Alexander I. Poltorak

Noah’s Ark — Three Layers of Reality

By Fer Gregory, licensed from Shutterstock

A light shalt thou make to the ark…with lower, second, and third stories shalt thou make it. (Genesis 6:16)

We mentioned in the previous posts that Noah’s ark (tevah) was a microcosm.[1] As we discussed in the previous post, “Noah’s Ark—Three Layers of Being Human,” most structural parallels related to Noah’s ark are based on its tripartite structure —that is, its having three tiers. In Chasidic thought, the three levels of Noah’s ark correspond to three worlds of BiYA—Beriyah (the World of Creation), Yetzirah (the World of Formation), and Asiyah (the World of Action). In this essay, we will investigate how the tripartite structure of Noah’s ark is reflected in the structure of reality.

We might say that the totality of existence comprises three layers—physical, informational, and spiritual. The classification of reality into three classes is not new. The Torah itself speaks of it in the first verse:

In the beginning God created the heaven and the earth. (Genesis 1:1)

The “beginning” can be seen as the temporal domain, whereas “the heaven” and “the earth” can be seen as references to the spiritual and the physical (or space and matter), respectively.[2] The other reference to a tripartite structure is the division of waters into “higher waters” and “lower waters,” separated by a firmament:

And God said: “Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.” (Genesis 1:6)

Another such tripartite structure is the ancient belief in heaven (Paradise), earth, and the netherworld (Sheol[3] or Gehenna[4]). Tripartite classifications appear in modern philosophy as well.[5] We shall examine here a different tripartite structure within the totality of existence: physical reality, information, and spiritual reality.

Physical Matter: The Lowest (First) Tier

Although the “spiritual” seems vague and ill-defined, no one has any doubts about what physical reality is. That said, the easiest (albeit too broad, as we shall see) way to clarify the word “spiritual” is to define it as “nonphysical.” That distinction requires, however, a careful definition of what “physical” is.

According to late Rabbi Aryeh Kaplan,

The main difference between the spiritual and the physical involves the concept of space. Physical space exists only in the physical world. In the spiritual domain, there is no concept of space as we know it.[6]

However, physical reality exists in three dimensions—space, time, and mass (or energy, which is proportional to mass: E = mc2). We see these three dimensions reflected in the basic units of physics—length (m), time (sec), and mass (kg).[7] Any physical unit is a combination of these three basic units. These three units can be metaphysically understood as being related to change: time is the measure of change, space is the lack of change, and mass, as the measure of inertia, is resistance to change. All these concepts are symbolized by various aspects of Noah’s ark. Change is symbolized by the raging waters surrounding the ark; flowing water is a classic metaphor for change and time in many cultures. (See the earlier post “Noah’s Ark—Sailing the Flood of Time.”)  The duration of the flood—one year—symbolizes time as the measure of change. In Hebrew, a year is shanah, which is etymologically related to the word shinui, that is, “change.” The dimensions of the ark given in the Torah symbolize length (or space). The ark made of solid gopher wood itself symbolizes mass.

These three base units—length, time, mass (or energy)—form a three-dimensional conceptual space. Any physical object exists in this three-dimensional conceptual space. In turn, space itself is three-dimensional. If we expand one dimension—length—in the three-dimensional conceptual space into three-dimensional physical space, we end up with a five-dimensional space made of four-dimensional space-time plus the fifth dimension of mass/energy.[8] This five-dimensional space is very similar to the five-dimensional space described in Sefer Yetzirah[9] dating to the first century CE.[10]

The reason we cannot define physical objects based on their spatial characteristics alone is that only solid objects have clearly defined spatial characteristics—shape and volume. Liquids, while maintaining their volume, lose their shape, and gases do not maintain their volume, either. The same object gradually loses its spatial characteristics in higher energies.[11] Thus, the nonsolid matter quickly sheds its spatial characteristics while retaining its physical nature.

The first (lowest) deck of Noah’s ark is parallel to physical matter.

Information: The Middle (Second) Tier

The second tier of the ark may correspond to information. We are familiar with the information when embedded in a tangible, physical medium—printed on paper, recorded on a tape or a vinyl disk, digitized and stored in non-transient memory, etc. However, when disembodied from such carriers, information in its abstract form is no longer physical.

