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The Second Derivative — The Secrets of The Double Cave

And he [Avraham] spoke with them, saying, “…Listen to me and entreat for me to Ephron the son of Zohar. That he may give me the Machpelah (Double) Cave, which belongs to him, which is at the end of his field…" (Genesis 23:8-9) double: A house with an upper story over it. Another interpretation: because it was doubled with couples (Er. 53a) (Rashi on Genesis 23:9) In the Torah portion Chayei Sarah, Avraham purchases a Double Cave, Machpelah, as the ancestral burial plot. Almost all classical Biblical commentators interpret Machpelah (that is, "double") to mean a cave with two chambers. Rashi takes an entirely different approach and states that the cave was known for a two-story house built on top of it. So, the word Machpelah refers not to the cave itself, but to [...]

By |2020-11-11T00:04:58-05:00November 7th, 2018|Bereshit, Chayei Sarah, Genesis, Mathematics, Parshah, Pentateuch (Chumash), Randomness, Uncategorized|0 Comments
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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 countries? Said G‑d: “Let Esther, the descendant of Sarah who lived 127 years, come and rule over 127 lands. (Esther Rabbah 1:8) The Midrash Ester Rabbah compares 127 years of Sarah’s life with 127 provinces that Esther ruled. How can one compare time with space? When the Midrash says that Adam gifted 70 years of his life to his descendant, King David, it’s understandable – a year for a year. But a year for a province? What’s the connection? Hermann Minkowski When, in 1905, Albert Einstein published his Special Theory of Relativity, it was nothing short of a scientific revolution. For the first time, Einstein showed [...]

By |2024-10-13T21:44:20-04:00November 4th, 2018|Bereshit, Chayei Sarah, Genesis, Pentateuch (Chumash), Physics, Relativity, Science, Space, Time, Uncategorized|1 Comment
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Wellsprings from Above and Wellsprings from Below

In the six hundredth year of Noah's life, in the second month, on the seventeenth day of the month… all the fountains of the great deep were broken up, and the windows of heaven were opened. (Gen. 7:11) In calculating the time of the dawn of Messianic revelation, the Zohar writes, And after six hundred years of the sixth thousand there will be opened the gates of wisdom above and the fountains of wisdom below, and the world will make preparations to enter on the seventh thousand as man makes preparation on the sixth day of the week, when the sun is about to set. (Zohar I, 117a) The Zohar calculates this based on the letters of the Tetragrammaton, but brings the verse from this parashah as the mnemonic: “In the six hundredth [...]

By |2022-05-30T22:03:48-04:00October 14th, 2018|Bereshit, Genesis, Kabbalah, Mashiach (Messiah), Names of G‑d, Noach, Parshah, Pentateuch (Chumash), Physics, Quantum Field Theory, Science, Uncategorized, Zohar|2 Comments
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Day Six – the State of Superposition

And G‑d saw all that He had made, and behold it was very good, and it was evening and it was morning, the sixth day. (Gen. 1:31)   The Biblical narrative of creation concludes with the above verse. Rabbi Shlomo Yitzchaki (a.k.a. Rashi) comments on this verse: the sixth day: Scripture added a “hey” on the sixth [day], at the completion of the Creation, to tell us that He stipulated with them, [“you were created] on the condition that Israel accept the Five Books of the Torah.” [The numerical value of the “hey” is five.] (Tanchuma Bereishith 1). Another explanation for “the sixth day”: They [the works of creation] were all suspended until the “sixth day,” referring to the sixth day of Sivan, which was prepared for the giving of the Torah (Shab. 88a). [...]

By |2018-10-10T14:40:55-04:00October 10th, 2018|Bereishit, Bereshit, Collapse of the wavefunction, Deuteronomy, Parshah, Pentateuch (Chumash), Quantum Theory, Superposition, Uncategorized, Wavefunction|1 Comment
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Shabbat Bereshit – Past, Present, and Future

In the last post, Tishrei—Past, Present, and Future, we discussed how all Tishrei holidays – Rosh HaShanah, Yom Kippur, Sukkot, and Simchat Torah – are connected by the same thread of time and, more specifically, the unification of past, present, and future. This cluster of Tishrei holidays is culminated and concluded with Shabbat Bereshit, when we start the new annual cycle of reading the Torah. Not surprisingly, Shabbat Bereshit follows the same pattern of unification of past, present, and future. The Torah starts with the creation of the world. The story of Creation, obviously, relates to the past. The word “bereshit,” means, in the beginning. The root of “bereshit" is “reshit” – beginning. Beginning, however, points into the future – to something that will follow the beginning in the future. The Lubavitcher [...]

