Alexander Poltorak

Isaac’s Blessing

Stars, Sand… and Silence Abraham’s blessings sparkle with cosmic imagery—stars above, dust below. But when God blesses Isaac, the patriarch of gevurah, something extraordinary happens:

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Isaac Digging Well

Digging Wells

The third aliyah of Parshat Toldot presents a profound metaphor through Isaac’s well-digging enterprise. Isaac re-opens his father’s wells, stopped up by the Philistines; then

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Isaac sawing the field

The Hundredfold Paradox

Dwell in this land. (Genesis 26:3). In famine, with every natural instinct pointing south toward Egypt, Isaac (Yitzḥak) is told to stay. The Midrash notes

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Hagar and Ishmael in the desert

The Well That Was Always There

(Parshat Vayeira, Genesis 21:14-21) Hagar and Ishmael are dying of thirst in the desert. In her despair, Hagar places her son under a bush and

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Silhouettes with glowing Hebrew letters at sunset.

The Fertility of Letters

When G‑d promises great wealth to Abram, after Abram refuses the spoils of war offered by the King of Sodom, Abram retorts: What can You

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Abraham refuses all spoils from the king of Sodom

The Thread That Transforms

Neither from a thread to a sandal-strap, nor will I take from whatever is yours… (Genesis 14:23) After defeating five kings, Abraham (then called Abram)

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Abraham Rescues Lot

Loyalty Despite Separation

When Abram heard that his kinsman had been taken captive, he mustered his trained men… and went in pursuit. (Genesis 14:14) Abraham just separated from

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A man feeding animals in a dimly lit barn.

Dominion After Service

Two diets framed early humanity. In Eden, humans ate only plants; meat was forbidden. The Talmud teaches: Rav Yehuda says that Rav says: Meat was

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Uniformed crowd before a towering structure.

The Tower of Babel

Quanta of Thought | Parashat Noach The story of the Tower of Babel seems, at first glance, like a triumph of human unity. All spoke

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Abstract painting with vibrant colorful brushstrokes

The Rainbow That Isn’t There

Everyone marvels at the beauty of a rainbow—its perfect arc, its radiant colors. Yet, in truth, the rainbow doesn’t exist out there. The spectrum of

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The Ark Within

When the world was overwhelmed by chaos, Noaḥ found grace in the eyes of G-d (Genesis 6:8). The Zohar explains that “grace” (ḥein) is a

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Robot and human hands reaching towards each other.

The Second Adam: From Dust to Silicon

Summary This essay proposes an allegorical (remez) interpretation of Genesis 2, reading the second creation narrative as a prophetic template for humanity’s creation of artificial,

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For Myself and For That Guy

This Simchat Torah was the most joyous I have felt in years. News of the hostages’ release on the eve of the holiday lifted mountains

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The Day of Superposition

Today is Hoshana Rabbah, the last day of Chol HaMoed Sukkot. Six years ago, I wrote “Chol HaMoed—Days in Superposition,” exploring how these intermediate days

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The Prophecy of Ha’azinu

TL;DR: Ha’azinu’s warning about a “no-people” (b’lo-am) finds chilling relevance in the modern “Palestinian” identity—a political construct created in 1964 by the KGB and Arab

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Gott’s Nomen

In many Ashkenazi communities, the day after Yom Kippur is nicknamed Gott’s Nomen, Yiddish for “G-d’s Name.” Chassidic sources associate the four days between Yom

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Ten Days of Penitence

The ten days between Rosh HaShanah and Yom Kippur are called Aseret Yemei Teshuvah (Ten Days of Penitence). As the prophet says: Seek G-d while

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Shanah Tovah!

Dear Readers and Friends, As we enter the new year, I extend to you heartfelt wishes for a שנה טובה וגמר חתימה טובה—may you and

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Curved lines and stars on a twilight sky.

