Pentateuch (Chumash)

/Pentateuch (Chumash)

Torah – Five Books of Moses

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 [...]

The Entangled Tenth

And all the tithe of the herd or the flock, whatsoever passeth under the rod, the tenth shall be holy unto the Lord.” (Leviticus 27:32) This Shabbat, I was called up to the Torah for the last aliyah (lit. “ascent”, meaning the reading from the Scroll) of the book of Leviticus. This portion talks about tithing animals, giving the precise procedure for doing so – every animal is released from a pen one by one while being counted – one, two, three, … , ten. The tenth animal is touch by the rode and consecrated as the ma’aser – tithe. The Torah states that every tenth animal is holy unto God. What is the state of the animals before counting? They have two possible states: (1) chulin, i.e., “not sacred” and (2) ma’aser, [...]

Unified Field Theory and the Dew of Resurrection

And ye shall take you on the first day the fruit of goodly trees, branches of palm-trees, and boughs of thick trees, and willows of the brook (Levit. 23:40) After completing his masterpiece, the General Theory of Relativity in 1916, Albert Einstein spent the rest of his life working fruitlessly on unifying gravity with electromagnetism. His quest was to develop a unified field theory that would unify his General Relativity, a theory of gravitational, with Maxwell electrodynamics. To his great dismay, Einstein never succeeded in developing a unified field theory. It was actually even worse. While working tirelessly on unifying two known classical fields – gravitational field and electromagnetic field – Einstein missed the incredible progress in quantum physics, of which he was one of the founders and for which he received his [...]

Adultery and Monogamy of Entanglement

And whosoever lieth carnally with a woman, that is a bondmaid, designated for a man, and not at all redeemed, nor was freedom given her; there shall be inquisition; they shall not be put to death, because she was not free. (Lev. 19:20) In Quantum physics there is a principle of monogamy of entanglement, which roughly means that if two particles (or objects) are entangled, neither can be entangled with a third particle (or object). A human parallel to this principle is obvious – if two spouses are married, neither can have any intimate relations with a third person. In other words, a marriage must be monogamous. It is because of this parallel that the physical relationship between entangled particles in quantum mechanics was named the monogamy principle, or monogamy of entanglement. In [...]

Ye shall be disentangled… but not disengaged

In my post, “Ye Shall be Disentangled,” I suggested that the verse: “Ye shall be holy, for I, the Lord, your God, am holy” (Levit. 19:2) may be interpreted as: “Ye shall be disentangled, for I, the Lord, your God, am disentangled.” I supported this proposition with the quantum monogamy principle (a.k.a. monogamy of entanglement) according to which, if two objects are entangled, neither of them can also be entangled with a third object. Consequently, if we wish to be entangled with God, we cannot also be entangled with the material world, as it would violate the monogamy principle. Thus, we must disentangle from the world, i.e., be holly. One may legitimately object to this interpretation because, in Judaism, we do not have monasteries; we do not have monks, we don't withdraw from [...]

Vectors, Spins, and Gender

Vectors, Spins, and Gender Speak to the children of Israel, and have them take for Me an offering; from every person whose heart inspires him to generosity, you shall take My offering. (Ex. 25:2) Every physics professor teaching physics 101 to freshmen spends the first lecture teaching vector algebra. Why vectors are so important? Because most quantities in mechanics (a branch of physics dealing with motion and forces) are vectors. A vector is a mathematical object that has a magnitude and a direction. For example, velocity is a vector – it shows not only how fast the object is moving, but also in what direction it is moving (it is different from “speed” which is an average velocity and is just a number). Similarly, acceleration is a vector, force is a vector, angular [...]

Jacob Meets Esau and his 400 men

And the messengers returned to Jacob, saying: “We came to thy brother Esau, and moreover he cometh to meet thee, and four hundred men with him.” (Gen. 32:7) Why does the Torah take pains to tells us the exact number of men accompanying Esau? Servants of Esau are of no particular significance. It is apparent that, by specifying the number of men in Esau's entourage, the Torah is trying to tell us something about Esau. It seems to me that Jacob understood the significance of the number 400. This number is a sum of the powers of 7 from 0 to 3: 70+71+72+73=400. This four powers of 7 hint at the lunar month that has, approximately, 28 days (4×7). The significance of this will become apparent later. 400 is a repdigit in base [...]

The Meaning of Life as Taught by Bayesian Angels

And he [Jacob] dreamed, and behold! a ladder set up on the ground and its top reached to heaven; and behold, angels of God were ascending and descending upon it. (Gen. 28:12) Rabbi Shneur Zalman of Liadi (a.k.a Baal HaTanya, or the Alter Rebbe) once remarked in Yiddish, “lieben mit di tzait” – live with the time, meaning one should live with Torah portion of the week.  Last week I was taught a lesson on how the current Torah portion affects my thinking, whether I know it or not. Last week I shared with my wife, who is a biophysicist, that while thinking about system biology, I realized that all organisms – from a single cell to multicellular organisms – are Bayesian systems. I knew that the brain is a Bayesian engine, but [...]

Second Derivative – Secrets of the Double Cave

And he [Avraham] spoke with them, saying, “…Listen to me and entreat for me to Ephron the son of Zohar. That he may give me the Machpelah (Double) Cave, which belongs to him, which is at the end of his field…" (Gen. 23:8-9) double: A house with an upper story over it. Another interpretation: because it was doubled with couples (Er. 53a) (Rashi on Gen. 23:9) In the Torah portion Chayei Sarah, Avraham purchases a Double Cave, Machpelah, as the ancestral burial plot. Almost all Biblical commentators interpret Machpelah-double to mean a cave with two chambers. Rashi takes an entirely different approach and states that the cave was known for a two-story house built on top of it. So, the word “Machpelah” (lit. “double”) refers not to the cave itself, but to the house [...]

Biblical Relativity

And the life of Sarah was one hundred years and twenty years and seven years... (Gen. 23:1) Why did Esther merit to rule over 127 countries? Said God: “Let Esther, the descendant of Sarah who lived 127 years, come and rule over 127 lands. (Esther Rabbah 1:8) The Midrash Ester Rabbah compares 127 years of Sarah’s life with 127 provinces that Esther ruled. How can one compare time with space? When the Midrash says that Adam gifted 70 years of his life to his descendant, King David, it’s understandable – a year for a year. But a year for a province? What’s the connection? Hermann Minkowski When, in 1905, Albert Einstein published his Special Theory of Relativity, it was nothing short of a scientific revolution. For the first time, Einstein showed [...]

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