Aron Katsenelinboigen


                                                                              Chapter 6




The mathematical terms manifold and singular variety are relevant to many systems, even though I use these terms in a vague way.[71] Among these systems are political, biological, and later, the Torah.



To gain a better understanding of the process of creation it is important to distinguish between the manifold, variety, and singular variety. I propose to approach the notion of a manifold as an entity whose components involve a diversity of objects and relations between them. Unlike variety that is a set of prioritized elements, a manifold is set of elements that are unranked (i.e., indistinguishable in terms of preference or priorities). A degenerate case of a variety (which strips it of its general significance) is singular variety.

The integration of a manifold and a singular variety is a very delicate problem. The idea of combining differentiation and integration that is offered by Jamshid Gharajedaghi (1999, pp.92-93) can be relevant to the integration of a manifold. This concept assumes an approach that preserves the diversity of objects in a manifold and avoids the temptation of a simplified version of integration via the uniformization of the objects. The integration of a singular variety assumes that each object has its own local internal value (e.g., utilities of an individual), and simultaneously, that a global value parameter can be formed for the whole field of the system (e.g., prices in an economic field). The fact that each object can be explicitly represented by a triple of parameters, which are the physical characteristics of an object, its local and global values, allows for the integration of a singular variety by different kinds of vertical and horizontal mechanisms (see my book, 1988).

A pluralistic mechanism is the leading one for the development and integration of a manifold and a singular variety. The performance of a pluralistic mechanism can be divided into the following stages: the creation of a growing manifold of components under the assumption that each component is taken not as truth but just a hypothesis of its nature; the selection of more valuable components from the manifold that could be better adjusted to a given area; the revision of the value of selected components in terms of their adaptation to the given area; and finally, if it is necessary, a replacement of those previously chosen components that are incorrectly adjusted by new ones from the expanding manifold.

A Manifold and a Singular Variety in a Political System

A manifold in this system contains a set of political programs that represent different paths of development of the country, because is impossible to find a complete link between each program and the future of the country as a whole. The relations between the programs are based upon independent organizations, as well as independent financial sources, to back them up. A preserved multiparty system fulfills this role.

A pluralistic mechanism is particularly intricate in countries with people who possess relatively low political culture. Even in these countries, the question is not whether to introduce a pluralistic mechanism or to prohibit it. The question is to what extent the scope of a pluralistic mechanism should be correlated with the political culture of the masses and with their participation in the political mechanism. If the political culture of the nation is sufficiently high and it possesses a deep understanding of pluralism, then pluralism is compatible with the extensive participation of the people. This is the case even in extreme situations, like England during the Second World War and Israel which throughout its history has had to face an extremely hostile environment. Meanwhile, in many countries, the conflict between pluralism and the participation of the masses in the political mechanism is resolved in a very painful fashion, e.g., the Weimar Republic turned out to be a disaster for Germany, because although it had an insufficiently mature political culture of the masses, the masses were allowed to participate in the political mechanism, and the majority of the population voted either for fascists or for communists that rejected pluralism.


   At the next step, it is necessary at any given moment to select one single program (or one combination of programs) in order to integrate a social system, for a system cannot function according to several programs simultaneously, i.e., to derive a singular variety from a manifold. It is outside my topic to discuss the stages of converting a manifold to a singular variety, of revision of the selected program, and its replacement if it is required.



As a matter of fact, the described principle of the integration of a manifold and a singular variety can also be helpful for better understanding the perennial debate between radical liberals and radical conservatives that centers on the coexistence of different ethnic groups. As racists, radical conservatives not only underscore ethnic distinctions, but also claim the superiority of one ethnos over another based on certain indicators. They go on to generalize and proclaim the universal superiority of one ethnos, while urging the limitation or even the eradication of inferior ethnic groups, i.e., they seek to obtain a singular variety avoiding the preservation of the manifold of ethnic groups. On the other hand, liberals who recognize the need to preserve diverse ethnic groups are unwilling to acknowledge a singular variety, that is, situational priorities of one ethnos over another as judged on the basis of certain criteria. In fact, radical liberals purport that the variations among the ethnic groups are fleeting and caused solely by the environment, because it propagates and aggravates differences. Perhaps inadvertently, radical liberals seem to advocate only a simplified uniformed manifold of ethnical groups.