However, physicists have long suspected that such abstract information, while not physical itself, may be the source of space, time, and matter. In the 1960s, physicist John Archibald Wheeler formulated the “It From Bit” program. A bit is the quantum of information and can have only one of two values—zero or one. In the context of Wheeler’s phrase “it from bit,” “it” represents physical matter, and “bit” represents information.

Theoretical physicist John Wheeler suggested that information is fundamental to physics. He formulated the “it from bit” doctrine, whereby all physical things originate from information:

It from bit. Otherwise put, every it—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. It from bit symbolizes the idea that every item of the physical world has at bottom—a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe. (John A. Wheeler, “Information, Physics, Quantum: The Search for Links.”)[12]

The last phrase, “a participatory universe,” refers to the notion that quantum mechanics require all observers to be participating observers that affect reality (for the specifics, see my paper, “Towards Reconciliation of Biblical and Cosmological Ages of the Universe”). Here Wheeler aptly observes that information is meaningful only so long as human beings, participating observers, give meaning to the information.

One might think that mathematics should also belong in this stratum of reality, along with information. However, mathematics is not a stratum of reality—it is a language used to describe every stratum of reality. Theoretical physics uses mathematics to describe physical reality. Shannon’s theory of information (as well as Fisher information) uses mathematics to describe information. As we shall see, spirituality can also be described mathematically.

There is room, however, to consider mathematics as a set of abstract ideas, rather than tools, in which case mathematics can also be viewed as occupying the second tier of reality alongside information.

In this metaphor, the middle (second) deck of Noah’s ark is parallel to information. It is interesting to note that Wheeler’s “It From Bit” paradigm fits well with our metaphor. Just as the waste housed in the third deck of the ark comes from the animals on the second level, the physical matter corresponding to the third deck of the ark, according to Wheeler, comes from information, which in our model is parallel to the second level of the ark. It also fits with our parallel between Noah’s ark and a living cell described in the previous post, “Noah’s Ark—A Model of a Living Cell“. Just as a physical body can be seen metaphorically as the waste of angels, so too in the present metaphor, can physical matter be seen as a byproduct (the waste) of information. There is also a close relationship between angels and information.

Spirituality: The Upper (Third) Tier

The upper—third—level of reality is occupied by the spiritual (in Hebrew, ruchniyut). Physicists cringe when they hear this word, spiritual, and for good reason—it is an extremely vague and ill-defined concept. What is spiritual? Well, the straightforward answer is that the spiritual is everything that is not physical. Although,  the term nonphysical smacks of something otherworldly, at least it is a rigorous definition.[i] Having defined physical matter as existing in a three-dimensional conceptual space (abstract space) with the dimensions of length (physical space), time, and mass/energy, we can say that spiritual matter exists outside of this three-dimensional conceptual space (or the expanded five-dimensional space, as discussed above).

This definition, however, is too broad, because it includes information and mathematics, each of which exists outside the three-dimensional conceptual space of length, time, and mass/energy.

Three different concepts are often lumped together into one category called spirituality. These three concepts are related to information, the wave function, and extra dimensions in a conceptual space.

As we discussed above, it is quite tempting to classify information as something spiritual, because it is . . . well, not physical. Information, disembodied from its physical medium, is an abstraction that lacks the indicia of physical matter. But in reality, information is an intermediary between the spiritual and the physical. In Kabbalah and Chasidut, it is called “physical of spiritual” (gashmiyut shebe-ruchniyut).

A good example of information treated as something spiritual and otherworldly occurs in the story of Jacob preparing to meet his brother Esau.

And Jacob sent messengers before him to Esau his brother unto the land of Seir, the field of Edom. (Genesis 32:4)

In the original Hebrew, “messengers” are malakhim, meaning either “messengers” or “angels.” Classical Torah commentator Rashi insists that these were malakhim mamash, that is, real angels. What was the mission of these angels/messengers?

And he commanded them, saying: “Thus shall ye say unto my lord Esau: Thus saith thy servant Jacob: I have sojourned with Laban, and stayed until now. And I have oxen, and asses and flocks, and men-servants and maid-servants; and I have sent to tell my lord, that I may find favour in thy sight.” (Genesis 32:5)

The only function of these “angels” was to transmit information. It follows that angels are indeed messengers—information carriers. There you have it: information and its transmission (the subject of Shannon’s Theory of Information) is couched in spiritual terms involving angelic beings.

