or forces in time; becoming and disappearing are "twin aspects" (Moles, p. 237). Flux is permanent.

Although the last four paragraphs may drop a heavy load on the reader, they contain nothing mysterious. Our problem is that 2500 years of the Socratic Judaeo-Christian metaphysic have caused us to think in terms of stasis, of an agent, of linearity, of cause and effect, of good and evil, of anthropomorphism, perfect forms, and the fall from paradise. I am convinced that such an ancient, powerful and prestigious origin of our misunderstanding was what made Nietzsche sometimes appear shrill in his frustration to express himself, to make us understand what he had seen and caused him to caution us to read him carefully. The nature of our analytic, of our methodology, of our problematic had been inherited from the very metaphysic we had to reject.

Nietzsche points out that the Will to Power (the glass bead game model) is against the "prevalent instinct and taste which would rather be reconciled even to the absolute fortuituousness, even the mechanistic senselessness of all events than to the theory that a will to power is operating" (GM II 12). This attitude Nietzsche calls a "democratic idiosyncrasy" (Ibid.). One may say that Eigen’s beads are pure activity which produce patterns, pure activity which is not adaptation because there is no reactive, adaptive mechanism. For Nietzsche, the "democratic idiosyncrasy" has robbed life of activity and "places ‘adaptation’ in the foreground...a mere reactivity" in which "life itself has been defined as a more and more efficient inner adaptation to external conditions" (Ibid.). Nietzsche, in effect, explains how Darwinian evolution works, in terms consistent with the glass beads. Adaptation, however, ignores "the essential priority of the spontaneous, aggressive, expansive, form-giving forces," and the " will to life is ignored" (Ibid.).

3. The nature of the states of the glass bead game.

In the bead game "Random Walk," we saw a square board with sixteen beads, eight white and eight black. Each player put his beads on his half of the board and a coin was tossed to determine who would lose a bead and who would gain a bead. The configuration of the board at the beginning of the game (i.e., eight white beads on one half and eight black on the other) we may call a "state," state 1, for example. After the coin is tossed and a white bead is replaced by a black bead which had been held in reserve we have another state, state 2. Each time the coin is tossed the configuration of the beads is yet another state, as long as we play the game, for n number of states.

In a more complicated game, "Limitation of Growth" (Eigen, p. 225), played on a square board with 64 beads, one version has 62 squares filled with black beads, one with a white bead, and one position empty. That is also a state, state 1, for example. Rolling the dice alternately for birth and death, one doubles the bead selected for birth and removes the bead selected for death, our rules dictating what was described earler as a conforming strategy. At every cast of the dice, the game exhibits a different state up to n number of states. "Random Walk" demonstrates the equilibrium of a conservative system and "Limitation of Growth" shows the population shifts until one of the colors disappears. But at present we are not interested in the outcome of the games, we are interested only in the relation between state 1 and state 2, no matter what the game being played.

The relation between or among states appears paradoxal. State 1 is not causally related to state 2 in a linear fashion. Yet is it still an expression or an instance of the same game, an instantiation of the operation of the laws of chance turned into order and meaning by the laws of the game, the law of large numbers, the influence of proximity, etc. Each state exists in isolation, having no predictable effect on the other state. Yet, the population of beads in a game may affect the rate of replacement (birth or death) of the game in a particular stage. The number of white beads on the board of "Random Walk" has nothing to do with whether the coin will turn up heads or tails. The number of green, yellow, red or blue beads in the grass-rabbit-fox-pelt game does not determine whether the dice will select a yellow bead, but autocatalytic actions in situations of proximity may affect the rate at which the game is diffusive. We are faced with a situation in which states are completely isolated from one another on the one hand (since they cannot affect the nature of chance), and on the other hand are intimately related by the rules which they may affect and which affect the unit itself. Isolated entities and configurations exist as members of the same game. Each state on the board has no destiny before the dice throw...yet, after the dice are thrown the state changes or may change according to the rules of the rate of change, the development of autocatalysis, the conditions of proximity, etc.

