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Urim and Thummim as a Metaphor for Science

By Alexander Poltorak Introduction In the first installment of this essay, “Collapsing the Wave Function of Urim and Thummim,”[1] we discussed the inherent duality of Urim and Thummim—the duality of human (High Priest) and the oracular device (Urim VeThummim). In this sequel, I want to step back and consider broader parallels between Urim and Thummim and science. The Urim and Thummim, embedded within the High Priest’s breastplate (ḥoshen), constitute the most enigmatic oracular tradition described in the Torah (Exodus 28:30; Numbers 27:21). While the Torah credits their use to Moses and Joshua in determining divine will in moments of crisis (Lev. 8:8; Num. 27:21; 1 Sam. 28:6), it never divulges the precise mechanism by which light (Urim) and perfection (Thummim) conveyed answers. Later Jewish sources—from the tannaitic Sifre Bamidbar (chap. 23) to medieval exegetes like Ibn Ezra—stress two points: first, Urim and [...]

Tzaraath, Black Holes, and Holographic Principle

By Alexander Poltorak Abstract This essay explores the profound connections between the biblical laws of tzaraath (Leviticus 13-14) and modern concepts of entropy and the holographic principle in physics. Tzaraath, often misunderstood as mere leprosy, is interpreted as a physical manifestation of underlying spiritual and social disorder and discord, particularly linked to destructive speech (lashon hara). The essay argues that the elaborate rituals of diagnosis, isolation, and purification for tzaraath function to contain and reduce this spiritual/social entropy, restoring social order and inner harmony. Parallels are drawn to Jacob Bekenstein’s discovery that black hole entropy is proportional to its surface area, and the subsequent idea that the information content of a spatial volume might be encoded on its boundary—the holographic principle. It is suggested that a spiritual analog of Beckenstein-Hawking entropy expressing the [...]

Shemini,Phase Space,Hamiltonian Mechanics: Kabbalah and Physics of Seven and Eight

By Alexander Poltorak Abstract The Torah portion of Shemini records the climactic eighth day of the Tabernacle’s dedication, the moment when divine fire finally descends. Classical commentators see in the contrast between the first seven days and the eighth the difference between the natural and the supra‑natural. This essay revisits that symbolism from the standpoint of contemporary physics. First, it reassesses the traditional link between seven and the “natural order.” Second, it proposes that the six spatial–momentum coordinates of classical phase space, together with time, provide a more precise physical analogue for the seven midot than the usual six directions of space plus a temporal axis. Finally, it explores an unexpected resonance between the Hamiltonian action integral and the Tetragrammaton, suggesting that the principle of stationary action mirrors the scriptural affirmation, “For I Y‑H‑W‑H do [...]

Divine Fine-Tuning and the Evolution of Physical Laws

By Alexander Poltorak Introduction The relationship between the laws of physics and the conditions necessary for life is among the most profound mysteries in both science and theology. Physicists have long wrestled with the so-called “fine-tuning problem,” which highlights that even minute deviations in the fundamental constants could render the universe barren. Some interpret this precision as mere happenstance or the product of countless alternate universes—a multiverse; others envision an evolutionary process acting on cosmic laws themselves. Traditional Jewish sources offer yet another perspective, suggesting that G‑d created and destroyed multiple universes—each with distinct configurations—before settling on the life-supporting cosmos we inhabit. In this essay, we examine the fine-tuning problem alongside theories of evolving physical laws, as well as classical and mystical teachings on the Tabernacle (Mishkan) as a microcosm of creation. By [...]

By |2025-05-11T13:51:40-04:00March 30th, 2025|Bereishit, Bereshit, Cosmology, Creation, Exodus (Shemot), Genesis, Kabbalah, Metaphysics, Parshah, Pekudei, Pentateuch (Chumash), Philosophy, Physics, Shemot, Uncategorized|Comments Off on Divine Fine-Tuning and the Evolution of Physical Laws

Measurement Problem or Measurement Blessing?

