Aerodynamics of Egyptian Hail

Something About Sforno  — A Short Dvar Torah on the Parsha — Va’era 5769

Aerodynamics of Egyptian Hail

US Air Force test pilot, Chuck Yeager, is credited as being the first person to break the sound barrier on October 14, 1947, in the Bell X-1. Many pilots before him died trying. It took test pilots and engineers many years to understand and overcome the many issues surrounding traveling faster than the speed of sound. Some scientists thought it was impossible and aircraft would break apart from the extreme pressure and vibrations as they approached the sound barrier.

In the early days of the cold war, the one critical element lacking in the development of nuclear missiles was known as “atmospheric reentry technology”. Scientists discovered that anything they sent into space or even the upper atmosphere would burn up on reentry. As such they needed to develop proper shielding technology to protect the “payload”.

Sonic booms and atmospheric reentry burnout were technological issues that were not even dreamed off until a few decades ago.

As such, it is outright incredible that Rabbi Ovadia Sforno describes both of these phenomena in his commentary about half a millennium ago.

In Exodus 9:23-24 the Bible recounts:

“And Moses outstretched his staff to the heavens, and God gave sounds and hail, and fire descended earthward, and God rained down hail upon the land of Egypt. And there was hail and fire together in the hail, very heavy, the like of which was not in Egypt since it’s becoming a nation.”

Sforno comments on the “fire descended”:

“The flaming air descended to the earth with the force of the movement of the hail that pressed on it (the air) during its descent.”

Sforno basically and accurately described atmospheric reentry during the same period of time when Leonardo Da Vinci was playing with his water engine.

Sforno continues:

“In the force of the movement of the hail during its descent, the air was flamed and produced sound.”

He’s talking about sonic booms!

Imagine an ongoing downpour of burning hailstones accompanied by continuous sonic booms. It’s no wonder Pharaoh is frightened out of his wits and begs for the noise to stop before mentioning the hail.

The fact that Sforno was able to describe scientific concepts that we think of as exclusively from our modern era simply leaves me awestruck.

May plagues continue to hail down on our enemies, and may we be spared, and like our ancestors may we witness redemption.

Shabbat Shalom,



To the memory of Dr. Irwin Rochwarger, a beloved mentor and teacher. As an engineer who designed and built satellites for NASA, amongst many other amazing technological feats, he would have appreciated very much Sforno’s insight.

Unfamiliar Terms?

The term sonic boom is commonly used to refer to the shocks caused by the supersonic flight of an aircraft. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion. Thunder is a type of natural sonic boom, created by the rapid heating and expansion of air in a lightning discharge.[1]


When an object passes through the air, it creates a series of pressure waves in front of it and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound, and as the speed of the object increases, the waves are forced together, or compressed, because they cannot “get out of the way” of each other, eventually merging into a single shock wave at the speed of sound. This critical speed is known as Mach 1 and is approximately 1,225 kilometers per hour (761 mph) at sea level.


The cracking sound a bullwhip makes when properly wielded is, in fact, a small sonic boom. The end of the whip, known as the “cracker”, moves faster than the speed of sound, thus resulting in the sonic boom.[3] The whip was the first human invention to break the sound barrier.[citation needed]

A bullwhip tapers down from the handle section to the cracker. The cracker has much less mass than the handle section. When the whip is sharply swung, the energy is transferred down the length of the tapering whip. In accordance with the formula for kinetic energy, the velocity of the whip increases with the decrease in mass, which is how the whip reaches the speed of sound and causes a sonic boom.

Einstein’s Shmitta: Theories and Divine Calculus

Einstein’s Shmitta: Theories and Divine Calculus

by Ben-Tzion Spitz


I was running, walking, crawling, jumping, through a constantly changing landscape of desert, mountains, forests, caves, beaches, and snow covered slopes of what could only have been Israel.

“Mr. Spitz. Mr. Spitz! Please wake up.” exclaimed Prof. Komar in our Modern Physics lecture.

