Alexander I. Poltorak

Quantum Cheshire Cat vs. Venomous Snakes

By Unknown author - The story of the Bible from Genesis to Revelation, Public Domain,

A Study in Form and Matter

And Moses prayed for the people.  And the Eternal said unto Moses: “Make thee a fiery serpent, and set it upon a pole; and it shall come to pass, that every one that is bitten, when he seeth it, shall live.” And Moses made a serpent of brass, and set it upon the pole; and it came to pass, that if a serpent had bitten any man, when he looked unto the serpent of brass, he lived. (Numbers 21:8-9)

The Torah portion, Chukat, tells a bizarre story. Jews complain against God and Moses. God gets angry and sends venomous snakes that bite and kill many Jews. The people repent and ask Moses to pray for them. In response to Moses’s prayer, God instructs him to make a fiery serpent and mount it on a pole, so that anyone bitten by a snake may gaze upon the fiery serpent and be healed. Moses makes a copper snake and mounts it on a pole. Bitten people gaze upon the copper snake and get healed. What a strange story! Every year, reading it in the Torah, I kept wondering: what is so special about a copper snake? How could it heal those bitten by a real, live snake? There is a ma’amar (discourse) by the Alter Rebbe[1] in Likkutei Torah,[2] where he explains the origin of evil and the secret of the copper snake pointing to the source of evil, which is goodness in disguise. I highly recommend studying this foundational ma’amar.

However, there is one question that remains unanswered. God commanded Moses to make a fiery serpent. Why then did Moses make a copper snake instead? This year, I finally understood the answer. But to explain it, we need a bit of background in Formation.

Tzurah and Chomer—Form and Matter

What does a copper snake have in common with a live snake? Only one thing—the form of a snake. Thus, the copper snake Moses made was meant to represent the snake form.

There is an ancient metaphysical doctrine, known as Universal Hylomorphism, that all things (substances) are composed of matter and form. This form-matter dichotomy also plays a significant role in Jewish philosophy and Kabballah. In Hebrew, form is tzurah, and matter is chomer.

Tzurah (form)  is the shape and function of an object, whereas chomer is the matter from which the object is fashioned. An object could have several forms defining it. For example, in the case of a wooden table, the wood of which the table is constructed is its chomer (matter). However, the tzurah (form) of the table consists of both its “tableness” based on its function—i.e., what all tables have in common—as well as its particular shape, whether round, square, or some other shape. Tzurah is an abstract principle, whereas chomer is matter that behaves according to the principle. Tzurah is a soul, whereas chomer is a body.[i]

The primary source of the Jewish understanding of form and matter can be found in the medieval work “Mekor Chayim” by Jewish philosopher Solomon ibn Gabirol,[3] which is devoted to this topic. Also known by its Latin title, Fons Vitæ, this philosophical treatise postulates that the basis of all existence is a combination of “matter” (materia universalis) and “form.” In general, he followed the Neoplatonism of Plotinus in his understanding of form and matter.[4]

Another medieval Jewish philosopher, Rabbi Joseph ibn Tzaddik,[5] borrows extensively from ibn Gabirol’s Fons Vitæ in writing about tzurah and chomer in his work Olam Katan.

Rabbi Abraham ibn Daud, known as Ra’ava”d I,[6] was the first Jewish Aristotelian philosopher. He adopts Aristotle’s notions of form, matter, and substance. He gives the example of a golden scepter that is turned into a golden coin, which in turn, is made into a ring and, finally, into a nose ring. He points out that the underlying matter in all these objects, gold, does not change. What differentiates each object is its form, which is imposed on the matter. [7]

Maimonides, following Aristotle, writes in his Guide, “Every physical body necessarily is composed of two things… form… and matter.”[8]

From there on, the notions of tzurah (form) and chomer (matter) became prominent features of Kabbalistic and Chasidic thought.[9]

To help develop an intuitive understanding of the difference between form and matter, or tzurah and chomer, here is a table with many examples from various disciplines:

  Tzurah Chomer (Matter)
Philosophy Ideal Form/Idea Matter
  Actual Potential
An object Geometrical shape of the object The material of the object
Classical Mechanics Energy A body or a system having the energy
Hamiltonian Mechanics Hamiltonian The System
Classical Field Theory Lagrangian The field (Electromagnetic or gravitational)
Optics Physical light The medium through which the light passes
Thermodynamics Entropy Gas, or another medium
Quantum Mechanics Wavefunction The System
Particle physics Charge, spin, and other characteristic of particles Particles stripped of their specific quantum-mechanical characteristics
Mathematics Axioms Interpretation of the axioms with mathematical objects
Human being Soul Body
Biology Genome DNA
Information / Communications Information Carrier of information, communication channel
Music Notes The sound produced by a musical instrument
Literature General structure/plot Specific storyline
Language Meaning Words
Gender Male Female


