Pentateuch (Chumash)

Torah – Five Books of Moses

A Girl in a State of Superposition

A Girl in a State of Superposition

In my essay "Secrets of the Talking Ass," I discussed the phenomenon of Bein HaShmashot (twilight or dusk), which is neither day, nor night, nor both, nor neither, but rather a distinct state having its own unique status and laws associated with it. What is interesting about Bein HaShmashot from our point of view is that it has uncannily similar to the quantum-mechanical state of superposition. As we discussed in that essay, an electron can be in a state of superposition of having its spin up and down (with angular momentum directed counterclockwise and clockwise) or a photon in a state of superposition of horizontal and vertical polarization, or the Schrödinger cat in a state of superposition of being alive and being dead. Just as Bein HaShmashot the cat is neither dead, nor [...]

By Alexander Poltorak|2023-07-14T12:09:33-04:00July 18th, 2014|Bamitbar, Husband and wife, Mattot, Numbers, Parshah, Pentateuch (Chumash), Superposition, Uncategorized|0 Comments

Phinehas – the Slayer of Uncertainty

Phinehas – the Slayer of Uncertainty

A strange episode at the end of the last Torah portion, Balak, where Phinehas (Pinchas) slain a Jewish prince caught in the act with a heathen woman, is rewarded in this week’s eponymous Torah portion with the priesthood. This begs the question, what is the connection between the act of zealotry by Phinehas and the reward of priesthood he receives for it? By way of background, as we read in the previous Torah portion, the evil king, Balak, fails to bring a curse on the Jewish people by Balaam (Bilam). According to Midrash, Balaam advises Balak to send most beautiful Midian women to seduce Jewish men (see Flavius Josephus's Antiquities of the Jews, Book IV, Chapter VI, Paragraphs 6-12). Balak heads the advice and uses Moabite and Midianite women to seduce Jewish men [...]

By Alexander Poltorak|2019-07-22T22:52:15-04:00July 11th, 2014|Collapse of the wavefunction, Entanglement, Numbers, Parshah, Pentateuch (Chumash), Pinchas, Superposition, Uncategorized|0 Comments

Secrets of the Talking Ass

And G‑d opened the mouth of the ass, and she said to Bilam: "What have I done to you, that you have struck me these three times?" And Bilam said to the ass: "Because you have mocked me; I would there were a sword in my hand, for now I would kill you." And the ass said to Bilam: "Am not I your ass, upon which you have ridden all your life to this day? Was I ever wont to do so to you?" And he said, "No." Num. 22:28-30 Despite the simple dialogue between Balaam (Bilam) and his ass in the Torah portion of Balak, this ass was no ordinary ass. This ass saw an angel where a prophet as great as her owner, Balaam, did not. It stands to reason that [...]

By Alexander Poltorak|2017-07-07T16:33:28-04:00July 6th, 2014|Balak, Bamitbar, Collapse of the wavefunction, Creation, Dreams, Numbers, Parshah, Pentateuch (Chumash), Quantum Theory, Shabbat, Superposition, Uncategorized, Wavefunction|1 Comment

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 unto Me seventy men of the elders of Israel, whom thou knowest to be the elders of the people, and officers over them; and bring them unto the tent of meeting, that they may stand there with thee. And I will come down and speak with thee there; and I will take of the spirit which is upon thee, and will put it upon them… And the LORD came down in the cloud, and spoke unto him, and took of the spirit that was upon him, and put it upon the seventy elders; and it came to pass, that, when the spirit rested upon them, they prophesied, but [...]

By Alexander Poltorak|2014-06-09T01:04:27-04:00June 9th, 2014|Bamitbar, Behaalotecha, Entanglement, Numbers, Pentateuch (Chumash), Quantum Theory, Uncategorized, Wavefunction|0 Comments

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) In the Torah portion Behaalotecha (Num. 8:1), Aaron is commanded to light the Menorah so that three light on the right and three lights on the left are directed towards the middle light. On the first blush, it appears to be a very strange commandment. Why would lights on the right and on the left need to be directed towards the center light? What is the significance of that? It seems to me that this unusual arrangement hints at fundamental structure of our world. Sefer Yetzirah states that this world is created in three domains – Olam (“World” – meaning space), Shanah (“Year” – meaning time) and Nefesh (“Soul” [...]