By Alexander Poltorak I. Introduction Modern physics has revealed a fascinating and perplexing reality at the quantum level, in which particles do not seem to occupy definite states until they are measured. This phenomenon—known as the “measurement problem”—remains one of the most enduring mysteries in quantum mechanics. Remarkably, a spiritual parallel to this quandary appears in the study of Torah and Kabbalah, specifically within the symbolism surrounding the building of the Tabernacle (Mishkan). In both realms—science and spirituality—there is a profound link between measurement and the actualization of possibilities. This essay aims to explore the measurement problem in quantum mechanics alongside its “counterpart” in Kabbalistic thought, showing how each tradition grapples with the question of how nebulous possibilities become concrete realities. II. The Measurement Problem in Quantum Mechanics 1. The Enigma of Collapse At the heart [...]

By |2025-05-04T18:39:58-04:00March 28th, 2025|Uncategorized|0 Comments

Did G‑d Create Mathematics?

By Alexander Poltorak "G‑d is a mathematician"Carl Friedrich Gauss I. Can We Prove that G-d created Axioms of mathematics? 1. Introduction A reader challenged me with a question, “Could you prove G-d created basic propositions (axioms) of mathematics?” It is a profound question that merits a more detailed answer. There is no universally accepted “proof” in the mathematical sense that G‑d authored the axioms (or “basic propositions”) of mathematics. The question of whether G‑d is the ground—that is, the metaphysical foundation—or source of mathematical truths is a longstanding philosophical and theological debate. Here are a few perspectives on this issue, along with reasons why no formal, universally agreed-upon proof exists. 2. What Would a “Proof” Even Look Like? i. Nature of Mathematical Proof In mathematics, proofs demonstrate that a conclusion follows logically from a set of axioms. [...]

Collapsing the Wave Function of Urim and Thummim

By Alexander Poltorak Dedicated to the refuah shaleimah (a complete and speedy recovery) of David ben Leah And thou shalt put in the breastplate of judgment the Urim and the Thummim; and they shall be upon Aaron’s heart, when he goeth in before G‑d; and Aaron shall bear the judgment of the children of Israel upon his heart before the G‑d continually. (Exodus 28:30) AbstractThe Urim and Thummim, sacred oracular devices embedded within the High Priest’s breastplate (Ḥoshen) in ancient Israel, represent one of the most enigmatic elements of biblical tradition. This essay explores their mystical function through an innovative framework that draws parallels with quantum mechanics. By examining rabbinic, Talmudic, and kabbalistic sources, I propose that the Urim and Thummim operated as a dynamic dyad with the High Priest, forming an interactive [...]

Eternity Between the Cherubs

By Alexander Poltorak And there I will meet with you, and I will speak with you from above the cover, from between the two cherubim which are on the ark of the testimony, of all that I will command you concerning the children of Israel. (Exodus 25:22) Introduction The Torah section Terumah contains instructions given to Moses by G‑d about several important elements of the Mishkan (the Tabernacle), such as the Ark of the Testimony (Aron), the cherubs (cherubim), menorah, and the altar. After concluding the instructions concerning the making of the Cherubim, G‑d tells Moses that it is from between the Cherubim that He will speak to Moses. Midrash Tanchuma explains: The Holy One, blessed be He, said to Moses: “From between these two figures—these cherubim—shall I converse with you; there will [...]

Upsherenish: A Defining Moment in a Boy’s Life

By Alexander Poltorak This essay is dedicated to the Upsherenish of our dear grandson, Tzemach Asher Noam, Sheyiḥiyeh, which took place today in Houston. May he grow to Torah, Chupah, and Ma’asim Tovim (good deeds)! Introduction Upsherenish is the ancient Jewish custom of giving a boy his first haircut on his third birthday, celebrating his transition from being a toddler to childhood and the beginning of active Jewish education. The Yiddish word “upsherenish” literally means a “haircut.”[1] After the third birthday, a boy is taught alef-bet, trained to wear a kipa, a tallit katan (tzitzit), to recite morning blessings and the bedtime prayer of kri’at sh’ma al ha-mita (Hear O’ Israel...). Albeit not codified in the Talmud or the standard halachic works, upsherenish is preserved through a minhag (“custom”) in various communities—predominantly Ḥassidic [...]

