Golden Beauty

“They shall make an ark... two and a half cubits its length, a cubit and a half its width, and a cubit and a half its height.”

 Uomo Vitruviano Vitruvian Man 1492 Leonardo Da Vinci. (photo credit: MAXPIXEL)
Uomo Vitruviano Vitruvian Man 1492 Leonardo Da Vinci.
(photo credit: MAXPIXEL)

In the first part of this article, we looked at the proportions of the Ark of the Covenant, the Altar and Noah’s Ark, finding that all of them are close to the golden ratio and are members of the Fibonacci sequence (see Table 1): 

Table 1 (Credit: Eduard Shyfrin)Table 1 (Credit: Eduard Shyfrin)

We also concluded that there is a connection between the Ark of the Covenant, the Altar and Noah’s Ark, and the Sefirah of Malchut from the realm of Atziluth.

The conclusion of the previous article posed a number of questions (see below), and this new article shall attempt to answer them:1 - Why, when the High Priest entered the Holy of Holies of the Temple on Yom Kippur, did he say the Almighty’s name Havaya, which pertains to the Tree of the Sefirot in general, and the Sefirah of Tiferet (Beauty) specifically?

2 - Why, when the Torah describes how Noah’s family entered the Ark (in the Noah chapter), does it say, ‘And the Lord (Havaya) shut him in?’

3 - Why is the golden ratio associated with the concept of beauty?

4 - What impact will our findings have on the philosophy of mathematics?


Fig. 1 depicts the Tree of the Sefirot as per Arizal’s teachings. Each Sefirah has a specific number of connections, both incoming and outgoing. The Sefirah of Tiferet has five incoming and three outgoing connections, which coincides with the proportions given in Table 1, and indicates the presence of a connection between the Ark of the Covenant, the Altar, Noah’s Ark, and Tiferet.

This fact calls for an explanation from the standpoint of the Kabbalah of Information. We must start, however, by reviewing the description of the Sefirah of Tiferet.

According to Kabbalah, each of the Sefirot corresponds to a specific Name of the Almighty, which determines His self-expression through Creation. At the same time, the entire Tree of the Sefirot in the realm of Atziluth corresponds to the Name Havaya (the Tetragrammaton). The Sefirah of Keter corresponds to the apostrophe over the letter yod, the Sefirah of Chokhmah corresponds to the letter yod, the Sefirah of Binah corresponds to the first letter hei, the Sefirot of Chesed, Gevurah, Tiferet, Netzach, Hod, and Yesod correspond to the letter vav, and the Sefirah of Malchut corresponds to the second letter hei. Each Sefirah also separately corresponds to a specific Name of the Almighty. For example, the Sefirah of Chesed corresponds to the Name E-l, and the Sefirah of Gevurah corresponds to the Name El-him. Notably, the Sefirah of Tiferet corresponds to the Name Havaya (the Tetragrammaton), i.e., the same name as the entire Tree of the Sefirot. The Sefirah of Tiferet also corresponds to the concept of Beauty.

This author believes that the most detailed description of the Tree of the Sefirot can be found in Sha’arei Orah (Gates of Light), a book by Rabbi Joseph ben Abraham Gikatilla. Below is a selection of quotes from this book that are relevant to the Sefirah of Tiferet:

“Know and understand that the Name Havaya (the Tetragrammaton) is the pillar to which the higher and lower Sefirot are tied. All systems of the world, their foundations and structures are built upon this Name.”

“Know that in the Name Havaya (the Tetragrammaton), all Sefirot are connected, and all is complete and flawless.”

“Know that all of His Names are included in the unique Name Havaya (the Tetragrammaton).”

“There is no Sefirah that is vested in all Names, except for the Sefirah of Tiferet, and this Name, as well as the Sefirah of Tiferet, includes all and governs all.”

“Know that the Sefirah of Tiferet is the complete structure of the entire Tree of the Sefirot.”

“Know that Havaya (the Tetragrammaton) is called You (Ata in Hebrew) and is the essence of everything that was created through the combinations and permutations of letters.”

Tree of the Sefirot (Credit: Eduard Shyfrin)Tree of the Sefirot (Credit: Eduard Shyfrin)

An important thesis of Kabbalah is the idea of a union between the Sefirot of Tiferet and Malchut. The implication here is that the Sefirah of Tiferet embodies nine of the Sefirot and the male principle, in a union with the tenth Sefirah, Malchut (the female principle).

