In the previous article (“And G-d said, ‘Let us make man in our image, after our likeness...”), we examined the Theory of likeness. Let us briefly recall some of the ideas expressed.
1. The Creation can be represented as an information space of concepts expressed in symbols.
2. In the information space, distance is determined by the difference in complexity (in the meaning of the concepts).
3. The distance between two identical concepts equals zero.
4. Once a certain critical distance is covered, the exchange of information stops. (Just as in our physical world, tactile information exchange stops at a certain distance; similarly, there are distances at which auditory and visual exchanges are no longer possible.)
5. The human soul has the image of the Tree of Life (Sefirot), and the ‘distance’ between the soul and the Tree of Life is determined by how much our mental concepts resemble the concepts of the Tree of Life.
In this article, we will look at the practical application of the Theory of likeness to find hidden connections in the Torah and gain a deeper understanding of its concepts. We will thereby try to reduce the distance between ourselves and the Tree of Life.
Instructions from the Most High
1. Terumah 25:10 reads, “They shall make an Ark of acacia wood, two and a half cubits long, a cubit and a half wide and a cubit and a half high.”
2. Terumah 25:17 reads, “Overlay this Tabernacle with pure gold and golden rings and poles to carry the Ark. You shall make a cover of pure gold with two gold Cherubim on both ends of the cover.”
3. Terumah 27:1 reads, “Build an altar of acacia wood, three cubits high; it shall be square, five cubits long and five cubits wide.”
4. In Noah 6:15, the Most High instructs Noah on how to build the Ark: “This is how you shall build it: the ark is to be three hundred cubits long, fifty cubits wide and thirty cubits high.”
Given that there is no superfluous information in the Torah, and each symbol has a deep meaning, it is essential to answer the question of why the Most High specified the dimensions above and what they mean.
To that end, let us journey into mathematics.
The Golden Ratio
Around 300 BCE, the founder of geometry, Euclid of Alexandria, offered the definition of a certain proportion, subsequently named ‘the golden ratio.’
The value of C is determined by the following formula: AB / AC = AC / CB. C divides segment AB proportionately: = 1.6180339887... is an irrational number. However, it turns out that, mystically, this number plays a major role in the Creation. We see it in geometry, the structure of galaxies, quantum physics, biology, the design of plants, in art and architecture.
It has been used intuitively by sculptors, artists, and architects who understand that this proportion is aesthetically pleasing to the human eye.
Numerous experiments were carried out in the 19th and 20th centuries to determine why the ‘golden ratio’ () is so pleasing to human perception, but no reliable results were obtained.
In 1202 Leonardo of Pisa, also known as Leonardo Fibonacci, released his book "Liber Abaci" (The Book of Calculation). Through this book, Europeans became acquainted with both the Indo-Arabic numeral system and with algebra. This precipitated a mathematical revolution. Over the course of his life, Fibonacci solved various mathematical problems. One of his many accomplishments is the identification of a sequence of numbers that was later named the ‘Fibonacci sequence.’
In the Fibonacci sequence, each number starting from the third represents the sum of the previous two numbers. It looks like this:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
The Fibonacci sequence is used to solve many practical problems and has a unique feature: as one moves along the sequence, the ratio of any number to the previous number is very close to the ‘golden ratio.’
Luca Pacioli, a medieval Italian mathematician and theologian, wrote a three-volume summa on the ‘golden ratio’ titled "Divina Proportione" (Divine Proportion). The book was released in Venice in 1509, and its main theme is the presence of the golden ratio in the structure of the Creation.
In his book ‘The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number,’ astrophysicist Mario Livio articulates the following questions:
1. How can the presence of the ‘golden ratio’ () in so many varied aspects of our life be explained?2. Why is the ‘golden ratio’ () considered to be a symbol of beauty?3. Does mathematics have an aesthetic component?4. Do mathematics and its principles exist independently of people and are simply being discovered (platonism), or is mathematics a product of human mental activity, thereby being invented (nominalism)?
To answer the above questions, let us return to the instructions of the Most High as presented at the beginning of this article.
The number of the Most High
Table 1 shows the measurements of the Ark of the Covenant, its covering, the Altar, and Noah’s Ark as determined by the Most High. All of them have the same ratios close to the ‘golden ratio’ ().