By |2018-10-07T17:42:31-04:00October 7th, 2018|Bereishit, Bereshit, Creation, Holidays (Yomim Tovim), Parshah, Rosh HaShanah, Simchat Torah, Sukkot, Time, Uncategorized, Yom Kippur|0 Comments
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Tishrei — Past, Present, and Future

The months of Tishrei is full of holidays, and they all share a common theme—the unification of time—past, present, and future. Picart, Blowing of the Shofars on Rosh Hashanah It all starts with Rosh HaShanah. Traditionally translated as the New Year, it literally means the Head of the Year. The word shanah has the same letters as the word shinui — “change.” As Aristotle famously wrote, time is change. The sages of Kabbalah agree—time, in its essence, is change. Thus, Rosh HaShanah can be translated as the Head of Time, or the Beginning of Time (since a related Hebrew word, reshit means the “beginning”). Indeed, it is all about time. Rosh HaShanah has three main themes—Ziḥronot (remembrances), Shofrot (Sounds of the Shofar), and Malkhiot or  Kabalat Ol Malkhut Shamayim (acceptance of [...]

By |2023-10-17T22:54:50-04:00September 29th, 2018|Bereishit, Holidays (Yomim Tovim), Kabbalah, Names of G‑d, Pentateuch (Chumash), Rosh HaShanah, Simchat Torah, Sukkot, Sukkot, Time, Uncategorized, V'Zot HaBerachah, Yom Kippur|0 Comments
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Scientists are Clarifying Witnesses

Listen, O heavens, and I will speak! And let the earth hear the words of my mouth! (Deut. 32:1) In this Torah portion Haazinu, Moses appeals to heavens and earth as witnesses. However, a few verses later, he extorts the Jewish people: “Ask your father, and he will tell you; your elders, and they will inform you” (Deut. 32:7) as if to confirm the testimony of heavens and earth. Why wasn’t the testimony of heavens and earth enough? Why did their testimony need to be corroborated by “your father” and “your elders”? The Lubavitcher Rebbe The Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, in one of his talks (see R’ Schneerson, M.M. Likute Sihot (Brooklyn, NY: Vaad L’Hafotzas Sichos, 1998) v. XIX, Devorim, pp. 188-196) discusses the Talmudic concept of two types of witnesses: [...]

By |2018-09-23T03:38:20-04:00September 21st, 2018|Creation, Deuteronomy, Devarim, Haazinu, Mashiach (Messiah), Parshah, Pentateuch (Chumash), Uncategorized, Witnesses|0 Comments
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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 time. Nefesh means "soul" and signifies the spiritual dimension. In another place, recognizing the space itself is three-dimensional, Sefer Yetzira speaks of five-dimensional space, a Minkowski spacetime with an addition of the fifth spiritual dimension. This construct is very similar to the Kaluza-Klein five-dimensional generalization of the General Theory of Relativity (a theory that is near and dear to my heart because, unaware of its existence, I independently rediscovered it as a teenager.) Kaluza-Klein, first forgotten, is now experiencing a revival as a special case of the string theory. Sefer Yetzirah In every one of these dimensions, G‑d created the domain of holy and the domain [...]

By |2024-10-13T21:41:24-04:00September 18th, 2018|Uncategorized|1 Comment
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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 |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
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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 upon the fledglings, or upon the eggs, thou shalt not take the mother with the young; thou shalt shoo away the mother, but the young thou mayest take unto thyself; that it may be well with thee, and that thou mayest prolong thy days. (Deut. 22:6-7) Many years ago, I was at a physics conference in Princeton in honor of the 85th birthday of John Archibald Wheeler. At the lunch break, I sat alone at a table to eat my kosher lunch (I was always uncomfortable eating this airplane food typically served at conferences whenever I order kosher food. The sound of unwrapping the cellophane attracts everyone’s attention [...]

