sefirot

Sukkot — Bringing Time into Space

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), and branches of the willow tree (aravot)—and wave them in all six directions (na’anuim) while holding the species together. The precise movements involve bringing the bunch to one’s heart, then moving them to and fro in all six directions, three in each direction, every time returning the bunch to the heart. A strange sight indeed… what could it possibly mean? I’ve written before that Sukkot has to do with bringing holiness into time and space. The seven days of dwelling in the sukkah-booth (a.k.a. tabernacle) is related to the most important cycle of time – 7: there are seven days in a week, seven years in a Sabbatical cycle (shemita), seven [...]

By Alexander Poltorak|2023-10-04T19:50:48-04:00October 18th, 2019|Sefirot, Space, Sukkot, Sukkot, Time, Uncategorized|3 Comments

Relational Space

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, the reader is referred to that post. My second Shavuot “epiphany” was that space is relational. Not that I realized that space was relational for the first time – I always thought so. But, for some reason, thinking about the meaning of the four faces of Chayot, the "living creatures" – the angelic beings described in the prophecy of Ezekiel that we read on Shavuot – made it absolutely clear in my mind. Isaac Newton The debate about the nature of space goes back at least to the times of Newton and Leibniz. Isaac Newton believed (as it is apparent from his mechanics and as it [...]

By Alexander Poltorak|2020-10-20T00:26:20-04:00June 17th, 2019|Ezekiel, Kabbalah, Mathematics, Mathematics, Names of G‑d, Physics, Relativity, Sefirot, Shavuot, Space, Time, Uncategorized|8 Comments

Space – Between the Future and the Past

Space – Between the Future and the Past

Meditations on the Maaseh Merkavah – I We do science by studying nature. We study physics in a lab, peering into space or working out mathematical models with pencil and paper to see if they fit experimental data. However, great mystics of the past were able to see how this world operates by gazing into spiritual worlds above. On Shavuot, the holiday when we celebrate the revelation on Mount Sinai, we read the prophecy of Ezekiel (the First Vision of Ezekiel) called Maaseh Merkavah (or Ma'aseh Merkabah)—Work of the Chariot. Masters of Kabbalah have taught us that understanding the Work of the Chariot gives the initiated an understanding of the works of nature. This Shavuot, studying and thinking about Maaseh Merkavah, I came to understand some profound insights about the physics of space [...]

By Alexander Poltorak|2025-03-03T22:43:27-05:00June 13th, 2019|Ezekiel, Fractals, G‑d, Holidays (Yomim Tovim), Kabbalah, Names of G‑d, Physics, Relativity, Science, Sefirot, Sefirot, Shavuot, Space, Spirituality, Tanakh, Time, Topology, Uncategorized|7 Comments

Ten Sephirot and Special Relativity

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 [...]

By Alexander Poltorak|2019-06-05T17:55:43-04:00June 2nd, 2019|Kabbalah, Mathematics, Mathematics, Physics, Relativity, Sefirot, Sefirot, Space, Spirituality, Symmetry, Uncategorized|4 Comments

The Entangled Tenth

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) This Shabbat, I was called up to the Torah for the last aliyah (lit. “ascent”, meaning the reading from the Scroll) of the book of Leviticus. This portion talks about tithing animals, giving the precise procedure for doing so – every animal is released from a pen one by one while being counted – one, two, three, … , ten. The tenth animal is touch by the rode and consecrated as the ma’aser – tithe. The Torah states that every tenth animal is holy unto G‑d. What is the state of the animals before counting? They have two possible states: (1) chulin, i.e., “not sacred” and (2) ma’aser, [...]

By Alexander Poltorak|2019-06-02T11:37:10-04:00June 2nd, 2019|Bechukotai, Collapse of the wavefunction, Entanglement, Leviticus, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Sefirot, Superposition, Uncategorized, Wavefunction|0 Comments

Fractal Tu B’Shevat

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 wielding an axe against them; for thou mayest eat of them, but thou shalt not cut them down; for is the tree of the field man, that it should be besieged of thee? (Deut. 20:19) On Tu B’Shevat we celebrate the New Year of the trees. There is much to be said about the legal, ecological, homiletical, and mystical meaning of this day. And, indeed, much has been written about this minor holiday from these perspectives. In this post, however, I’d like to focus on the mathematical and biological aspects of this holiday that, to my knowledge, had not been discussed until now. When the Torah rhetorically asks, [...]