It seems that we put ourselves in a tragic bind by opposing radical liberals’ uniformity and radical conservators’ racism. Once we recognize certain ethnos-specific qualities (i.e., the manifold of ununiformed components), we are in a position to promote the culture of each ethnos and then integrate them. Reluctance on the part of liberal circles to recognize certain qualities that are peculiar to each ethnos, especially those of ethnic groups living in the same country, leads to a virtual imposition of the dominant culture upon all other groups. The consequences of such an attitude may be dreadful.

The fact that racists spotlight certain ethnos-specific traits is not evil per se. Their vision is flawed because they ignore the fact that the differences are limited, meaning they fail to reflect the full range of qualities intrinsic to a given ethnos. Racists also tend to exaggerate the importance of certain traits and even falsify facts to confirm their statements. The pronounced value judgment that they make is at best situational, for the performance of any given trait depends on the prevailing circumstances, and a shift in the environment may cause certain traits considered negative to become positive. This rejection of variety may also lead to tragic consequences.

A Manifold and a Singular Variety in a Biological System

In the initial stage, the manifold of living creatures is formed. This stage supports the creation of old and new living beings. Relations between the species are implanted in individuals and expressed through their interaction. For example, carnivores are hunting for herbivores. The relationship between carnivores and herbivores, between a pike and a carp, could not be evaluated unconditionally, because it could have a negative value, from the point of view of killing, and a positive one, from the point of view of sanitation, i.e., the extermination of sick beings that could cause an epidemic disaster.   

 In the second stage, the manifold of creatures and their relations "lives and works" in an environment where the creatures' capacities to interact are actually realized. At this stage, the manifold converts to a singular variety that defines the different degrees of importance of living beings in a specific environment from the point of view of their survival. The third stage reveals how well the selected set of living beings copes (and thus develops) in a given environment. In the fourth stage, the manifold of creatures undergoes a restructuring of the ratios of various species, and then there is continuous interaction with the environment. Naturally, there is feedback from all of these stages.

The creation of a manifold is the leading part of biological evolution, because it is frequently impossible to determine what the role of a certain being will be and what its relationships will be in different situations in space and time. Often the same living being can play a variety of roles in different environments. For example, bacteria bring illness as well as provide benefits in the digestive process. The term virus has a negative connotation, because it is associated with diseases. Nevertheless, viruses also play a positive role. It is known that viruses can cause a recombination of the cell's genetic code in a manner similar to the way a male cell acts upon a female cell. These kinds of recombination can be of a very orderly nature and can even lead to transformations in an organism that are better adapted to the environment.

As Konstantin Umansky mentioned in his book (1984):

… one feature shared by all respiratory virus infections is that they are seasonal and correspond to changes in the environment (Fall/Winter and Spring seasons). It is important to note that these outbursts are not "calendar specific" but correspond to the extremum points of the changing environment, i.e., time frames when adaptive reorganization is most urgent, especially so for respiratory organs. These observations lead us to conclude that certain respiratory viruses are factors that partake in the organisms' adaptive acclimatization. (p. 30)

The following famous example of the survival of a certain type of butterfly shows how important it is to preserve a manifold under unexpected, day- to-day changes in the environment. In the state of Michigan (USA) and in England, there is a kind of a butterfly that mutated into white and gray varieties. In the time prior to the Second World War, the white variety prevailed, because the bark on the trees that the butterfly used was light, and predatory birds could not see them. Meanwhile, the more vulnerable gray butterfly also appeared. After the War, trees became gray as a result of unexpected pollution. In the new situation, the gray butterfly became the most adaptive. Meanwhile, the white butterfly continued to appear.

The major drawback of biological science is its inability to understand the mechanisms of the creation of a manifold. Leading biological theories are based on the idea that the creation of something new occurs through the mechanism of random mutations that are caused by such external factors as chemicals, radiation, and viruses. Together, the new living beings form a manifold, because their importance cannot be judged from the standpoint of an unforeseeable future. With regard to the current situation, in which the actual environment is determined, different mutations possess different degrees of adaptability. The hereditary mechanism works so that the mutations with the greatest chance of survival in the existing environment will prevail. Some biologists (for example, E.K Tarasov, 1979) have shown that the probability distribution of mutations after changes in the environment are not totally random, i.e. the process of mutation is somewhat regularized, so that the manifold is ordered to a certain extent.