“I’m sorry Prof. Komar. I must have dozed off” I apologized quickly as he continued deriving yet another of Einstein’s equations on relativity.

The place was Yeshiva University’s Science Building. It must have been around 6pm on a Thursday night in the winter of 1989/90. I was in a class with only two other students, so it was uncomfortably easy to be spotted doing anything else, especially my favorite classroom effort of catching up on some sleep.

Prof. Komar had a very distinctive personality and appearance as anyone who was in YU at that time might remember. He always wore black; black shoes, black pants and a black button down shirt. What was even more distinctive was that though at the time he must have been in his fifties, he had very thick snow white hair on his head that stood straight up and a neatly trimmed white beard that framed his pale face. The contrast of the constant black garments versus the sharp almost albino features made Prof. Komar memorable even to those that weren’t in his class.

One of Prof. Komar’s claims to fame was that he was a student of Einstein’s during his tenure in Princeton University. My classmates and I (though I was probably the leader in this effort) would often question Prof. Komar about Einstein and would elicit stories about him to pass the time and distract him from going through more equations. I think Prof. Komar also enjoyed reminiscing. To this day I proudly proclaim that I have good ‘Yichus’ (pedigree) when it comes to my physics education (I can’t claim much else), as I am a student of a student of Einstein.

Einstein is of course renown for thinking of, popularizing and formalizing the “Theory of Relativity” and the most famous equation of conservation of mass and energy: E=mc2.

I believe though that these principles were well known to Chazal (the Rabbis) millennia before Einstein and that they form a founding basis for many Biblical and Talmudic accounts. Furthermore, the Rabbis added a further dimension (which mathematicians have theorized mathematically, but have not named). Besides the spatial and temporal dimensions, the Rabbis always considered the spiritual dimension.

Spatial & Temporal Distortion

The first place I came across the concept that spirituality or holiness has an effect on physical reality was in an article by Stephen Greenman in the book “Encounter: Essays on Torah and modern life” (a companion volume to Challenge), edited by H. Chaim Schimmel and Aryeh Carmell, Feldheim Publishers 1989. This was a perception altering article for me.

One of the effects that the equations of relativity predict is that the closer one gets to the speed of light the shorter dimensions become to an observer. Just to illustrate: if Harry Potter was flying on a broomstick and he was approaching the speed of light, his broomstick would appear shorter (he’d get thin too and would probably not survive flying at such speeds – but this didn’t trouble Einstein – so I won’t worry either).

Taken to its logical and mathematical extreme, anything traveling at the speed of light would be reduced to a dimension of zero. For those of you thinking that this would be a fantastic weight-loss program, there is unfortunately a converse but parallel effect. The closer one gets to the speed of light, the heavier one gets and at the speed of light ones weight would become mathematically infinite. A better known angle to these equations is that the faster one moves the slower time passes, and at the speed of light, time would stand still.

I used to think to that if I walked faster I would age slower, but this only works at velocities approaching the speed of light. Needless to say, these laws have little practical day-to-day relevance and Sir Isaac Newton’s more simplistic view of the universe still serves us quite well centuries later.

Rabbi Greenman, however suggests in his article a novel concept and the consideration of another factor or dimension – that of holiness. He demonstrates in his article, based on a discrepancy in the measurements of articles in the Temple, that there was a relativity effect occurring. The closer one got to the epicenter of the Holy of Holies (in this case the spiritual equivalent of the speed of light) the shorter dimensions in the Temple become. His proof is that the same utensils that are closer to the Holy of Holies are indeed recorded as being shorter. The jackpot of his proof is that in the Holy of Holies itself, there is a tradition that the Ark took up no space whatsoever – in exact agreement with his interpretation of Einstein’s equations.

From this vantage point we can then better understand multiple other cases of spatial distortion throughout the Bible and the Talmud. While there are traditionally considered miracles, we can now better understand the method to these ‘miracles’.

