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Joseph and His Brothers

I grew up In Russia and was raised on the metric system based on the decimal arithmetic. When we immigrated to the U.S., I had to learn a new to me (but, actually, very old) Imperial system of measurements having 12 inches in a foot. I still struggle with it (decimal system, apparently, was hardwired in my brain). There are many number systems or positional notation systems. Ancient Babylonians used base-60, Hindu-Arabic system uses familiar decimal base-10 system, Mayans used base-20 system. There are base-2 binary, base-12 duodecimal, and base-16 hexadecimal systems, to name a few. Aside from the binary system used by computers, we humans mostly use decimal and, sometimes, duodecimal systems. The all-familiar decimal system is used in the metric system of measurements. In base-10 positional notation there are 10 decimal [...]

Entangled Sisters

Vayeitzei 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 of 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 twins (Seder Olam Rabbah). As twins, who emerge from the same womb, they were entangled.  They were somewhat opposite—one is introvert, the other is extrovert; one is beautiful, the other has weak eyes. Rachel and Leah are earthly embodiments of spiritual partzufim (configurations of sephirot—Divine emanations).  Kabbalah teaches that in spiritual realms, there is Partzuf Rachel and Partzuf Leah, which are two aspects of the Nukva—the feminine aspect of Godliness.  Partzuf Rachel represents [...]

By | November 8th, 2013|Entanglement, Parshah, Symmetry, Vayetze|0 Comments

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 [...]