We may say then, based on the nature of the states of the glass bead games, that each state is fully what it is without the [linear] influence of the other states, that it is an independent state which maximizes the conditions available to it from the rules of the game, and that it fully actualizes itself, drawing its ultimate consequence from the potential that it exhibits as an instantiation of the rules of the game...the rules of the game which are the rules for the recombination of particles-energy centers. The states of the glass bead games are identical in nature to the distributions of the forces of the Will to Power"At any precise moment of a force, the absolute conditionality of a new distribution of all its forces is given it cannot stand still" (WP 1064). Any distribution of the forces of the Will to Power (any consecutive state of a glass bead game) is not caused by a previous distribution of forces (a previous state of the game) but is an entirely fresh creation of the Will to Power. Any instance of the localized distribution of forces of the Will to Power is related to another local distribution of forces only in the sense that the Will to Power is the totality all the strategies that local aspects of the Will to Power may manifest, with the understanding that these forces are not totalized or totalizable into some universal pattern or necessity. "At any moment of a force, the absolute conditionality of a new force is also given, a new inner balance of power. At any given moment of a force, therefore, the necessity of a new moment is already granted. One moment displaces another, continually and without end" (Moles, p. 235). Moles could just as well be describing the glass bead games.

However, if such a summation of strategies had been totalizable, then within an eternity of time (to conform to the thinking of Nietzsche) they would already have been totalized and a teleological process would have already led us to some such condition as the Omega point of Teilhard de Chardin. Biological evolution would long ago have been at an end. We must come back to this point later but for the present we must insist that such a situation in which each distribution of the forces of the Will to Power is linearly unrelated to any other distribution of forces (that the Will to Power creates anew at each instantiation) suggests that biological evolution does not and could not have developed algorithmically; had there been an algorithmical progression within the eternity of time, evolution would have had the inevitable nature of a Turing machine, a supercomputer, and the inalterable perfection of an end product would already have been reached. The universal Turing machine which would simulate true life would have to incorporate the capacity for incompetency and occasional foolishness, for taking wrong roads and risking catastrophe and extermination. When one moment of force is constantly displaced by another, as in the concept of time in Nietzsche (v. Moles, p. 234 ff), and when moments of temporality reflect the same displacement by other moments of time, then we have cracked apart the necessary connections in causality and temporality, we have destroyed the basis for the privileges of the logos, and we have made the challenges to traditional logic that will be clarified by the philosophical implications of quantum mechanics. We have a system which, as Serres likes to point out, works because it does not work! We will discuss this later when we are concerned with the algorithimic nature of machine language, how machine language and computer programs are related to the social structure of power, and how the logos would require necessary connections between states of the glass bead games and the configurations of the Will to Power. We shall soon see that time creates some problems for Nietzsche.

Earlier we saw the introduction of the mutation into Eigen's game "Selection." Yet, mutation as a source of change "always takes its rise from a sequence of events that is completely independent of any evaluating mechanism" (Eigen, p. 163), That is to say that mutations do not come about as a result of a perceived or even an autocatalytic systemic need of the organism for adaptation. There is such a thing as adaptation, but it does not work that way, that is, as a response to an identified problem. Isolated events are intimate parts of the system. Readers of Nietzsche have long ago seen where this discussion is going The rules of the game are the Will to Power. "Equilibrium will tend to occur more frequently once it has been established, and it will occur less freequently in periods of greater deviation" (Eigen, p. 39). Nietzsche expressed a similar idea by saying that the Will to Power acts through the maximization of its power; it acts using all games and all strategies.