In the book Or Ne’erav by Rabbi Moses Cordovero, we find a passage saying that the creation of souls also depends on the Sefirah of Tiferet, which is the hidden sign of the union between the Sefirot of Tiferet and Malchut.

The prominent Medieval Kabbalah scholar Menahem Recanati believed that the two cherubim depicted on the Ark of the Covenant corresponded to the Sefirot of Tiferet and Malchut, respectively.

It is also very important to note that, according to Kabbalah tradition, the name of our forefather Jacob corresponds to the Sefirah of Tiferet, the name of our forefather Abraham corresponds to the Sefirah of Chesed, and the name of our forefather Isaac corresponds to the Sefirah of Gevurah.

As a brief intermediary review, we can conclude that the Sefirah of Tiferet is a ‘node’ of the entire Tree of the Sefirot and embodies the concept of Balance.

In order to explain the connection between the proportions of the Ark of the Covenant, the Altar and Noah’s Ark, on the one hand, and the proportions describing the Sefirah of Tiferet, on the other hand, let us consider how the interaction between the Sefirot is described in Kabbalah.

Let us look at the current opinions:

1 - In his book Kabbalah, Moshe Idel cites the thoughts of one of Kabbalah’s founders, Rabbi Abraham ben David. According to Rabbi Abraham ben David, before Creation, the opposite Sefirot (like Chesed and Gevurah) were joined into a single whole, part of the Almighty’s essence (Ein Sof), which now allows them to interact.

The way I interpret this, Rabbi Abraham ben David is hinting that, despite their opposing concepts, these Sefirot have retained some shared traits, and it is thanks to these shared traits that they can interact.

2 - In his commentary on Sefer Yetzirah, Rabbi Aryeh Kaplan writes, “In the spiritual world, it is utterly impossible to bring two opposites together... Two opposites can then be brought together by being bound to physical objects. In the physical world, space exists, and two opposites can literally be pushed together.” He further notes that the Sefirot are not physical objects and are not bound to any physical concept. Which raises the question: how do they interact? It is obvious that the only possible way of doing that is through interacting with the physical world, as Rabbi Aryeh Kaplan concludes.

However, I believe that this is incorrect, as, according to the principles of the Kabbalah of Information, there is no division between the spiritual and the physical: the physical and the spiritual are merely manifestations of the same substance: information.

Equally incorrect is the assumption that space exists only in our physical world. According to the Kabbalah of Information, all of Creation is a single information space.

3 - In his book Kabbalah, Gershom Scholem mentions that the notion of each Sefirah containing all the others, in an endless sequence of self-similarity, began to emerge in the teachings of the Kabbalists from the 13th century onward. Essentially, this implies that the Sefirot have a fractal structure.

Rabbi Moses Cordovero elaborated on the aforementioned notion further, seeking to explain the mechanism behind the interactions of the Sefirot.

In Or Ne’erav, he writes, “The beginner should know that the joining of the Sefirot and their union, despite the fact that they represent Judgment and Mercy, results from the inclusion of Gevurah into Chesed. For this reason, Gevurah is joined with Chesed in one of two possible ways. The first way is through the essence of Gevurah, which is contained in Chesed, and the second is through Chesed, which is contained n Gevurah. The Sefirah of Tiferet is joined with the Sefirot of Chesed and Gevurah through the part of the Chesed and Gevurah that it, Tiferet, contains, as well as through the part of Tiferet contained in Chesed and Gevurah.”

In order to explain the interactions between the Sefirot, Rabbi Moses Cordovero made the following suggestion: each Sefirah contains an endless multitude of ‘aspects,’ the main purpose of which is to ensure inter-Sefirah interactions. Furthermore, all of the aspects are interconnected by cause-and-effect links. The number of aspects is both immense and finite as, at one point, one Sefirah is inevitably followed by another. Essentially, Rabbi Moses Cordovero found himself dealing with the mathematical concept of limit: when a function approaches a certain value in an infinite sequence but never reaches it. He postulated that the first Sefirah, Keter, asymptotically ‘approaches’ the Almighty in its essence but never becomes identical to Him.

In Or Ne’erav, we read: “The beginner must know that Ein Sof is not identical to the Sefirah of Keter, He is the reason for Keter. The Sefirah of Keter is the first derivative of Ein Sof, from which the process of further emanation develops.”

To explain how different ‘aspects’ interact with each other, Rabbi Moses Cordovero used the concepts of ‘channels,’ namely ‘direct and reflected light.’ ‘Direct light’ allowed a given Sefirah to influence the next, and ‘reflected light’ enabled the opposite effect.