By Alexander Poltorak|2019-01-21T08:54:47-05:00January 21st, 2019|Biology, Fractals, Holidays (Yomim Tovim), Mathematics, Mathematics, Science, Sefirot, Tu B'Shvat, Uncategorized|1 Comment

The Beard of the Long Face is Found

The previous Lubavitcher Rebbe, the Rebbe Rayatz (a.k.a. the Fridriker Rebbe) told the story about his father, the Rebbe Rashab. Once the brother of Rebbe Rashab, Rabbi Menachem Mendel (a.k.a. the RM”M) told him that he read in a magazine an article that stated that scientists found a nerve in the brain regulating the cognitive function so that when a person needed to remember something he would tilt his head looking up, whereas when the person needed to concentrate, he’d tilt his head down. The Rebbe Rashab took his brother to his study, took from the shelf a book by the Second Lubavitcher Rebbe, the Mittler Rebbe, in which it stated the same thing. The Rebbe Rashab said to his brother, “You’d think he was a doctor, but he wasn’t. He saw Adam [...]

By Alexander Poltorak|2018-11-10T23:01:55-05:00August 31st, 2018|Bereshit, Biology, Genesis, Kabbalah, Neuroscience, Parshah, Pentateuch (Chumash), Science, Sefirot, Sefirot, Toledot, Uncategorized, Zohar|4 Comments

Breaking Symmetry

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 their sides; on the one side and on the other were they written. And the tables were the work of G‑d, and the writing was the writing of G‑d, graven upon the tables… And it came to pass, as soon as he came nigh unto the camp, that he saw the calf and the dancing; and Moses' anger waxed hot, and he cast the tablets out of his hands, and broke them beneath the mount. (Ex. 32:15-19) The Torah portion Ki Tisa (Ex. 30:11-34:35) is, perhaps, has one of the most enigmatic episodes in the Torah—the breaking of the Tablets of the Covenant. The sin of the Golden [...]

By Alexander Poltorak|2018-03-04T18:54:42-05:00March 4th, 2018|Uncategorized|2 Comments

Five Worlds

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 Rebbe. On the day of his yartzeit, it is customary to study his last maamar (Chassidic discourse), Basi LeGani. One of the themes expounded in the first chapter of this discourse is the concepts of four worlds: Atzilut, Beriah, Yetzirah, and Assiyah (collectively referred to as ABYA). Actually, in Kabbala and Chassidic philosophy, we speak of five worlds and the “world,” which precedes Atzilut is call Adam Kadmon (Primordial Man, often referred to by its acronym as the A”K). In this post, I will draw a parallel between these spiritual worlds and stages of the creation of our physical world. Why do that? It is axiomatic in Jewish mysticism [...]

By Alexander Poltorak|2017-05-23T19:06:38-04:00February 6th, 2017|Collapse of the wavefunction, Creation, Kabbalah, Physics, Quantum Theory, Science, Sefirot, Sefirot, Space, Spirituality, Time, Uncategorized, Wavefunction|0 Comments

The Fifth Force

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 force, electromagnetic force, strong (nuclear) force, and the weak force (beta decay). Newton first described the gravitational force in his famous universal law of gravity. Today, we use Einstein’s General Theory of Relativity to describe gravitation fields. Electromagnetism was described in the 19 c. by Faraday and Maxwell. Strong and week forces were discovered much later, in the second half of the 20 c. Since Albert Einstein started a search for unified field theory, unsuccessfully trying to unify (describe by a single theory) gravity and electromagnetism, the quest for a unified field theory – the “Theory of Everything” – became the holy grail of theoretical physics. Strong and [...]