Five-Hundred-Year-Journey

Alexander Poltorak Abstract This essay addresses the anigmatic statement of the Jewish Sages, stating that G-d created this world with the letter Heh and the

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Ten Systems—Ten Sefirot

… mi‑b’sari echezeh Elokah—From my flesh I behold G‑d (Job 19:26) Introduction – “In His Image” The Torah’s initial description of humanity is both profound and enigmatic:

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Korach’s Revolt: a Tale of Symmetry

Korach Revolt Korach, the proto‑egalitarian, cried: All the community are holy… so why do you exalt yourselves? (Numbers 16:3). Chassidut explains that holiness is indeed

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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

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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

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The Exclusion Principle

Like most Jewish families worldwide, last Shabbat, the conversation revolved around the situation in the Middle East and the war in Gaza. The question was,

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Principle of Least Action I

The least action principle is an expression of teleological reasoning where the initial states of the system are determined by the endpoints—the beginning and the

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Quantum Torah WhatsApp Discussion Group

‎Open this link to join my WhatsApp Group: https://chat.whatsapp.com/HzeLLjGb05THGWBuQzgj87. This Group is dedicated to the discussion of posts on this blog, issues related to the

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The Standard Model II

In the first installment on the Standard Model, we uncovered a curious parallel between the arrangement of the elementary particles in the Standard Model (a.k.a.

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The Standard Model

Introduction What could the Standard Model of particle physics possibly have in common with biblical accounts of the Israelites’ travels in the Sinai Desert, Kabbalistic

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Light Above and Light Below

Einstein’s Special Theory of Relativity (STR) is broadly misunderstood by the public. In most popular science books, relativity theory is hailed for introducing relativity to

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The Flood—a Quantum Metaphor

Noah’s flood was a cataclysmic event with no parallels in recorded history. All of humanity (along with flora and fauna)—except for Noah and his family

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The Captive Beauty

In the proposed allegorical interpretation, the soldier in the war is a metaphor for the Jewish people, who are all “soldiers” in G‑d’s army Tzivot

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The Many Secrets of Mezuzah

This week we study the Torah portion of Eikev, which we will be reading this Shabbat in synagogues. This Torah portion contains the second section

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Three Donkeys

And Abraham rose early in the morning, and saddled his ass. Geneses 22:3 And Moses took his wife and his sons, and set them upon

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Zettaflood

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

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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

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The Paradox of Steven Weinberg

The world has lost one of the greatest theoretical physicists of our time—Steven Weinberg (1933–2021). I never met him in person. But I studied his

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Ball_Bearing

A Wheel Within a Wheel

Now as I beheld the Chayot [living creatures], behold one Ophan [wheel] at the bottom hard by the living creatures, at the four faces thereof. The

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Lag BaOmer Tragedy

A day of joyful festivities turned into a day of tears and mourning. When tragedy strikes, it is not the time for analysis or finger-pointing.

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Collapse and Revelation

The collapse of the wave function is the process of revealing hidden possibilities. Reducing uncertainty reveals information. Until the wave function collapse, the system is

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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

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Akeida in Parallel Universes

Michael Frayn’s 1998 play, Copenhagen, concerns a meeting between two great physicists, Niels Bohr and Werner Heisenberg, in 1941 in Copenhagen. In this play, the

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Let There Be Light

And G‑d said: “Let there be light.” And there was light. And G‑d saw the light, that it was good; and G‑d separated between the

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Moritz_Daniel_Oppenheim_-_Shavuot_(Pentecost)

Shavuot (in Russian)

Шавуот Праздник Дарования Торы Aлександр Полторак    Закончился праздник Песах.  Все евреи поспешно убрали пасхальную посуду в особые шкафы или на чердаки до следующего Песаха.

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The Soul is in the Blood

For the life of the flesh is in the blood.” (Leviticus 17:11) The word translated here as “life” in the Hebrew original is nefesh, i.e.,

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Counting Weeks and Days

There is a Biblical Commandment to count the days between the Passover and Shavuot, the “Feast of Weeks” (a.k.a. Pentecost). We start counting on the

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Cosmology and the Tetragrammaton

As we discussed in the previous post “Singularity and Paradise,” Paradise offers a beautiful metaphor for modern cosmology wherein Eden is the initial singularity preceding

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Singularity and Paradise

These are the chronicles of the heaven and of the earth when they were created, in the day that the Eternal G‑d made earth and

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The Tree of Life and Wave Mechanics

As we discussed in the earlier post, The Tree of Knowledge as a Metaphor for Superposition of States and Heisenberg’s Uncertainty Principle, the Heisenberg uncertainty

