And G-d said, 'Let us make man in our image, after our likeness'

The reader is offered a series of articles where I will discuss the aspect of the Kabbalah of Information that I deem the most important: The Theory of Likeness, which is the universal aspect of Creation. I will then apply this theory to explaining the nature of life and death, good and evil, and beauty, as well as providing commentary on multiple scenes from the Torah.

I would like to apologize in advance for the slight academic terminology overload in the first article; that said, I believe that such terminology is essential for a proper understanding of the matters that I touch upon.

This series of articles will be exploring the key law that governs interactions between humanity and the Almighty: The Law of Likeness. 

For the reader's reference: according to the Kabbalah of Information, Creation is a hierarchical information-based structure, and the main prerequisite for its existence is the exchange of information between the Almighty and humanity. Kabbalah stipulates that human beings determine how this exchange will be taking place.

Louis Jacobs notes in his foreword to ‘The Palm Tree of Deborah,’ a book by Rabbi Moses Cordovero, one of the most prominent scholars of the Kabbalah, “The most striking and far-reaching of the Kabbalistic doctrines is the role ascribed to man because man mirrors the world of the Sefirot [and] his behavior influences that world. He is the purpose and the summit of Creation, and by his deeds, he determines the flow of Divine grace here below. By his sin, he brings about an unbalance among the Sefirot. If he is virtuous, he helps to unite the upper and lower worlds. To use the well-known expression of the Zohar, ‘the impulse from below calls forth that from above’”.

In his Gates of Light, Rabbi Joseph Gikatilla writes, “If the sons of Israel are righteous... the wellspring shall be filled with life-giving waters, coming from the higher emanations, and all shall prosper and be filled with goodness. But when the sons of Israel sin, the water ceases to flow, and the wellspring becomes dry land (yabasha in Hebrew). Then the sons of Israel hunger and thirst, and lose their connection to the Divine.”

From the Kabbalah of Information standpoint, the nature of interactions between humanity and the Almighty is dictated by the Law of Likeness, which I will review below.

Likeness

I believe it is possible to base the description of Creation’s information-based structure on the information space model, which was suggested by Richard Hamming and described by Manfred Eigen in his book, From Strange Simplicity to Complex Familiarity. Important clarification: I by no means believe that G-d's Creation can be adequately described in mathematical terms; what follows is just an approximation. 

Hamming's model pictures information space as a set of concepts, represented by a sequence of symbols; space is a hypercube with n dimensions (where n is the number of symbols used for representing a given concept).

Each concept is located at its own vertex of the hypercube. Hamming also introduces the notion of distance within the information space. Let us elaborate on that. 

In some theological circles, there is a widespread assumption that the spiritual realms do not have any “distance” the way it exists in our physical realm. But I believe that this assumption is fundamentally wrong. In the book ‘Etz Chaim’ (the teaching of the Arizal, written by Rabbi Chaim Vital), it is written that “the world ‘Yetzirah’ does not receive its light from the world ‘Beriah’ except through the curtain and the distance.  The world ‘Asiyah’ does not receive from ‘Yetizrah’ except through the curtain, the distance, and that lessening.” 

The main idea in the Kabbalah of Information is that the laws of Creation are universal and that its laws apply to all possible realms (information-based structures). 

1 - In Hamming's model, the shortest distance between two concepts is defined as the minimal difference in their symbolic representation (for instance: 1-1-0 and 1-0-1). 

2 - The distance between two identical concepts equals zero. 

3 - According to Hamming, movement within this information space follows the edges of the hypercube, and since there are several sides extending from each vertex, the number of possible combinations is immense.

Richard Hamming proposed his model with a purely practical task in mind: controlling how accurately messages are relayed and eliminating errors. In order to describe the information-based structure of Creation, Hamming's model needs to be reworked, specifically as follows: 

1 - The distance between the concepts is defined by the differences in their information content (Understanding).

2 - A distinction must be made between the Almighty's understanding of concepts, which is absolute, and the human understanding of concepts, which is relative. 

3 - Hamming's model is static. Creation, however, is dynamic: its dynamics constitute an infinitely changing chain of concepts.

4 - In this information space, movement (the movement of a soul) can be defined as a change in understanding.

5- The movement between concepts that are known to us is easy and unobstructed. 