Acknowledging the enormous role of the mechanism of random mutations, it is reasonable to ask whether this mechanism is always capable of transforming existing species into new species that are based on new principles. Assuming that random mutations only support small changes, the nascence of new forms of life via continuous, gradual, evolutionary transitions is often topologically impossible.

A feasible hypothesis that could help solve this problem is that there may exist an internal mechanism of change in the structure of the genome that leads to the creation of new forms of organisms. In other words, the genome itself might possess a genetic program to change the first-level genetic program that directly shapes the living organism. It is difficult to say how many levels of such genetic programs there are, i.e. programs that change programs that change programs, which in turn change programs, and so on, until we get to the first-level program. In any case, the hypothesis of multilevel programs, even if their number is limited to two, seems quite valid. As I have shown in my book (1997a, Chapter 5), several facts may serve as the first signs announcing the forthcoming proof of the existence of an internal mechanism of change. These facts include: the existence of a major set of genes whose role is unclear, i.e., the so-called "junk" genes; the existence of regularities in this set of genes; the existence of jumping genes, as discovered by Barbara McClintock; and the ability of a DNA molecule to be an enormously powerful computer, as designed by Leonard Adelman.


Preservation of the Manifold of Living Beings

Whatever guided the authors of the Torah is founded upon creating and preserving a manifold of components, i.e., material components and the relations between them. What is crucial here is the presence of certain classes of objects, since each class fulfills some particular function that is important for the operation of other objects in the system. It is quite possible that the authors of the Torah were thinking about what we would call in modern terminology the ecological harmony of the world, and by this, I mean the interrelationships and mutual dependence among different living organisms.

Different values of different components were not set in the beginning, although the whole manifold was evaluated. Creation of all components in the first six days was declared to be very good (Genesis 1:21). My interpretation of beauty in the Torah as the value of the whole manifold is to a great extent close to the interpretation of inclusive beauty by Stephen Ross (1998a):

Beauty here carries a double meaning, inclusive and exclusive. In the exclusive, restricted sense, it pertains to how things appear, their manifestations, and to the joys human beings experience when presented with beautiful things: human bodies, artifacts, natural creatures, and things.  Relevant questions here are always what kinds of things are beautiful and what are not, what qualities make something beautiful.  In the inclusive sense, beauty pertains to anything worthy of approbation, to human virtues and characters, to nobility and goodness, to hidden things and truths, to the natural and the divine worlds.  Almost anything may be regarded as beautiful, and beauty may include almost any quality.  In the exclusive sense, it is important to distinguish what is beautiful from what is not. In the inclusive sense, beauty resists binary oppositions, joins disparate and opposing terms.  As different as these two meanings may seem today, they have not traditionally been kept distinct. (p.237)

Ross’s statement that “almost anything may be regarded as beautiful” (my italics, A.K.) ruins the purity of his concept, because for a strong concept, exceptions are not allowed. When exceptions emerge, either a broader concept should be developed that incorporates the exceptions, or new concepts should be developed in order to handle the exceptions.

After the creation of the universe, the manifold of created components is converted to a singular variety where good and bad components are evident. The interpretation of the process of the creation of the universe as a set of predispositions resolves the well-known inconsistency that during the first six days of creation, all objects are good, but as the process unfolds, a division emerges between good and bad. Using my terminology, the judgment “everything that God had made, and, behold, it was very good” is based on fully unconditional values. These values are essential from a long-range point of view, because the role of any species in the future is unknown, and it is therefore necessary to preserve the whole diversity of species. In the process of development, taking into account different degrees of conditionality in different kinds of situations, corresponding rewards and punishments can be assigned to different objects in the frame of a species. Again, I repeat that the diversity of species has to be preserved as a strategic constraint. So, whatever guided the authors of the Torah, this document is founded upon the idea of a developing God who preserves the diversity of species while eliminating some living beings of a given species.