4 - Among the key principles in the teachings of Rabbi Isaac Luria (Ari) is the concept of Partzufim, each of which includes all Sefirot. The Partzufim are as follows:

The Sefirah of Keter; Atik Yomin and Arich Anpin; the Sefirah of Chokhmah: Abba; the Sefirah of Binah: Imma; the Middot (Chesed, Gevurah, Tiferet, Netzach, Hod, Yesod); Zeir Anpin; the Sefirah of Malchut: Nukvah.

The Ari also introduced the concept of tiers. In his book Etz Chaim, we read: “And you must know that the Nukvah of the Partzuf Zeir Anpin in the realm of Atziluth contains ten Sefirot and that each Sefirah has three tiers: the Face, the Back, and the Middle.”

Etz Chaim further writes that the Partzuf Zeir Anpin in the realm of Atziluth contains ten Sefirot, each of which possesses three Vessel qualities: the Outer, the Middle and the Inner. In all, there are thirty Vessels: ten Inner Vessels within ten Middle Vessels, within ten Outer Vessels.

Furthermore, Arizal introduces an important idea: the Outer tier of a given Sefirah is also the Inner tier of the next, similar Sefirah.

Arizal’s theory is incredibly complex, with many subtle implications and things remaining unsaid, but the general conclusion that we can draw is that it is consistent with the theory of Rabbi Moses Cordovero and states that each Sefirah contains elements of other Sefirot, through which interaction takes place.

Aram Tzova Crown (Credit: Wikimedia Commons)Aram Tzova Crown (Credit: Wikimedia Commons)

The stance of the Kabbalah of Information

Before we start, a reminder for the reader: according to the Kabbalah of Information, Creation is an information space built out of concepts of varying degrees of complexity. The distance between concepts in the information space is determined by the difference in their content and complexity. Specifically, the distance between identical concepts equals zero, and the distance between opposing concepts equals the maximum. There is also the concept of critical distance: when it is reached, information interaction ceases.

The above concerns the static part of this information space. The dynamics in this information space are determined by pulses (ratzo v’shov).

Since the Tree of the Sefirot in the realm of Atziluth corresponds to the Almighty’s Name Havaya (the Tetragrammaton), which, in turn, also corresponds to the Sefirah of Tiferet in the realm of Atziluth, we can conclude that the distance between the concept of Tiferet and the concept of the entire Tree of the Sefirot equals zero; in other words, they are identical to one another. This conclusion needs to be elaborated further.

The 2-D illustration of the Tree of the Sefirot is highly simplified; it does not reflect the inter-Sefirah connections in full. In truth, the Tree is a multidimensional information space, where the concept of distance differs dramatically from what we are accustomed to. In this space, there are no such things as up, down, left or right. The Sefirot may be extremely close to one another in certain information planes and extremely distant from one another in other information planes. In order to properly analyze the Tree of the Sefirot, the reader needs to cast aside the traditional notions of two or three dimensions and try to achieve a fairly advanced level of abstract thinking.

Kabbalah suggests that before the realm of Atziluth, there was the realm of Tohu (Nekudim), the world of points. The Kabbalah of Information interprets this as follows: in Nekudim, each Sefirah was expressed through a single concept – a point in the information space. The distance between opposing concepts (such as between Chesed and Gevurah; see above) was at its maximum, and the Sefirot did not interact. There were no intermediary concepts. The number of possible combinations and concepts was at its minimum. In other words, we could say that the realm of Tohu was the concept of the Absolute Self.

In the book Torah Ohr, written by Rabbi Shneur Zalman of Liadi, we read that from the realm of Akudim comes the realm of Nekudim, where each Sefirah exists separately, which is why the ten Sefirot of this realm are referred to as the ten’ points.’ In the realm of Tohu (Nekudim), the Sefirot (for example, Chesed and Gevurah) did not penetrate into one another, meaning that they could not interact.

According to Arizal’s Kabbalah, the realm of Tohu underwent Shevirat ha-Kelim (Breaking of the Vessels). As a result, each Vessel from the realm of Tohu shattered into small pieces, which contained fragments (sparks) of Tohu’s Divine Light. Later, writes Arizal, these fragments descended into the realms of Creation, where the so-called Kelipot (sources of Evil) formed out of them. These Kelipot embody the Absolute Self.