Let’s ponder that further: all of these ratios correspond to the ratios of the three numbers in the Fibonacci sequence: 3, 5, and 8 (8/5 =1.6, 5/3 =1.66...)
Essentially, we can say that these ratios correspond to the ‘golden ratio’ () but do not exactly match as the measurements determined by the Most High are expressed in whole numbers.
So, the question arises – What kind of conclusion can be drawn from the fact that these proportions coincide with ()for the Ark of the Covenant, its covering, the altar, and Noah’s Ark?
To answer this, we need to examine the structure of the Creation and the Tree of Life.
We will delve into the question in more detail in the ‘Theory of the Kabbalah of Information’ section. Below is a brief description.
The Structure of the Creation
According to the Kabbalah of the Arizal, the sequence of the Creation is described as follows:1. Tzimtzum2. Adam Kadmon3. Akudim4. Nekudim (Tohu) 5. Atziluth
The five worlds mentioned above are Emanations.
The three worlds of the Creation follow:
1. Beriah (Creation)2. Yetzirah (Formation)3. Assiah (Action)
The area of division between the worlds of Emanation and the worlds of the Creation is the Sefira Malchut of the world of Atziluth. We will analyze its nature a little later on.
Since the Sefira Malchut separates the five worlds of Emanation from the three worlds of the Creation, we can say that one of its information dimensions is the ratio of 8/5 = 1.6 and 5/3 = 1.66 ..., which coincides with the proportions of the Ark of the Covenant, the Altar and Noah’s Ark.
It should be noted that, according to the Theory of likeness, the distance between identical concepts in the information space is zero.
Thus, we can preliminarily conclude that, as per the aforementioned parameters, the Ark of the Covenant, the Altar, and Noah’s Ark correspond to Sefira Malchut of the world of Atziluth in the information space.
To understand the significance of this connection and its meaning, it is crucial to analyze the nature of the worlds of both Emanation and Creation as well as the Sefira Malchut of the world of Atziluth.
Key Area of Creation (1)
Figuratively, the worlds of Emanation can be likened to the Thought of the Most High and the worlds of the Creation to His Speech and Action.
The most important difference between the worlds of Emanation and the worlds of the Creation is that it is impossible for essence to exist within its ‘Ego’ in the worlds of Emanation.
In his book "Torah Or," Rabbi Shneur Zalman of Liadi says, “In the world of Atziluth, the existence of anything but Light is beyond belief.”
The area in the information space that separates the worlds of Emanation from the worlds of the Creation is the Sefira Malchut of the world of Atziluth.
The Sefira Malchut of the world of Atziluth is essentially the Sefira Keter of the world of Beria, which is, in fact, the area of the Creation.
In the book "Etz Chaim" (the teachings of Rabbi Yitzhak Luria), we read, “The permanent order is that Malchut of one world is Keter of another.”
In "Or Neerav" by Rabbi Moshe Cordovero, we read, “Malchut (of the world of Atziluth) is the place (Keter) of the world of Briah.”
In "Torah Or", we read, “Sefira Malchut, which is also called the Word of G-d, or the Word that constantly creates worlds.” Ibid. ‘ In the Torah we read (Parashat Ekev) “Not by bread alone does man live, but rather by everything that comes from the mouth of God does man live.” It is known that the Sefira Keter serves as a ‘mediator’ between the higher and lower worlds. In other words, this Sefira is a lower scale of a higher world as well as the beginning and source of the lower world. Thus, Malchut of the world of Atziluth is Keter of the world of Briah.” The "Torah Or" also writes, “For all the worlds, the upper and the lower, are derived from the Sefira Malchut.”
Sefer Yetzirah (1:10) reads,
“Second, from the Spirit
he made Air and formed for speech
and Twelve Elementals, but the Spirit is
first among these.”
Aryeh Kaplan comments, “This is Malchut (kingdom), the lower of the ten Sefirot; it is counted right after Keter, according to the wording of Sefer Yetzira, ‘and their end enters their beginning.’ Moreover, Kabbalah considers the axis of Keter Malchut to be primary in the Tree of Life.”
The Ark of the Covenant contained two tablets with the commandments of the Most High. The commandments are the expression of the Will of the Most High. In the information space, Sefira Keter identifies with the concept of the Will and Desire of the Most High.
As such, we can draw an important conclusion that the Ark of the Covenant is directly related to the Sefira Malchut of the world of Atziluth (Keter of the world of Beria) through mathematical proportions and informational content.