Now I will develop the analysis of the singular variety. Very soon after creation of the world, God begins to distinguish the values of different living beings. God implicitly sets a negative valuation on Adam and Eve after they violate God’s restrictions, but this evaluation is made to only exile them from the Garden of Eden, thereby allowing for the preservation of their lives. This supports the idea of creating a singular variety while preserving the manifold, as does the attitude that is taken toward the serpent. To the authors of the Torah, the serpent is the subtlest of all the land animals created by God (Genesis 3:1). The serpent makes a lot of trouble for God. It challenges God by seducing Adam and Eve, who were created in the image of God. Nevertheless, God does not erase the serpent as a species but only puts a curse on it by saying,

            upon thy belly shalt thou go, and dust shalt thou eat all the days of thy life. (Genesis 3:14)

The Ark

After the living beings multiplied in huge quantities God found that the majority of them was bad. He became disappointed with his creations and decided to exterminate them. And God saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.

And it repented the LORD that he had made man on the earth, and it grieved him at his heart. And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them. (Genesis 6:5-7)

Meanwhile, God preserved the manifold of living beings. First, he found among people the righteous ones, such as Noah and his family, and Lot and his family. Next, he corrected the singular variety by punishing many living beings or even by exterminating them with the flood. He still used other methods that he, for example, applied to Sodom and Gomorrah (Genesis 14:10) and Admah and Zeboim (Deuteronomy, 29:23). 

The legend of Noah clearly illustrates the four steps of the integration of a manifold and a singular variety. After the creation of the universe, a huge manifold of human and living beings has been developed. This manifold, as I have mentioned above, has been converted to a singular variety. Observing this singular variety, God becomes furious and decides to correct it by choosing from the manifold only a very limited number of living beings and exterminating all others, i.e., eliminating the undesirable living beings, while preserving the manifold of all species. In other words, the integration of the manifold and the singular variety means the preservation of all living beings as species along with the extermination of many individuals in each species. To implement this decision, God chooses righteous people such as Noah. As the Torah says, "Noah found grace in the eyes of the Lord" (Genesis 7:2). God asks Noah to create an Ark so that Noah, his family, and representatives of all other species will be saved during the flood. God says to Noah,

And of every living thing of all flesh, two of every sort shalt thou bring into the ark, to keep them alive with thee; they shall be male and female. Of fowls after their kind, and of cattle after their kind, of every creeping thing of the earth after his kind, two of every sort shall come unto thee, to keep them alive. (Genesis 6:19-20)

Subsequently, God says to Noah:

Of every clean beast thou shall take to thee by sevens, the male and his female: and of beasts that are not clean by two, the male and his female. Of fowls also of the air by sevens, the male and the female; to keep seed alive upon the face of all the earth.' (Genesis 7:2-3)

On the first glance the two accounts of life being saved look contradictory. As famous writer and scholar Chaim Potok (1989} mentioned:

Often I wondered how the biblical editors had regarded the Bible’s contradictory material. How had they fell as they read, for example, the two flood stories (the animals brought to the Ark in sevens and in pairs in Genesis 7:2, and the animals brought only in pairs in Genesis 7:9)?

Naturally, I wondered what criteria they had brought to the editing process: I found it all intellectually exhilarating.

In a private conversation, my friend Michael Levins convinced me that there was no contradiction between these two flood stories. The first story (Genesis 6:19-20) concerns the genders of the animals, i.e., the claim to take a pair of each animal - a male and a female (and this is repeated in the second story Genesis 7:2). The main concern of the second story is the proportions of different kinds of animals (clean and unclean) that have to be saved. As a matter of fact, in the Rashi’s commentaries of the Torah we don’t find any hints to treat these two statements as contradictory.

 Anyway, in case when a pair of each kind is saved, we talk about a manifold, i.e. a set comprised of objects that are indistinguishable in value. The unequal number of clean and unclean animals saved in the second version suggests that the preference was shown for the clean ones. In both cases, however, the general amount of the saved species is kept qualitatively intact.

The legend of the Ark brought forth a huge literature that includes an analysis of this legend (Mayr, 1982), and even a scientifically valid story of an attempt to find the Ark on the Mount Ararat (Corbin, 1999). The literature related to the Ark also pays a lot of attention to comparisons of the biblical legend of the ark, the Mesopotamian version of the ship that preserves living beings during the flood, and the character of Noah, etc. The legend of Noah immediately stimulates at least two questions. First, “If God is omniscient, omnipotent, and ubiquitous why did he create so many bad creatures?” Second, "Why did God prefer to destroy the offspring of his own creations instead of preventing their bad actions?”