After analyzing the gematria of the word merachefet (hovering) from the passage “The spirit of G-d was hovering over the face of the water (Bereishit 1:2),” Arizal concluded that there were 288 fragments in all.

The reason for the Breaking of the Vessels, as cited in Kabbalah, was that the light was ‘strong’ and the vessels were ‘weak.’

A detailed description of the Breaking of the Vessels is found in Torah Ohr. The book explains that the Divine vessels (of the realm of Tohu) were shattered into a great many small pieces, which were scattered over the realms of Creation (Beri’ah, Yetzirah, and Assiyah. The lower they descended, the more they shattered.

Written by Rabbi Shneur Zalman of Liadi, it also notes that the 288 sparks that fell into Atziluth (during the Breaking of the Vessels) made their way into the realms of Creation. They split into countless minuscule particles, which were the seeds of all the elements of Creation that have their own Self.

As per the Kabbalah of Information, the main difference between the Sefirot of the realms of Atziluth, Creation and Tohu lies in the following:

1 - In Tohu, a Sefirah is a concept expressed in the most precise, condensed way possible. The distances between the Sefirot in this information space are at their maximum.

2 - In the realms of Atziluth and Creation, a Sefirah is a family of concepts with similar content but some minor differences. Two consecutive concepts within the same given Sefirah are located at a minimal distance.

In light of the above, we cannot help but ask how the transition from one Sefirah to another occurs in the realm of Atziluth or in the realms of Creation. Answering this question requires examining genetics and information theory.

Error threshold

For the reader’s reference: one of the key concepts of Claude Shannon’s theory is information entropy, which can be defined as the degree of uncertainty. Mathematically, it is expressed as a base 2 logarithm for the possible states of the system.

While working on his theory (the Mathematical Theory of Communication), Claude Shannon had a purely practical goal: to ensure the transmission of information messages in the most cost-effective way with a minimal number of errors. But with time, the academic community came to understand that Shannon’s theory is, in fact, universal in the same way like the theories of Newton, Maxwell and Einstein.

What prompted such conclusions was the acknowledgment that information lies at the foundation of reality. The principles of Shannon’s theory function equally well in thermodynamics. When discussing the number of microstates of a system; in information transmission; when discussing the number of possible combinations of symbols in a given language; or in genetics, when discussing the various combinations of nucleotides in gene chains.

Information theory asks the following fundamental question: At what point in changing its information state does the system (be it a physical body, a message in a given language, or a gene) transition to a qualitatively different state?

The answer to this is provided in From Strange Simplicity to Complex Familiarity, a book by Nobel Prize winner Manfred Eigen.

While studying mutation processes, Manfred Eigen introduced the concept of ‘error threshold.’

In his book, he wrote that the presence of an error threshold is one of the most definitive properties of various sequences. He looked at a macromolecular sequence consisting of a finite number of different classes of monomer. Its reproduction in nature is always associated with a finite error rate. The higher the error rate, the more mistakes will occur and need to be removed with the help of some error-correction mechanism. He then asks: Why is there an error threshold, passing which results in a complete destruction of information?

As the book mentions further, we know from biology that even the smallest genes are sequences that contain 10, 100, or even more possible combinations. The only way of producing a given sequence is to copy one that already exists. This process is accompanied by errors.

As for the actual mutation process, Manfred Eigen describes it as follows: at a zero-error rate, only the basic sequence exists; at the same time, development and evolution cannot occur. As the number of errors increases, we can observe the emergence of a family of sequences. However, when the error threshold is reached, the information contained in this family of sequences undergoes a qualitative change.

It is vital to note that whatever kind of development or evolution can only occur when approaching the error threshold.

Manfred Eigen points out that sequence disintegration at the error threshold can be compared to ‘dissolution’ of information or a phase transition (melting, evaporation).

The presence of the error threshold in all biological organisms is a known scientific fact with solid experimental proof. In conclusion, Manfred Eigen writes, “Semantic information can only come about by selection.” Selection is physically based on replication (reproduction). In other words, replication performs two tasks: the first task is to conserve information, while the second task is to provide a basis for a phase transition in order to create unlimited amounts of new information.

According to Manfred Eigen, similar processes occur during mental information processing.

Tiferet as balance

Having taken the above into consideration, let us now return to the matter of transition between one Sefirah and the next in the information space.

The Sefirot of the realm of Atziluth are a family of concepts with minor differences, separated by a short distance (information-wise). As concept changes accumulate, the error threshold is reached (see above), and the information content of the concept changes radically, bringing closer to the concepts of another Sefirah.