Tzurah (Form) acts upon chomer (matter) to produce a substance, i.e., objects we can observe and interact with. It is tzurah that gives individuality and existence to each thing. Tzurah relates to chomer as the male relates to the female.[10]

The Quantum Cheshire Cat

Let us recall, as first predicted by Yakir Aharonov in 2013, it should be possible to separate a quantum particle (chomer) from its properties—i.e., its “personality,” or tzurah only to reunite them at a later time. Just as a Cheshire Cat can be separated from its grin, so a quantum particle may be separated from one of its quantum characteristics, such as its charge, spin, or magnetic momentum. As we discussed at length in the post “Quantum Cheshire Cat and Resurrection,” it has been demonstrated in experiments that particles (chomer) can indeed be stripped of their properties, such as charge and spin (tzurah), only to be reconnected later, to form reconstituted particles with their original characteristics.

The Universe of Tohu and the Universe of Tikun

Perhaps the earliest references to tzurah and chomer can be found in one of the oldest books of Kabbalah, Sefer haBahir, which writes:

Rabbi Berachiah said: It is written (Genesis 1:1), “The earth was formless (Tohu) and Desolate (Bohu). What is the meaning of the word “was” in this verse? This indicates that the Chaos existed previously. What is the Chaos (Tohu)? Something that confounds (Taha) people. What is desolation (Bohu)? It is something that has substance. This is the reason that it is called Bohu, that is Bo Hu—“it is in it.” (Bahir 2)[11]

Abraham bar Chiyya[12] (12th century) was the first Jewish philosopher to interpret the tohu and bohu of Gen. 1:2 as meaning “matter” and “form,” following the above quote from the Bahir. He wrote:

Matter, being void of all reality, requires form to give it existence. Now the union of these two by the will of God, which brings them from a state of potentiality into one of actuality, is Creation, time itself being simultaneously produced with the created things. Both matter and form consist of two different elements. There is pure, and there is impure matter. So also, there is form too sublime to mingle with matter, such as that of the angelic or the upper world; and form which, being receptive and hollow, is susceptible to mixture with matter. The upper world, while gazing upon the lower and radiating its higher light, causes the mixture of matter with receptive form, the “tohu va-bohu”; and out of pure matter the celestial bodies, and out of impure matter the four elements, were evolved. (Hegyon ha-Nefesh)

Nachmanides insisted that only the initial matter created on the first day of Creation was created ex nihilo. Commenting on the first verse of the Torah, “In the beginning, God created the Heavens and the Earth.” (Genesis 1:1), the Nachmanides writes:

Now listen to the simple and proper explanation of the verse. God created all creations from nothing… [yet] not everything that is found in Heaven and Earth was originally from nothing. Rather God first created out of absolute nothingness a very fine matter, which had no tangible element to it. It was simply potential that could be formed into something. It was something that was ripe to accept form, and to thus be actualized. This matter was the first thing created, and is called Hiyuli by the Greeks. After the Creation of this matter, God did not create anything else ex nihilo, but rather Formed things… (Nachmanides on Genesis 1:1)

This primordial matter, hiyuli, is, of course, chomer—the matter that would be Formed into specific creations after being merged with the respective form of that Creation.

The original Universe of Tohu (“Chaos”) is identified with chomer, an unformed matter that is impossible to imagine, which, therefore, confounds (taha) human mind. This universe did not survive, which is why the verse refers to it as it “was.” The vessels (sefirot) in the Universe of Tohu were unrectified because they were not inter-included. Therefore, they could not withstand the Infinite Light, Ohr En Sof, and shattered. This breaking of the vessels (shevirat hakelim) is the defining characteristic of the Universe of Tohu. The shards of the broken vessels of Tohu fell in the Universe of Tikun and formed the source of evil. The Universe of Tohu is associated with the eight kings “who ruled in the land of Edom before any king ruled the children of Israel.” (Genesis 36:31) These kings die one after another, as recorded in the Torah. Therefore, the Universe of Tohu in its unrectified state can be viewed as associated with suffering (shevirah—brokenness) and death.