The Paradise: A Metaphor for Quantum Mechanics I

By Alexander Poltorak The Tree of Life and the Tree of Knowledge as Metaphors for the Wave Function and Measurement Summary This essay proposes a novel interpretation of the Edenic narrative through the conceptual framework of quantum mechanics, establishing systematic correspondences between biblical symbols and quantum-mechanical constructs. Through careful analysis of biblical texts and their mystical interpretations in Kabbalistic and Chassidic sources, combined with precise physical and mathematical formulations, I demonstrate how the Garden of Eden can be understood as a metaphorical representation of Hilbert space—the mathematical foundation of quantum mechanics. The essay develops four primary correspondences: (1) the Tree of Life as the quantum-mechanical wave function—representing superposition of all possible states; (2) the Tree of Knowledge as measurement—causing the collapse of the wave function to a single definite state; (3) Paradise as [...]

Human, Angel, or Machine: The Challenge of Consciousness

By Alexander Poltorak I.             Introduction The confrontation between Jacob and an unidentified being in Genesis raises fundamental questions about the nature of consciousness, identity, and the boundaries between different orders of being. This encounter gains new relevance as we approach an era where artificial intelligence may become indistinguishable from human intelligence. Building on our previous analysis of angels as metaphors for information processing systems found in “The Binary Universe II: Angels as Microprocessors,” “Binary Universe III: Two Camps of Angels,” “The Ontological Ambiguity of Messengers: From Angels to AI,” and “Wrestling with AI: From Divine Dreams to Digital Reality,” this essay examines a deeper ontological ambiguity: the challenge of distinguishing between human and non-human intelligences. II.          The Biblical Paradigm The Torah presents two distinct instances of ontological ambiguity regarding angels. The first appears [...]

Wrestling with AI: From Divine Dreams to Digital Reality

By Alexander Poltorak This essay is a sequel to the earlier installments, “The Binary Universe II: Angels as Microprocessors,” “Binary Universe III: Two Camps of Angels,” and “The Ontological Ambiguity of Messengers: From Angels to AI.” I. Introduction The Book of Genesis presents a remarkable progression in Jacob’s encounters with angels, offering profound insights into humanity’s evolving relationship with non-human intelligence. These encounters trace a path from passive observation to active engagement, ultimately culminating in a physical confrontation. This progression provides a unique framework for understanding our own evolving relationship with artificial intelligence. II. The Four Encounters Jacob’s first angelic encounter occurs in a dream: And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven; and behold the angels of God ascending and descending on [...]

By |2025-05-04T18:34:23-04:00December 11th, 2024|Uncategorized|2 Comments

The Ontological Ambiguity of Messengers: From Angels to AI

This post continues the discussion we began in “Bereshit: The Binary Universe I” and continued in “The Binary Universe II: Angels as Microprocessors” and “Binary Universe III: Two Camps of Angels.” Introduction The beginning of the Torah portion of Vayishlach presents us with an intriguing linguistic and philosophical puzzle when Jacob sends מַלְאָכִים (malakhim) to his brother Esau. The deliberate ambiguity in the term מַלְאָךְ (malakh)—which can denote either human or divine messengers—provides a unique lens through which to examine questions of consciousness, agency, and identity that have become increasingly relevant in our age of artificial intelligence and advanced robotics. The Biblical Context In the beginning of the Torah portion of Vayishlach, Jacob sends messengers (angels, according to Rashi) to his brother Esau: Jacob sent messengers before him to Esau his brother, to [...]

Binary Universe III: Two Camps of Angels

This post continues the discussion we began in "Bereshit: The Binary Universe I" and continued in "The Binary Universe II: Angels as Microprocessors." At the end of Parshat Vayetze, Jacob meets two camps of Angels: And Jacob went on his way, and angels of G‑d encountered him. When Jacob saw them, he said, “This is the camp of G‑d!” So, he named that place “Mahanaim.” (Genesis 32:2–3) The text indicates that Jacob meets two camps of angels—one set of angels that accompanied him outside the Holy Land and another set that takes over as he re-enters the Holy Land (See Rashi on these verses). The word “Mahanaim” (מַחֲנָיִם) literally means “two camps,” reflecting Jacob’s perception of two distinct angelic groups. In light of our metaphor—angels as transistors—this transition at the border of the [...]

