sephirot

Principle of Least Action III — History

Principle of Least Action III — History

The spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements. Pierre Louis Maupertuis (1744) Among the more or less general laws, the discovery of which characterize the development of physical science during the last century, the principle of Least Action is at present certainly one which, by its form and comprehensiveness, may be said to have approached most closely to the ideal aim of theoretical inquiry. Its significance, properly understood, extends, not only to mechanical processes, but also to thermal and electrodynamic problems. In all the branches of science to which it applies, it gives, not only an explanation of certain characteristics of phenomena at present encountered, but [...]

By Alexander Poltorak|2024-10-13T21:24:17-04:00September 10th, 2023|G‑d, Kabbalah, Mathematics, Mathematics, Physics, Principle of Least Action, Science, Sefirot, Teleology, Time, Tzimtzum, Uncategorized|0 Comments

Yom Kippur—The Day of Pure Delight

Yom Kippur—The Day of Pure Delight

Yom Kippur means “The Day of Atonement.” Some view it as a frightening day full of regrets of the past and anxiety for the future. However, Chasidic philosophy sees Yom Kippur as the day of pure delight. On a simple level, Yom Kippur is the day of forgiveness--the day when we all going to be forgiven, cleansed, and atoned. What is not to be happy about? Moreover, it is a day when we get our personal rendezvous with our Heavenly Father, and with ourselves. The last prayer of Yom Kippur is called Neila ("closing"). It is usually interpreted as the closing of the doors of prayers when the penitent feverishly trying to squeeze another prayer before the doors are shut. In Hassidic teachings, the Neila is viewed completely differently—it is the most cherished [...]

By Alexander Poltorak|2023-09-24T00:35:40-04:00September 15th, 2021|Uncategorized|0 Comments

Noah’s Ark—Three Layers of Reality

Noah’s Ark—Three Layers of Reality

A light shalt thou make to the ark…with lower, second, and third stories shalt thou make it. (Genesis 6:16) We mentioned in the previous posts that Noah’s ark was a microcosm.[1] As we discussed in the previous post, “Noah’s Ark—Three Layers of Being Human,” most structural parallels related to Noah’s ark are based on its tripartite structure —that is, its having three tiers. In Chasidic thought, the three levels of Noah’s ark correspond to three worlds of BiYA—Beriyah (the World of Creation), Yetzirah (the World of Formation), and Asiyah (the World of Action). In this essay, we will investigate how the tripartite structure of Noah’s ark is reflected in the structure of reality. We might say that the totality of existence comprises three layers—physical, informational, and spiritual. The classification of reality into three [...]

By Alexander Poltorak|2024-06-23T21:53:15-04:00October 28th, 2020|Age of the Universe, Bereshit, Collapse of the wavefunction, Fractals, Genesis, Kabbalah, Mathematics, Mathematics, Noach, Parshah, Pentateuch (Chumash), Physics, Sefirot, Space, Spirituality, String Theory, Superposition, Time, Uncategorized, Wavefunction|1 Comment

Salt: The Covenant of the Opposites

Salt: The Covenant of the Opposites

And every meal-offering of thine shalt thou season with salt; neither shalt thou suffer the salt of the covenant of thy G‑d to be lacking from thy meal-offering; with all thy offerings thou shalt offer salt." (Leviticus 2:13) Torah dictates that all offerings to G‑d must be brought together with salt. Classical commentators ask: What is so special about salt that it is an indispensable ingredient of any sacrifice? Moreover, why is it called the covenant of salt? Nachmanides explains: The Torah also uses this covenant as a model for other covenants, as both the priestly covenant[1] and the Davidic covenant[2] are called “covenant of salt” because they are upheld just as the sacrificial covenant of salt…. I am of the opinion that the significance is that the salt is water, which [...]

