There is a famous saying: “God works in mysterious ways!” Meanwhile, I am so ambitious that will try to speculate concerning the ways of God’s creativity.

A COMMON APPROACH TO THE CREATION OF THE UNIVERSE

This approach could be based on two assumptions. The first assumption is that God has a final goal, and the second is that God has a program to achieve it. God's final goal may even be eschatological, assuming that the world God has created is a stationary system.

I did not find any explicit expression of a final goal in the Torah, but some Jewish scholars, and Neil Gilman, in particular, have found eschatology in the Jewish religion.

God's redemptive power is the centerpiece of Jewish eschatology (from the Greek: eschaton = last things; logos = discourse), the umbrella term for the body of teaching that describes the events that will occur at the end of days, at the culmination of history as we know it. Jewish eschatology is a singularly complex and imaginative body of teachings because it purports to discuss events that no human eyes have ever witnessed. This doctrine also evolved throughout Jewish history. In its fully developed form, dating from the talmudic period, it describes events that will take place in three dimensions: a universal dimension (events that will affect the entire cosmos), a national dimension (affecting the Jewish People), and an individual dimension (affecting each individual). In one way or another, each of these scenarios describes God as the initiator of the drama. All eschatologies stem from one common impulse: the sense that things as they are now are deeply flawed. The redemptive scenarios then proceed to describe how at the end of time God will transform the flawed into the perfect. All speak of a God who saves, rescues, and delivers people or, ultimately, the cosmos as a whole, from an imperfect state. (pp. 168-169)

The idea that the purpose of God is redemption has been developed mainly by Christian theologians, among them Jonathan Edwards (1703-1758), and more recently Oscar Cullmann (for example, in his book of 1968).[27] I do not object to the idea that redemption is one of God's directives in the post-creation development of the universe, but in order to speak about the purpose of God, one should take into account both the process of the creation of the universe as well as its performance. The concept of redemption is related only to the performance of the universe.

When I speak of a program, I mean a protracted path of stages that are completely and consistently linked as opposed to a plan, which is a protracted path of stages with disjointed relations between the steps in each stage.[28] I did not find in the Torah any explicit statement concerning the development by God of a program or a plan, but some scholars characterize God’s activities as being planned. For example, Robert Sacks (1979) mentions,

[W]e must consider the general plan for Creation as a whole. On  day one light was called into being; on day two the sky was made and the water divided. The third day was devoted to the appearance of dry land together with the production of the plants. On day four the sun. moon, and stars will be made, and on the fifth day the denizens of the sky and the water will come to be, while day six is given to the land-dwelling beings, including man. …In addition to this general plan which relates the first three days to the last three days there is a general transition from simple motion to motion of a more complicated character. Enough has been seen so far concerning the order of Creation to reach some answer to our original problem of why the words and it was good had to be deferred from the second day to the middle of the third day. Simple and elegant as the above plan is, not even God was capable of completing the seas before making the dry land since the limits of the sea are the same as the limits of the land. Unlike many mythological accounts, the author does not imply any great and tragic necessity against which God must struggle. The difficulty is nothing more than a simple problem of topology. However, it is a problem which even God Himself must face, and the plan cannot be fulfilled in its simple and most immediate sense. (p.39)

So, in my mind, the authors of the Torah do not explicitly present God as someone who possesses a plan or a final goal. If we assume that God did not have a final goal or a plan and God is acting in a protracted process that have only goals for each stage, it is reasonable to raise the question: “How are intermediate goals presented”? The answer to this question immediately brings me to the analysis of methods of creation in general, and in particular, in protracted systems.

Classical methods like dynamic programming (R. Bellman, 1957) are quite adequate in situations where we can start at the end (the final state) and link it to the current state in a complete and consis­tent manner by a fixed program. Such a link could be made even if the initial information about the problem can be given in terms of probabilities based on statistical ob­servations of frequencies.

By the same token, especially if there is a law, one is able to start at the beginning (the initial state) and proceed until the system reaches a signal to terminate the procedure. For example, a writer (a poet) in the process of composing may have a final goal, which is best expressed by the term closure (Smith, 1968).