Individual and elementary physical events when they are taken in isolation are not determinate, but they are manifested according to the law of large numbers. Chance and necessity work so closely together that they seem to be inseparable. "The activity of the will to power at any constantly to change chance into necessity and give meaning to accident" (Moles, p. 219). As we shall have occasion to study later on in this essay, the relation (identity) of chance and necessity even operates in the domain of the spiritual, within the unique solution Nietzsche offers to the mind-body problem and the nature of Nietzschean "spirit." The advent of the friend as the anticipation of the overman will be seen to be purposeful, " the becoming of good through evil, as the becoming of purpose out of accident" (Z I, 16). We will come back to this problem when we deal with the axiosphere as an evolutionary development of the Will to Power, or as a "rational" development in the sense of morphogenesis, as defined earlier. The Will to Power is not disorder, whether in the inorganic, the organic, or the moral-ethical world. And here we must insist that order is the nature of things, and that chaos is very, very difficult to find. True chaos could exist only if the universe consisted of one single particle. Given a second particle, a second energy center, then position, proximity, cooperativity, relation and statistical behavior arise. Then we have the rules for an elementary game. (Lévy expressed the same idea in political terms when he said that power is born in the contact between two individuals, and that power is the primal event of human relationship.) We must return to this point when we discuss the Eternal Recurrence for we see that the Will to Power does not operate according to naked chance. It channels chance, maximizing its states and the potential of those states. "Matter's capacity for self-organization has been underestimated rather than overestimated" (Eigen, p. 169). Moreover, power itself expands by its own laws, as Jacques Ellul very well saw in his analysis of technique and the technological society (1954), as Deleuze saw in his essay on capitalism (1972), and its nature is autocatalytic (v. Eigen, p. 248). Again, as we shall see later, the concept of chaos is irrefragably calqued on theology and modern physicists searching for it found the elegance of fractals.

We may now see how the glass bead games give us a perspective on Nietzsche. Nietzsche had criticized Spinoza because the latter gave ontological status to rationality, logic becoming the mechanism whereby the divine essence produces the universe. Moles does not think Nietzsche is fair to Spinoza in this instance.

Nietzsche insists that rationality is an exception in the universe of forces. But, despite his opposition to Spinoza on this point, his own conception of necessity appears to have an inherent logical structure. The configuration of forces at any point, he claims, is such that a new configuration is straightaway created; this new configuration is also the only configuration possible, given the nature of will to power as self-maximizing. A sort of logical possibility is suggested here, especially when it is remembered that Nietzsche talks about the tautology that all events are necessary (Moles, p. 217).

But when we see the Will to Power in terms of the comportment of the states of the glass bead games, then we understand that rationality is simply not necessary, particularly in Spinoza's ontological sense, that rationality is not a productive or useful concept, and the sort of logical possibility that Moles suggests in the self-maximization of the configuration of forces resulting in a new configuration which is likewise the only one possible is best explained by the principles governing the relations of states of games described above. Rationality is not necessary nor a priori. I have been waiting for this point in our discussion to arrive in order to insist that Nietzsche's analytic in terms of the Will to Power is consistent with modern game theory, molecular biology, etc., and to suggest therefore that Nietzsche is the first major modern thinker, having come to conclusions that later scientists and mathematicians reached with laboratories and the developments of modern technology. The philosophy of perfect forms, the 2500 years of the Socratic-Judaeo-Christian metaphysic, has caused our method, our problématique, to conform so closely to the requirements of an a priori rationality that we have been unable to see the development of the universe in terms of a new a posteriori "rationality" of statistical and autocatalytic actions and it helps to explain why the apparent logical contradictions of quantum mechanics are so confusing. In the idea of rationality which we got from the Greeks there is the lurking figure of an agent. Rather than rationality, "morphogenesis" would even be a more appropriate term. These are the kinds of conclusions I had intended to get from the confrontation of Nietzsche and Eigen, a path we will pursue.

This relation between the states of the glass bead games and the states of the Will to Power clarifies the nature of chance for Nietzscheit always operates within parameters, which channel it, parameters which it may create or alter catalytically. It blurs the distinction between chance and necessity, chance becoming merely a break in the pattern of necessity which prevents necessity from becoming static and rigidly algorithmic like a computer, a computer which reflects, as we shall see later, the logos, the politico-rationalist values of the techno-capitalist society and the Socratic-Judaeo-Christian metaphysic. This relation between the states of the glass bead games redefines cause and effect, and requires that we look differently at time and space. "The universe as a whole does not maximize itself" (Moles 218), or it would mean the end of flux, the end of change and evolution. To use Nietzsche's terminology, we could say that Newtons's physics maximized the Will to Power on a cosmic scale it therefore stabilized the universe, and was thus cosmically consistent with Christianity (v. Prigogine on the role of Newton). It has been suggested that the prevailing cultural values reflect the accepted theories of physics, but in the case of Newton it was the prevailing religio-cultural values which were reflcted in a well-oiled universe lubricated by the chrism itself.