The wave function in and of itself is not physical. The wave function is a distribution of probabilities to find a physical object in a particular state. This is a mathematical abstraction related to a physical object, but it is not a physical object itself. In Kabbalah and Chasidut, it is called “spiritual of physical” (ruchniyut shebe-gashmiyut). Both the spiritual of physical and the physical of spiritual are two levels in the Olam HaAsiyah Ruchni (the spiritual stratum of the World of Action)[13]. Physical matter is also part of the World of Action (Olam HaAsiyah)—it is the lower stratum of this world. The upper stratum of this world— the spiritual of physical and the physical of spiritual—are the intermediary levels connecting the spiritual and the physical. For this reason, we will not classify these two categories—information and the wave function—as spiritual, although neither is physical.

A good example of the wave function been described as spiritual is the dispute between tana Nehunya ben HaKanah and the Ari regarding the sabbatical cycles—shemitot. Rabbi Nehunya ben HaKanah maintained that this world was preceded by six sabbatical cycles, each lasting seven thousand years (or, according to Kabbalist Isaac of Akko,[14] much longer—approximately 15 billion years in total[15]). According to the Ari, these previous sabbatical cycles (shemitot) took place in the spiritual world. As I discussed in my essay, “Two Beginnings,” the world initially existed in a superposition of states with the universal wave function evolving some 13+ billion years before the appearance of the first observers—Adam and Eve—who collapsed the universal wave function and brought the world into tangible existence as we know it today. From this point of view, what the Ari called “spiritual” was certainly not physical, but a well-defined state—the wave function describing the world in a superposition of states.

Another example may be the statement of the Ari that, prior to the sin of the Tree of Knowledge, Adam was a spiritual being with his body made of light that spread across all four worlds of ABiYA.[16] According to the Ari, when he ate the fruit of the Tree of Knowledge, his stature was “diminished,” and he became a physical being.[17] In contemporary terms, this describes the wave function (“light” wave) of Adam spread across Hilbert space, which the Ari identifies with various spiritual realms. When Adam partook of the Tree of Knowledge and acquired sufficient knowledge to be a “participating observer,” he collapsed his own wave function and became a physical being with a well-defined location. The “diminishing” of his stature alludes to the collapse of his wave function. These two examples demonstrate that what we now call the wave function, or the superposition of states, mystics of old called, for lack of a better word, “spiritual.”

What is truly spiritual is described in Sefer Yetzirah (the “Book of Formation”)—it is an extra dimension in a conceptual space. Sefer Yetzirah writes:

A depth of beginning, a depth of end;
A depth of good, a depth of evil;
A depth of above, a depth of below;
A depth of east, a depth of west;
A depth of north, a depth of south.[18]

Each line in this passage defines one dimension in a five-dimensional conceptual space by describing the opposite extremes or two opposite infinities (“depths”) of each direction. For example, “A depth of beginning, a depth of end” defines the dimension of time extending infinitely into the past and into the future (from the reference point of the observer, who is in the present). Similarly, “a depth of good, a depth of evil” defines a spiritual or “moral” dimension. The other lines describe our physical three-dimensional space. In this picture, our four-dimensional physical space-time continuum is embedded in five-dimensional conceptual space, in which an extra dimension is a spiritual or moral dimension, as shown in the following table.

Dimension – ∞ + ∞ Meaning
Time A depth of beginning (past) A depth of end (future) Physical time
Moral dimension A depth of good A depth of evil Spiritual dimension
Up-Down direction A depth of above A depth of below Three-dimensional physical space
East-West direction A depth of east A depth of west
North-South direction A depth of north A depth of south


Based on this recipe in Sefer Yetzirah, if we want to describe the spiritual dimension in mathematical terms, all we need to do is to add another dimension (a spiritual/moral dimension) to our familiar space-time.

This is, however, what we call in physics the first order of approximation. The single spiritual dimension can be expanded into many dimensions, depending on how many degrees of freedom we wish to consider. We have a similar situation in the three-dimensional conceptual space made of three fundamental units—length, time, and mass/energy. The first dimension, length, representing the spatial degree of freedom, should be expanded into three spatial dimensions.[19] So the resulting space becomes five-dimensional space containing four-dimensional space-time plus the fifth dimension—mass/energy.