Guided by this closure, the creator organizes the entire structure of the work, and in the extreme case he or she does so completely and consistently. On the other hand, the writer may proceed without having any concrete, fixed, a priori image of the final goal; he or she finds the beginnings and develops them, eventually arriving at the final destination (E. Said, 1975). The writer does not stipulate this destination in advance. The writer may even suffer from the realization that if he or she follows the permissible behavior of the hero, the writer would be compelled to kill him in the end. But in any case, starting from the beginning assumes that there are laws that will drive the author to the destiny state.

What can be done if “the time is out of joint”? (Hamlet, Act 1, Scene 5) That is, what can be done when a case occurs where it is impossible to find a complete and consistent process of creation especially in the absence of a final goal?  One of the major steps under these conditions is to elaborate a direction of development.

Direction of Creation and Development of the World in the Torah

In a very interesting way, Nahum Sarna (1966) emphasizes God's role in directing the creation of the universe, as it is represented in the Torah:

One of its seemingly naïve features is God's pleasure at His own artistry, the repeated declaration, after each completed act of creation, that God saw how good …But this naiveté of idiom cloaks a profundity of thought that marks off the mood of Hebrew civilization from that of Mesopotamia in a most revolutionary manner. The concept of a single directing Mind behind the cosmic machine, with all its ethico-moral implications, emancipated Israel from thralldom to the vicious cycle of time. In place of a fortuitous concatenation of events, history has become purposeful and society has achieved direction. A strong streak of optimism has displaced the acute awareness of insecurity. The all-pervasive pagan consciousness of human impotence has given way to a profound sense of the significance of man and the powers he can employ. …This basic belief in the essential goodness of the universe was, of course, destined to exert a powerful influence upon the direction of the religion of Israel and to affect the outlook on life of the people.  (p.18)

I                                            

It seems to me that the most general form for the direction of any developing system is expressed in the phenomenon as entropy.[29] It is widely held that growing entropy is paramount in closed systems. It is also widely held that the principal characteristic of development in open systems is an increase in the degree of order, i.e. the growth of negentropy (Bertalanffy, 1968). Moreover, a closed system can also strive towards greater negentropy if it possesses mechanisms of self-perfection. That is, it may turn out to be equivalent to the openness of the system as far as the inflow of new energy is concerned. In other words, the growth of entropy is associated not only with the closeness of a system, but also with the fixed nature of the rules that govern interactions among its elements. Perfection in this context really means a change in the rules of interaction. 

It deserves to be mentioned that some authors use the idea of entropy for the interpretation of the Torah when it concerns the process of the creation of the universe. Leon Kass (2003) uses this idea in a very interesting manner, even though it is not a basic concept for him. (I assume it is not a basic concept for him, because he does not even include  "entropy" in the Index of his book.) Assuming that creation increases order, Kass emphasizes the influence of initial entropy on creation:

Life and freedom are only the most obvious principles of disordering and change. A scrupulously close look at the text suggests even more fundamental principles of change. First, there is the formless, watery chaos out of which everything came to be. How well does it accept form and order? Are all its native entropic tendencies abolished by the process of separation to which it is subjected? Or does its chaotic character persist beneath the forms of the world, making any order unstable? Does Genesis 1 subtly teach what was once known as the recalcitrance of matter? (p.49)

The answers to Kass’s questions require deep involvement in the murky concept of entropy that is behind my book.

One aspect that is usually not taken into account in measuring entropy-negentropy is the level of the diversity of a system. We should note that, in the introduction to his book (1954), Norbert Wiener describes the growth of entropy as involving not only an increase in chaos, but also an increase in uniformity.

As entropy increases, the universe, and all closed systems in the universe, tend naturally to deteriorate and lose their distinctiveness, to move from the least to the most probable state, from a state of organization and differentiation in which distinctions and forms exist, to a state of chaos and sameness. Wiener never elaborates upon the idea of entropy as a function of two independent variables: order and diversity. For Wiener, as far as I can understand him, these two variables are clustered and not separated. Jamshid Gharajedaghi (1985) constructed the negentropy function with regard to living systems as a function of two variables: complexity (diversity, differentiation) and order (integration), i.e., Gharajedaghi treated the variables complexity and order as a two-dimensional entity rather than as a dichotomy in a one-dimensional structure. There is a range of values that each of these parameters can assume. Although each one can vary independently of the other, development implies some sort of coordinated change in each variable. Viewing greater differentiation as an increase in complexity and the growth of integration as an increase in order, Gharajedaghi (1985) notes,

[M]ovement toward complexity and order is the essence of the negentropic processes in living systems (p.40).[30]

So, we have entropy represented as a function of two variables: differentiation (diversity, complexity) and integration (order).