6 - The movement towards concepts that are unknown to us is more challenging. I will talk about it in more detail in future articles.

The nature of information exchange between the soul and the Sefirot system depends on the distance between them. 

When a certain "critical distance" is reached, interactions between the soul and the Sefirot system are minimized and distorted.

The distance between the soul and the Sefirot system is defined by the soul's Likeness to the Sefirot system. The greater the Likeness, the shorter the distance.

Let us now consider the concepts of Likeness and Understanding.

Likeness

In the Alter Rebbe's theory, the soul is structured the same way (has the same image) as the Tree of the Sefirot. 

I believe that the Likeness of the soul to the Tree of the Sefirot depends on the soul's information content, i.e., the understanding of the Tree's concepts. This can be illustrated with an example from geometry. All triangles have the same image, but only those with the same angles can be called similar triangles, or triangles with a "likeness." Therefore, in order to bring ourselves closer to the Tree of the Sefirot, we must perceive and understand its concepts, which are relayed in the Torah, the Prophecies, and the Commandments.

It is important to bear in mind that we will never be able to grasp the concepts completely, the way the Almighty is capable of doing; otherwise, the distance between the soul and the Almighty would have equaled zero, which is absurd. This statement can be reaffirmed with a quote from Kohelet (Ecclesiastes), as recorded by King Solomon: “Also the [wisdom of] the world He [the Almighty] put into their hearts, save that man should not understand the work which G-d did, from beginning to end.” 

UnderstandingThe notion of Understanding is subjective and immensely complex and has not been defined in modern research. 

In 1949, Claude Shannon and Warren Weaver published a book called ‘The Mathematical Theory of Communication.’ The aim of their theory was to solve a practical task: namely, to find a way of communicating information as efficiently as possible, with minimal error. However, with time, the research community realized that the provisions of this theory go far beyond the technical process of information exchange and are, in fact, the underlying principles of our reality. The Shannon–Weaver model of communication deserves to be equated in importance to fundamental physics theories by Newton, Maxwell, and Einstein.  

The key concept of Shannon and Weaver's theory is information entropy, which defines how much information we do not yet know; in other words, entropy describes the degree of our uncertainty. 

As Claude Shannon said, “Information is the resolution of uncertainty.”

Shannon's theory is indeed fundamental; at the same time, it only describes the quantitative aspects of information and does not touch upon the concept of Understanding. The theory introduces a unit of measurement (bits) for the amount of information conveyed in a single symbol, but there is no such thing as a specific amount of Understanding per symbol. 

In his book ‘Torah Or,’ the Alter Rebbe writes that letters play the role of inanimate matter, contrasting against the mind that is “clothed” in them. 

From my point of view, the Understanding of a predefined specific concept lies in the awareness that it is connected to other concepts that we already know, as well as the ability to start using this concept in logical chains together with these known concepts during the information exchange process. 

Consequently, Understanding can, roughly speaking, be represented as a branching structure, made out of the sides of the information space hypercube, which are linked to one another and connect a specific concept (the target of our Understanding) with other known concepts.  

In Hamming's model, if the concepts are expressed with n symbols, the size of the information space (the number of the hypercube's vertices) equals 2 to the degree of n (for a binary system). If the number of symbols increases by 1, the size of the information space will equal 2 to the degree n+1, i.e., it expands twofold. 

If we assume that the complexity of a concept is, in some way, proportionate to n (the number of symbols used to express it), we will see that, as the concept grows more complex, the information space expands exponentially. Correspondingly, the number of hypercube sides extending from a single vertex also increases substantially, which, as described above, significantly hinders the Understanding of this concept.  

The physical realm that we live in is an information space zone that contains concepts with relatively "simple" information content. The information content of "spiritual" realms is much more complex. As we move to the first phase of Creation (Tzimtzum), concept complexity steadily increases. And when it comes to the nature of the Almighty (Ein Sof), this information concept transcends our understanding, i.e., its complexity is infinite.  

It is written in Etz Chaim, “It is mandatory that there should be a middle level between the Emanator and the emanated for there is a distance between them such as the sky from the earth.” 

Some points to illustrate the above.

1 - Albert Einstein used to say, “Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.”

2 - The Unity of Human Knowledge lecture by Niels Bohr, one of the founders of quantum physics, mentions that the description of an experiment and the analysis of the observations obtained must be provided in a simple, easy-to-understand language.