Joshua’s prophecy reads, “This is the Ark of the Covenant of the Lord (Adon, Heb.) of all the earth.”
In the information space, the Sefira Malchut of the world of Atziluth corresponds to the Name of the Most High, Ad-noy.
It is clear that the information in the prophecy matches the above conclusions about the connection between the Ark of the Covenant and the Sefira Malchut of the world of Atziluth, which were obtained by applying the Theory of likeness.
In Genesis (Bereshit), there is a description of the third day of the Creation: “And G-d said, Let the water under the sky be gathered to one place, and let dry ground appear. And it was so.”
During the Flood, the opposite took place: the land disappeared and became covered with water.
In this sense, the Flood reverses the Creation (which is noted in many Jewish sources) to the state before the third day of the Creation.
It is also important to note that both the Creation and the Flood were carried out through the Word of the Most High (creative and destructive), which are derived, as noted above, from the Sefira Malchut of the world of Atziluth.
Thus, the conclusion about the connection between Noah’s Ark and the Sefira Malchut of the world of Atziluth in the information space, which was obtained by applying the Theory of likeness, is clearly confirmed through analyzing the sequence of time of the Creation.
The connection between the altar and the Sefira Malchut of the world of Atziluth will be analyzed in a separate paper.
Key Area of the Creation (2)
Let us look at the nature of the Sefira Malchut of the world of Atziluth in more detail.
Each Sefira is an area of information space containing a family of similar concepts. For example, Sefira Chesed is about the concepts of love, kindness, and expansion, and Sefira Gevura implies the concepts of power, judgment, and contraction, etc.
Each Sefira corresponds to the Name of the Most High, reflecting His expression in the world of Creation.
The fundamental difference between the Sefira Malchut and the other Sefirot is that there is no family of concepts inherent to this Sefira.
The Sefira Malchut is an area in the information space where all other concepts of the Tree of Life are being implemented and identified with the Name of the Most High Ad-Noy, reflecting the concept of justice.
In a figurative sense, we can imagine the Sefira Malchut of the world of Atziluth as a screen onto which the light projects sequences of concepts that create events.
In his book "Sha’are Orah" (Gates of Light), the outstanding Spanish Kabbalist Rabbi Joseph Gikatilla writes, “Know that the attribute of Ad-Noy, since he receives energy from above, has different qualities: to give life, bring death, destroy or heal. It all depends on the energy this attribute receives. He acts throughout the Creation according to the energy he receives. Sometimes he is given the name of the attribute from which he receives the energy.”
He continues, “Sometimes, Ad-Noy is described as Yam (sea) because all divine emanations of energy flow into Him, just like rivers flow into the sea: “All rivers flow into the sea” (Kohelet).”
Gershom Scholem, in his book ‘Kabbalah,’ writes, “...Each Sefira fulfills its essential functions, except for the last Sefira (Malchut), which does not have such an active power but has all the Sefirot within itself and represents a special principle that unifies all active powers without adding any of its own characteristics.” Sefira Malchut of the world of Atziluth is essentially a key area of the Creation, for it is where the separation of the worlds of Emanation and Creation takes place (i.e., figuratively, the transition from thought to speech and action).
It is important to understand that the Creation of all the aforementioned concepts is carried out at the level of Eyn Sof (the level of the Creator).
In the book Etz Chaim we read, “One should know that the expansion of Eyn Sof takes place throughout the world of Atziluth down to the quality of Malchut.”
The main task entrusted to Sefira Malchut of the world of Atziluth is the transformation of the above sequence of concepts into informational commands for implementing Divine Providence in the Worlds of Creation and controlling all their activity, including angels, souls, plants, animals, inanimate nature – everything. Below, we will try to understand how this happens.
According to Kabbalah, the above transformation takes place when the light of the world of Atziluth passes through the parsa, which is located between the world of Atziluth and the world of Briah (in Sefira Malchut).
"Torah Or" reads: “The point is that in the Holy Temple, the main source of G-d’s influence and the revelation of Shekhinah was a place called the “Holy of Holies.” However, G-d’s influence could not fully spread further. After all, if it could, the same high unity would reign everywhere as in the Holy of Holies, and, therefore, the influence of Shekhinah was ‘leaking,’ so to speak, through the veil (parochet, Heb.) that separated the Holy of Holies, the place of the full revelation of Shekhinah, from the Sanctuary, where Shekhinah revealed itself to a lesser extent. Onkelos translates the word ‘parochet’ as “parsa,” which means ‘screen’ in Aramaic. Here, a ‘partition’ is implied, separating the higher spiritual world from the lower one.”