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Stress-testing the judgment

And Abraham drew near, and said: ‘Wilt Thou indeed sweep away the righteous with the wicked? Perhaps there are fifty righteous within the city; wilt

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Cosmic Symphony

Strings vibrate, Souls tremble, Angels are running and returning, G‑d is touching and not touching – The rhythms of the universe… Nothing stays still… all

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Noah — the First Inventor

At the end of the first chapter of the Torah, Genesis (Bereshit), G‑d regrets, as it were, creating humanity that became depraved: And the Lord

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Sukkot — Bringing Time into Space

Jews have a very strange custom to take four species (Heb. arba’a minim)—a fruit of a citron tree (etrog), a branch of a date palm (lulav), boughs from the myrtle tree (chadassim),

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The Land We Married

And the Lord spoke unto Moses, saying: ‘Command the children of Israel, and say unto them: When ye come into the land of Canaan, this

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Daughters of Zelophehad

Then drew near the daughters of Zelophehad …. of the families of Manasseh, the son of Joseph; and these are the names of his daughters:

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Collapse of the Wave Function

Meditations on the Maaseh Merkavah – III This is the third installment in the series of posts related to the Ezekiel’s prophesy, Maaseh Merkava, “The

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Relational Space

Meditations on the Maaseh Merkavah – II This post is a sequel to my previous post, “Space – Between Future and Past.” For background information,

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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)

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Eugene_Wigner

Wigner’s Friend Paradox

Amicus est Socrates, magister meus, sed magis est amica veritas. “Socrates is my friend but a greater friend is truth” – Plato c. 428-348 BCE.

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The Puzzle of Pi

March 14 is celebrated by nerds around the world as the Pi Day. When written in digits, 3/14 represents first three digits of the number

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Quantum Torah Film Premiere

Welcome to the premiere of our first film, Quantum Torah. You can watch the film here:   Don’t forget to subscribe to my channel here:

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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

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Fractal Tu B’Shevat

When thou shalt besiege a city a long time, in making war against it to take it, thou shalt not destroy the trees thereof by

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About Midnight

And Moses said: “Thus saith the Lord: About midnight will I go out into the midst of Egypt; and all the first-born in the land of

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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

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Brit Milah in Six Dimensions

Sefer Yetzira speaks of three dimensions: Olam, Shanah, and Nefesh (Sefer Yetzirah, 6:4.)  Olam means “world” and signifies space. Shanah means “year” and signifies the dimension of

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Shoo Away the Mother Bird

If a bird’s nest chances before thee in the way, in any tree or on the ground, with fledglings or eggs, and the mother sitting

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Sanctuary in Five Dimensions

In my last post, Tisha B’Av on Shabbat – A Relativistic Perspective, I wrote that G‑d created His sanctuary in four dimensions — Bet HaMikdash

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Passover Seder—The Arrow of Time

The Passover Seder is called seder, i.e., “order” not without a reason. It is a highly structured and orchestrated ceremony that follows the ancient script—Passover

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Breaking Symmetry

And Moses turned, and went down from the mount, with the two tablets of the testimony in his hand; tablets that were written on both

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Grand Unification

In physics, we seek Grand Unification, also known as the Theory of Everything. The Standard Model describes three out of the four fundamental forces: the

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Joseph—the Master of Time

The story of Joseph’s incarceration ends with his successful interpretation of the dreams of the Pharaoh’s chief butler and the chief baker.  He ingeniously interpreted ordinary

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Holiday of G‑d’s Name

According to the tradition passed down to us from the Baal Shem Tov, the day after Yom Kippur is called the Holiday of G‑d’s Name.