By Alexander Poltorak|2014-06-09T00:08:13-04:00June 8th, 2014|Bamitbar, Behaalotecha, Numbers, Pentateuch (Chumash), Shabbat, Space, Spirituality, Time, Uncategorized|0 Comments

G‑d Collapses Sotah’s Wave Function

G‑d Collapses Sotah’s Wave Function

The story of Sotah, a suspected adulteress, is very troubling on the first blush. Why would a woman be subjected to such humiliation? The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, points out that, to the contrary, the story of Sotah is the story of the boundless love of the Creator for his people. Notwithstanding the strict Biblical prohibition of erasing G‑d’s name, to vindicate the wrongly accused woman, G‑d allows and, indeed, decrees to erase His holy Name by dissolving the scriptural verses written on a parchment in the water that the woman would drink to clear her name. For as long as a woman is being suspected of infidelity, she cannot be intimate with her husband. It takes a Divine intervention, whereby G‑d sacrifices His honor in allowing erasing His holy Name, [...]

By Alexander Poltorak|2020-05-24T16:51:13-04:00June 1st, 2014|Bamitbar, Collapse of the wavefunction, Entanglement, G‑d, Husband and wife, Names of G‑d, Naso, Numbers, Parshah, Pentateuch (Chumash), Quantum Theory, Superposition, Tanakh, Wavefunction, Witnesses|1 Comment

Suspected Adulteress as a Schrödinger Cat

Suspected Adulteress as a Schrödinger Cat

In quantum mechanics, the state of a physical system is described by the so-called wave function (or the "wavefunction"). All attempts by Schrödinger, who first introduced the wave function, and others to interpret it as a scalar potential of some physical field, or as the de Broglie wave (as in particle-wave dualism) were not successful. In 1926, Max Born noticed that the squared amplitude of the wavefunction of a particle in a given region gives the probability of finding the particle in this region. He suggested that the wavefunction represented not a physical reality but rather our knowledge of the quantum state of an object. The wave function represents our knowledge of all possible quantum-mechanical states of an object and their probabilities. In other words, the quantum-mechanical state of a physical system is [...]

By Alexander Poltorak|2020-05-24T16:41:26-04:00May 30th, 2014|Bamitbar, Collapse of the wavefunction, Entanglement, Husband and wife, Naso, Numbers, Parshah, Pentateuch (Chumash), Quantum Theory, Shavuot, Superposition, Uncategorized, Wavefunction|2 Comments

Creatio ex Nihilo and the Number Theory

As we began this Shabbat reading the Fourth Book of Torah—Numbers, I thought, it would be appropriate to post on this blog an excerpt from my article Creatio ex Nihilo, Number Theory, Quantum Vacuum, and the Big Bang, originally published in B’Or HaTorah (Jerusalem: 2007, No. 17, p.115). Introduction The kabbalistic principle of yesh m’ayin or creatio ex nihilo—creation of something from nothing—is difficult to fully understand because we have no experience of creating something from nothing. Although many human creative activities seem to create something new, in fact, they merely change the form or nature of things. Never do we create something from nothing. A sculptor takes a preexisting slab of marble and shapes it according to his imagination. So does a potter, who molds pottery out of clay; a glassblower, who forms liquid [...]

By Alexander Poltorak|2014-05-26T12:34:27-04:00May 25th, 2014|Bamidbar, Bamitbar, Creation, Mathematics, Numbers, Science, Uncategorized|2 Comments

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 the congregation of the children of Israel, and say unto them: Ye shall be holy; for I, the Lord, your G‑d, am holy. Leviticus 19:2 The gist of this commandment is “Be kadosh (or pl., kedoshim) because I, the Lord, your G‑d, am kadosh.” The question is, what does the word “kadosh” mean. It is usually translated as “holy.” The word “holy” means sacred, sanctified, blessed, divine. But this translation presents a problem. It would be a tautology to say that G‑d is divine. It is also self-understood that G‑d is holy. He is the definition and the source of all that is divine and holy, i.e., godly. [...]

By Alexander Poltorak|2019-05-08T09:58:17-04:00April 25th, 2014|Entanglement, G‑d, Kedoshim, Leviticus, Names of G‑d, Parshah, Pentateuch (Chumash), Space, Spirituality, Uncategorized, Vayikra, Wavefunction|0 Comments

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 waving pictures of John Kerry chanting “Flip-flop, flip-flop…” referring to Kerry’s ever changing position on the war in Iraq (“First I voted for it, before I voted against it”) and other political issues. Former Governor of New York State, George Pataki, said there, “This year, we will win one for the Gipper, and they will lose one with the Flipper.” Kerry lost, as flippers usually do. This Haftorah (weekly portion of Prophets read publicly in Synagogues) starts with an astonishing statement of Elyahy Hanavi (Elijah the Prophet), “How long will you waver between two ideas? If the Lord is G‑d, follow Him, and if the Baal, follow him.” (Melachim-I [...]

