Gazing at the Shekhinah

In his commentary on this week’s Torah Portion, Yitro, Rabbi Chayim Vital, writing in the name of his teacher, the Ari-zal, states that Abel was punished for gazing at the Shekhinah—the divine presence.[1] But what relevance does this have to the Torah portion retelling the greatest event in Jewish history (and, indeed, the history of human civilization)—the Sinaitic epiphany—the giving of the Torah? This is the Torah portion, where we read the Ten Commandments. What is the relevance of the sin of Abel to the Ten Commandments? More generally, what is Abel’s connection to this Torah portion? That is easy to understand. The Torah portion Yitro starts with the story of Jethro (Yitro), Moses’s father-in-law, coming to Moses in the Sinai desert with his daughter—the wife of Moses—and her two children. Rabbi Chayim [...]

Principle of Least Action III — History

The spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements. Pierre Louis Maupertuis (1744) Among the more or less general laws, the discovery of which characterize the development of physical science during the last century, the principle of Least Action is at present certainly one which, by its form and comprehensiveness, may be said to have approached most closely to the ideal aim of theoretical inquiry. Its significance, properly understood, extends, not only to mechanical processes, but also to thermal and electrodynamic problems. In all the branches of science to which it applies, it gives, not only an explanation of certain characteristics of phenomena at present encountered, but [...]

Entrainment by the Red Heifer

And for the unclean they shall take of the ashes of the burning of the purification from sin, and running water shall be put thereto in a vessel. Numbers 19:17 In my essay “Paradox of the Red Heifer,” I proposed a mechanism by which the ashes of the red heifer remove the impurity of death, where I analogized the procedure with resuscitation using a defibrillator.[1] In this essay, I propose an additional mechanism based on the phenomenon of entrainment, which I will explain below. Entrainment In physics and biology, entrainment refers to the synchronization of two or more rhythmic cycles.[2] This concept can apply to various systems, from physical phenomena to biological rhythms. Here are a few examples: Physics. In mechanical systems, entrainment refers to the process whereby two interacting oscillating systems assume the [...]

The Tree of Knowledge as a Quantum-Mechanical Metaphor

To Mendel Almost three years ago, in December of 2019, I posted an essay, "The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle." The manuscript of that essay contained an addendum with a short primer on the superposition of states in quantum mechanics and quantum-mechanical treatment of the primordial sin. It expressed the ideas of Maimonides about primordial sin in precise mathematical formulas proving the exact parallel between the fruit of the tree of knowledge of good and evil and a quantum eraser. Realizing that only people familiar with the formalism of quantum mechanics would understand that part of the essay and fearing losing my readers, I decided to omit the addendum entirely. However, the addendum is arguably the most interesting part of the essay, because it [...]


In the six hundredth year of Noah’s life, in the second month, on the seventeenth day of the month, on the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.Genesis 7:11 As the Torah tells us, at the dawn of human history, the flood swept the world. Most people, except for Noah and his family, drowned in that flood. Today, we too are drowning in a flood of a different kind—the informational flood. To put the current flood in perspective, consider this: according to one estimate in 2003, between the beginning of human civilization and the spread of computers, humanity generated cumulatively about 12 exabytes (12x1018 bytes) of data. However, in 2002 alone, we generated 5 exabytes of data. According to another estimate, [...]

Fill the Earth

And G‑d created man in His own image, in the image of G‑d created He him; male and female created He them. And G‑d blessed them; and G‑d said unto them: “Be fruitful, and multiply, and replenish the earth, and subdue it . . . .Genesis 1:28 G‑d created man, male and female, and commanded them to be fruitful and multiply, fill the earth, and subdue or conquer it. While the literal meaning of this verse is apparent—fill the earth with your progeny by procreating[1]—it begs a question. Specifically, the phrase “fill the earth” seems superfluous—wasn’t it enough to say “Be fruitful and multiply”? Indeed, the Hebrew word milupim[2] (“to multiply”) is etymologically related to the word mil’u[3] (“to fill”).[4] If humans were to multiply, as commanded by G‑d, they would naturally fill the earth. It seems [...]

Egyptian Exile as a Metaphor for Compactification in String Theory

And they made their lives bitter with hard service, in mortar and in brick…Exodus 1:14 On a literal level, the Egyptian exile (Galut Mitzrayim) is a story of the Jewish people’s enslavement in ancient Egypt, where they were forced to do hard labor making mortar and bricks, and building cities for the Pharaoh. On a deeper level, it is axiomatic in Jewish mysticism that suffering is usually a means to purify and rectify a sinner’s soul in this or past incarnation. It is also axiomatic that any sin damages the sinner’s soul and some supernal spiritual levels that obstruct the flow of the divine benefice into the world, impeding the blessing and, therefore, causing suffering to the sinner. Technically, it works as follows. When a sin committed below causes damage above, the resulting [...]

Noah’s Ark—Three Layers of Reality

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 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 [...]

Tzimtzum III—Renormalization—Sweeping Infinites Under the Rug

Sweeping Infinities Under the Rug—or Renormalization Having dealt with internal contradictions in the previous section (see Physics of Tzimtzum I — The Quantum Leap and Physics of Tzimtzum II — Collapse of the Wave Function), we are left with another problem—infinity. Although G‑d concealed His self-contradictory nature by “sweeping paradoxes under the rug” in the process akin to the collapse of the wave function, the Light of the Infinite (Ohr Ein Sof) filled the whole of existence with infinite Divine emanation. This infinite radiation left no room for any finite creation to emerge. What was G‑d to do? Having aced the exam on quantum field theory with flying colors, G‑d employed the favorite trick of theoretical physicists in sweeping infinities under the rug using what is called “renormalization.”[1] Roughly speaking, renormalization solves the [...]

Physics of Tzimtzum I — The Quantum Leap

Introduction “In the beginning G‑d created the heavens and the earth.” (Genesis 1:1) “In the beginning G‑d created the heavens and the earth,” the Torah says. However, what was before the “beginning”? It is like asking, What was before the Big Bang? In physics, until relatively recently, such questions were discouraged. The prevailing wisdom was that time and space had been created by the Big Bang, and there was no “before” before the Big Bang. Mishnah discourages such thinking, too. The sages point out that the first letter of the Torah, the letter bet, is open on the left and closed on the right:[1] The text of the Torah and the history of the world proceed from that opening on the left. The closed right side of the letter bet visually walls off [...]




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