Similarly, one spiritual dimension of Sefer Yetzirah can be expanded into a multi-dimensional space. Since every sefirah comprises all ten sefirot, a logical choice would be to replace each point on the one-dimensional spiritual line with ten-dimensional spaces wherein each dimension corresponds to a single sefirah. This would model Olam HaTohu (the “Universe of Chaos”) where all sefirot are independent of each other (not interincluded, as in Olam HaTikun—the “Universe of Rectification”).  To model Olam HaTikun would require much more complicated fractal geometry, because all sefirot are interincluded (each of the ten sefirot includes all ten ad infinitum).

During the early part of the twentieth century, a group of philosophers and scientists who called themselves “logical empiricists” formed the Vienna Circle.[20] They tasked themselves with formalizing analytical philosophy by replacing words with mathematical symbols and formulas. The day is nigh when the study of spirituality will also be well-defined and formalized, removing ambiguity and otherworldliness from it. When spiritual concepts are expressed in mathematical terms, the barrier between science and spirituality will, at last, be removed.


[1] See, for example, Rabbi Yitzchak Ginsburg (2007), “Noah’s Ark and the Gift of Cosmic Speech,” Chabad of Central New Jersey,, retrieved on October 22, 2020; David W. Cotter, Berit Olam, Studies in Hebrew Narrative and Poetry, Genesis. (Liturgical Press, 2003), 55, 59; Martin Kessler and Karel Adriaan Deurloo, A Commentary on Genesis: The Book of Beginnings. (Paulist Press, 2004), 81; Aleida Assmann, “Cultural Memory and Western Civilization” (Cambridge University Press, 2011), 101; Joseph Triolo, “The Tabernacle as Structurally Akin to Noah’s Ark: Considering Cult, Cosmic Mountain, and Diluvial Arks in Light of the Gilgamesh Epic and the Hebrew Bible,” 2019, SBL Pacific Coast Regional Conference, Fullerton, California,, retrieved on October 22, 2020; “Noah,” Wikipedia,, retrieved on October 22, 2020; “Reynikung Flood Narrative,” ” Fandom [Constructed Worlds Wiki],, retrieved on October 22, 2020; “Genesis Flood Narrative,” Wikipedia,, retrieved on October 22, 2020; Noah’s Ark, The Multilingual Encyclopedia,, retrieved on October 22, 2020.

[2] See Nachmanides on Genesis 1:1.

[3] See Numbers 16:31–34; 1 Samuel 2:6; 2 Samuel 22:5–19; Job 7:7-10, 10:18–22; Jonah 2:3–8; and Psalms 88:2-10, 30:4, 94:17, 143:3, and 115:17.

[4] Babylonian Talmud, tr. Eruvin 19a:16.

[5] One of the most influential philosophers of science, Karl Popper, for example, proposed three worlds: World One—the physical world (or physical states); World Two—the world of mind (or mental states, ideas, and perceptions); and World Three—the body of human knowledge, or the products of the Second World (ideas) expressed in the tangible materials of the First World (i.e., books, papers, paintings, sculptures, music, etc.). See Karl Popper, “Three Worlds, The Tanner Lecture on Human Values,” The University of Michigan, 1978.

[6] Rabbi Aryeh Kaplan, “Innerspace: Introduction to Kabbalah, Meditation, and Prophecy, 2nd ed. (Moznaim, Jerusalem, 1990), p. 191, n. 33.

[7] All units are given in SI—the International System of Units based on the metric system.

[8] In 1973, while in high school, I proposed to generalize four-dimensional space-time in the special theory of relativity with five-dimensional space, where the fifth dimension is energy. Unbeknownst to me, fifty-some years earlier, a similar five-dimensional theory was proposed by Theodor Kaluza (1921) and Oskar Klein (1926), known as Kaluza–Klein theory (or KK theory). This theory was completed in the 1940s by Einstein and his colleagues at Princeton; Thiry in France; Jordan, Ludwig, and Müller in Germany; and Scherrer in Switzerland. KK theory is considered a precursor to modern string theory.

[9] The five-dimensional space described in Sefer Yetzirah is a four-dimensional space-time plus a fifth, moral (spiritual) dimension.

[10] The dating of Sefer Yetzirah to the first century is based on the attribution of its authorship to tana Rabbi Akiva. However, most traditional sources attribute this first book of Kabbalah to the patriarch Abraham, who was born, according to Jewish tradition, in 1813 BCE.

[11] If we start with a cube of ice, it has volume and shape. If we heat the ice and melt it, water no longer maintains its shape, only keeping its volume. When we heat it further to evaporate the water, the resulting vapors will have neither shape nor volume.