Commentators claim that when our Patriarch Jacob went to sleep in the town of Bet-El the entire land of Israel compressed itself and his body encompassed an area that was previously thousands of square miles. While on the surface, this may not seem to make any sense, or may be attributed to some other underlying symbolic reason, according to what we might call the “Spiritual Laws of Relativity”, it makes perfect sense.

Jacob had his first divine revelation; he was at a heightened state of prophecy and spirituality. It is therefore entirely logical that a relativistic effective such as shorted spatial distances should occur.

I’m sure that the reader, armed now with this viewpoint can identify multiple other ‘miracles’ that are recounted by Rabbinic commentaries, that can link the relativistic effect to the recipients spiritual state.

“Dune”, the best-selling science-fiction classic by Frank Herbert, has as one of its central themes the search for the “Kvisatz Haderach”. According to Herbert the “Kvitsatz Haderach” is the man that will be able, with his mind, to jump through and bridge the dimensions of time and space and therefore enable interstellar travel. Rashi uses almost the exact same phrase when explaining what happens to Jacob on his journey to Haran where he transverses a mutli-day journey in the space of a single day.

This is yet another example of the intertwining of the ‘miraculous’ with the “Spiritual Laws of Relativity” and how these concepts have already entered popular culture to an extent.

To Einstein and mathematicians, time was just another dimension; the fourth to be precise. We have shown so far that there is a relativistic connection between space, time and holiness. This connection is not more apparent than in the land of Israel.

Israel as a Holiness Gauge

Countless Biblical, Talmudic and Rabbinic sources speak about the holiness of the land of Israel. This holiness, besides for the relativistic effects we discussed above, is demonstrated by its relationship to the inhabitants. The Bible speaks about the land of Israel having to “kick out” the previous Canaanite inhabitants because of their sins and immorality. The land of Israel is meant for the children of Israel because of their shared holiness. However, when the children of Israel sin overmuch, the land can’t “handle” them either, and the result is exile. Some commentators discuss how the commandments cannot be completely fulfilled outside of the land of Israel and that Israel is the only place where a Jew can be complete. On the flip side there is a higher level of spiritual accountability.

In Beit Hannassi (The President’s Residence) in Jerusalem, one can see the original correspondence between Ben Gurion and Einstein when they requested he serve as the first President of the State of Israel. Einstein declined, but I wonder if one of the reasons might have been out of concern for the Spiritual Relativistic Laws that are most pertinent in Israel and the responsibility they engender.

Perhaps the clearest connection between holiness and the land of Israel are the laws of Shmitta (the agricultural sabbatical year).

The Bible commands the children of Israel a number of times to let the land lie fallow on the seventh year. Besides being good agricultural practice in terms of letting the soil regain lost nutrients and providing for better productivity, there are also a host of social and economic benefits for the broader community.

An interesting facet of Shmitta is that the year and its resulting produce are considered ‘Holy’, comparable to the holiness of the seventh day of the week. The spiritual accounting that occurs with Shmitta and its correlation between the people of Israel and the land of Israel seems quite stringent. The prophets themselves berate the people when they don’t adhere to the precepts of Shmitta and describe exile from the land as its punishment. The punishment is calculated with mathematical precision, where the exile apparently lasts for as many years as the Shmitta went unheeded.

While not keeping Shmitta can lead to a mathematically precise divine retribution, adherence to Shmitta, we are told in the Bible itself, will lead to a clear yet ‘miraculous’ multiplication of benefit. A farmer who refrains from working the land for one year, but is concerned about his income, is promised that his produce will be guaranteed, for not one, not two, but for three years.

E=mc2 as a formula for reward and punishment

In Einstein’s formulation, E stands for Energy, m stands for Mass and c is the speed of light, which is a constant.