By Alexander Poltorak|2020-04-01T23:00:14-04:00March 31st, 2020|Chemistry, II Kings, Kabbalah, Leviticus, Parshah, Pentateuch (Chumash), Science, Sefirot, Uncategorized, Vayikra, Vayikra, Zohar|2 Comments

The Primacy of the Prime Numbers

And the messengers returned to Jacob, saying: “We came to thy brother Esau, and moreover he cometh to meet thee, and four hundred men with him.” (Genesis 32:7) On this blog, we primarily focus on structural parallels between Torah and Physics and, more specifically, quantum physics. Today I would like to explore an interesting parallel between this Torah portion and the number theory. In my previous essay on the Torah Portion Vayishlach, “Jacob Meets Esau and his 400 men,” I wrote “Esau and his 400 men together were 401 strong. 401 is a prime number that is the sum of seven consecutive prime numbers (43+47+53+59+61+67+71).” In that essay, I focused on the significance of the number seven. Let us now focus on the significance of the prime number. The structural parallel I see [...]

By Alexander Poltorak|2019-12-15T00:54:15-05:00December 13th, 2019|Bereshit, Genesis, Mathematics, Mathematics, Parshah, Pentateuch (Chumash), Randomness, Sefirot, Uncategorized, Vayishlach|3 Comments

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

Daughters of Zelophehad

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: Mahlah, Noah, and Hoglah, and Milcah, and Tirzah. And they stood before Moses and before Eleazar, the priest, and before the princes and all the congregation at the entrance to the Tent of Meeting, saying: “Our father died in the desert, …. and he had no sons. Why should our father's name be done away from among his family, because he had no son? Give unto us a possession among the brethren of our father.” (Numbers 27:1-4) In the Torah portion that was read last Shabbat in the Diaspora, Phineas (Pinchas), we read the story of the five daughters of Zelophehad who brought the claim for inheritance in [...]

By Alexander Poltorak|2022-04-21T14:21:49-04:00July 28th, 2019|Bamitbar, Kabbalah, Mashiach (Messiah), Names of G‑d, Numbers, Parshah, Pentateuch (Chumash), Physics, Pinchas, Quantum Field Theory, Science, Sefirot, Standard Model, Uncategorized|8 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 Future and Past

Space – Between Future and 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|2024-06-09T17:14:43-04:00June 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|6 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

Three-and-a-half Hakafot — Topology of Simchat Torah

Three-and-a-half Hakafot — Topology of Simchat Torah

Why is this night different from all other nights, asks a child on the Seder night. On this Simchat Torah I asked a different question—why is the day different from the night? Indeed, on the night of Simchat Torah, we dance seven hakafot-circuits. However, during the morning service of the next day, we only dance three-and-a-half hakafot. What is the meaning of this number—three and a half? There are a few instances the Torah, Talmud, and Rabbinic instances where this number is mentioned (e.g., during the Gaonic period, c. 590–1000 CE, in some communities in the Land of Israel, the Torah reading cycle was completed in three and a half years; Maimonides rules that only half of the tzitzit string should be dyed blue leaving three and a half strings white), but none of them [...]

By Alexander Poltorak|2017-10-16T02:32:29-04:00October 15th, 2017|Holidays (Yomim Tovim), Kabbalah, Mashiach (Messiah), Mathematics, Sefirot, Shabbat, Simchat Torah, Sukkot, Sukkot, Time, Topology, Uncategorized|0 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

Chayei Sarah – where Kabbalah meets physics

And these are the years of the life of Ishmael: one hundred years and thirty years and seven years (Gen. 25,17) You might say the ‘hand of G‑d’ wrote that number [137] – Richard Feynman The mystery about α is actually a double mystery. The first mystery – the origin of its numerical value α ≈ 1/137 has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized. — Malcolm H. Mac Gregor, M.H. MacGregor (2007). The Power of Alpha. World Scientific. p. 69. Kabbalah is the esoteric level of the Torah. The word “kabbalah” (קבלה) literally means “receiving” or “received [wisdom].” The gematriah (numerical value) of the word “kabbalah” is 137: Kuf (100) + Bet (2) + Lamed (30) + Heh (5) = 137. This number appears explicitly for the first time [...]

By Alexander Poltorak|2018-10-28T19:58:33-04:00November 27th, 2016|Atomic Theory, Bereshit, Chayei Sarah, Genesis, Kabbalah, Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Science, Soul, Spirituality, Uncategorized|3 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

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