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The Pilot Wave

And on the day that the tabernacle was reared up, the cloud covered the tabernacle, even the tent of the testimony; and at even there

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Purim: Celebrating Randomness

Ultimately, I suppose Einstein was right—G‑d does not play dice. So when Haman reached that spiritual level through casting the lots, he discovered the true

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Entangled Cherubs

And thou shalt make two cherubim of gold; of beaten work shalt thou make them, at the two ends of the ark-cover. And make one

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Five Worlds

Today, Yud Shvat, is the yartzeit (anniversary of passing) of the sixth Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn, a.k.a. the Rebbe Rayatz, or the Frierdiker

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Joseph’s Sons

And now thy two sons, who were born unto thee in the land of Egypt before I came unto thee into Egypt, are mine; Ephraim

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Big Bang

בְּרֵאשִׁית בָּרָא Genesis 1:1 The Torah starts with two words—Bereshit bara—“In the beginning, G‑d created…” (or, as Rashi translates it, “At the beginning of creation

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Lubavitcher_Rebbe_with_Arba_Minim

Unified Field Theory… and Practice

Albert Einstein had a lifelong quest—to develop a unified field theory—the theory that would describe as a single field gravity and electromagnetism (just as Maxwell

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The Fifth Force – Epilog

This post is a continuation and the conclusion of the previous post, THE FIFTH FORCE. Aside from the connection with the last week’s Torah portion,

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The Fifth Force

Now, therefore, write ye this song for you, and teach thou it the children of Israel.” (Deut. 31:19) The four known fundamental forces are: gravitational

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Standing and Moving

According to the Saadia Gaon, these two Torah portions – Nitzavim and Vayelech – are really one portion, which sometimes is split into two.  In the

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Fractal Patterns in the Torah

In the Torah portion Emor (Leviticus 21:1–24:23), we are instructed to abstain from work every seventh day on Shabbat. Next week’s Torah portion, Behar, continues

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Shabbat in Numbers

Last week Torah portion, Emor, speaks about the prohibition of working on Shabbat. In fact, the Talmud enumerates precisely 39 categories of labor forbidden on

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Relativity of Manna

This is the thing which the Lord hath commanded: Gather ye of it every man according to his eating; an omer a head, according to

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Fig of Rabbi Akiva

What came first, the Schrödinger cat or the fig of Rabbi Akiva? You be the judge. Today we present a guest post by Rabbi Dr. David

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String Theory

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,

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On Change

We all know that we leave in a three-dimensional world. Up-down, right-left, forward-backward – these are well-familiar to us directions in three dimensions of space

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The V-Day

We frequently discuss on this blog the state of superposition – the mixed state unique to quantum mechanics, in which the system can be in

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The End of Days II

This post is a continuation of the earlier post, The End of Days I. In this Torah Portion, Shemot, we read about the encounter between

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The End of Days I

In this Torah portion, Vayechi, Jacob, gathers his children to reveal to them “Ketz HaYamim”–“the End of Days.” Rashi explains that Jacob’s intention was to

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Joseph and His Brothers

I grew up in Russia and was raised on the metric system based on decimal arithmetic. When we immigrated to the U.S., I had to

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Mezuzah in Three Dimensions

The mezuzah is one of the few miẓvot ([divine] “commandments”) for which the Torah states its reward. In this case, the reward is a long

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The Final Frontier

In this Torah portion, Devarim (Deuteronomy 1-3), Moses recalls the travels through the Sinai desert when G‑d told him: Be not at enmity with Moab,

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We will go in front of our brothers…

Rabbi Schneur Zalman of Lyadi (the first Rebbe of Chabad and the author of Tanya), known as the Alter Rebbe once said, we must leiben min hatzait – live with the time,

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Prophesy by Entanglement

…And they prophesied in the camp. (Num. 11:27) In the Torah portion Behaalotecha, there is an interesting narrative: And the Lord said unto Moses: ‘Gather

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Menorah

Speak unto Aaron, and say unto him: “When thou lightest the lamps, the seven lamps shall give light in front of the menorah.” (Num. 8:1)

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613 Degrees of Freedom

Passover has ended. All Jews hastily return their Passover dishes to storage in special cabinets or the attic until the next Passover. After an eight-day

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Ye Shall be Disentangled

Ye shall be holy, for I, the Lord, your G‑d, am holy. Leviticus 19:2 This Torah portion begins with an astonishing statement: Speak unto all

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From Purim to Passover

The Shulchan Aruch – the Code of Jewish Law – states that 30 days before Pesach (Passover) one needs to start learning the laws of

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Thou Shall Not Be a Flipper

Reading the Haftorah this Shabbat brought to mind scenes from the 2004 Republican National Convention in Madison Square Garden in New York City where attendees where

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Global or Local?