One of the realizations that came out from this formula which is what helped usher in the nuclear age is that the conversion of Mass to Energy is an incredibly powerful phenomenon.The most powerful energy is when mass is completely converted into energy, such as in an antimatter reaction (this is real stuff, though Star Trek popularized it). In an antimatter reaction there is complete annihilation of the matter and complete conversion to energy. Multiplying mass by c2 leads to a lot of energy. Just for comparison, let’s look at how much energy is produced by these different processes:

Burning Petrol:9.1 million joules/kg

Nuclear fission of Uranium:82 million million joules/kg

Antimatter reaction:90,000 million million joules/kg

The same mass can give very different energy levels depending on the type of mass and the efficiency of the conversion process.

If we attempt to use the E=mc2 formulation in the spiritual realm, we could propose as follows:

c would stand for closeness to God, doing what’s right, or being Holy. In this realm approaching (the speed of) light would be parallel to approaching God (except that in our formula it would not be a constant.

m would stand for the material, the resources, the intentions and the effort that go into any particular activity and parallels the mass that is invested into any process.

Finally, E would stand for the results. It is not only the Energy that is created as in the physical world, but rather all of the positive (or negative) effects that occur in this world and the next. The point is that the reward (or punishment) is a geometric function (multiplication of a square) and not a linear one.

Einstein once explained relativity as follows: “Put your hand on a stove for a minute and it seems like an hour. Sit with that special girl for an hour and it seems like a minute. That’s relativity.”

Our Rabbis understood relativity and geometric reward quite well, when they stated millennia ago: “Greater is one hour of repentance and good deeds in this world, than the entire life of the World to Come; and greater is one hour of spiritual bliss in the World to Come than the entire life of this world.”


The Bible, Talmud and later Rabbis all understood the concept that we modernly call ‘relativity’. Einstein, the man who popularized it, applied it and his famous equations to a strictly physical world. We have seen ample evidence that these can be applied in the spiritual world, where one strives for holiness and closeness to God. Shmitta, the original agricultural Sabbatical year in Israel is a particularly concrete manifestation of the divine operating via the physical. The commandments in general and this one in particular call for our attention and understanding and to appreciate them beyond the obvious aspects of their performance. A scientific view of the Torah can only enhance a deeper connection to its precepts.

Einstein himself would have participated in the effort. At a symposium on the topic of Science and Religion, he succinctly summarized his philosophy: “Science without religion is lame, religion without science is blind.”

The Diamond in the Cesspool

Something About Sforno  — A Short Dvar Torah on the Parsha — Shmot 5769

The Diamond in the Cesspool

The Egypt of our ancestors was apparently one of great moral depravity. Egyptian culture was submerged in a superficial, materialistic, hedonistic, idol worshipping, incestuous reality. A by-product of such a society was many unwanted births and a cheapening of life.

In the beginning of the Book of Exodus, the Children of Israel have evolved from honored guests and royal protégés, to feared enemies and eventually downtrodden slaves. The low point of this progression is perhaps the draconian edict to kill all newborn Jewish boys.

Into this environment Moses is born. Fearing for his life, the mother of Moses takes the desperate measure of placing the three-month old into a basket to float on the river. Moses’ sister, not without hope, keeps an eye on the basket (Exodus 2).

Pharaoh’s daughter spots Moses’ basket while bathing in the Nile. She investigates and is surprised to find baby Moses within.

At this point Rabbi Ovadia Sforno asks as to why Pharaoh’s daughter would claim Moses. Sforno explains that it was apparently common practice for Egyptians to discard unwanted children into the river, and there would be a plethora of abandoned children to be claimed.

Sforno answers that the “goodness” of Moses was “shinning” and was clearly visible for anyone to see. Pharaoh’s daughter said to herself: “This is not some bastard or unwanted child. This is a beautiful Israelite child. He is so stunningly gorgeous that I must claim him for myself.”

Sforno continues to explain that Moses was visibly outstanding because of the “ingredients” put into him. Following is a translation of Sforno’s comment regarding the reaction to the birth of Moses by his mother, that “he was good”:

“She noted that he was more beautiful than normal, and thought that this was for an intended purpose from his Creator, for the beauty of the form indicates the quality of the ingredients and the complete power of the Designer.”