What is the meaning then of such a statement as "To recognize the active force, the creative force in the chance event--chance itself is only the clash of creative impulses" (WP, 673)? Moles explains that the forces in Nietzsche's universe are relational, "creating themselves only in relation to other outer forces" (Moles, p.219). In addition, however, and what is probably more important to the discussion at hand, within a universe of chance, necessity can be generated internally by the force itself. i.e., a force can be eventually overcome by pressures within itself. For this reason, no force (read state) can become a generally perfected cosmic state" force can grow to encompass the world within itself forever" (Moles, p. 219).

What one force makes part of itself by necessity cannot at the same timme be made part of an external force by the same necessity. From the perspective of the external force, this new development is chance.. . . Chance is the stimulus by which necessities grow. . . . Every local necessity (finite force) [read "state"] seeks to conquer this chance, but chance triumphs over every local necessity in the end. Yet, since this triumph is always the work of another force, it too always proceedsnecessarily. At the local level, chance is found everywhere; but when the whole univese is considered, every event is strictly necessary (Moles, p. 219).

What is this chance which is not really chance but which lies at the origin of necessity? What is this force which is one force in a relational universe of forces and to which it relates holistically, yet can and must change itself internally to the point that it cannot be generalized as a perfected cosmic state? What is this force which can change itself internally but cannot pass this change along to the other forces to which it is related holistically? Commentators have struggled to describe Nietzsche's idea and it appears that Nietzsche struggled to communicate his intuition on this point. Now, the whole problem could have been stated very clearly if Nietzsche had known about the non-linear, autocatalytic, self-regulating nature of out-of-equilibrium dissipative systems, because that is just what the Will to Power is--an astronomically large collection of localized autocatalytic dissipative systems which are independent and related at the same time. (We will later have occasion to insist on this Nietzschean non-linear development when we consider the Übermensch and the evolutionary axiosphere, pursuing the idea of a Nietzschean holism which goes from the inorganic to the moral and providing a solution to the mind-body problem, a problem which is an illusion necessary for the maintenance of the Socratic Judaeo-Christian metaphysic.)

This chance described above by Moles in his most excellent summary of the problem, this chance which is the essential nature of the universe, this chance which always proceeds necessarily, this internal alteration of a force by itself is none other than autocatalysis. . . and even on occasion mutation. The energies and forces of chance are creatively channeled by internal changes related to the nature of all other forces relating to the force; the glass bead games of Eigen, the evolution-devolution of Darwin, the Will to Power of Nietzsche, the parasites and palimpsests of Michel Serres, the autoproductive unconscious and the desiring machines of Gilles Deleuze and Félix Guattari, Lévi-Strauss' Nature as combinatory matrix, perhaps even the signifier chains of Derrida and the psychic dynamism of Freud, are autocatalytic structures of channeled chance. But the autocatalytic structures of channeled chance which the Will to Power is . . . was first of all the intuition of Friedrich Nietzsche in the 19th century--and that makes him the first modern since Heraclitus, and the first physician to innoculate us against the plague of Platonist idealism!

The Will to Power is expressed in the internal changes in the growth rate of the rabbit population because of the lack of grass and the appetite of foxes, which happend by the chance which is not chance and then affects the whole system of grass-rabbits-foxes-pelts. The changes are not even inevitable because the whole rabbit population may die out and the whole system come to an end; the survival of the human race is not inevitable in the holistic scheme of the Will to Power. The rabbits are an independent force on one level, related to the independent force of the foxes on another level; both are related to the independent force of the system (force) grass-rabbits-foxes-pelts and the latter force (system) is related to every other manifestation of the Will to Power. If the hunters who depended on the fox pelts would learn to fertilize the grass so that the system of separate but related forces would continue to produce fox pelts, then we would have a metabolic system, a hypercycle whose periodic and graphable highs and lows fit the definition of an Eternal Recurrence and justifies Nietzsche's claim that the ewige Wiederkehr is a starkly scientific reality.