Only with the assumption that God is absolute and, thus, knows the future and applies the combinational style while interacting with the world can one assert that the bad creatures were created and destroyed just to teach the rest a lesson. Otherwise it would be logical to assume that God had no knowledge of how his creatures would develop in the future since he wouldn’t be able control their free will. As the history of mankind reveals,  the removal of bad beings does not prevent the appearance of new ones. It is sufficient to mention the case of Sodom and Gomorrah, which occurred after the flood and the growth of homosexuality in the present times.

The creation of a singular variety by God is based upon the diversity of individual beings and their ability to perform different actions. It seems to me that individuals from various "nations" (ethnic identities) differ in the following sense. Each ethnos is composed of individuals with unique mentalities. At the same time, in each ethnos there exists an active group of individuals sharing similar mentalities. This core group of people forms what is called a “national character.” The core could be relatively small, but it is sufficient to preserve the existence and development of the given ethnos. The diversity of individuals in each ethnos creates a potential for different actions in different environments, actions that could be good or bad.  Free will is the realization of this potential.

Free Will

Let me give my definition of the category of free will. Will is, first of all, a desire to realize plans and make achievements; hence, will power is a measure of this desire. Free will means that one can vary his will power in pursuing his objectives in life. A lack of free will means that the will power is fixed, so that any controlled change in one’s behavior is categorically ruled out.

The last statement is illustrated by the problem of determining how much responsibility a human being should bear for his actions. On the one hand, the environment imposes certain restrictions upon an individual. The restrictions are expressed in social values, such as thou shall not murder, thou shall not steal, etc. An individual may possess other values and enjoy killing others, but the liability he possesses for his actions is determined by his capacity to perceive the requirements that are imposed by the environment that he could adjust his behavior appropriately.


 If an individual is incapable of such adjustments, he is not held responsible. Indeed, insane people are regarded as not being responsible for their actions, precisely because their program of behavior fails to fulfill all or just one of the necessary conditions for responsibility.  Those conditions are (1) the internalization of external constraints and (2) the generation of a proper behavioral response. A given society deems someone a criminal because he is considered capable, at least in principle, of altering his conduct according to the dictums of the environment, but he fails to do so because he possesses individual values that are opposite those of society, and it gives him greater satisfaction to fulfill his own values and ignore society's dictates. Punishing the criminal is actualizing for him the potential system of punishment. This may prod him to curb his individual values and avoid crime in the future.

I would like to elaborate on the category of free will in the framework of the types and the levels of the processes that run living beings. First, processes differ in their sources of origination. There are natural processes that are innate, and there are cognitive processes that are acquired by one throughout his life. Both types have different levels structured by different degrees of power. Behavioral processes that, according to Herbert Simon, directly govern the behavior of creatures are denoted as zero-level processes. They can be altered by the first-level processes that, subsequently, can be modified by the second-level processes, and so on.

Of course, if the hierarchy of processes is truncated at the first level, and if the first-level processes are fully fixed, the zero-level processes could also eventually become fully fixed. However, if the hierarchy has at least three levels, and if it allows for change-inducing feedback between different levels, the whole picture changes dramatically.

The described hierarchy of processes resembles the system of education. Their affinity is revealed if we consider that as a result of learning, which is based upon one's own experiences and deliberations as well as the experiences and deliberations of others, a given-level process causes changes in adjacent-level processes.

In either case, a lack of free will in living beings results in all kinds of psychological disorders, be it a maniacal pursuit of the zero-level program if will power is strong, or total inability to do anything to realize an objective if will power is weak. In the latter extreme case, any attempt at attaining one's goal produces complete physical and nervous exhaustion.

In general, natural processes seem to be more conservative and rigid than cognitive ones, for they reflect a long list of accumulated experiences of living organisms acquired through interaction with the environment. Natural programs are largely hereditary. We can clearly see that different types of beings in nature have not perceptibly changed over the millennia.[72]

With respect to cognitive programs, they do change quite rapidly under the impact of a fluid, artificial, man-made environment, that is, new kinds of food, weapons, etc. For example, the sensations that we feel from eating are biologically determined and seem to be correlated with our need for different kinds of foodstuffs. These sensations are not likely to have changed much in the course of human history. Civilization, however, has produced foodstuffs that have a heightened effect on our gustatory sensations, inducing us to eat more than physiologically necessary. The tension between the biologically-determined gustatory sensations and artificially manufactured products causes a full-scale war between intellect and will on one side, and biological drives on the other, with the latter often winning by suppressing both intellect and will.

