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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 reveal the date of the coming of Mashiach (Messiah). Jacob called for his sons and said, "Gather and I will tell you what will happen to you at the end of days. (Gen. 4:1) However, he proceeds rebuking his sons without revealing to them the Ketz — End of Days. Rashi says that Jacob looked into the future and saw his children being in exile for a long time. Rashi says that the word “ketz” (end)—spelled in Hebrew Kof-Tzadik—has the numerical value of 190. (Kof=100, Tzadik=90. 100+90=190). Jacob gazed 190 years into the future and saw his children still enslaved in Egypt. He became depressed and Shechinah (Divine Presence) left him. [...]

By Alexander Poltorak|2017-01-13T15:54:32-05:00January 2nd, 2015|Genesis, Mashiach (Messiah), Names of G‑d, Pentateuch (Chumash), Sefirot, Uncategorized, Vayechi|1 Comment

Septuagint—Collapsing the Wave-function of the Torah

Today is the eighth day of the month of Tevet. On the 8th of Tevet of the Jewish year 3515 (246 BCE), the Torah was translated into Greek. In the ancient times, this day was commemorated by fast. Seventy sages translated the Torah into Greek for King Ptolemy. That day was as difficult for the people of Israel as the day on which the [Golden] Calf was made; for the Torah could not be fully translated. (Babylonian Talmud, Tr. Sefer Torah, 1:8) Why does the Talmud compare translation of Torah into Greek to the tragedy of Golden Calf that brought terrible retribution the consequence of which we still suffer today? According to Medrash Tanchuma, Moses translated Torah into seventy languages before Jews crossed Jordan river on the way to the Promised land. Moreover, [...]

By Alexander Poltorak|2014-12-30T19:52:29-05:00December 30th, 2014|Collapse of the wavefunction, Pentateuch (Chumash), Uncategorized|1 Comment

Joseph and His Brothers

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 learn a new for me (but, actually, very old) Imperial system of measurements. 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 the base-60 system; the Hindu-Arabic system uses the familiar decimal base-10 system; the Mayans used the 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 digits—0, 1, [...]

By Alexander Poltorak|2020-12-10T20:20:44-05:00December 14th, 2014|Bereshit, Chanukah, Genesis, Holidays (Yomim Tovim), Husband and wife, Kabbalah, Mashiach (Messiah), Mathematics, Mathematics, Names of G‑d, Parshah, Pentateuch (Chumash), Science, Sefirot, Uncategorized, Vayeshev|1 Comment

On Tzimtzum, Sefirot and Cardinal Numbers

Today is Yud Tes Kislev -- Rosh HaShanah of Chasidut. Today I received two gifts, which I'd like to share. Lately, while learning Samach Vov, I've been struggling to understand the meaning of Sefirot Ein Keitz. Today, during shacharis shemone esreh, it donned upon me that the literal meaning of Sefirot Ein Keitz is infinite numbers. I suddenly realized that while Sefirot after the Tzimtzum are ordinary numbers, Sefirot before Tzimtzum—Sefirot Ein Keitz—are cardinal numbers developed by the mathematician Georg Cantor at the end of the 19 c. Later during the day, I got the second epiphany that Tzimtzum is the collapse of the universal wavefunction describing the creation. Before Tzimtzum, all creations were in the state of "yecholot" -- potentialities. After the Tzimtzum, i.e., after the collapse of the wavefuction, these potentialities actualized in specific [...]

By Alexander Poltorak|2016-01-24T12:30:41-05:00December 11th, 2014|Collapse of the wavefunction, Creation, Mathematics, Quantum Theory, Superposition, Uncategorized, Wavefunction, Wavefunction of G‑d|1 Comment

Schrödinger May Have Been Born Today

A man once came to a rabbi with said news – his cat just died. Rabbi politely expressed his sympathy to the owner of the deceased cat. He thanked the rabbi and asked if he could say kaddish (memorial prayer) for his cat. Rabbi was taken aback – a kaddish for a cat?! This is sacrilege! The man offered to donate to the synagogue a thousand dollars, if the rabbi would allow him to say kaddish for his cat, but to no avail. He offered two thousand, five thousand, but rabbi was unmoved. When the man finally offered ten thousand dollars, the rabbi exclaimed, “Why didn’t you tell me your cat was Jewish?!” Ervin Schrödinger I am not sure if the cat in this old Jewish joke was Jewish, but the [...]

By Alexander Poltorak|2014-08-10T17:21:35-04:00August 12th, 2014|Collapse of the wavefunction, Quantum Theory, Superposition, Uncategorized, Wavefunction|0 Comments

The Final Frontier

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, neither contend with them in battle; for I will not give thee of his land for a possession. (Deuteronomy 2:9) To put this into context, let us recall the covenant of the pieces (or covenant between the parts, Heb. Brit Bein HaBetarim), when G‑d promised Avraham: On that day the Lord made a covenant with Abram, saying: “Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates; the Kenite, and the Kenizzite, and the Kadmonite, and the Hittite, and the Perizzite, and the Rephaim, and the Amorite, and the Canaanite, and the Girgashite, and the Jebusite.” (Genesis 15:19-21) The medieval [...]

