Alexander I. Poltorak

Tzitzit, Korach, and Wave-Particle Duality

The Lord spoke to Moses, saying: Speak to the children of Israel and you shall say to them that they shall make for themselves fringes on the corners of their garments, throughout their generations, and they shall affix a thread of sky blue [wool] on the fringe of each corner. (Num. 15:37,38)

They [Korach and his men] assembled against Moses and Aaron, and said to them, “You take too much upon yourselves, for the entire congregation are all holy, and the Lord is in their midst. So why do you raise yourselves above the Lord’s assembly” (Num. 16:3)

The Torah portion Shlach, which we read last Shabbat, deals primarily with the fiasco of the spies sent by Moses to scout out the land of Canaan. The portion ends, however, seemingly out of place, with the commandment to wear tzitzit (fringes, tassels, or strings) on a four-corner garment. The following Torah portion, Korach, deals with another disaster, the rebellion of Korach. What is the connection between these two Torah portions? Why does the story of Korach follow the commandment of Tzitzit? The Jerusalem Talmud (as well as some ancient anonymous sources referred to as Pseudo-Philo sources, Liber Antiquitatum Biblicarum) already links the commandment of Tzitzit with Korach. To understand this, let us examine the meaning of tzitzit.

The Torah instructs Jewish men to wear tzitzit (fringes, tassels, or strings) on the corners of a four-corner garment. The performance of the precept requires two main components: the beged, i.e., the garment with four corners, and tzitzit, the strings attached to the four corners of the beged. Another notable detail is tekhelet – the blue (or turquoise) string:

…and they shall affix a thread of sky blue [wool] on the fringe of each corner.”

The blue string is added to the white strings, which we will discuss later. For now, let us focus on the big picture – the garment (beged) with the fringes (tzitzit) at the corners.

The garment could be of any shape and color. There are very few requirements, only that it has four corners and must have a minimum size (to qualify as a garment, rather than, say, a scarf or a handkerchief). The tzitzit, on the other hand, have many detailed requirements related to the number of strings, the number of knots, the manner in which the knots are tied, and the color of the strings.

Today, Jewish men wear two types of garments with fringes: tallit gadol used during prayer, and tallit katan worn as an undergarment the whole day. The difference is only the size—tallit gadol is large, and tallit katan is small, although in kabbalah they represent two different types of the surrounding light, makif (far makif and near makif) Both are made of a rectangular piece of cloth with tzitzit-strings attached to its four corners.

Image result for Tekhelet talitThe primary feature of this commandment—the juxtaposition of strings over a whole piece of cloth—is symbolic of the juxtaposition of klal (whole) and prat (part). Klal, usually translated as “general,” (as opposed to particular), “whole,” (as opposed to a part), or a community (as opposed to the individual members of the community), represents a holistic view, the view of the whole forest, as opposed to the trees. Prat, on the other hand, means “particular,” i.e., a detail or an aspect of a whole, a tree in the proverbial forest.

The dynamic of klal and prat is at the center of Torah Hermeneutics. Any concept, object, or a Biblical verse could be analyzed as a whole, from a more general, holistic point of view, or it could be viewed as a sum-total of its parts, in which case the focus is on details and particulars. The Oral Torah provides thirteen rules for biblical exegesis. These rules were formulated by Rabbi Yishmael in the Baraita as the introduction to Sifra. Of the thirteen principles, eight principles (Nos. 4-11) involve the dynamics of klal and prat. One might say klal and prat is the central theme of Torah exegesis. It is this dialectic tension between klal and prat, between general and particular that is responsible in large measure for the body of Oral Torah as expounded in Mishna and Talmud.

The commandment of wearing tzitzit is emblematic of klal and prat, because the beged (the garment itself) represents the klal, whereas the tzitzit (fringes) represent particulars. One without the other is deficient. A garment that has four corners but no tzitzit is forbidden to wear. Tzitzit-tassels by themselves are worthless if not attached to a beged (garment). Wearing tassels alone (say attached to the belt) does not accomplish anything—it is not a mitzvah. Only wearing them together, with tzitzit attached to the four corners of the garment, as prescribed by Halachah, the Jewish ritual law, one can fulfill this Biblical precept, a mitzvah.

Aside from the klal and prat dynamics, the other major theme of this commandment is the blue thread, tekhelet:

…and they shall affix a thread of sky blue [wool] on the fringe of each corner.”

This means that out of eight half-strings to be attached to each corner of a garment, at least one (but no more than half) should be blue. This color combination creates a tension between white and blue colors.  It is reasonable to ask what is the connection between these two themes: klal and prat, on the one hand, and blue and white on the other.