Thus, free will may be viewed as the ability of a being to carry out its zero-level program and to change a program of a given level through changing a higher-level program. The Torah can be interpreted by using examples of free will in different beings that were created in the process of the creation of the universe. The presence of a free will in human beings is not mentioned at all in Chapter 1 of Genesis but it is easy to conclude that free will exists from the behavior of Adam and Eve. The existence of free will in other beings can even be surmised from the text concerning the creation of universe, i.e., Chapter 1 of Genesis.

An intricate interpretation of the Torah imbues plants with free will as well:

And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree [emphasized by A.K.] yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and  the tree [emphasized by A.K.] yielding fruit, whose seed was in itself, after his kind: and God saw that it was good. (Genesis 1:11-12)

A number of scholars, among them Or Ahaim, Rumban, and Baal Ahaturim, have pondered the difference between verses 11 and 12 in Genesis 1. God asks for the creation of a fruit tree, and the earth produces just a tree. This disparity can be interpreted as proof that the earth has a free will.[73]

Leon Kass (2003), using some ideas from Robert Sacks (1979), brought a broader list of cases confirming that, in the process of creation, different objects possess a free will:

The text speaks twice of each creative act, once to call forth ("Let there be"), once to report the act as performed ("And there was"). Only in the case of the creation of light is the report of the creative act letter-for-letter perfectly identical to the call for the creative act: "Let light be" and "Light be." Only in this case is God's speech precisely and perfectly efficacious in its mode of creative and revealing "letting be." In all other cases, there is a clear difference between command and performance. For example, God asks the earth to "grass grass," but the earth instead "put forth" [totse'] grass (1:11-12)—leading the rabbis long ago to remark that the earth was first in disobedience. A second example: God, perhaps now mindful of the earth's recalcitrance, later asks the earth to "put forth" [totse’] the terrestrial living creatures (1:24), but it turns out that God has to make" ['asah] them Himself (1:25). In fact, resistance to order may be present even earlier: at the very start, after God has fully separated the light from the dark, calling the one Day and the other Night, the text reports that there was evening and there was morning: the separated Day and Night, quite on their own, had drifted partially back together, blurring the boundaries between them. The recalcitrance of matter, like the mischievous propensities of life, promise massive changes, even for God's created order. (pp.49-50)

So, it is possible to explain the behavior of God concerning the extermination of beings on the basis that all of them have a free will. However, such an explanation would be cumbersome, because it resorts to various logical manipulations.[74]

 Unexpected Outcomes and Mistakes

It is more elegant to approach the behavior of God that relates to the Flood with the assumption that God is a developing entity who employs a positional style that precludes definitive, fully-certain predictions. This style suggests a possibly incomplete and inconsistent process of the creation of predispositions that may be associated with unexpected outcomes. The latter should not be confused with mistakes, because this term suggests that the creator possesses proper knowledge of the process but mishandles the implementation of it (like a mistake in spelling).  Moreover, the recognition of God as a developing entity is consistent with such attributes of God as omnipotent, omniscient, and so on, in the following sense: God is able to recognize unexpected outcomes as sdoon as they have happened, evaluate them, and on the basis of a created predisposition, channel them along a desirable course.

Allow me to briefly repeat and enlarge the aforementioned myth about the Flood using an approach that will shed some new light on this story as told in the Torah. The discovery of "badness" in the conduct of many people and living beings may represent an unexpected outcome for God. God repents the creation of Man and animals by unleashing a flood (Genesis 6:6-7). God bears down upon the life God has created with all God’s destructive power, while channeling God’s constructive force to save the righteous Noah and his family and animals (Genesis 6:8, 17-22, 7:1-24, 1-19). The destruction inflicted upon the world by God was so great (an unexpected outcome) that it made God think of what was done; it made God look deeper into the motives behind human behavior; and it caused God to change own behavior in the future. This point is explicitly stated by the authors of the Torah:

and the Lord said in his heart, I will not curse the ground any more for mans sake; for the imagination of mans heart is evil from his youth; neither will I again smite any more every thing living , as I have done. (Genesis 8:21)

To make good on the God’s promise, God establishes a covenant with Noah and his descendants. (Genesis 9: 8-17).