By Alexander Poltorak|2014-02-18T22:04:11-05:00February 18th, 2014|Collapse of the wavefunction, Entanglement, Exodus (Shemot), G‑d, Ki Tisa, Parshah, Pentateuch (Chumash), Shemot, Superposition, Tanakh, Uncategorized, Wavefunction, Wavefunction of G‑d|0 Comments

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 and nonlocality. Theoretical physics was born when Isaac Newton published his Philosophiæ Naturalis Principia Mathematica in 1687, where he formulated his laws of motion and the universal law of gravity. The law of gravity says that two masses attract each other proportionally to the product of their masses and inversely proportionally to the square of the distance between them. This law said nothing about the nature of the gravitational interaction, it did not explain the mechanism of this attraction at a distance. Newton was bothered by the question of how one body can act on another body far removed from it with nothing in between, i.e., the notion of “action [...]

By Alexander Poltorak|2019-02-06T16:45:19-05:00February 2nd, 2014|Exodus (Shemot), G‑d, Pentateuch (Chumash), Physics, Quantum Theory, Science, Shemot, Terumah, Uncategorized|3 Comments

Convergence of Science and Torah

Convergence of Science and Torah

The Torah portion of Yitro (Ex. 18), is the high point of the story of Exodus—the giving of the Decalogue on Mount Sinai. In a strange digression, the progressive narrative of the Exodus from Egypt is interrupted by the side story of Jethro (Yitro), the father-in-law of Moses, who comes to Sinai desert to join the Jewish nation. After hearing Moses’ account of all the miracles G‑d performed for Jewish people, Jethro exclaimed: Now I know that the Lord is greater than all deities. (Ex. 18:11) Jethro said confidently, “I know,” because, as the chief priest of Midian, he indeed knew all pagan cults and all deities worshiped in his time. Moreover, in antiquity, priests were expected to possess all secular knowledge as well (sadly, it is no longer the case). They needed to [...]

By Alexander Poltorak|2019-01-20T14:55:32-05:00January 20th, 2014|Exodus (Shemot), G‑d, Mashiach (Messiah), Parshah, Pentateuch (Chumash), Science, Shemot, Uncategorized, Yitro|2 Comments

Manna – Superposition of All Tastes

While traveling in the Sinai desert, Israelites were fed by the heavenly bread – the manna. The Torah portions – parshat Beshalach – states that raw manna tasted like wafers that had been made with honey: וַיִּקְרְאוּ בֵית-יִשְׂרָאֵל אֶת-שְׁמוֹ, מָן; וְהוּא, כְּזֶרַע גַּד לָבָן, וְטַעְמוֹ, כְּצַפִּיחִת בִּדְבָשׁ. And the house of Israel called the name thereof Manna; and it was like coriander seed, white; and the taste of it was like wafers made with honey. (Ex. 16:31): However, in Numbers, it says that it tasted like cakes baked with oil: כְּטַעַם לְשַׁד הַשָּׁמֶן The taste of it was as the taste of a cake baked with oil. (Num. 11:8) The Talmud (Yoma 75b) reconciles this discrepancy by explaining that the tastes varied depending who ate the manna – to small children it tasted [...]

By Alexander Poltorak|2017-02-10T17:47:09-05:00January 13th, 2014|Beshalach, Collapse of the wavefunction, Exodus (Shemot), Parshah, Pentateuch (Chumash), Quantum Theory, Shemot, Superposition|0 Comments

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 a hint? Still no idea? Okay, here is the answer: Yes, the first figure represents two doorposts and the lintel marked with the blood of Passover sacrifice, as it says: וְלָקְחוּ, מִן-הַדָּם, וְנָתְנוּ עַל-שְׁתֵּי הַמְּזוּזֹת, וְעַל-הַמַּשְׁקוֹף--עַל, הַבָּתִּים, אֲשֶׁר-יֹאכְלוּ אֹתוֹ, בָּהֶם And they shall take of the blood, and put it on the two side-posts and on the lintel, upon the houses wherein they shall eat it. (Ex. 12:7) The second picture is of the splitting of the sea, as it says: וַיָּבֹאוּ בְנֵי-יִשְׂרָאֵל בְּתוֹךְ הַיָּם, בַּיַּבָּשָׁה; וְהַמַּיִם לָהֶם חוֹמָה, מִימִינָם וּמִשְּׂמֹאלָם And the children of Israel went into the midst of the sea upon the dry ground; and the [...]

By Alexander Poltorak|2019-01-16T05:59:50-05:00January 12th, 2014|Beshalach, Collapse of the wavefunction, Dreams, Entanglement, Exodus (Shemot), Parshah, Pentateuch (Chumash), Quantum Theory, Shemot, Superposition, Time, Uncategorized, Uncertainty Principle|0 Comments

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 is says: וְלָקְחוּ, מִן-הַדָּם, וְנָתְנוּ עַל-שְׁתֵּי הַמְּזוּזֹת, וְעַל-הַמַּשְׁקוֹף--עַל, הַבָּתִּים, אֲשֶׁר-יֹאכְלוּ אֹתוֹ, בָּהֶם And they shall take of the blood, and put it on the two side-posts and on the lintel, upon the houses wherein they shall eat it. (Ex. 12:7) The second picture is of the splitting of the sea, as it says: וַיָּבֹאוּ בְנֵי-יִשְׂרָאֵל בְּתוֹךְ הַיָּם, בַּיַּבָּשָׁה; וְהַמַּיִם לָהֶם חוֹמָה, מִימִינָם וּמִשְּׂמֹאלָם And the children of Israel went into the midst of the sea upon the dry ground; and the waters were a wall unto them on their right hand, and on their left. (Ex. 14:22) And both have to do with time. But this is a [...]