By |2023-08-25T10:06:23-04:00August 24th, 2018|Deuteronomy, Devarim, Ki Teitzei, Parshah, Pentateuch (Chumash), Uncategorized|1 Comment
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Sabbatical Year – when the Wavefunctions are Collapsed

The Torah portion, Re’eh, talks about the Sabbatical Year—in Hebrew, Shemitah—the Seventh year. When the Sabbatical year comes, all loans are forgiven, and Jewish servants go free. This is difficult to understand. Why would a lender forgive a loan just because it’s the seventh year in the Shemitah cycle? Why would slaves be set free just because it’s the Sabbatical year? Another question is why do we translate Shemitah as the “Sabbatical year”? Besides the fact that it is the seventh year, and Shabbat is the seventh day, what connects the word “shemitah” with Shabbat? As Rabbi Yehoshua Steinberg writes in Biblical Hebrew Etymology, (see Re’eh: The Slippery Year? – The Wonders of the Holy Tongue), the three-letter root of the word “shemitah” – Shin-Mem-Tet – connote falling, collapsing, slipping, weakening, or disintegration. The two-letter [...]

By |2018-08-17T12:28:16-04:00August 17th, 2018|Collapse of the wavefunction, Deuteronomy, Devarim, Parshah, Passover (Pesach), Pentateuch (Chumash), Re'eh, Superposition, Uncategorized, Wavefunction|0 Comments
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Re’eh – the Power of Seeing the Blessings

The Torah portion Re’eh, begins with the verse: Behold, I set before you this day a blessing and a curse. (Deut. 11:26) The first word of this verse, re’eh, literally means “see” in Hebrew. So, literally, this verse should be translated as: See, I set before you this day a blessing and a curse Spoken words are heard, not seen. Why did Moses implore people to see, as he was about to set before them a blessing and a curse? To understand this, we need to look at the following verses defining the blessing and the cure: The blessing, if ye shall hearken unto the commandments of the Lord your G‑d… (Deut. 11:27) …and the curse, if ye shall not hearken unto the commandments of the Lord your G‑d… (Deut. 11:28) Does this [...]

By |2019-08-26T16:42:26-04:00August 12th, 2018|Collapse of the wavefunction, Deuteronomy, Devarim, Parshah, Pentateuch (Chumash), Quantum Theory, Re'eh, Superposition, Uncategorized, Wavefunction|6 Comments
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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 (preceded by the Mishkan in the desert) in the three spatial dimensions, and Shabbat in the fourth dimension, time. I emphasized four dimensions because that was all we needed to explain the connection between the Temple and Shabbat and why we do not fast when Tish B’Av falls on Shabbat (but, instead, fast on the following day—Sunday). In truth, however, G‑d created His sanctuary in five dimensions. As we discussed in several posts on this blog (On the Nature of Time and the Age of the Universe, The Fifth Force, The Fifth Force – Epilog, Tumah and Taharah), Sefer Yetzirah, the oldest surviving book of Kabbalah, describes our [...]

By |2024-10-13T21:51:42-04:00July 27th, 2018|G‑d, Mathematics, Shabbat, Soul, Space, Spirituality, Uncategorized|3 Comments
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Tisha B’Av on Shabbat – A Relativistic Perspective

Yesterday was the 9th day of the month of Av or, in Hebrew, Tisha B’Av. Usually, Tisha B’Av is marked by mourning and fasting. Yesterday, however, we ate festive meals, drank wine and were prohibited from fasting or displaying any signs of mourning. Because yesterday was Shabbat. Shabbat pushes off the observances of Tisha B’Av by a day. Indeed, today, Sunday, we fast and mourn the destruction of the First and the Second Holy Temple  – Bet Hamikdash – in Jerusalem, we remember the Holocaust and many other tragedies that befell the Jewish people. Why couldn’t we observe Tisha B’Av on Shabbat? After all, that was the day when on the 9th of Av, both Temples were destroyed! The simple explanation, of course, is that on Shabbat there is no mourning. On Shabbat, [...]