4. Nietzsche and Chance.

What Nietzsche calls chance is not chance at allit is his term (Zufall ) , which describes the nonlinear periodic autocatalytic behavioral relations between entities (whether these entities are particles or "energy centers," a very useful expression preferred by Schacht). As such, his word chance is an aspect or even a synonym of the Will to Power! The Will to Power is merely the behavior of chance (Zufall ) within the parameters it has itself created. As such, his use of the word "chance" has caused difficulty for scholars. What Nietzsche calls "chaos" is not really chaos. No wonder Nietzsche, despite the agony of his illness, felt at home in the universe. He was convinced it was a universe in which he belonged and which would be again. Now it begins to make more sense when we read Deleuze's claim (1962) that Nietzsche is a fellow who wins everytime the dice are thrown.

5. The Will to Power and the problem of time.

Although we have touched on the problem of time above, it is a thorny question when dealing with Nietzsche and requires more comment. The problem lies largely in the difficulty of identifying discrete pieces of time within the continuum of time, i.e., within the flux, and with the conception of time as continuum in the first place. When we dealt earlier with the configurations of the discrete forces in the Will to Power (i.e., with the separate but related states of the glass bead games in the game model), we were able to see all the possible states of the game within the overall picture of the rules of the game and to see the independent but relational nature of the states of the game. We saw that each configuration was necessary (in the way we defined necessity), but that it also left the way open for a new state every relational distribution of forces sets the stage for a new relational distribution of forces. With time, however, it is a little harder to decide what makes up a piece of temporal stuff and then to relate these so-called discrete units of time in a Nietzchean relational model which reflects adequately the satisfaction we had with the relations of energy centers and glass beads. Time is likewise complicated by the problem of duration (biological, existential, anthropomorphized "subjective" time) versus scientific "objective" time, space-time, irreversibility within the framework of the Big Bang theory, and the question of whether time is eternal or whether time began only with the Big Bang. If this creative explosion happened between ten and fifteen billion years ago, then we are faced with deciding whether time began only then, in which case talking about eternity becomes a fishy business, or whether there was a Platonist time as an a priori formal reality, which recreates the very metaphysical problems we are trying to avoid with Nietzschean relationalism. Although it may not yet be apparent, we have to deal with the nature of thermodynamic systems and point out that entropy guarantees the stasis of equilibrium in a closed system, that for dissipative systems to avoid equilibrium they must have a constant contribution of energy, and that closed thermodynamic systems exist only in the laboratory.

6. Reconstructing a Nietzschean theory of time.

Since Nietzsche's account of time is occasionally unsatisfactory, we have to see, as Moles suggests (p. 226), whether we can reconstruct a Nietzschean theory of time which is consistent with his view of the nature of things. In order to fulfill the claims made earlier in this essay about the contribution the game model can make toward the clarification of Nietzsche's thought, we must simply state that time is a function and an expression of a dissipative model and that Nietzsche's insistence on human reality as the reality of the body emphasizes that, for our purposes, the body is a metabolic-dissipative out-of-equilibrium system which is the very image of the functioning of the Will to Power in general and which is therefore consistent with the dissipative model.