3 - Simplicity and elegance are considered one of the most important characteristics of any theory in physics. Just think back to Albert Einstein's famous E=mc2.

4 - Rabbi Shneur Zalman of Liadi (the Alter Rebbe) tells the following story in his ‘Ma'amar Admor Hazaken:’ 

One Saturday, Rabbi Isaac Luria (the Arizal) fell asleep at noon. His student, Rabbi Abraham Ha-Levi, noticed that he was muttering something in his sleep. When the Arizal awoke, Rabbi Abraham asked him to explain the meaning of what he had been saying. He answered to his student that while he slept, his soul had ascended to higher realms and explored the secrets of the Torah. Rabbi Abraham asked him to share at least one of those secrets. But the Arizal only smiled and said, “I swear upon the heaven and the earth, even if I had lived for 80 years and spent all of these years talking about what I learned of Balaam's she-donkey, I would not have been able to retell it all.” 

1 - The information-based interactions between the human soul and the Tree of the Sefirot are defined by the distance between the two.

2 - The distance between the soul and the Tree of the Sefirot is defined by the former's Likeness to the latter.  

3 - The soul's Likeness to the Tree of the Sefirot is defined by the information content and the understanding of the Tree's concepts.

This matter calls for further discussion, with a special focus on why the likeness of the soul to the Tree of the Sefirot gets distorted.

The Problem of Evil is one of the central problems discussed in the Kabbalah. There are countless interpretations and explanations, mostly boiling down the idea that Evil is the Sitra Aḥra (literally, the other side), the complete opposite of the realm of the Sefirot. The book of Zohar mentions ten "anti-Sefirot." One of the fundamental aspects of the Arizal's Kabbalah is the "Shattering of the Vessels" of the Tohu realm. According to this theory, the Shattering was what created the Kelipot of Evil. The Alter Rebbe, in Torah Or, mentions that the Sitra Aḥra and the Sefirot mirror one another. Modern philosophy has a theory that, essentially, a wicked person and a righteous person are each other's reflections. These concepts will be explained below. 

In my previous article, ‘What Is Evil. An Exact Definition,’ I defined the concept of Evil. Allow me to refresh the reader's memory: 

1 - Evil (or the actualization of Evil) is a violation of at least one of the six hundred and thirteen commandments listed in the Torah (or at least those commandments that can be feasibly followed in the modern world).  

2 - There are no evil deeds (actualizations of Evil) that are not in some way connected to a violation of at least one of the six hundred and thirteen commandments from the Torah. 

3 - Consequently, the violation of at least one commandment from the Torah is a necessary and sufficient prerequisite for Evil to actualize itself. 

Creation as an information space comprises concepts and dimensions expressed as designated symbols (letters of the Hebrew alphabet and numbers). In light of the aforementioned definition, the side of Good can be depicted as an information space segment that contains 613 concepts (commandments). The side of Evil (Sitra Aḥra), in turn, can be depicted as an information space segment that contains 613 identical commandments, except with a negation, universal for this entire segment.A brief explanation:

1. instruction commandment: "do..." 1. Sitra Aḥra: "do not..."

2. prohibition commandment: "do not..." 2. Sitra Aḥra: "do not not..." (i.e., "do...")

This gives us a mirror-like structure of Good and Evil in the information space.

The discussion above is reaffirmed in the works of scholars of Kabbalah from various historical periods.  

1. One of the most quintessential Kabbalah books, Sefer Yetzirah

1.1. Verse 2:2

The foundations are the 22 letters:

Engrave them, 

carve them 

weigh them,

permute them,

and with them depict the soul of all that was formed and all that will be formed in the future. 

1.2 Verse 2:4

22 foundation letters:

They are set in a circle

as 231 Gates.

If the sphere be rotated forward, Good is implied, if in a retrograde manner, 

Evil is intended. And this is the sign: 

There is no Good higher than Delight,

and there is no Evil lower than plague (punishment).Note: In Hebrew, Delight is abbreviated as ONG (letters Ayin, Nun, Gimel) and plague/punishment as NGO (letters Nun, Gimel, Ayin). The difference is that one letter, Ayin, is moved from the beginning of the word to its end.

The excerpts above clearly illustrate the formation of information concepts in Creation.