Tohu is formless; hence, it is identified with primordial matter—chomer. The following word, bohu, signifies tzurah (form). In Kabbalah, Tohu refers to the vessels (sefirot) of the Universe of Tohu that shattered—chomer, whereas Bohu refers to rectified vessels of the Universe of Tikuntzurah.

The Universe of Tohu exists above time (which first appears in Malchut of Atzilut—the first world of the Universe of Tikun). Consequently, the shattering of the vessels (shevirat hakelim) continues to happen at all times (that which exists above time, appears to us—temporal creatures—as something that exists all the time). This continuous shattering of the vessels of Tohu, which is the source of evil, manifests itself in death, illness, suffering, and other problems in this world.

The Universe of Tikun is the Universe of Rectification, where shattered vessels (sefirot) of Tohu get reconstituted, mended, and rectified. Therefore, the Universe of Tohu (Chaos), where shattering of the vessels (shevirat hakelim) continuously takes place, as we said above, is the source of all illness, tragedies, and suffering. The Universe of Tikun, on the other hand, where these shattered vessels get rectified, can be viewed as the “Universe of Healing.” The word tikun, which means “fixing,” “repairing,” “mending,” or “rectifying,” can be viewed as the principle of healing. Indeed, from the point of view of systems biology, disease is usually the loss of homeostasis due to tissue damage or a break in communications between systems due to breaking of feedback loops—i.e., chaotic behavior outside of the boundaries of homeostasis. All these properties are characteristic of tohu. Healing is the process of repairing tissue, restoring feedback loops and orderly behavior on the cellular and system levels, and reinstating homeostasis. All these functions are characteristic of tikun. Thus, tikun is the metaphysical principle of health and healing. It is the foundational principle of the Universe of Tikun, which is why I refer to it as the Universe of Healing.

The Conclusion

Now we can understand the secret of the copper snake. The bite of a venomous snake, causing incurable illness, suffering, and, ultimately, tragic death, is a manifestation of the ongoing shuttering of the vessels (shevirat hakelim) in the Universe of Tohu. Recall, however, that the Universe of Tohu is identified in the Book of Bahir with chomer (matter). The Universe of Tikun—the Universe of Healing—is identified with tzurah (form).

As we said earlier, the copper snake represents the tzurah of a snake. Furthermore, God told Moses to make a fiery serpent (“saraf”), but instead, Moses made a copper snake (“nachash”). Why? A fiery serpent (whatever it is) and a copper snake have different chomer (fire vs. copper) but the same tzurah. Serpent (saraf) and snake (nachash) are two different words that have the same meaning. The particular letters and sounds that comprise words are chomer, but their meaning is tzurah. This substitute is to further emphasize the separation of tzurah from chomer and the superiority of form (tzurah) over matter (chomer)!

As in the Quantum Cheshire Cat experiment, the copper snake separated form (tzurah) from matter (chomer). Raised on a pole, the copper snake connoted of the superiority of form (tzurah) over matter (chomer). Instead of being fixated on the suffering caused by the bite of a snake and on imminent death that are emblematic of the Universe of Tohu, a person would gaze at the artificial snake held by Moses, thereby focusing on the tzurah that is the principle of tikun. On a spiritual level, this act decoupled the person from the Universe of Tohu—the Universe of the Shattering of the Vessels, which was the source of his suffering—and reconnected the person to the Universe of Tikun—the Universe of Healing—thereby saving the person from imminent death and healing him from his suffering.

As we find ourselves in the middle of the COVID-19 pandemic, which, as any illness, is yet another manifestation of shevirat hakelim, may all those who suffer from this, or any other, illness be reconnected to the source of healing in the Universe of Healing (Tikun) and be healed immediately!


[1] Rabbi Shneur Zalman (Baruchovitch) of Liadi (1745–1812), also known as the Alter Rebbe, Admur HaZoken, Baal HaTanya, or the Rav, was one of the principal students of Rabbi Dov Ber of Mezeritch (the Mezeritcher Maggid) and the founder of the Chabad school of Hassidism. .

[2] Likkutei Torah, on Parshah Chukat, Vayaas Mosheh Nachash Nechoshet…, p. 61b

[3] Solomon ibn Gabirol or Shlomo Ben Yehuda ibn Gabirol was an 11th century Jewish Neoplatonic philosopher and a paetan ( liturgical poet). Published under his Latin name, Avicebron, his works had a significant influence on the development of Jewish Neo-Platonic philosophy, as well as, l’havdil, Christian and Islamic scholarship. As a devout Jew and  mystic, he authored many of the selichot read on fast-days and kinot read on Tisha B’Av. Ibn Gabirol was born c. 1021-1022, in Málaga, Spain, but his date of death is unknown. He died very young—according to some accounts before the age of 30 (c. 1058) and according to others, at the age of 48.