It is important to emphasize that passing the error threshold is not accompanied by the information compression that occurs when moving between worlds in the Sefirah of Malchut. The content is the only thing that changes.

The concept of the error threshold is universal and can be applied to the transition between any of the Sefirot. But the transition to Tiferet does have its own specifics. Each Sefirah can be described through its key information concept. Notably, eight of the nine Sefirot (except for Malchut) are described through concepts associated with a certain kind of action, and Tiferet is the only one that is expressed through the concept of beauty, which is not directly related to any action. Instead, the concept of beauty is described as harmony, completion and balance.

Based on the above, we can conclude that the family of concepts from the Sefirah of Tiferet is a unique part of the information space: a part that contains balanced concepts only. The balance is achieved between the concepts of all Sefirot: mercy and judgment, wisdom and understanding, will and humility, etc.

Torah Ohr tells us that the above allows us to understand why not only the Light but also the vessel of Tiferet corresponds to the Name Havaya, unlike other vessels. The fact is that the interaction between the Sefirot in the realm of the world of Correction (Atziluth, Tikkun)) occurs along the ‘median’ line: Keter — Tiferet — Yesod — Malchut. The ‘median’ line corresponds to the Sefirah of Tiferet and the forefather Jacob. The Sefirah of Tiferet is also referred to as the Letter of Truth; in other words, this Sefirah links different Sefirot together and ensures that they interact in order to avoid a situation where each Sefirah exists in complete separation.

Therefore, the Kabbalah of Information postulates information space through a static element: a concept. The dynamic element of the same information space is based on pulses (ratzo v’shov), during which the concepts get linked into chains and form events, which, in turn, get linked as well. This process — the process of actualizing an event — takes place in the zones of the Keter — Malchut information space and is initiated both by Ein Sof and humans.

In the realm of Tohu, where each Sefirah represented just one concept, there was no notion of balance, so we can conclude that any disruption of balance comes from Tohu.

In Kabbalistic tradition, our forefather Abraham is associated with the ‘unbalanced Chesed’ property, which resulted in him begetting Ishmael; our forefather Isaac is associated with the ‘unbalanced Gevurah’ property, which resulted in him begetting Esau; and only our forefather Jacob is associated with the Sefirah of Tiferet, i.e., with the concept of absolute balance.

We can conclude from the above that, through the Holy of Holies in the Tabernacle) and, through the Temple in Jerusalem, the Jewish people had a direct connection with the Malchut from the realm of Atziluth, which, as we explained in the previous article, is the space of Creation, as well as with the Sefirah of Tiferet from the realm of Atziluth, which is the space of absolute balance.

In practice, this means that, during the existence of the Temple, the Jewish people lived under a balanced Divine Providence (balanced reward and balanced punishment); furthermore, the Jewish people were spiritually connected with the highest realm of Creation via specific planes. The notion of balanced Providence requires additional commentary.

Five opposite five

Balanced Providence can be described as the process of actualizing the concepts found in the Tiferet information space: the space of balance.As a reminder to the reader, we must highlight that in the realm of Tohu, each Sefirah corresponded only to one concept, expressed in its strongest, most concentrated and unbalanced form. Therefore, the actualization of the concept of Providence from the realm of Tohu can be called ‘unbalanced Providence.’

What happens, in this case, is the actualization of concepts from the information space of the Sefirah of Keter from the realm of Atziluth, which is also simultaneously the Sefirah of Malchut from the realm of Tohu. In illustrations of the Tree of the Sefirot, the Sefirah of Tiferet is positioned between Keter and Malchut. That said, the illustrations of the Tree of the Sefirot are highly simplified. In the information space, there is no concept of ‘between.’ Therefore, the actualization of the concept from the Sefirah of Keter may occur directly in the Sefirah of Malchut (in Sefer Yetzirah, we read that their end is part of their beginning).The unbalanced state of the Tree of the Sefirot is described in Kabbalah through the notion of ‘five opposite five.’

Sefer Yetzirah says:“Ten Sefirot of Nothingness:The number of the ten fingers,Five opposite five.”

In Rabbi Aryeh Kaplan’s commentary on Sefer Yetzirah, we find the following explanation for this passage. Although the ten Sefirot are usually divided into three pillars, they can also be arranged as two pillars, right and left. The ‘male’ ones (Chasadim) are located on the right, the ‘female’ ones (G’vurot) are on the left. When the Sefirot are in their normal state, as three pillars, they are balanced. But when the Sefirot on the central line veer too much to the right or the left, this creates strong tension, and the powerful spiritual energy is channeled and directed.