2. Etz Chaim, a book written by Rabbi Chaim Vital to record the teachings of the Arizal, contains the following passage:

“We find that Kelipah and righteousness, from the beginning of the world of Atziluth and until the end of the world of Asiyah, look like the images of two people: one of them is righteous, and the other is wicked.” 

3. In Torah Or, there is a passage where the Alter Rebbe cites a verse from Kohelet (Ecclesiastes), “G-d has made one against each other,” and notes that the six Sefirot from the Zeir Anpin partzuf, representing the masculine essence, have their mirror-like counterparts in the realm of Kelipot (Evil). 

4. In his commentary on the Torah verse “Behold, I set before you today a blessing and a curse,” the Seventh Lubavitcher Rebbe analyzes two translations of this verse into Aramaic, by Rabbi Jonathan ben Uzziel and Onkelos, respectively.  

Onkelos translates the original word klala as "curse.” In Rabbi Jonathan ben Uzziel's version, klala becomes "transmutation" (realignment transformation). 

In other words, he interprets the verse “Behold, I set before you today a blessing and a curse” as “Behold, I set for you today a blessing and a transmutation.” The Lubavitcher Rebbe believes that the use of the word "transmutation" proves that the "blessing" and "curse" concepts have the same underlying nature. 

Let us ponder this a little further. 

In information theory, a blessing can be interpreted as the act of opening channels for information exchange with the realm of the Sefirot. Notably, the Hebrew word for blessing, "bracha,” has the same root as "brecha" (waterway, channel). 

A curse also opens channels for information exchange, albeit with the Sitra Aḥra (the segment of the information space that contains the concepts of Evil). 

This makes it possible to conclude that the only difference between the "blessing" and "curse" is their vector (the negation operator). 

This conclusion is entirely consistent with the structure of the Good and Evil concept segments of the information space suggested above. 

In order to understand and explain the interactions between the human soul and the Tree of Sefirot, let us take a closer look at the Law of Likeness.

The necessary and sufficient prerequisite for following the principle of Likeness is to comply with the 613 commandments of the Torah. 

Any violation of the commandments makes Evil (an anti-commandment) take root in the soul, abruptly increasing the distance between the soul and the Tree of the Sefirot. Thus, the Likeness is lost. 

It is written in Etz Chaim, “When Israel sins, then it causes the distance of the superior Ima (Sefirah Binah) from above the children (6 Sefirot Zeir Anpin), and then they (Kelipot forces of evil) can suck from their inner light of Zeir and Nukva (Sefirah Malchut).”

2. There are different degrees of Likeness.  

As noted above, the realms of Creation are an information space made out of hierarchically structured concepts (the hierarchy is based on concept complexity, i.e., how difficult the concepts are to understand). Understanding more complex concepts decreases the distance, increasing the Likeness between the soul and the Tree of the Sefirot.

Provided that mandatory condition No. 1 (following the commandments) is met, the increase in Likeness (and the reduction in the distance) is determined by the intellectual effort invested into understanding the concepts, as well as by the soul's position on the main dimension of the information space: bitul. 

The bitul dimension can be roughly represented as a line, with the concept of the Almighty at one end and the concept of the person's self at the other end. The closer the soul to the Almighty, the greater the bitul degree, and vice versa. 

As mentioned above, the concept of Sitra Aḥra is an information space segment that houses the "anti-Commandments." By nature, the realm of Sitra Aḥra is passive. The Sitra Aḥra concepts actualize themselves when the person's soul is at the Self end of the bitul line. In turn, the Self end of the bitul line is where the Kelipot are. The reader probably remembers that, in Arizal's Kabbalah, the Kelipot formed when the vessels in the Tohu realm were shattered. The Tohu realm's defining feature was the lack of interaction between the Sefirot: in other words, each Sefirah embodied a very strong concept of Self. Arizal's Kabbalah and the Alter Rebbe's theory stipulate that the "shards" of the shattered vessels transformed into the Kelipot, as well as into the nascent seeds of all information-based entities with their own sense of Self, i.e., souls. 

The statements above must be confirmed by examples from the Torah.

“And Abraham approached” (Genesis, Vayeira) 

When studying the Torah, it is important to be aware that the personalities of its central characters are not static; on the contrary, they develop dynamically within the context of their experiences, affected by the surrounding circumstances and the trials and punishments that the characters are subjected to by the Almighty. 

