Kabbalah of Information, Part 2: Arizal, Maimonides and Entropy

Kabbalah of Information, What Everything is Made of
Arizal, Maimonides and Entropy

To continue exploring the problem of what everything is made of, let us consider the description of the process of creation described in Kabbalah. 

Zohar

A line from Zohar (1) reads as follows: “At the head of the King’s authority he carved out of the supernal luminescence a lamp of darkness. And there emerged out of the hidden of hidden – the mystery of the Infinite – an unformed line, embedded in a ring…measured with a thread…” 

Arizal on the tzimtzum process

Arizal (2), describing the tzimtzum process, writes:

Know that before the emanations were emanated and the creatures were created, there was one simple supernal light that filled the all existence. And there was no empty place, no empty space or void, all reality was filled with that simple infinite light. There was no category of beginning, no category of end. All was one, unified, simple, undifferentiated, ubiquitous, and homogenous infinite light called Or Ein Sof. 

When it arose in His simple will to create worlds and emanate emanations, to bring to light the perfection of His actions, His Names and His attributes, for the purpose for creating all the universes… He constricted His infinite essence away from the center point of His being, that is, from the very center of His light. He thus constricted that light, distancing it to the extremities around this center point, leaving a vacated space and hollow void.

Behold, after this constriction, which resulted in the creation of a vacated space and hollow void in the very midst of the Infinite Light, there was a “place” for all that was to be emanated, created, formed and completed. He then drew forth a single, straight ray from His infinite encompassing light into the vacated space.

Subsequently, Arizal’s description of the tzimtzum (“constriction”) was complemented by Moses Zacuto (3), who introduced the concept of the reshimu (“mark” or “trace”), meaning that the divine light had not been completely removed from the empty space, but had left a trace — reshimu — in that empty space. 

The above prompted a discussion between kabbalists on how to interpret the concept of tzimtzum. Should it be understood literally, as a total elimination of the divine light and the creation of a completely empty space? Or should it be understood figuratively, by replacing the idea of elimination of light with the idea of its concealment.

Both interpretations had their supporters and detractors. The idea of interpreting tzimtzum as a concealment was first proposed by Rabbi Abraham Cohen de Herrera (4) and then further developed by the founder of the Chabad movement, Rabbi Shneur Zalman of Liadi (the Alter Rebbe)(5). The thrust of this approach is a kabbalistic dualism, which presumes that the Almighty is transcendental and immanent to His creation at the same time.

The main opponent of this approach was Rabbi Immanuel Ricchi (6). He claimed that divinity had been eliminated from the empty space. This, despite the Zoharic principle that “There is no place empty of God,” which obliged Rabbi Immanuel to propose an interpretation of this passage which explained its meaning that there was no place devoid of the Divine providence. Ricchi wrote: “I propose this idea not as a result of a philosophical study of the nature of the Almighty, but because it is more pleasing to my soul.”

I find it necessary to mention my own opinion on this matter, which involves interpreting the process of tzimtzum figuratively, as a form of concealment.

Analysis of the tzimtzum and possible conclusions

  From the description of the process of tzimtzum we can make a number of observations: 

1. The process of tzimtzum is an absolute “leap” from complete uncertainty (since we have barely any information about Ein Sof) to a rather certain situation. 
2.  In the process of tzimtzum we observe breakage of uniformity (for us). 

3. The concept of “event” is introduced.
4. The concept of “temporal succession” is introduced (pulsation, restriction—expansion)
5. It is apparent from the description of the tzimtzum that the entire reality has been created from the ray of light, without any other “building materials.” This point leads to the conclusion that there is no multiplicity in Creation, and no fundamental difference between spiritual and material.
6. The process of concealment is the process of concealing one kind of light using another.

The above points raise a logical question: What did kabbalists mean by “light”? Let’s refer to original sources. 

Rabbi Moshe Chaim Luzzatto (RaMCHaL) (7) wrote: “In truth, no word, name or term is adequate to apply to Godliness. But since it is impossible to speak without words, we must call it by some name. So we choose one that is somewhat less remote from Godliness than others. Light is the finest and most subtle of all physical phenomena, and accordingly, it is less remote from Godliness than other phenomena. Hence, ‘radiation of light’ is the closest term we can choose. Even so, you must understand that we are not talking about the radiation of physical light. We are applying the term ‘radiation of light’ only to give it some name.”

In Kabbalah, “light” also represents God’s manifestation or self-expression. To my mind, the tzimtzum represents a categorical leap from complete uncertainty to a rather certain situation, i.e. an infinite decrease in uncertainty.

The only way to reduce the uncertainty in the created reality is by obtaining information. Therefore, it’s logical to conclude that we can substitute the concept of light with the concept of information. This conclusion is also supported by the fact that any manifestation and expression takes place in our reality by means of exchange of information. It is important to know that in the theory of information, the notion of data is defined as a breakage of uniformity. Hence, we can conclude that the tzimtzum introduces the notion of data to us.

This leads us to another question: for whom does the concealment in the tzimtzum take place? Who was the recipient of the information that was withheld? We will discuss these questions later on, but for now I would like to invite the reader on a short excursion into the realm of science.

Informational entropy

In 1942, American scientist Claude Shannon (8), who worked for Bell Labs, came up with a Mathematical Theory of Communication. Shannon’s goal was to achieve an optimized encoding of information and its transmission to the recipient in an undistorted form, despite the presence of background noise.