This approach to entropy generalized to any system based on the concept of creative universe, ensures infinite development, because it concerns itself with the direction, or course, of development rather than focusing exclusively on the end goal.  In other words, this approach focuses on the structures of development rather than the end. I start to clarify the structure of development from the analysis of the changes in the network of God’s and human activities.

PREDISPOSITIONING AS THE LEADING METHOD OF CREATION AND PERFORMANCE OF THE UNIVERSE

Janus Process

Let us consider one simple case: a system composed of the production chains of different kinds of final goods. As man evolved, there emerged multistage production chains between nature and the final product. The production chains were largely separate and relatively short until intermediate products be­came more versatile, and this tangle of production chains was transformed into a uni­fied net­work.

As long as this network remained relatively simple, a change in any one of its nodes could be completely and consistently traced directly to the end re­sult, that is, the final products. Therefore, with respect to the domain of a system, which yields consistent and complete links between initial and future states, changes can originate both at the end and at the beginning. This means that the process of devel­opment is driven by a well-defined practical objective, namely, the creation of new products or technologies that are integrated in the overall network in a rather complete and consistent manner.

At some stage of human development a question arose that marked a revolution in its history: "Why not proceed in a parallel fashion, taking any arbitrary link as a starting point, even if the output cannot be completely and consistently linked with the final outcome”? However, this parallel development exacts a heavy toll. The problem is that, at the beginning, the potential worth of any given under­taking may be entirely unclear. For this reason, the efforts that have been made in the initial link can eas­ily lead to a dead end. To help the reader understand this problem, I will explain it in the context of the so-called Janus process.

Janus, the Roman god of beginnings and endings, has two faces looking in opposite directions: one in the front of his head and the other at the back. Thus, the Janus process denotes a pro­cess where the changes in the system are triggered both at the end and at the be­ginning. More than any other system, the history of mathematics has exhibited such two-ended development (see my book 1997b). On one end, there was the need to solve practical problems; on the other, there was the desire to explain the harmony of numbers and lines and such. Contrary to the pragmatic Egyptian mathematicians, the Greek mathematicians, like Euclid, Pythagoras, and their followers, professed purity of mental constructs and aloofness from reality. Certainly, this kind of development raises many difficult problems for mathematics. One of them is the judgment of an unsolved problem that starts from the beginning.

A famous example of this situation is the problem of Euclid's fifth postulate, which for a long time seemed to be a minor scholarly issue. Only in the nineteenth century did several mathematicians resolve this problem. Its solution had a revolutionary impact on mathematics and its applications, shaping in particular the mathematical apparatus for Einstein's relativity theory. (A broad description of Euclid's fifth postulate may be found in the book by Voldemar Smilga, 1970).

Certainly, as soon as we start from the beginning of a disjointed protracted system, the basic problem we face concerns the criterion for judging the validity of the first steps. Here, I want to make a preliminary remark. A typical mistake that occurs during these judgments is the attempt to measure the value of the objects that are developing from the beginning by the same criteria as the objects that are developing from the end. In fact, there is some confusion about how to properly judge some nascent developments in science and art. Specific cases include the attitude toward functional analysis in mathematics in the early decades of the twentieth century and the evaluation of atonal music. The methods that are the first candidates for judging initial stages of development are probabilistic methods, which are based on fixed and repetitive cases. Even if the authors of the Torah had an intuitive notion of probability,[31] previous experience in determining the frequency of a given event would be required in order to make this sort of determination. In accordance with the Torah, God probably lacked such experience, because God was creating the world for the first time. That is, in the Torah, there is no hint of God having any previous experience in creating other worlds.

But, what should be done in intermediate situations if they are unique? I think that the creation of predispositions that are evaluated in terms of beauty is one of the proper answers.

Predispositions

The concept of a predisposition that I have developed in the last thirty years is based on my understanding of the categories of determinism-indeterminism including its degree. (See more in my books 1997b and 2003.)