And let them make me a Sanctuary that I may dwell among them (Ex. 25:8) In modern physics, there are two paradigms usually expressed as locality

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Splitting of the Sea

Do you like riddles?  Here is a riddle – what do these two figures represent in the context of Exodus?   No Idea?  How about

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Riddle — the answer

And the answer is… (drum roll, please)   Yes, the first figure represents two doorposts and the lintel marked with blood of Passover sacrifice and circumcisions as

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Riddle — a hint

There were some good ideas expressed in the comments.  Close, but no cigars.  Here are some hints for you folks: 1. These two pictures express

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Riddle

I’ve never done this before on this blog, so this a first — a riddle: What do these two figures represent? Please post your answers in the Comment

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Mezuzah and Time

Bo: Exodus 10:1 – 14:16 The Erev Shabbat parshat Bo (the Eve of Sabbath of the week when we read the Torah section Bo) 2014

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Carpe Diem

As we have discussed in the post, It’s the time, stupid, Pharaoh never got the message that it’s all about mastery of time.  To make

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It’s the Time, Stupid!

There is a continuous thread about the mastery of time that weaves through the last chapters of the book of Genesis (Bereshit) and continues through

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Sensing Spirituality

It is unsurprising, then, that spiritual phenomena have never been experimentally detected in a laboratory setting. Spirituality, by definition, is non-physical. Consequently, no physical laboratory

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Joseph_tells_his_dreams_to_Jacob_Rembrandt

Interpreting Dreams

In the Torah portion Vayeishev (Gen. 37:1–40:23), we read about Joseph interpreting dreams of the Pharaoh’s chief butler and the chief baker: And the chief butler told

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Body Chemistry

Reading the Torah, sometimes, can give a false impression of reading a story, albeit the greatest story ever written. This Divine drama involves colorful characters,

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Entangled_Sisters

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

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The Entangled Twins

Entanglement is often called the most baffling and quintessential phenomenon in quantum mechanics. What is entanglement, in a nutshell? Two particles born from one reaction

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Cave_of_Machpelah

Maarat HaMachpelah – Double Cave

Give me the Machpelah (double) Cave Genesis 23:9 The first legal acquisition of land in Israel takes place in this Torah portion, Chayei Sarah, when Abraham

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Saved by Randomness

Some people may be fooled by randomness but, when we realize that randomness opens the door to the Divine, we are saved by randomness. It

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Cosmological Rosh HaShanah

This Rosh HaShanah I had the strangest dream. I dreamed that I was giving a lecture in cosmology at a university when I suddenly realized

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Witnesses

Massei — Bamidbar-Numbers 35 Whoever kills a person, based on the testimony of witnesses, he shall slay the murderer. A single witness may not testify

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Paradox of the Red Heifer

Speak to the children of Israel and have them take for you a perfectly red unblemished cow, upon which no yoke was laid… The cow

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Tumah and Taharah

The Hebrew words taharah and tumah, which are the subjects of the Torah portion of Chukat (Numbers 19:1–22:1), are usually translated as ritual purity and

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Koraḥ Disentangled

Koraḥ the son of Yitzhar, the son of Kehos, the son of Levi took [himself to one side] along with Dasan and Aviram, the sons

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Holy Smoke

And the entire Mount Sinai smoked because the Lord had descended upon it in fire, and its smoke ascended like the smoke of the kiln…

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Schrödinger Pots

Vaikra-Leviticus 14:35-36 (Metzora) 35.  and the one to whom the house belongs comes and tells the kohen, saying, “Something like a plague has appeared to

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Jacob's_Ladder

Jacob’s Ladder

And he dreamed, and behold! a ladder set up on the ground and its top reached to heaven; and behold, angels of G‑d were ascending

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Two Beginnings

B’reshit bara Elokim et hashamaim v’et haaretz… In the beginning, G‑d created heaven and earth… Alternative translation: With two beginnings G‑d created heaven and earth…

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Tale of Entangled Goats

And he shall take the two he goats, and place them before the Lord at the entrance to the Tent of Meeting. And Aaron shall

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Leprous Cats and Angry Birds

In the Torah portion Tazriah (Leviticus 13), the Schrödinger cat[1] gets leprosy. Well, it’s not really leprosy, it’s a mysterious supernatural disease called tzara’as, nowadays translated

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