As we all know, Moses was indeed intended for supreme greatness, even amidst the decadence and immorality of Egyptian culture.

May we all transcend the negative environments around us, and like Moses, take the great ingredients that are a part of us – and shine.

Shabbat Shalom,



To the recovery of 2nd Lieutenant Aharon Karov of the IDF Paratrooper Brigade. Aharon is from the community of Karnei Shomron. He left to Gaza the morning after his wedding to lead his soldiers. He was critically injured from a blast within a booby trapped home in Northern Gaza. Please pray for him – Aharon Yehoshua ben Chaya Shoshana. May our soldiers be safe, may the wounded recover and may the mourners be comforted.

Unfamiliar terms?

Drawn from Wikipedia, the free encyclopedia

The Nile is a major north-flowing river in Africa, generally regarded as the longest river in the world.[1]

The northern section of the river flows almost entirely through desert, from Sudan into Egypt, a country whose civilization has depended on the river since ancient times. Most of the population of Egypt and all of its cities, with the exception of those near the coast, lie along those parts of the Nile valley north of Aswan; and nearly all the cultural and historical sites of Ancient Egypt are found along the banks of the river. The Nile ends in a large delta that empties into the Mediterranean Sea.

The Nile (iteru in Ancient Egyptian) was the lifeline of the ancient Egyptian civilization, with most of the population and all of the cities of Egypt resting along those parts of the Nile valley lying north of Aswan. The Nile has been the lifeline for Egyptian culture since the Stone Age. Climate change, or perhaps overgrazing, desiccated the pastoral lands of Egypt to form the Sahara desert, possibly as long ago as 8000 BC, and the inhabitants then presumably migrated to the river, where they developed a settled agricultural economy and a more centralized society.

Sustenance played a crucial role in the founding of Egyptian civilization. The Nile is an unending source of sustenance. The Nile made the land surrounding it extremely fertile when it flooded or was inundated annually. The Egyptians were able to cultivate wheat and crops around the Nile, providing food for the general population. Also, the Nile’s water attracted game such as water buffalo; and after the Persians introduced them in the 7th century BC, camels. These animals could be killed for meat, or could be captured, tamed and used for ploughing — or in the camels’ case, travelling. Water was vital to both people and livestock. The Nile was also a convenient and efficient way of transportation for people and goods.

The structure of Egypt’s society made it one of the most stable in history. In fact, it might easily have surpassed many modern societies. This stability was an immediate result of the Nile’s fertility. The Nile also provided flax for trade. Wheat was also traded, a crucial crop in the Middle East where famine was very common. This trading system secured the diplomatic relationship Egypt had with other countries, and often contributed to Egypt’s economic stability. Also, the Nile provided the resources such as food or money, to quickly and efficiently raise an army for offensive or defensive roles.

The Nile played a major role in politics and social life. The pharaoh would supposedly flood the Nile, and in return for the life-giving water and crops, the peasants would cultivate the fertile soil and send a portion of the resources they had reaped to the Pharaoh. He or she would in turn use it for the well-being of Egyptian society.

The Nile was a source of spiritual dimension. The Nile was so significant to the lifestyle of the Egyptians, that they created a god dedicated to the welfare of the Nile’s annual inundation. The god’s name was Hapy, and both he and the pharaoh were thought to control the flooding of the Nile River. Also, the Nile was considered as a causeway from life to death and afterlife. The east was thought of as a place of birth and growth, and the west was considered the place of death, as the god Ra, the sun, underwent birth, death, and resurrection each time he crossed the sky. Thus, all tombs were located west of the Nile, because the Egyptians believed that in order to enter the afterlife, they must be buried on the side that symbolized death.

The Greek historian, Herodotus, wrote that ‘Egypt was the gift of the Nile’, and in a sense that is correct. Without the waters of the Nile River for irrigation, Egyptian civilization would probably have been short-lived. The Nile provided the elements that make a vigorous civilization, and contributed much to its lasting three thousand years.

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