 

 

The key component that defines determinism-indeterminism is the program that links the inputs of a system with its outputs. The degree of indeterminism depends on the potential possibility of avoiding this program. In the case of determinism, the program that links the inputs and the outputs is unavoidable. That is why even if the output is uncertain the system could be deterministic if the process of interaction between the inputs and the outputs is fixed (as in quantum mechanics, for example).

The degree of indeterminism can be expressed in certain stages depending on the potential abilities to be avoided.  Combination, predisposition, chaos, mess, and mishmash are among these stages.

Mishmash could be defined as an entity that consists of undistinguishable components (like a mashed potato is different from the set of potatoes that have been used to prepare the first one.) 

Mess is defined by Webster’s Dictionary as “a disorderly or confused collection or mass of things.”

Chaos does have some regularity, as expressed by fractals, strange attractors, and Feigenbaum numbers.

A combination assumes a narrow, well-defined goal and an unavoidable program that completely and consistently links the goal with the initial conditions.

Multidimensionality is a system’s approach that could in the best way to clarify the meaning of a predisposition. Such an approach allows for a multifaceted observation of an object.[32] Some different aspects of the observation of an object are the following types:  functional, structural, operational, operatorial, and genesis.

These aspects are very well-known, but they have typically been used with the assumption of unidimensionality, meaning that one of them is an independent variable that can be controlled, while all the others are dependent variables. The systems approach assumes that all these aspects are independent variables. That is, the systems approach is based on multidimensionality. This means that if one aspect is fixed, the others still maintain a certain degree of freedom.

By embedding an object in such a multidimensional space, one can better see the object as a whole and escape one-sidedness in its contemplation.  Unnecessary arguments among scholars in the same field frequently arise as a result of the fact that each of them views the system from a single aspect, that is, on the basis of unidimensionality.

As I will show below, one could dissect a system via multidimensionality and then revive it. Now let us apply the multidimensional approach to the category of a predisposition.

From a functional aspect, a predisposition could be recognized as an entity that characterizes the strength of the influence of a given stage on future development. To be more specific, from the functional point of view, a predisposition should: 1) induce the environment in a certain way, for example, aggressive or defensive, extroverted or introverted 2) absorb unexpected outcomes in its own favor 3)  minimize the harm from unexpected outcomes and mistakes

From the structural point of view, a predisposition is based upon the concept of a position that contains as independent variables a set of material and relational objects. In their physical presentation, these objects form the set of initial components. Measurement of the components of a given position is made up of dual variables that are unconditional values.  To put it more precisely, these values are degrees of unconditionality. I will explain in detail the meaning of these values when I discuss the problem of ethics in the Torah in Chapter 5.

Now, I will define the operational dimension. This dimension refers to the formation of a predisposition as a concept that relates to an intermediate stage in a disjointed system in such a way that it is possible to find some links between past, present, and future. The means by which a predisposition is created could be called predispositioning. This method assumes a deep dissection of a system's state into its con­stituent components, which I detailed when I described the structural aspect of a predisposition. Here, we face a taboo against dissecting a system's state, because there is the possibility of losing the holistic, or synergetic, effect.

To solve this problem, we need a very different approach to dissection, an approach that will allow us to reassemble the components afterwards in order to preserve the holistic effect. The major features of this procedure are the following: First, one finds the material and relational objects of a stage. Second, one measures them in unconditional values. Some progress has been made in the creation of new mathematical methods for disjointed systems. These methods appeared under the guise heuristic programming and – in Herbert Simon’s works – satisficing solutions. Notable are computer chess programs, which are based primarily upon exhaustive (brute force), disjointed, incremental searches (C. Shannon, 1950). However, a general formalized concept that is relevant to predispositioning has not been developed.[33]

An operatorial aspect emphasizes subjectivity. I define subjectivity as the total evaluation of a predisposition by an operator.  This operator cannot be separated from the operator that implements this predisposition.

From the point of view of genesis, the formation of a predisposition in a developed case is a non-Markovian process, because it takes into account in possible future situations the past trajectory of development. The development of beauty can be treated as a general, non-Markovian process, because it takes into account influence on the present state from the future as well as from the past.