The point I want to stress is that the authors of the Torah did not think of God's fairness as a static category that is instilled within God to the limit. Initially, God is less fair or, to be more precise, his actions are more arbitrary, because he does not always realize his own limitations and he does not foresee the possible consequences of his own actions. God's moral stature grows as he accumulates experience and becomes conscious of his own actions.

So, the flood can be viewed as a result of God's limitations in foreseeing the future. Here we are facing a very important problem: “Are the limitations inherent in God’s nature, or are they set by God”?

Neil Gillman (2000) solved this problem in the following way:

God accepts Moses' arguments and renounces the punishment (Exodus 32:14). So much for God's vaunted omnipotence! De jure, God has all the power, but de facto, that power is limited by God's public image and by promises God has freely made. This God seems to be a limited God, not by God's own essence but rather by specific extrinsic factors. This is not an intrinsically limited God but rather a self-limiting God. (p.39)

I think that God is limited by his own essence. Indeed, if God could have foreseen the consequences of his own actions he would not have destroyed his creations later. This concerns not only human beings, but fauna and flora, as well. The repentance of God over the flood is a clear confirmation of it.

God's inability to foresee the far future may be also interpreted as a presence of some other limitations, such as, for instance, his inability to speed the process of development. Still, the Torah explicitly reveals God's desire to expand his sphere of influence. It therefore becomes necessary to simulate development over some fixed period of time and risk the possibility of unexpected outcomes. The creation of a predisposition for future development allows us to reduce the risk and make necessary corrections in the course of development.

This practice can be interpreted as God’s intention to eliminate undesirable, unexpected outcomes arising in the course of development of the world. This, however, has nothing to do with the idea of God correcting his mistakes. Indeed, as I have mentioned, the notions of a mistake and an unexpected outcome are quite different.

That is why I don’t share the opinion of some scholars who interpret some of God’s actions as mistakes when they could be interpret as unexpected outcome. Allen Dershowitz’s writings concerning the flood (2000) are an example of the interpretation of the flood as a mistake.                                                                                                                                                 

… the God of the Jewish Bible is a learning God as well as a teaching God, and perhaps He was wrong in flooding the world. He seemed to have acknowledged His error by "repenting" his decision to destroy the world just as He had earlier "repented" His decision to create man. When God made His covenant with Noah after the flood, He promised never again to bring any floods to destroy the world. Yet He knew that people would turn bad again. Indeed, He expressly promises never to "curse the soil again on humankind's account, since what the human heart forms is evil from its youth"(8:21). Nevertheless, He absolutely precluded Him-self from bringing another flood. This certainty suggests that God may have realized He made a mistake, one He did not want to repeat. When God saw how evil man could be, He had a shock of self-realization: He had created this evil creature in His very own image, so maybe He too has the capacity to do evil—a capacity He must learn to control. Like a person who understands that he needs to make a public promise in order to control his destructive instinct, God bound Himself never to flood the earth again. Even God needs rules. (pp. 65-66)



     [71]. Here I will provide a simple example that illustrates the accepted mathematical terminology of a manifold and a singular variety. Let us take a circle. Each point on the circumference has a neighborhood that is typically equivalent (homeomorphic) to the same topological structure, namely an open interval on a straight line. Structures of this type will be called a manifold. Now take a curve shaped like a figure eight (8). It has one singular point (point of self-intersection) the neighborhood of which is topologically different from the neighborhoods of other points. This type of structure will be called singular variety. We can think of the figure 8 as being derived from a circle by the following process:


[72].That is why some theatre directors, to emphasize the unalterable nature of human nature, dress their actors playing ancient Greeks in modern-day costumes.

      [73].I am grateful to Ilya Mayzel who called my attention to the above statement.

[74]. This situation reminds me of the interpretation of the planetary system by Claudius Ptolomaeus  (2d century A.D.) as a geocentric system and by Nicolaus Copernicus (1473-1543) as a heliocentric system. Both interpretations allow the calculation of orbits, but the first one does so in a cumbersome way, the second in an elegant one.