The Puzzle of Pi

March 14 is celebrated by nerds around the world as the Pi Day. When written in digits, 3/14 represents first three digits of the number traditionally represented by the Greek letter “π” (pronounced pi) – 3.14. Pi Day is celebrated by eating pie and discussing the significance of π. Some folks who have too much time on their hands compete at memorizing decimal digits representing the value of pi. The record presently stands at 67,890 digits! While eating pie is optional, discussing the significance of π is truly mandatory. So, what is π and why is to so important? π is arguably the most famous mathematical constant, expressing the ratio between the circumference of a circle and its diameter. If you take a circle with a diameter of 1, the circumference of this [...]

Quantum Torah Film Premiere

Welcome to the premiere of our first film, Quantum Torah. You can watch the film here:   Don't forget to subscribe to my channel here:

Quantum Torah — Film Premiere

I am excited to announce that the premiere of our film "Quantum Torah" is scheduled for this Friday, March 1st. You can see the trailer at Not to miss the premiere, subscribe to my channel, Quantum Torah on YouTube at: I look forward to your comments. See you on YouTube!  

Vectors, Spins, and Gender

Vectors, Spins, and Gender Speak to the children of Israel, and have them take for Me an offering; from every person whose heart inspires him to generosity, you shall take My offering. (Ex. 25:2) Every physics professor teaching physics 101 to freshmen spends the first lecture teaching vector algebra. Why vectors are so important? Because most quantities in mechanics (a branch of physics dealing with motion and forces) are vectors. A vector is a mathematical object that has a magnitude and a direction. For example, velocity is a vector – it shows not only how fast the object is moving, but also in what direction it is moving (it is different from “speed” which is an average velocity and is just a number). Similarly, acceleration is a vector, force is a vector, angular [...]

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, [...]

Chanukah Menorah – the River of Time

In a Kabbalistic meditation on lighting Chanukah Menorah, the Arizal links the menorah lights with a supernal river (see Candle on the River). The Arizal’s principal disciple, Rabbi Chaim Vital, writes in Shaar HaKavanot, Inyan Chanukah: One should meditate on the idea that the initials of the words ‘…l'hadleek ner Chanukah [to light the Chanukah candle]’ are the holy name called ‘Nachal’.” It is easy to see that the first letters of  “l'hadleek ner Chanukah” are three letters, Lamed (L), Nun (N), and Chet (Ch). Rearranged, these letters spell the word NaChaL – a stream or a small river. As I wrote in my essay “On the Nature of Time and the Age of the Universe” and more recently in the post “Joseph—the Master of Time,” a river has been the metaphor for time across many cultures. Does [...]

The Meaning of Life as Taught by Bayesian Angels

And he [Jacob] dreamed, and behold! a ladder set up on the ground and its top reached to heaven; and behold, angels of God were ascending and descending upon it. (Gen. 28:12) Rabbi Shneur Zalman of Liadi (a.k.a Baal HaTanya, or the Alter Rebbe) once remarked in Yiddish, “lieben mit di tzait” – live with the time, meaning one should live with Torah portion of the week.  Last week I was taught a lesson on how the current Torah portion affects my thinking, whether I know it or not. Last week I shared with my wife, who is a biophysicist, that while thinking about system biology, I realized that all organisms – from a single cell to multicellular organisms – are Bayesian systems. I knew that the brain is a Bayesian engine, but [...]

Second Derivative – 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…" (Gen. 23:8-9) double: A house with an upper story over it. Another interpretation: because it was doubled with couples (Er. 53a) (Rashi on Gen. 23:9) In the Torah portion Chayei Sarah, Avraham purchases a Double Cave, Machpelah, as the ancestral burial plot. Almost all Biblical commentators interpret Machpelah-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” (lit. “double”) refers not to the cave itself, but to the house [...]

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 God: “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 [...]



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