Let me now illustrate the role of a predisposition through the game of chess. It is impossible, generally speaking, for a chess player to link in a complete and consistent manner a current move with the final outcome of the game, because he would have to take into account 10¹²⁰ possible positions that could appear during the game, and he would have to do this in the absence of algorithms that could find an optimal solution to the game in an reasonable period of time. As a result, players have to play the major part of the game from start to finish without knowing the consequences of a given move.

 

 

 

 

This uncertainty makes the formulation of an intermediate goal that is pursued by a given move the crucial aspect of move selection. Many ingenious devices have been invented to deal with this problem, especially in the middle game. One of them was the combinational style, which was the prevalent until the end of the nineteenth century. The positional style is now the prevailing style for the middle game. The philosophy of the positional style is actually based upon a deep understanding of the indeterministic character of development, which is the absence of a fixed method for acting. Therefore, the master of the positional style forms his position in such a way that it could be beneficial in the future (the development of which cannot be predicted). The evaluation of the strength of a position had been done in a formal way by Claude Shannon (1950) via a weight function. The function f for some chess position π could look as follows

:   f(π) = 200(K – K’) + 9(Q - Q') + 5(R - R') + 3(B - B' + N - N') + (P - P') -.5(D-D' +S-S' +I-I’)+.1(M -M')+ ...,

where K, Q, R, B, N, P are White's extant king, queen, bishops, knights, and pawns; D, S, I = doubled, backward, and isolated white pawns; and M = White's mobility (measured, for example, by the number of legal moves available to white pieces)The letters followed by an apostrophe (K') refer to black pieces. The coefficients 200, 9, 5, 3, and 1 are the widely accepted semi-conditional valuations of relevant chess pieces; the coefficients .5 and .1 are the rough-and-ready valuations of positional components proposed by Shannon.

The stronger the position is, the better it helps a player to induce the environment in the most favorable direction. Besides, a strong position may successfully adapt all kinds of occurrences or, at least, decrease their harm.

The positional style does not eliminate the combinational one. A developed position becomes “pregnant” with combinations, and they could be relatively easily revealed in a short number of moves.[34]

Certainly, I do not claim that the positional style could exhaust the answers to the large set of questions concerning the Torah. My method of analysis is meant to apply only to some responses to a selected set of questions. By using this method of analysis, I hope to enlarge the manifold of different approaches to the unsolved problems in this field. I will take one more step before I come to the formation and the evaluations of stages of creation in the Torah. This step concerns the presentation of aesthetic value by the well-known U.S. mathematician George Birkhoff (1884-1944). Birkhoff’s (1956) formula for the aesthetic measure M is a function of two variables: C = complexity and O = order. Here is how he clarifies these measures:

The typical aesthetic experience may be regarded as compounded of three successive phases: (1) a preliminary effort of attention, which is necessary for the act of perception, and which increases in proportion to what we shall call the complexity (C) of the object; (2) the feeling of value or aesthetic measure (M) which rewards this effort; and finally (3) a realization that the object is characterized by a certain harmony, symmetry, or order (O), more or less concealed, which seems necessary to the aesthetic effect. (pp. 2185-2186)

To illustrate his ideas, Birkhoff uses the example of a convex polygonal tile. The measure of its complexity is determined by the number of its sides and the measure of order, and by such parameters as repetition, similarity, contrast, equality, symmetry, balance, and sequence. Formally, Birkhoff’s variables look as follows: C = ra + sb + tc + ..., where a, b, c = indices of tension that take place r, s, t times and that the nervous system must perform for the “material” objects to be perceived). These indices have a negative sign, because perception here is impossible without sustained interest

0 = ul + vm + wn + . . .,where l, m, n = indices of tone of feelings repeated u, v, w times. Feelings could be positive, negative, or indifferent. Ambiguity, undue repetition, and unnecessary imperfection produce clearly negative feelings.

The correspondence of Birkhoff’s evaluation function and Shannon’s function is clear. The components involved in complexity are the same as the material components, and the components involved in order are the same as the positional components. The feelings in Birkhoff’s evaluation function play the same role as the values used in Shannon’s weight function.