By Alexander Poltorak|2019-10-03T17:33:39-04:00October 11th, 2016|Deuteronomy, Devarim, G‑d, Names of G‑d, Parshah, Pentateuch (Chumash), Physics, Science, Sefirot, Sefirot, Uncategorized, Vayelech|4 Comments

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 this theme and instructs us to abstain from agricultural work every seventh Sabbatical year, Shmita. And the Torah doesn’t stop there. It instructs us to count seven Shmitas and then observe a Jubilee, Yovel. Do you notice a pattern? Every seven days, every seven years, every seven Shmitas… Furthermore, the Midrash states the world will exist for seven thousand years with the seventh millennium being a thousand years of the kingdom of Mashiach (Messiah)—yom shekuloy Shabbat—one long Shabbat. A second-century sage, Rabbi Huniah ben HaKanah, interprets this Midrash to mean that the world will last seven Cosmic Shmitas, i.e., 49 thousand years (which, according to a prominent 13th–14th [...]

By Alexander Poltorak|2019-05-15T17:51:30-04:00May 31st, 2016|Behar, Emor, Fractals, Mathematics, Omer, Parshah, Pentateuch (Chumash), Sefirot, Sefirot, Space, Time, Uncategorized, Vayikra|1 Comment

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 Shabbat. But why 39? Rabbi Shimon b’ Rabbi Yossi ben Lakunya (Shabbat 49b) suggests that the number 39 can be derived from the number of times the various forms of the word “melacha” (work) appear in the Torah. Unfortunately, it’s not easy to see how this works out. In his commentary on this passage, Rabbi Hananel ben Hushiel (990-1053) already pointed out that this word appears 61 times in the Torah, not 39! Actually, this word actually appears 63 times! Another Talmudic Sage, Rabbi Chanina of Sepphoris derives the number 39 homiletically strenuously computing gematria of the phrase, “These are the things.” (Shabbat 7:2) The lack of clear [...]

By Alexander Poltorak|2019-03-26T16:25:51-04:00May 22nd, 2016|Creation, Emor, Husband and wife, Kabbalah, Leviticus, Parshah, Pentateuch (Chumash), Sefirot, Shabbat, Sukkot, Uncategorized, Vayikra|2 Comments

Jacob’s Sheep—Particles, Fields and Strings

Jacob’s Sheep—Particles, Fields and Strings

And it came to pass at the time that the flock conceived, that I lifted up mine eyes, and saw in a dream, and, behold, the he-goats which leaped upon the flock were streaked, speckled, and spotted. (Gen. 31:10) This week’s Torah reading, Vayeitzei (Gen. 28:10-32:3) talks about three kinds of sheep: streaked, speckled, and spotted. Streaked Sheep Streaked sheep (“akudim”) were ankle-ringed. They looked as if their ankles were bound together with a black rope. Hence the name—"akidim" (Hebrew world for streaked, “akud” means bound as in “Akeda”—binding of Isaac). Speckled Sheep Speckled sheep (Heb. “nekudim” from sing. “nakod”.) were sheep with black dots. Spotted Sheep Spotted or flecked sheep (Heb. "berudim") were blotched. What is the significance of these streaks, speckles and blotches that the Torah devotes [...]

By Alexander Poltorak|2017-11-24T14:57:34-05:00November 20th, 2015|Bereshit, Genesis, Kabbalah, Parshah, Pentateuch (Chumash), Physics, Quantum Field Theory, Quantum Theory, Science, Sefirot, Uncategorized, Vayetze|0 Comments

Yom Kippur – Disentangling the Entangled

When G‑d created the first humans, Adam and Eve (Chavah), He created them as one. And G‑d created man in His own image, in the image of G‑d created He him; male and female created He them. (Gen. 1:27) Actually, as Midrash Rabbah (Gen. VIII:1) explains, Adam and Eve were created as one being as Siamese twins—attached by their side. When the story of the creation of Adam is repeated in the next chapter, it seems as a very different story: And the Lord G‑d caused a deep sleep to fall upon the man, and he slept; and He took one of his ribs, and closed up the place with flesh instead thereof. And the rib, which the Lord G‑d had taken from the man, made He a woman, and brought her unto the [...]

By Alexander Poltorak|2017-09-24T22:38:12-04:00September 24th, 2015|Creation, Entanglement, Holidays (Yomim Tovim), Mashiach (Messiah), Randomness, Superposition, Uncategorized, Yom Kippur|0 Comments

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

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

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

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

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

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