By |2018-07-24T14:20:03-04:00July 22nd, 2018|Holidays (Yomim Tovim), Kabbalah, Mathematics, Mathematics, Physics, Science, Space, Time, Tisha B'Av, Uncategorized|0 Comments
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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 Haggadah. The Seders is a play in four acts: Kiddush (sanctification), Magid (telling the story of the Exodus), Shulchan Orech (the festive meal), and Nirtzah (Hallel—the prayer for the Messianic redemption). This sequence sets the natural arrow of time past-present-future. The Past. During the Magid part of the Seder, we retell the story of the Exodus of the Jewish people from Egypt—the narrative of our history. Eating of the matzah, drinking four cups of wine and other "simonim" (symbols) of the Seder table—bitter herbs, an egg, a bone, charoset, etc.—are all symbols that have historical significance. This part of the Seder clearly represents the past. The Present. During [...]

By |2019-04-14T16:45:56-04:00March 30th, 2018|Passover (Pesach), Time, Uncategorized|1 Comment
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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 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 |2018-03-04T18:54:42-05:00March 4th, 2018|Uncategorized|2 Comments
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Purim—the Day when We Celebrate Spontaneous Symmetry Breaking

This is what Haman did not understand. Even at the highest level, where there is a complete symmetry between Jacob and Esau, G‑d chooses Jacob—a spiritual example of the spontaneous symmetry breaking: "I loved you, said the Lord, and you said, “How have You loved us?” Was not Esau a brother to Jacob? says the Lord. And I loved Jacob. And I hated Esau…" (Malachi I, 2-3). Haman failed the test on quantum field theory and ended up hanging on a gallows.

By |2024-03-20T23:07:19-04:00March 2nd, 2018|Holidays (Yomim Tovim), Physics, Purim, Quantum Field Theory, Quantum Theory, Randomness, Symmetry, Uncategorized, Yom Kippur|0 Comments
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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 strong (nuclear) force, the weak force (beta decay), and the electromagnetic force. The gravitational force, described by the General Theory of Relativity, does not fit into the Standard Model. Developing a quantum theory of gravity, and unifying gravity with the other three forces is the holy grail of theoretical physics. Jewish people are also in need of Grand Unification. There is a schism that runs through the history: it is the schism between Joseph (Yosef) and Judah (Yehuda). Judah represents a “shtetl yid,” a Jew who lives in a ghetto, who sits in a yeshivah, who learns Torah, and who sees the world outside as hostile, as a [...]

By |2018-12-10T23:07:02-05:00December 23rd, 2017|Bereshit, Chanukah, Deuteronomy, Ezekiel, Holidays (Yomim Tovim), Kabbalah, Mashiach (Messiah), Parshah, Pentateuch (Chumash), Physics, Quantum Theory, Resurrection, Science, Uncategorized, Vayigash|0 Comments
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Dreams of Pharaoh—A Lesson in Symmetry

In the Torah portion Miketz, Pharaoh has two dreams. He wakes up agitated and calls on all the wise men of Egypt to interpret his dreams. Nobody is able to come up with an acceptable interpretation, so they fetch Joseph from prison and he successfully interprets the dreams of Pharaoh—that there will be seven years of plenty followed by seven years of famine. Joseph proceeds to instruct Pharaoh on how to prepare for the seven years of famine. In the previous posts, "Interpreting Dreams" and "Joseph—the Master of Time," we already explained how Joseph was able to interpret dreams in terms of units of time and why Pharaoh appointed Joseph as the viceroy of Egypt. This story, however, still has mysteries to unlock. Perhaps it can teach us more lessons. In Talmudic and [...]

By |2020-12-20T14:57:57-05:00December 16th, 2017|Bereshit, Dreams, Genesis, Mathematics, Miketz, Parshah, Pentateuch (Chumash), Physics, Quantum Field Theory, Symmetry, Uncategorized|2 Comments
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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 objects (tendrils of grapes and baskets of bread) as symbols of the units of time (Interpreting Dreams). Even greater insight was Joseph’s understanding that the engagement in time, manifested by 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. Conversely, the passivity of the chief baker, who dreamt of baskets of bread sitting on his head, with birds eating from the baskets, symbolized the opposite of life.                                                  Girolamo Brusaferro [...]

By |2020-12-17T20:11:21-05:00December 14th, 2017|Bereshit, Dreams, Genesis, Miketz, Parshah, Pentateuch (Chumash), Time, Uncategorized|0 Comments
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