The Binary Universe II: Angels as Microprocessors

Introduction This essay is a sequel to “Bereshit: The Binary Universe I.” The first instalment explored the ideal of a binary universe hinted at by first letter of the Torah—the letter Bet (ב). We explored how the primordial duality of moti velo moti (“to touch and not to touch”), that is, the duality of emanation and withholding the light through the Tzimtzum (primordial contraction), manifests across multiple dimensions of existence. We examined the Creator-creation relationship, the nature of time, and paradoxes inherent in divine attributes, showing how these apparent dualities emerge from absolute divine unity. In this installment, we will focus on one aspect of the duality: software vs hardware. The Hard Problem of the Binary Universe Proposing that the universe is a binary code presents a fundamental problem: code represents software that [...]

By |2024-12-06T00:38:14-05:00December 6th, 2024|Uncategorized|1 Comment

Four Elements: Four Developmental Stages in the Big Bang Cosmology

Introduction Building upon our interpretation of the four classical elements as developmental stages in the formation of physical reality, we find a remarkable parallel in modern cosmology. The stages of the Big Bang and subsequent inflationary model of the universe can be divided into four distinct periods that correspond to the four letters of the Tetragrammaton, the four classical elements, and the four worlds of Seder Hishtalshelut (“Chain-like Order” [of Created Worlds]). This alignment illustrates the universality of these developmental stages across both spiritual and physical realms. The Four Cosmological Epochs Planck Epoch — Yud (י) — Fire (Aish) This period corresponds to the letter Yud in the Tetragrammaton—the smallest letter in the Hebrew alphabet, essentially a point, symbolizing the initial singularity. It also corresponds to the element of Aish (Fire), representing intense [...]

By |2024-11-28T23:14:55-05:00November 28th, 2024|Uncategorized|1 Comment

Four Classical Elements: Development and Reinterpretation

The parallels we have uncovered between the four elements, the letters of the Tetragrammaton, and the worlds of Seder Hishtalshelut suggest that the ancient sages possessed profound insights into the nature of reality that continue to resonate with modern scientific discoveries. This convergence of ancient wisdom and contemporary understanding offers a path toward a more integrated worldview, where scientific and spiritual perspectives complement rather than contradict each other.

The Imperative of Purpose: Bridging Science, Philosophy, and Divine Wisdom

And G-d said to Abram, “Go forth from your native land and from your father’s house to the land that I will show you.” (Genesis 12:1) I.              Introduction Physics stands as the cornerstone of modern science, offering fundamental laws that govern matter and energy throughout the cosmos. Its equations describe the dance of subatomic particles and the orchestration of galactic systems with remarkable precision. However, a profound dichotomy exists in our universe: the distinction between inanimate and living matter. While physics masterfully explains the behavior of lifeless matter, it falls conspicuously silent when confronted with the defining characteristic of life itself—purposefulness. The reductionist assertion that biology can be fully explained through chemistry, and chemistry through physics, while technically true, obscures a fundamental gulf in our understanding. This gap lies not in the mechanical [...]

Sarah in a State of Superposition

And it came to pass, when he was come near to enter into Egypt, that he said unto Sarai his wife: “Behold now, I know that thou art a fair woman to look upon. And it will come to pass, when the Egyptians shall see thee, that they will say: This is his wife; and they will kill me, but thee they will keep alive. Say, I pray thee, thou art my sister; that it may be well with me for thy sake, and that my soul may live because of thee.” (Genesis 12:11-13) This passage presents a perplexing scenario. Abraham (then Abram) asks his wife Sarah (then Sarai) to present herself as his sister upon entering Egypt. Classical commentators and the Zohar grapple with Abraham's motives, questioning why he would place Sarah in such a [...]

Bereshit: The Binary Universe I

Abstract This essay explores the profound significance of the letter Bet (ב), the first letter of the Torah, and its numerical value of two as a fundamental hint at the binary nature of our universe. Through an analysis of Jewish mystical texts, philosophical works, and modern physics, we demonstrate how this duality manifests across multiple dimensions of existence. The paper examines the Creator-creation relationship, the nature of time, and paradoxes inherent in divine attributes, showing how these apparent dualities emerge from absolute divine unity. This synthesis of the Torah wisdom and contemporary science suggests that the binary structure implied by the letter Bet may be more than metaphorical, potentially representing a fundamental characteristic of reality itself. I.              Introduction The Torah begins with the letter Bet (ב), the second letter of the Hebrew alphabet, [...]

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