Rabbi Aryeh Kaplan believes that proof of the above lies in the fact that the Tablets of the Law contained five Commandments each. He also cites the prophecy that was given to our forefather Abraham amid the animal carcasses divided in the middle.

In the Kabbalah of Information, the information space lacks concepts like up, down, left, right, or between, meaning that the Sefirot do not move.

The state of ‘five opposite five’ is a state of unbalanced Providence, in which the concepts from the Keter information space are actualized in the Malchut information space.

Examples of unbalanced Providence

As per Kabbalah, the word ‘I’ spoken by the Almighty (Ani in Hebrew) corresponds to the Sefirah of Malchut, while the Hebrew Anokhi (‘I,’ ‘I am’) corresponds to the Sefirah of Keter. The word ‘You’ (Ata in Hebrew), spoken when we address the Almighty, corresponds to the Sefirah of Tiferet. The word ‘He,’ used to describe the actions of the Almighty (Hu in Hebrew), corresponds to the Sefirah of Keter:

1 - The Flood

The Flood was a completely unbalanced punishment for the world.In Parashat Noah (Genesis 7:4), we read, “For in another seven days, I will make it rain upon the earth.” The Hebrew word used here is ‘Anokhi,’ corresponding to the Sefirah of Keter.

The punishment came from the realm of Tohu.Torah Ohr explains this as follows: “Therefore, the world had to obtain sensation through cleansing waters. This required, in the words of sages, ‘the power of rain’ from the realm of Tohu.’” Torah Ohr further says that the waters of the Flood poured down from Heaven in a stormy torrent, with extraordinary power characteristic of the realm of Tohu. These waters were the manifestation of the Sefirah of Chesed from the realm of Tohu, because if the Earth was to be truly cleansed, this required the strongest light from Tohu, a realm above the realm of Atziluth.

2 - The destruction of Sodom and Gomorrah

The destruction of Sodom and Gomorrah was also a completely unbalanced punishment.The Torah in Parashat Vayeira (Genesis, Chapter 19:25) tells us: “And He (the pronoun from the Sefirah of Keter) turned over these cities and the entire plain, and all the inhabitants of the cities, and the vegetation of the ground.”

3 - The Death of the Firstborn

The Death of the Firstborn likewise, is a completely unbalanced punishment, enacted from the tier of Self, of I (Anokhi, corresponding to the Sefirah of Keter in the realm of Atziluth).While the section in Parashat Bo does not elaborate on the subject, we do find some information in Parasha Lech-Lecha. While telling Abraham that his descendants will be enslaved, the Almighty says (Bereishit 15:14), “And also the nation that they will serve will I judge” (Dan Anokhi in Hebrew).

4 - The Shema Yisrael

The Shema Yisrael prayer tells us, “You shall love the L-rd your G‑d with all your heart, with all your soul, and with all your might. And these words which I (Anokhi in Hebrew) command you today shall be upon your heart.”Anokhi symbolizes the Sefirah of Keter: what is promised to the Jewish people is either a blissful existence for fulfilling the orders and commandments of the Almighty or complete destruction for worshiping idols. There is no in-between.

5 - In Parashat Lech-Lecha (Chapter 15:1), we read: After these incidents, the word of the L-rd came to Abram (Abraham) in a vision, saying, “Fear not, Abram; I am (Anochi) your Shield; your reward is exceedingly great.”The Almighty speaks from the Keter tier, promising Abraham complete and unconditional protection.


We began this chapter with four questions. I attempted to answer the first two in this article, specifically:

1 - The reason why the High Priest spoke the Tetragrammaton (the Almighty’s Name Havaya), as he entered the Holy of Holies of the Temple on Yom Kippur, is because (as demonstrated above) many dimensions of the Ark of the Covenant and the Altar coincide with the proportions of the Sefirah of Tiferet, which is associated with the Name Havaya and is the realm of information concepts relevant to balanced Providence.

2 - When Noah and his family entered the Ark, the Torah tells us, “And the Lord (Havaya) shut him in.”As demonstrated above, Noah’s Ark also matches many of Tiferet’s proportions within the information space. It is important to emphasize that, while the rest of the world suffered a punishment from the Sefirah of Keter (unbalanced Providence), Noah and his family experienced balanced Providence.

In the next article, I will attempt to answer the questions about the concept of Beauty and the philosophy of mathematics.

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