Image result for Tekhelet talit

The connection is rather obvious—both represent the tension between the sefirah of Chesed (love, kindness) and the sefirah of Gevurah (strength, strict judgment). As late Rabbi Aryeh Kaplan writes in the Inner Space, the dialectic tension between the opposites is represented in each of the three triads of the sefirotic tree: thesis-antithesis-synthesis. In the second sefirotic triad, Chesed-Gevurah-Tiferet, Chesed represents a thesis, whereas Gevurah represents the antithesis. The wholesomeness of the klal (general, whole) symbolized by the beged (garment) represents Chesed. On the other hand, the prat (particulars), which breaks the klal into its constituent parts and detail symbolized by the strings, represents Gevurah.

The same Chesed-Gevurah dynamic plays out in the colors of the tzitzit strings: white symbolized Chesed, whereas blue symbolized Gevurah (Zohar Vol. 3 p. 227a; Likutei Torah, Shelach). As the Psalmist says:

Sur merah v’aseh tov” – run away from evil and do good. (Psalms 37:27)

Sur merah (run away from evil) represents gevurah, whereas aseh tov (do good) represents chesed. As I wrote in my post, “String Theory,” Jewish Sages tell us that white strings symbolize the aseh tov (do good), which is the attribute of chesed, whereas the blue string, tekhelet, symbolize the sur merah (run away from evil), which is the attribute of gevurah.

It seems that there is even a deeper connection between the dynamics of klal and prat, on the one hand, and white and blue, on the other. To explore this connection, however, we must take an excursion into quantum physics.

In physics, we also find a similar tension between klal and prat, between general and particular. It is the wave-particle dualism. It is not coincidental that, in the English language, the words “particle” and “particular” share the same root, as they both come from Latin particula meaning “little bit” or “part.”

In quantum physics, every object could be viewed as a wave or as a particle. In our everyday life, we encounter particles and waves separately. Some objects can be idealized as point-like objects or particles. When we look at the surface of a lake or an ocean, we see waves, which are spread in space. These familiar concepts of particles and waves fail us when applied to the microworld of subatomic particles. Just as a beged without tzitzit or tzitzit alone without a beged are worthless, concepts of “wave” and “particle” by themselves are inadequate to describe the reality of the subatomic objects, which are neither particles nor waves, but possess properties of both. Only wave-particle duality, where the concepts of “wave” and “particle” are taken together, produces the correct description of sub-atomic particles. Einstein said it best:

We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.” (Albert Einstein, Leopold Infeld (1938). The Evolution of Physics)

As Louis de Broglie realized in 1924, all particles, not just quanta of light, possess wave properties, such as frequency and wavelength. I wrote about wave-particle duality in my earlier posts, Jacob Teaches Wave-Particle Duality and First Fruits and the Wave-Particle Duality of Nature, and will not further elaborate on it. Here, I would like to stress only the connection of the quantum-mechanical wave-particle dualism with the notion of klal and prat in general, and with the commandment of tzitzit in particular.

I associate waves with klal (“general” or whole) because they are spread out in space. Therefore, one cannot see a wave by focusing on a particular spot.  To see waves, one needs to take a broad and expansive view of the wave as a whole (at least, one whole cycle of the wave from one crest to the next crest, or from one trough to the next trough).

On the other hand, particles are localized in space. One can zoom in on a particle to investigate its properties disregarding the global picture. That is why particles represent the prat aspect of the klalprat dynamics.

A quantum particle is represented by a wave packet

Wave-particle duality inevitably leads to the Heisenberg Uncertainty Principle.

All periodic processes can be analyzed using the Fourier transform. The Fourier transform decomposes a function of time into its constituent frequencies. This is a mathematical technique well-familiar not only to physicists and mathematicians but to many engineers as well, as it is widely used in signal processing and acoustics. The French mathematician Fourier showed that all complex periodic processes, such as soundwaves, for example, may be represented as a sum of simple sinusoid functions of different frequencies. Furthermore, Fourier developed a technique to simplify the analysis by transforming it from the time domain to the frequency domain.  Without delving into the mathematics behind it, suffice it is to say that the wave-particle duality and the Heisenberg uncertainty principle follow naturally from Fourier formalism.

Image result for Fourier transform
The Fourier Transform (FT)

Going back to our muttons, one might say that the beged (klal – general) vs. strings (prat – particular) dynamic., which is parallel to wave-particle duality, is conceptually parallel to the Fourier transform formalism.

A careful reader will notice that the Fourier transform applies only to periodic functions describing periodic processes. Where do we see any hint on periodicity in the mitzvah of Tzitzit? The strings, of course!