By Alexander Poltorak|2024-08-08T23:04:41-04:00August 3rd, 2014|Deuteronomy, Devarim, Devarim, Habakkuk, Mashiach (Messiah), Parshah, Pentateuch (Chumash), Uncategorized|0 Comments

Forty Two Journeys to the Answer to the Ultimate Question of Life, the Universe, and Everything

Forty Two Journeys to the Answer to the Ultimate Question of Life, the Universe, and Everything

These are the journeys of the children of Israel… (Numbers 33:1) When G-d brought the Jews out from Egypt, He brought them out with the mystery of the 42-letter name, just as He created heaven and earth… (Zohar Chadash) The forty-two “stations” from Egypt to the Promised Land are replayed in the life of every individual Jew, as his soul journeys from its descent to earth at birth to its return to its Source. (Rabbi Israel Baal Shem Tov) Torah portion Massei (Num. 33-35) recalls forty-two journeys of the Children of Israel in the Sinai desert after the Exodus from Egypt. This is not the first time the concept of forty-two journeys appears in the Torah. Commenting on the Biblical verse, "And G‑d said, 'Behold, I Will Cause to Rain Bread from Heaven for You,’” (Ex. 25:5) [...]

By Alexander Poltorak|2019-07-30T21:26:13-04:00July 27th, 2014|Creation, G‑d, Massei, Mathematics, Names of G‑d, Numbers, Omer, Pentateuch (Chumash), Uncategorized, Yom Kippur|4 Comments

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, i.e., with the current Torah portion. The Torah portion we read this Shabbat – Mattos – talks about the tribes of Reuben and Gad who did not wish to cross Jordan (Yarden). They had a lot of cattle and seeing that the land of Sichon and Og was lush and suitable for cattle, they ask Moses for permission to build houses for their cattle, their children and wives in this land. They asked that this territory be given to them as a hereditary land instead of the portion of the land in Canaan on the other side of Jordan. Moses was furious with them. He accused them of repeating [...]

By Alexander Poltorak|2014-07-20T10:31:42-04:00July 20th, 2014|Uncategorized|0 Comments

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

613 Degrees of Freedom

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 break, home becomes filled with the aroma of freshly baked bread. Passover leaves us with the pleasant taste of burnt matzot, memories of the Seder spent with family, and stories of the Exodus. But did Passover really end? In the Mishnah (the precursor to Talmud), the holiday of Shavuot ("Pentecost") is called Atzeret. This word is familiar to us from Shemini Atzeret—the holiday that follows immediately after the seven days of Sukkot, often simply viewed as the last day (or, in the diaspora, the last two days) of Sukkot. Either way, Shemini Atzeret is the conclusion of the festival of Sukkot. By designating Shavuot as Atzeret, the Mishnah seems [...]

By Alexander Poltorak|2024-06-09T16:13:49-04:00June 6th, 2014|Freedom, Passover (Pesach), Shavuot, Space, Spirituality, Time, Uncategorized|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

Four Cups and Three Matzoth

On Seder night we drink four cups of wine and eat three matzoth. Why four cups and not three? Why three matzoth and not four? The same numerical relationship exists among our forefathers. We have the patriarchs – Avraham (Abraham), Yitzchak (Isaac) and Yaakov (Jacob). But we have four matriarchs – Sarah, Rivkah (Rebeca) Rachel, and Leah. This dynamics also manifests itself in the holiest name of G‑d – Tetragrammaton – Y‑H‑W‑H. Why does the four-letter Name have only three unique letters, Yud, Heh, and Vav? According to Sefer Yetzirah – a classic text of Kabbalah attributed to Abraham or to Rabbi Akiva – there are three letters of Hebrew Alef Bet called mothers: Alef, Mem, and Shin, which are considered to be “primary” letters. The three mothers represent the basic logical triad [...]

By Alexander Poltorak|2017-04-09T23:10:01-04:00April 20th, 2014|Freedom, Holidays (Yomim Tovim), Names of G‑d, Passover (Pesach), Science, Time, Uncategorized|1 Comment

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 Pesach. The simple meaning of this directive is clear – the laws are many and complicated and there is a lot to learn – so one needs to start early. There may be a deeper meaning in this, however. Let us recall that Pesach and Purim are exactly 30 days apart. To start learning about Pesach 30 days before, means to start learning about Pesach on Purim. Or, perhaps, the message is that from Purim we can learn about Pesach. The word Purim means “lot.” The story of Purim is about throwing lots. Evil Haman threw one lot to choose a month for the pogrom against Jews of [...]

By Alexander Poltorak|2017-04-10T15:36:48-04:00April 19th, 2014|Freedom, Passover (Pesach), Purim, Randomness, Uncategorized, Yom Kippur|0 Comments

Pesach – Time of our Freedom

The holiday of Passover – Pesach – is called zman cheruteinu– time of our freedom. As we have discussed many times on this blog (see Interpreting Dreams; It’s the time, stupid! Carpe Diem; Mezuzah and Time; Riddle — the answer; Splitting the Sea), freedom can only be obtained by mastering time. Everything about celebrating Passover is related to time. It all starts on the Rosh Chodesh Nissan (the New Moon, the beginning of the month of Nissan – marked by the renewal of the monthly lunar cycle – during which we celebrate Passover). On that day, the very first commandment was given to the Jewish people – the commandment to set the calendar by the lunar cycle, i.e., the commandment of keeping time. Classical commentators ask: Why the Torah (which means “Instruction”) does not have as [...]

By Alexander Poltorak|2017-04-10T16:28:20-04:00April 18th, 2014|Freedom, G‑d, Holidays (Yomim Tovim), Names of G‑d, Passover (Pesach), Rosh Chodesh, Time, Uncategorized|0 Comments

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