Predispositions as Goals

As we can see, the process of creation in the Torah is presented as being a multistage process. There is a whole spectrum of methods of performance involved in different stages. One of them is the creation of predispositions as stages with certain evaluations and directions for development.  This does not, however, preclude the authors of Torah from assuming that God varied the structure of a predisposition. In general a predisposition contains material and relational components. But sometimes could be mentioned either material or relational components.  Below I will consider only the time dimensional differences concerning creation of predispositions. In specifying the overall course of the creation and the development of the universe, the authors of the Torah delineate the stages (steps) set up by God in these processes. One can see the stages as time periods of varying durations, and each stage has its own goals.

I distinguish two factors in goal formulation. One refers to the time allotted for its attainment. This method of goal formulation prevails in the Torah. The other variety of goal formulation in the Torah specifies the desired state; here, the actual amount of time needed to reach it is an unknown variable.[35] Also note that even if the time period set aside for a certain stage it may be evident from the text that it requires a process of considerable duration, and in that case I include it among the long-lasting stages. So the duration of some stages is explicitly stated in the Torah, while for others it is not. Meanwhile, the latter stages still yield to the order of the magnitude of the time period required for their completion. (It would be interesting to explore which goals were assigned time and which were not.)

These ideas are illustrated in Figure 2.1 in the form of a 3x3 matrix. The axes of the matrix are the duration of a stage and the specificity of the goals to be achieved at a given stage. Although each of the two variables in the matrix is continuous, we can split them into three intervals corresponding to stages within the range of each variable.

The entries in the Figure 2.1 are examples taken from the Torah. I shall discuss some of them in detail. One of the entries in this matrix is empty. A reader familiar with the Torah can fill in this empty slot.

Now, I will discuss the ideas I have just discussed with respect to individual (in terms of time) stages that are distinguished on the basis of the essential parameters that are stressed at a given stage. The duration of a stage may range from hundreds of years to decades, single years, months, or days. The history of the Jewish people, as it is written in the Torah, does not follow a strict durational hierarchy, i.e. a short stage may be followed by a long stage. For instance, Abram did not have any children with his wife Sarah. God tells Abram that in one year he will have a successor "that shall come forth out of thine own bowels" (Genesis 15:3). When God promises a one hundred year old Abram and his ninety year old wife Sarah that they will bear a son by the name of Isaac "at this same time in the next year." (Genesis 17:21) God performs a miracle. At the same time, the authors of the Torah, referring to God, speak of the Jews coming to the Promised Land only after a hundred years:

And in the fourth generation they shall come back hither; for the iniquity of the Amorite is not yet full. (Genesis 15:16)

And He said unto Abram: ‘Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years.’  (Genesis 15:13)

It is also stated in the Torah:

Now the sojourning of the children of Israel, who dwelt in Egypt, was four hundred and thirty years. And it came to pass at the end of the four hundred and thirty years, even the selfsame day it came to pass, that all the hosts of the Lord went out from the land of Egypt. (Exodus 12:40-41)[36]

According to the authors of the Torah, when God sets specific goals, even remote ones, God does not announce a specific program for achieving these goals. God proceeds stage by stage, with some stages lasting for decades. For instance, the final stage of Jewish migration to the Promised Land is to last 40 years (Numbers 14:33-34). Some events last for years. For example, to "move" the Jews to Egypt in order to save them from starvation, Gods exercises foresight through the sale of his son Joseph to the Egyptians (Genesis 45:5-8). When the time comes, God, in the opinion of the authors of the Torah, sets a specific goal of getting the Jews out of Egypt and delivering them to the Promised Land. The immediate reason for God's decision was the desperate situation of the Jews in Egypt. Other events last for months.  Seeing the pain and the suffering of his people, God sets the goal ”to deliver them out of the hand of the Egyptians, and to bring them up out of that land unto a good land and a large, unto a land flowing with milk and honey” (Exodus 3:7-9, also see 2:24-25). Again, God proceeds step by step in carrying out the exodus of the Jews. God formulates relatively short-term objectives requiring days, or even hours, never revealing the entire plan ahead of time. God eventually does achieve own goal of delivering the Jews out of Egypt with the gold, silver, and clothing of their neighbors (Exodus 3:22).

To sum up what I have said, I would like to note that the authors of the Torah considered all the goals set by God as having been achieved. Meanwhile, the road to achieving them is neither clear nor smooth.

Now I am prepared to analyze in detail the creation of a predisposition in the Torah including its evaluation via beauty.