As I wrote in my post, “String Theory,” the dynamics of sur merah (run away from evil) vs. aseh tov (do good) creates the “vibrations of the strings.” Indeed, as we discussed before, in his vision of Maaseh Merkavah, “the Work of the Chariot,” Ezekiel sees angels running and returning (Heb. rotzoh v’shav). The concept of aseh tov (do good) is a manifestation of rotzoh (running towards doing good), whereas sur merah (running away from evil) is a manifestation of shav (returning). As I wrote in my posts “Paradox of the Red Heifer,” rotzoh v’shav sets off the basic rhythm of creation.

So, it is the dynamics of white strings vs. blue strings (tekhelet) that set off the rhythm that is responsible for the klal-prat dynamics of beged (garment) vs. tzitzit (strings). It took physics and mathematics to uncover this hidden connection.

The story of Korach is the continuation of the story told in the commandment of Tzitzit – the story of the tension between klal (general) and prat (particular), between beged (garment) and tzitzit (strings).

What is Korach’s complaint to Moses?

the entire congregation are all holy… So why do you raise yourselves above the Lord’s assembly?”

What Korach says is that everybody (klal-congregation) is holy — so why do we need Moses and Aaron as leaders (prat) to be above the congregation? Korach does not see klal-prat dynamics, nor does he understand the need for particulars (prat). He only sees the generalities (klal).

The Midrash elaborates further that Korach asked Moses, if the room is full of Torah scrolls, does the room require a mezuzah? Moses answered in the affirmative and Korach, and his company laughed. Korach failed to see the need for a particular section of the Torah written on a mezuzah scroll (prat) when the room is full of Torah scrolls (klal).

Jerusalem Talmud quotes a Midrash, according to which Korach dyed a garment blue and brought it to Moses. He asked if the whole garment is dyed blue, does it require tekhelet, the blue string? Moses answered, “Yes.” Hearing this, Korach claimed that Torah was not given by God, Moses was not a prophet, and Aaron was not the High Priest (Jerusalem Talmud, tr. Sanhedrin 10:1). Once again, Korach failed to see the import of a particular blue string in view of the whole blue garment. The reference to tzitzit and tekhelet in the debate between Korach and Moses is not coincidental – this is a hint at the previous Torah portion and the commandment of tzitzit, which is symbolic of the dynamics of klal and prat that is lost on Korach.

Moses, who, unlike Korach, understands klal-prat dynamics, argues with God, raising the question of collective responsibility: if one person (prat) sins, would God punish the entire community (klal)? Like Abraham in Genesis 18:23, Moses urges God to limit the punishment only to the guilty and spare the innocent—this is the prat approach, as the antithesis to the klal approach advocated by Korach. Similarly, God tells Moses and Aaron:

Separate yourselves from among this congregation.” (Num. 16:21)

referring to Korach and his band, and telling Moses and Aaron to separate (prat) from this evil congregation (klal).

Korach and his cohort, on the other hand, were punished (measure for measure) in accord with the principle of klal (which, in Korach’s opinion, negated prat) — they were punished with their wives and small children.

And the earth opened her mouth and swallowed them up, and their households, and all the men that appertained unto Korach, and all their goods. (Num. 16:32)

Moreover, the verse concludes, “they perished from among the assembly.” (Ibid, 33) again emphasizing the punishment in the mode of klal, as a measure for measure.

The Punishment of Korah — detail from the fresco Punishment of the Rebels by Sandro Botticelli (1480–1482)

Let us recall that the wave-particle duality exists in the state of superposition. Once the wave function is collapsed, either the wave OR the corpuscular properties are manifest. For example, in the double-slit experiment, an electron is in superposition of states of being a wave and a particle until we measure it – if we monitor which slit it goes through, it behaves as a particle; but if we focus our attention on the second screen (behind the screen with two slits), the electron behaves as a wave. By denying klal-prat dynamics, Korach denied wave-particle dualism and, therefore, the notion of superposition. Korach was punished by the earth opening its mouth and swallowing him and his band. The Ethics of the Fathers (Pirke Avot) states that this was one of ten miracles created on the twilight of the first Friday of creation. As I have written before, Twilight is a time in the state of superposition—not day, not night, not both, not neither, but the fifth unique state. Thus, it was fitting (measure-for-measure) to apply this punishment to Korach.

The klal-prat dynamic manifests itself in spiritual realms, as we see in the Biblical narrative of Korach’s rebellion and the commandment of tzitzit, as well as in our physical reality, as we see in wave-particle duality.

Originally published on

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.
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