Symmetry

Home/Symmetry

Jacob and Esau—Thermodynamics of Order and Chaos

And these are the chronicles of Isaac… (Genesis 25:19) So Esau went unto Ishmael, and took unto the wives that he had Mahalath the daughter of Ishmael Abraham’s son, the sister of Nebaioth, to be his wife. (Genesis 28:9)   This Torah portion is called Toledot. In Hebrew, toledot means “generations” or “chronicles.” Indeed, this Torah portion starts with the phrase, “These are the chronicles of Isaac.” This is not the first or the last time this word appears in Tanakh (the Hebrew Scriptures). It appears for the first time in the opening verse of chapter 2 of Genesis: These are the chronicles of the heaven and of the earth when they were created, in the day that the Eternal God made earth and heaven. (Genesis 2:4) The second time it appears in [...]

Steering Isaac’s Blessing

And Rebekah spoke unto Jacob, her son, saying: “Behold, I heard thy father speak unto Esau thy brother, saying: Bring me venison, and make me savoury food, that I may eat, and bless thee before the Eternal before my death. Now, therefore, my son, hearken to my voice according to that which I command thee. Go now to the flock, and fetch me from thence two good kids of the goats; and I will make them savoury food for thy father, such as he loveth; and thou shalt bring it to thy father, that he may eat, so that he may bless thee before his death.” And Jacob said to Rebekah his mother: “Behold, Esau my brother is a hairy man, and I am a smooth man. My father peradventure will feel me, [...]

It Is Not Good For Man To Be Alone

And the Eternal God said: “It is not good that the man should be alone; I will make him a helpmate opposite him.” (Genesis 2:18)   The end of this verse is rather puzzling. Why would the woman designated as a helpmate for Adam be opposite (literally “against”) him? One can perhaps soften things by translating the Hebrew eizer kenegdo as “counterpart.” However, in a literal translation, the question remains. A simple explanation is well known: if a man is worthy, his wife would be his best friend, ally, partner, companion, and helpmate. If the man is not worthy, however, his wife would be his opponent and antagonist. An esoteric interpretation offered by Rabbi Shneur Zalman of Liadi, in his commentary on this verse in “Torah Ohr,”[1] provides a deeper meaning. He writes [...]

Ten Sephirot and Special Relativity

The Special Theory of Relativity, published by Albert Einstein in 1905, was a game changer. It ushered the era of new physics dubbed by some as the “Jewish physics.” And Jewish physics it was. At the core of Special Relativity is the notion of the relativity of motion – all motion is not absolute, as Newton thought, but is relative to something else, to a particular point of view. In physics, we define a point of view as a frame of reference. If you are standing in a moving train, leaving the railroad platform, in your frame of reference (which is always at rest) the train is at rest relative to your frame of reference. The railroad platform, on the other hand, is moving with respect to your frame of reference. For someone [...]

Purim—the Day when We Celebrate Spontaneous Symmetry Breaking

The Zohar compares Yom Kippur to Purim stating that Yom HaKipurim may be interpreted as “a day like Purim” (k-purim in Hebrew means “like purim”).  On Purim we feast; on Yom Kippur we fast—what the two can have in common? Indeed, Purim and Yom Kippur have something very important in common.  Both days share a common root—pur—meaning  a “lot” (or pl. purim—“lots”). On Yom Kippur, two lots were placed in a wooden  box—one say “to God”, and the other “to Azazel.”  (See my post, “Tale of Entangled Goats”). The High Priest relied on a lottery to choose which goat would be used for a sacrifice to God and which to atone for the sins of Jewish People. On Purim, Haman threw two lots to determine the month and the day of a pogrom, [...]

Dreams of Pharaoh—A Lesson in Symmetry

In the Torah portion Miketz, Pharaoh has two dreams. He wakes up agitated and calls on all the wise men of Egypt to interpret his dreams. Nobody is able to come up with an acceptable interpretation, so they fetch Joseph from prison and he successfully interprets the dreams of Pharaoh—that there will be seven years of plenty followed by seven years of famine. Joseph proceeds to instruct Pharaoh on how to prepare for the seven years of famine. In the previous posts, "Interpreting Dreams" and "Joseph—the Master of Time," we already explained how Joseph was able to interpret dreams in terms of units of time and why Pharaoh appointed Joseph as the viceroy of Egypt. This story, however, still has mysteries to unlock. Perhaps it can teach us more lessons. In Talmudic and [...]

Symmetry and Love — Jewish Chromodynamics

Ye are standing this day all of you before the Lord your God: your heads, your tribes, your elders, and your officers, even all the men of Israel, your little ones, your wives, and thy stranger that is in the midst of thy camp, from the hewer of thy wood unto the drawer of thy water; that thou shouldest enter into the covenant of the Lord thy God—and into His oath—which the Lord thy God maketh with thee this day. (Deut. 29:9-11) The above verses at the beginning of the Torah portion Nitzavim that is always read in the week preceding the Jewish New Year, Rosh HaShanah, are usually interpreted in terms of the unity of Jewish people: You are standing this day all of you [read: standing together in perfect unity]. This is not [...]

Entangled Sisters

The story of entangled twins is continuing in the Torah portion Vayeitzei (Genesis 28:10–32:3.)  Structurally, it is very similar to the story in the previous Torah portion, Toldot (see “Entangled Twins”).  In this portion, we again read about two entangled siblings—albeit, this time, sisters—about deception and spontaneous symmetry breaking. Two sisters were Rachel and Leah. Moreover, according to Midrash, Rachel and Leah were also twins (Seder Olam Rabbah).[1] As inseparable twins, they were “entangled,” as it were. They were somewhat opposite—one introvert, the other extrovert; one beautiful, the other, perhaps not so much (she had “weak eyes”): Now Laban had two daughters: the name of the elder was Leah, and the name of the younger was Rachel. And Leah’s eyes were weak; but Rachel was of beautiful form and fair to look upon (Genesis 29:17). Rachel and [...]

The Entangled Twins

Entanglement is often called the most baffling and the most quintessential aspect of quantum mechanics. What is entanglement, in a nutshell? Two particles born out of one reaction (or two particles that interacted through a collision) remain connected, no matter how distant from each other. A change in the status of one particle instantaneously causes a change in the status of the other particle. Einstein called it "spooky action at a distance." Entanglement is often associated with a certain symmetry and corresponding conservation laws. For example, the law of conservation of angular momentum requires that the spin (the quantum-mechanical analog of the angular momentum) of two entangled particles always point in the opposite directions. This means that, if two entangled particles have their spin in a state of superposition of Up (↑) and Down (↓), and we collapse [...]

Archives

Categories

DON’T MISS A BEAT

Be the first to know when we publish a new post.

Go to Top