The key concept of the Mathematical Theory of Communication was “informational entropy.” Here is a simplified version of it.

E = log2.p

where E stands for informational entropy and P is the number of letter combinations in a message of particular length, subject to language constraints. This definition of entropy was similar to the definition of entropy in statistical mechanics developed by Ludwig Boltzmann (9).

E= klnW

where k is the Boltzmann constant and W is the number of a system’s different microstates that cannot be distinguished on a macro level. Let’s take a simple example. If we’re looking at a stone, its microstates that depend on coordinates and impulses of atoms are constantly changing, but its external (macro) state for us remains invariant. 

 Although Shannon’s work was aimed at effective information coding and transmission, his concept of informational entropy has a much broader interpretation in modern information theory as a measure of informational uncertainty. Here’s another simple example. If we flip a coin with two tails, the outcome is pre-determined, since we are dealing with one state: “tails.” In this case, Shannon’s entropy, or informational uncertainty, is defined by the following equation:

E= log21=0      

If we flip a coin with heads and tails, the result is undefined and we are dealing with two states: “heads” and “tails.”  In this case Shannon’s entropy is defined by a different equation — the bit formula:

E= log2=1

Let’s go back to Kabbalah. From the point of view of Shannon’s theory, the absolute leap from complete uncertainty to a certain state that occurred with the tzimtzum can be considered an infinite decrease in entropy or an infinite reduction in our uncertainty. Manfred Eigen (10), a prominent scientist of the 20th century, provided a brilliant definition of informational entropy. Eigen wrote: “Informational entropy is the measure of what we don’t know after we’ve accounted for everything we do know.”

The similarity between informational and thermodynamic entropy is striking. It’s obvious that increasing informational entropy (our uncertainty) conceals information. Increasing thermodynamic entropy conceals information as well.

For example, imagine you have a container divided by a heat-proof partition in the middle. There are equal amounts of the same gas in both parts of the container, but their temperatures are different (let’s say, 100° and 300°). If we remove the partition, the entropy of the system will increase and the temperature will even out. As a result, the gas in the container will have the temperature of 200° — an average between 100° and 300°. But if we can only see the end state of the system — a container with 200° gas, there is no way for us to know what the initial state of it was, because there is an endless number of options: 100° and 200°, 50° and 250°, 25° and 375°, and so on, ad infinitum. 

Maimonides (11) provided a brilliant description of the process of information concealment in his Guide for the Perplexed, written in the 12th century well before concepts like thermodynamics and entropy had been developed. Maimonides expressed his disagreement with Aristotle (12): “We, the community of the followers of Moses our Master and Abraham our Father, may peace be on them, believe that the world was generated in such and such manner and came to be in a certain state, which came after another state. Aristotle, on the other hand, begins to contradict us and to bring forward proofs against us based on the nature of what exists, a nature that has attained stability, is perfect, and has achieved actuality. As for us, we declare against him that this nature, after it has achieved stability and perfection, does not resemble in anything the state it was in while in the state of being generated and that it was brought into existence from absolute nonexistence.”

In the same chapter, Maimonides stressed: “No inference can be drawn in any respect from the nature of a thing after it has been generated, has attained its final state, and has achieved stability in its most perfect state, to the state of that thing while it moved toward being generated.”

The analogy with the statement about how increased entropy conceals earlier information is clear. Dwelling on the thoughts of Maimonides (and Shannon), we can conclude that based on our current knowledge of the world, even taking into consideration the information we have about the tzimtzum process, we cannot draw any conclusions about the Almighty as Ein Sof. This confirms Kabbalah’s key idea that Ein Sof completely transcends human understanding.

Footnotes:
1. The foundational work on Kabbalah is believed to have been written by Shimon bar Yochai, a prominent rabbi of the 2nd Century AD.
2. Arizal, or Isaac Luria (1534–1572) — founder of one of the main schools of Kabbalah, Lurianic Kabbalah
3. Moses ben Mordecai Zacuto (1620–1697) — philosopher, Kabbalist and poet, lived most of his life in Venice
4. Abraham Cohen de Herrera (1570–1635) — religious philosopher and kabbalist. Adherent of Lurianic Kabbalah
5. Shneur Zalman of Liadi (Alter Rebbe) (1745–1812) — rabbi, kabbalist, founder of the Chabad Hasidic movement.
6. Raphael Immanuel ben Abraham Ḥai Ricchi (1688–1743) — Italian rabbi and kabbalist who moved to the Land of Israel
7. Moshe Chaim Luzzatto (1707–1746) — rabbi, philosopher, and kabbalist; author of dozens of books on Kabbalah and Jewish ethics.
8. Claude Shannon (1916–2001) — American engineer, cryptographer, and mathematician. Known as “the father of information theory.”
9. Ludwig Boltzmann (1844–1906) – Austrian theoretical physicist, founder of statistical mechanics and the kinetic theory of gases
10. Manfred Eigen (1927–2019) — German physicist and chemist, winner of the 1967 Nobel Prize in Chemistry.
11. Moses ben Maimon (Maimonides, Rambam) (1135–1204) — prominent Jewish religious philosopher and scientist
12. Aristotle (384–322) — ancient Greek philosopher. The most influential ancient philosopher. Laid the foundation for modern natural science.