After arriving in Canaan, Abraham comes down to Egypt and falls under the power of Evil. The life journey that follows his miraculous escape can be viewed from the standpoint of Abraham's relationship with the surrounding evil and his progress towards bitul.  

After leaving Egypt and returning to the Holy Land, Abraham parts ways with his nephew Lot, who symbolizes the inclination towards evil (Yetzer Hara). 

Notably, Abraham refuses to accept gifts from the King of Sodom after the war with the four kings. 

This requires further commentary.  

Previously, Abraham did, in fact, accept gifts from Pharaoh and Abimelech. His rejection of gifts from the King of Sodom is motivated by his refusal to have anything to do with an accursed people (which is what sets him apart from Lot).

The scene where Abraham rejects gifts from the King of Sodom prompts an important conclusion that there is a great difference between sinners in general (even arch-villains) and sinners that have been cursed by someone righteous. Arch-villains like Pharaoh and Laban still have a chance to repent. The Torah tells us:  

“And Laban arose early in the morning and kissed his [Jacob's] sons and daughters and blessed them, and Laban went and returned to his place.” 

It would be absurd to imagine the heads of the Twelve Tribes of Israel receiving a blessing from an arch-villain. The teachings of Hasidic Judaism note that when giving his blessing, Laban ascended to the high holiness level (the ‘white’ level; Laban is Hebrew for white) and then returned to his place, i.e., descended back to the arch-villain level.

In the Torah portion of Lech-Lecha, we read: “After these incidents, the word of the Lord came to Abram in a vision, saying, "Fear not, Abram; I am your Shield; your reward is exceedingly great." 

To which Abraham (Abram) responds, "O Lord G-d, what will You give me, since I am going childless...?"

A little further along in the same chapter, we read: “And He said to him, "I am the Lord, Who brought you forth from Ur of the Chaldees, to give you this land to inherit it.”

To which Abraham's response is, “O Lord G-d, how will I know that I will inherit it?”In both examples above, Abraham uses the words "me" and "I" when addressing the Almighty, thus emphasizing to some degree that he is removed from Him. But as the story progresses, Abraham's position on the Self — G-d scale shifts. 

After the circumcision and the visit from angels (the Torah portion of Vayeira), the Almighty and Abraham have a conversation. The Almighty informs Abraham of His decision to destroy Sodom and Gomorrah.

Further in the Torah, we read: “And Abraham approached ["Vayigash" in Hebrew] and said, "Will You even destroy the righteous with the wicked?".' 

It is evident that "Vayigash" here must be interpreted as a movement forward in the information space, i.e., Abraham's comprehension of more profound, complex concepts.

A further passage reads, “And Abraham answered and said, "Behold now I have commenced to speak to the Lord, although I am dust and ash.” In this line of dialogue, Abraham also uses the word "I," but he does so to emphasize how small and insignificant he is, compared to the Almighty. This fact is proof that Abraham has made significant progress into the bitul zone. 

A short while after Isaac is born, Abraham parts ways with Hagar and Ishmael. It is only after this event that Akedah (the binding of Isaac) occurs, and it is the Akedah that brings Abraham to an absolute bitul state. 

In this article, I began my exploration of the Law of Likeness, which is the universal principle of Creation. This law can explain the nature of the relationship between humanity and the Almighty and shed light on the concepts of life, death, love, beauty, and many others. This is what I will attempt in future articles. The Law of Likeness will be further supplemented with examples from the Torah.

In conclusion, I would like to highlight a very important consequence of the Law of Likeness. The discussion in this article allows us to understand why those who are Righteous are punished even for "minor" transgressions.

Unlike a regular everyday person, a Righteous person is at a minimal distance to the Tree of the Sefirot, leading to maximal Likeness. Therefore, every sinful act (i.e., interaction with the concept of Evil), even the most trivial one, rapidly creates a gap between the Righteous person and the Tree of the Sefirot, essentially destroying the Likeness. In the case of a regular person, such "jumps" are much smaller, as the distance to the Tree of the Sefirot is still quite sizeable, and the Likeness is small. 

There is another possibility as well. If a Righteous person with a high degree of Likeness (understanding) decides (G-d forbid!) to reach out to the side of Evil, the consequences can turn devastating. That is the reason why Adam and Ḥawwāh (Eve) were banished from Gan-Eden.