By Alexander Poltorak|2014-01-11T23:39:35-05:00January 10th, 2014|Beshalach, Bo, Exodus (Shemot), Parshah, Pentateuch (Chumash), Shemot, Time, Uncategorized|0 Comments

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 ideas described in the current and the previous sidrot (weekly Torah portions); 2. Don't focus on the differences in these pictures, focus on similarities. 3. The answer has to be expressed in two psukim (verses) -- one from the last parshah and the other from the current parshah describing each respective picture. 4. Last but not least, here are these pictures again with some details:

By Alexander Poltorak|2014-01-10T11:57:37-05:00January 10th, 2014|Beshalach, Bo, Exodus (Shemot), Parshah, Pentateuch (Chumash), Shemot, Uncategorized|0 Comments

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 was my lucky day – I seem to have found an answer to a nagging question of many years. During several years from 1989 to 1996, I had been working on a book on Mezuzah. This was not a book about halachot (ritual laws) of mezuzah – there were many books on that subject – this was a book about the meaning of mezuah – its significance in Jewish history, philosophy, ethics, and mysticism. By 1996, the book was finished and I signed a contract with the leading publisher of English Judaica – Jason Aronson. I was supposed to deliver the finished manuscript in a few months, but [...]

By Alexander Poltorak|2017-02-02T22:34:18-05:00January 5th, 2014|Bo, Exodus (Shemot), G‑d, Names of G‑d, Parshah, Pentateuch (Chumash), Shemot, Time, Uncategorized|0 Comments

Carpe Diem

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 sure Jews did get this message, G‑d gave them the very first commandment—the commandment of keeping time, of marking new months: This month shall be unto you the beginning of months; it shall be the first month of the year to you.(Ex. 12: 2) It is important to note that Jews were not only commanded to keep time, they were commanded to “make” time. Indeed, in Biblical times, the new month was not calculated according to a calendar, as it is done today, it was proclaimed by a Bet Din (an ecclesiastic court) based on the testimony of two live witnesses, who observed [...]

By Alexander Poltorak|2018-01-19T06:54:12-05:00January 2nd, 2014|Bo, Collapse of the wavefunction, Exodus (Shemot), Holidays (Yomim Tovim), Omer, Parshah, Passover (Pesach), Pentateuch (Chumash), Quantum Theory, Rosh HaShanah, Shabbat, Shavuot, Shemot, Spirituality, Superposition, Time, Uncategorized, Wavefunction, Witnesses|0 Comments

It’s the Time, Stupid!

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 the beginning of the book of Exodus (Shemot). The story of Joseph’s incarceration ends with his successful interpretation of the dreams of the Pharaoh’s chief butler and the chief baker. Joseph's genius was not only in interpreting ordinary objects (tendrils of grapes and baskets of bread) as symbols of the units of time but in understanding that the engagement in time (manifested in the chief butler’s personally squeezing the grapes into the cup and placing the cup in Pharaoh’s hand) symbolized life for the chief butler and the passivity of the chief baker (who dreamt of baskets of bread sitting on his head, with birds eating from the baskets) [...]

By Alexander Poltorak|2021-01-14T23:27:27-05:00December 31st, 2013|Dreams, Exodus (Shemot), Parshah, Pentateuch (Chumash), Time, Uncategorized, Vayeira|0 Comments

Interpreting Dreams

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 his dream to Joseph, and said to him: “In my dream, behold, a vine was before me; and in the vine were three tendrils...” And Joseph said unto him: “This is the interpretation of it: the three tendrils are three days.” (Gen. 40:9-12) How did Joseph know that three tendrils are three days? The story repeats itself with the chief baker: When the chief baker saw that the interpretation was good, he said unto Joseph: “I also saw in my dream, and, behold, three baskets of white bread were on my head…” “This is the interpretation thereof: the three baskets are three days.” (Gen. 40:16-18) Joseph interpreting [...]

By Alexander Poltorak|2020-12-10T23:14:45-05:00November 24th, 2013|Bereshit, Dreams, Genesis, Miketz, Parshah, Pentateuch (Chumash), Time, Uncategorized, Vayeshev|3 Comments

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