7. Human Reality as Thermodynamic Model.

Human reality as body is a dissipative-metabolic model which lies at the origin of duration. It is possible to suggest that in this sense duration is the anthropomorphization of a physicist's space-time which is the real time of the universe, or even of a Platonist formal time; but we cannot prove this assertion without first proving or at least positing the reality of a real and absolute time for the external world of which duration is but an aspect. Such a positing puts us into an idealist and Newtonian mode and is, in fact, not necessary if we are willing to be satisfied with duration as the spin-off of a dissipative system. But if we extend the idea of the Will to Power to universal process, then the universe as an out-of-equilibrium system likewise spins off time, so that by this little exercise in (a) making body as human reality a dissipative model spinning off duration, and (b) making the cosmic Big Bang a dissipative model spinning off objective time or space-time, we have therefore (c) dissolved away the apparent incommensurability between duration and "objective"time (i.e., the modern physicist's idea of the "real" time of the external world, which is as near absolute time as we can get without falling into Newtonism or idealism) by making duration and non-anthropomorphized time the same kind of time, namely the nature of and the product of a dissipative system. In other words, there is no difference between duration and time, i.e., between subjective and objective time, because all time, whether duration or "real" time is a spin-off of the Will to Power in its local configurations from an overall view of a cosmic Will to Power. The term spin-off is not a particularly happy term, but in this context I would prefer it to "epiphenomenon" which would create a lot of problems. This, then, is the solution I would propose to resolving the distinction between subjective and objective time within the framwork of Nietzsche's ideas. The psychological time of the herd-man is a spurious time compared to objective time but it is a useful fiction.

This idea ought to come as no surprise because it is just what Nietzsche had in mind with the Will to Power as the nature of the universe in its every configuration of forces, (whether human, animal, inorganic, etc, which Moles has extensively documented) and accounts for the fact that Nietzsche felt at home in the universe of the Will to Power with a joy so profound and such a convinced scientific mysticism--a mysticism which shows up in 20th century biologists with a similar lyric conviction. We must remember the profound causes for this conviction when we come to deal with the problem of the Eternal Recurrence and the scientific reality which Nietzsche gives to it. In any sense that Kaufmann found Nietzsche to be an existentialist, it was certainly not an existentialism in which man knew the exile from nature of Camus or Sartre, that massive indifference of the universe toward man. An intimate part of the Will to Power, man is part of nature and cannot conceive of it as indifferent toward him without being indifferent toward himself--i.e., sinking into nihilism.

8. Equilibrium and decadence the origin of the moral.

Equilibrium models and Random Walks are part of the Will to Power just as are diffusive, dynamic, creative models. By extrapolating from Nietzsche's system, it becomes evident that he valorized the diffusive models as creative-positive and damned the equilibrium models as conservative, negative, destructive and sick. This is a game-model theory for the origin of Nietzschean values and the enhancement of life for the type Mensch. Morality and ethics are thus seen to be differential valorizations of equilibrated vs diffusive systems. Equilibrated systems preserve their weaknesses at the risk of stasis and catastrophe. In Nietzschean terms, Christianity, Buddhism, nationalism, etc., are such conservative, equilibrated systems. There are no equilibrated survivable models in biological evolution, and even though certain organisms appear stable they lead a precarious existence and become evolutionary dead ends. Rats and cockroaches are successful biologically because they are not equilibrated systems. Genetic and moral stasis guarantees catastrophe.

The idea of the diffusive lowers the usefulness, the value, the reputation of stability. The diffusive makes variation possible. Prigogine states it this way in the language of chaos theory"The ‘attractor’ which dominated the behaviour of the system near equilibrium may become unstable, as a result of the flow of matter and energy which we direct at the system. Non-equilibrium becomes a source of order. New types of attractors, more complicated ones, may appear, and give to the system remarkabale new space-time properties..." (Hiley and Peat, p. 206) (my emphasis).

9. Cosmic Equilibrium and the Big Bang.

There cannot be equilibrium even in our solar system unless all energy sources are extinguished. The directionality of force since the Big Bang guarantees irreversibility. "If irreversibility ceased to exist, we would never know it, for the very assymetry of unachieved equilibrium is one of the essential premises of all life. The disappearance of this assymetry would mean 'heat death' for the entire universe and therefore the end of all life" (Eigen, p. 157). It appears that our cosmos is in the very early stages of development and that ..."we are very far from reaching equilibrium. Our consciousness of time, too, oriented to mutability and inherent in the life rhythm of our brain cells, is rooted in the irreversibility posited in the second law of thermodynamics." (Eigen, p. 156).