"Etz Chaim" reads, “...subsequently, the world of Briah was created, which is illuminated through the “curtain,” the earth (Sefira Malchut), which is the foundation of the Palace of the world of Atziluth.”
"Torah Or" also reads, “Therefore, the light of the world of Atziluth reaches the world of Briah when passing through the veil, when the Sefira Malchut of the world of Atziluth becomes Keter of the world of Briah.”
According to the Kabbalah of Information, in the Sefira Malchut of the world of Atziluth, there is an abrupt transition between the multidimensional and complex information space of the worlds of Emanation and the information space of the worlds of Creation, which has a much lower number of dimensions and is less complex. This process had its parallel in the Mishkan. Moses our Teacher received his prophecies between the two Cherubim placed on the cover of the Ark of the Covenant, in very lofty and complicated form – incomprehensible to other Jews. After that, Moshe left the Mishkan, passing through the curtain on his way out, and transmitted the prophecy to the Jews, but in a much less complicated, and a more comprehensible form. This process precisely parallels the one which takes place in the Sefirat Malchut of the world of Atziluth.
We will analyze this transition in more detail in subsequent articles.
It is worth noting that this transition can be characterized as Tzimtzum (concealment), similarly to the Tzimtzum that the entire Creation resulted from.
"Torah Or" reads, “The world of Briah originates from the world of Atziluth in a completely different way because, in this case, the Tzimtzum is of a much lower level, which is implemented through the parsa (separating veil).”
It is, of course, to be understood that the result of this transition is not a simple decrease in the intensity of information. Here, a radical change in the structure of the information space and the complexity of its concepts takes place. In the physical world, this phenomenon can be conventionally compared with a phase transition process (for example, the freezing of a liquid), where the phase structure of degrees of freedom, entropy, and other parameters change abruptly.
Rabbi Shneur Zalman of Liadi (Torah Or) brilliantly described the above: “The light penetrating from the world of Atziluth through the veil of the parsa has a nature different from that of light that has not yet penetrated the parsa. After penetrating the parsa, it is a completely new, “born-again” light.”
1. Using the Theory of likeness, we have come to the conclusion that the Ark of the Covenant and Noah’s Ark are directly related to the Sefira Malchut of the world of Atziluth, which is the key area of the Creation.2. Many Kabbalists have come to a similar conclusion without turning to the Theory of likeness.3. The connection between the Ark of the Covenant and Sefira Malchut of the world of Atziluth is confirmed by the above prophecy.4. Scientifically, the fact that independent scientific theories arrive at the same conclusions confirms the correctness of the conclusions and the correctness of the theories. 5. The meaning of Paragraph 1 is that Moshe Rabbeinu, unlike other Prophets, received prophecies from the key area of the Creation (Sefira Malchut of the world of Atziluth).6. Paragraph 1 also implies that the Jewish people, by the grace of the Most High, through the Holy of Holies in the Mishkan (Tabernacle) and the Holy of Holies in the Temple in Jerusalem, had a direct connection to the key area of the Creation (Sefira Malchut of the world of Atziluth), bypassing all intermediate stages.
However, our research does not end here, since there are still questions left unanswered, namely:1. When entering the Holy of Holies of the Temple on Yom Kippur, why did the High Priest pronounce the Name of the Most High Havaya, which refers to the Tree of Life in general and to Sefira Tiferet (Beauty) in particular?2. Why, when describing the entry of the Noach family into the Ark, does the Torah use the words, ‘And Havaya shut behind him’ (see Parashat Noach)?3. Why is the ‘golden ratio’ associated with the concept of beauty?4. What consequences do our conclusions bring for the philosophy of mathematics?
These questions will be answered in the following article.
To purchase Eduard Shyfrin’s book ‘From Infinity to Man: The Fundamental Ideas of Kabbalah Within the Framework of Information Theory and Quantum Physics’ please click here. To purchase Eduard Shyfrin’s book ‘Travels with Sushi in the Land of the Mind’ please click here.