[12] John A. Wheeler, “Information, Physics, Quantum: The Search for Links,” in Wojciech Hubert Zurek (ed.), “Complexity, Entropy, and the Physics of Information” (Addison-Wesley, 1990).

[13] Olam HaAsiyah is the lowest of the three worlds of BiYA (Beriyah, Yetzirah, and Asiyah). The world of Asiyah is the world we live in, whereas the other words, Beriyah and Yetzirah, are spiritual worlds. (We left Atzilut, because it is not a world per se, although it is often counted as the first of four worlds of ABiYA). The World of Asiyah has two strata—the physical (Olam HaAsiyah Gashmi) and spiritual (Olam HaAsiyah Ruchni). The so-called “spiritual” stratum of the world of Asiyah is not really what we would call “spiritual.” It is the domain of ideas, music, mathematics, and information. Truly spiritual is the domain of the higher realms of Atzilut, Beriyah, and Yetzirah.

[14] Rabbi Isaac ben Samuel of Acre (13th–14th century), a Spanish Kabbalist of note and a contemporary of Moses de Leon. Rabbi Isaac was one of the central figures in the controversy surrounding the discovery of the Zohar by Moses de Leon. He investigated the authenticity of this claim and concluded that the Zohar was indeed written by Rabbi Shimon bar Yochai.

[15] According to Rabbi Aryeh Kaplan, who based his calculation on the words of Rabbi Isaac, the world is 15,340,500,000 years old. See Aryeh Kaplan, Immortality, Resurrection and the Age of the Universe: A Kabbalistic View (KTAV Publishing House, 1993).

[16] The worlds of seder hishtashlelut: Atzilut, Beriyah, Yetzirah, and Asiyah.

[17] See Moshe Wisnefsky, Apples from the Orchard: Gleanings from the Mystical Teachings of Rabbi Yitzchak Luria-the Arizal on the Weekly Torah Portion, (Thirty Seven Books, 2nd ed. 2008).

[18] Sefer Yetzirah 1:5; English translation by Rabbi Aryeh Kaplan, Sefer Yetzirah (Samuel Weiser, 1990), 44.

[19] In differential geometry, it is called a fiber-bundle, when every point in a space is replaced with another space. A good visual example of this would be a string from which many balloons are hung, so that every (well, almost every) point on the one-dimensional string corresponds to (or is replaced by) a three-dimensional balloon. We can even imagine a string put together of many deflated balloons strung together. When we start blowing through an opening in the string, all balloons become inflated, replacing all the points on the (approximately) one-dimensional string with three-dimensional balloons.

[20] The Vienna Circle was a very influential group of philosophers, scientists, and mathematicians, led by philosopher and physicist Moritz Schlick, who gathered at the University of Vienna from 1924 to 1936. The Vienna Circle included the philosophers Rudolf Carnap, Otto Neurath, Herbert Feigl, Felix Kaufmann, Viktor Kraft, and Edgar Zilsel; physicist Philipp Frank; and mathematicians Kurt Gödel, Hans Hahn, Richard von Mises, Karl Menger, and Friedrich Waismann. Ludwig Wittgenstein and Karl Popper were in close contact with the Vienna Circle. The Vienna Circle profoundly influenced twentieth-century philosophy in general and, particularly, the philosophy of science and analytic philosophy.


[i] In the language of the set theory,  spiritual objects can be defined as the elements in a complement to the set of physical objects. Let U be the universal set comprising all objects (physical and nonphysical). Let P be a set of all physical objects P = {p}. Then the set of all nonphysical objects is the absolute complement of P: S = Pc, Pc = U\P. Pc = {s ∈ U | s ∉ P}. In other words, set S contains all elements that are not in P.


Keywords: Noah, parshat noach, Noach, Noah’s ark, Noach’s ark, tevah, teivah, tripartite, ABiYA, BiYA, Beriyah, Beriah, Yetzirah, Asiyah, physical, informational, information, spiritual, spirituality, nonphysical, Genesis 1:1, Genesis 6:16, Gen. 1:1, Gen. 6:16, Bereshit 1:1, Bereshit 6:16, Genesis 1:6, Gen. 1:6, Bereshit 1:6, microcosm

Originally published on on 10/28/2020.

About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
Related Topics
Related Posts