[4] However, he disagreed with Plotinus that there were two types of matter—corporeal and incorporeal (spiritual). For ibn Gabirol, there is only one type of matter, spiritual matter, that underlies both material and non-material substances.

[5] Joseph ibn Tzaddik was a 12th century Spanish rabbi, poet, and philosopher.

[6] Abraham ibn Daud (c. 1110 – c. 1180)—a Spanish-Jewish philosopher, astronomer, and historian, who flourished in Cordoba. His philosophical work, Emunah Ramah, originally was written in Arabic and later translated into Hebrew. Being a true Arisotelian, ibn Daud vigorously opposed ibn Gabirol, who was a Neoplatonist.

[7] Emunah Ramah 1:2.

[8] Moreh Nevuchim (“Guide for the Perplexed”) 2, intr. prop. 22. Maimonides further writes there that only matter is subject to decay and deterioration, whereas form is not, as it is eternal. Identifying tzurah (form) with the soul, and chomer (matter) with the body, Maimonides proves that only the body (matter) is subject to death and decay, whereas the soul (tzurah-form) is eternal.

[9] See, for example, Rabbi Chaim Vital, Eitz Hadas Tov 290; Rabbi Shneur Zalman, Likkutei Torah, Ner Mitzvah: Chanukah I; Rabbi Menachem Mendel of Lubavitch (The Tzemach Tzedek), Derech Mitzvotecha, Tzitzit ch. 1; Rabbi Dovber of Lubavitch (Rebbe Rashab), Hemshech Rosh Hashanah, Sefer HaMaamarim 5710 [1950], p.15ff.

[10] The Maharal writes that Avraham was tzurah whereas Sara was chomer (Gur Aryeh on Geneses 11:29) See also Moses Almosnino, Tefilah LeMosheh, pp. 26a, 35a; Isaak Aroyo, Tanchumot El, p. 74 as quoted in History of Jewish Philosophy, edited by Daniel Frank and Oliver Leaman.

[11] The Bahir. Translation, Introduction, and Commentary by Aryeh Kaplan. Samuel Wiser, Inc. York Beach, Main. 1979. p. 1.

[12] Abraham bar Chiyya (c. 1070 – 1136 or 1145), also known as Abraham Savasorda, Abraham Albargeloni, or Abraham Judaeus, was a Jewish mathematician, astronomer and philosopher, who lived in Barcelona, Spain.


[i] The Theory of Forms — or Ideas, which he equated to forms —originated with Plato. According to Plato, the world of ideal forms exists independently from matter. Plato viewed primordial matter as potential, which is only actualized upon merging with a form.

Plato viewed forms as the non-physical essence of all things. Physical objects are viewed as mere imitations and approximations of forms. Socrates, through whom Plato introduces these notions in his Dialogues, posits that these forms are the only objects of study that can provide true knowledge.

Plato’s forms are the answer to the problem of universals. Universals are qualities or relations found among a plurality of objects. The problem of universals is a metaphysical question: Should the properties an object has in common with other objects, such as color and shape, be considered to exist beyond those objects? And if a property exists separately from objects, what is the nature of that existence? Philosophers generally agree that people can talk and think about universals, but disagree if universals exist in objective reality, outside thought and speech.

Plato’s realism was criticized by Diogenes of Sinope, who said, “I’ve seen Plato’s cups and table, but not his cupness and tableness.”

The Jewish notion of form and matter is very close to the Platonic one.

According to Aristotle, Form and matter are two aspects of every physical thing, which he calls substance. Form determines what the substance is, while matter fills the form. In a dynamically changing substance, only its form changes, while its matter remains unchanged. Because the form makes the object (substance) what it is, form is equated with actuality, whereas matter with potentiality. Aristotle also identifies form with specie and matter with genus.

Plotinus, who was a Neoplatonist, generally accepted Aristotle’s construct of form and matter and extended it to spiritual realms. He reasoned that, since non-material (i.e., spiritual) substances can also be defined in terms of species and genus, they can also be composed of form and spiritual matter. Only God, Plotinus maintains, cannot be thought of as having form and matter.

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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