In Nietzschean terms, the out-of-equilibrium localized maximization of the Will to Power which is manifested in the configuration of our snyapses and dendrites exists relationally with all other possible configurations of localized, maximized and relational energy centers which make up the Will to Power. It is the functioning of this diffusive system of the body-which-is-reality which produces duration, i.e., which is duration, and which demands energy input.

Any possible deviation of entropy from equilibrium value has anegative sign. Entropy can only increase as equilibrium isreestablished, regardless of the direction the shift of the chemical equilibrium has taken. Near the point of equilibrium,then, the distinction between past and future cannot be derived from the behavior of entropy. Our awareness of the passage of time is due to the fact that the realm of the universe in which we live is still nowhere near a state of equilibrium. The overall equilibration process is not far advanced, ...our world is still 'relatively young' (Eigen, p. 155).

In view of the above, I would like to give a slightly different interpretation to Nietzsche's statement that "in a state of equilibrium 'the clock of existence would be at a standstill' " (Moles, n. 90, p. 396). Moles sees in this remark an insignificant lapse on the part of Nietzsche and a suggestion of the absoluteness of time. I would like to exploit the same remark to suggest that Nietzsche's intuitions about the nature of time are consistent with the the preceding remarks about the nature of out-of-equilibrium systems (and the Will to Power as dissipative out-of-equilibriium system) and the idea that time itself is not absolute but is irrefragably connected to dissipative systems, that the concept of the Will to Power is consistent with the behavior of thermodynamic systems and the notion of entropy, that the existence of time depends on out-of-equilibrium systems and the contribution of energy which prevents entropy from falling toward the stasis of equilibrium and heat death, and once more to insist that Nietzsche is among the first of truly modern thinkers. We can likewise see in this context of out-of-equilibrium systems why it is necessary that Nietzsche's energy centers (what I will later call force-spacesv. section 49) be described in terms of the configurations of dominant and submissive force systems the concept of dominion and submission is a translation of thermodynamics into moral or quasi-moral terms.

10. Entropy and morality.

In summary, Eigen's game models help us clarify the idea that time is a function of the Will to Power as dissipative, out-of-equilibrium system. It likewise allows us to see that Nietzsche's morality is linked to a valorization of dissipative systems; it is a morality of anti-entropy. Nietzsche's moral theory may thus be summed up very briefly, and we must return to this later In moving beyond good and evil, we see that the good is anti-entropic; the decadent and sick are entropic. The dissipative is life; equilibrium is death. Total and universal equilibrium is the end of change and the death of the universe in the terms of the most modern and scientific physics. This is the profound meaning of Nietzsche's admonition to live dangerously, out of equilibrium, the profound meaning of his enormous disgust with ideololgies which promote safety and happiness as the goal of human efforts, and of his assertion that self-preservation is not necessarily the major motive of human effort or even of the Will to Power (after all, biological evolutionary dead ends regularly occur). "Happiness and virtue are no arguments...Something might be true while being harmful and dangerous in the highest degree" (BGE 39). This opting for life is likewise at the basis of Nietzsche's claims to scientific validity, and at the basis of his project to develop a genealogy of morals. It is likewise at the root of his ire at Kant, who "discovered a moral faculty in man" (BGE 11), who by his categorical imperative had made morality metaphysical and static and had therefore rendered a true science and genealogy of morals impossible and thus, in Nietzsche's eyes, had trivialized the whole moral problem and enabled man's continued nastiness toward his fellow man to continue without a possible solution short of preaching and moral indignation. Nietzsche thus had little respect for the indignant man. The concept of the Will to Power as dissipative dynamic system subsumes the spiritual, contributes to a solution of the mind-body problem, and is something we must consider later with Michael Ruse's work on Darwinian epistemology and ethics. However, Moles has identified problems with Nietzsche's conception of time which should be evaluated in terms of the above.

Moles describes and analyzes (pp. 223-245) Nietzsche's effort to provide an alternative to the mechanistic conception of time in order to avoid the absolute, quantifiable and inevitable time of Newton's classical mechanics, a conception of time consistent with linear, continuous and infinite Euclidean space. In the above I have proposed a Nietzschean alternative in terms of dissipative systems.