Dynamic Equilibrium (Parashat Pinchas 5778)

Balaam encourages the Midianite women to prostitute themselves in a concerted effort to turn Jewish men to Midianite Paganism. The Midianite ploy is extremely successful and in order to staunch the tide of converts, Hashem strikes Am Yisrael with a plague in which 24,000 die. After the plague, Hashem commands Moshe to count the nation in order to assess the damage[1]. After the census data is collected, the total number of Am Yisrael [Bemidbar 26:51] comes to 601,730 men between the ages of twenty and sixty.

601,730? Wait a minute – that number sounds familiar! Indeed it should. Only a few weeks ago, we read Parashat Bemidbar and we can still remember that most of that parasha pertained to a census. After the census data is collected, the total number of Am Yisrael [Bemidbar 1:46] is 603,550 men between the ages of twenty and sixty. The two censuses differ by only 1820 people, a difference of 0.3%. It sounds almost too close to be true. The closeness of the two results is even more striking if we note that while the two censuses are separated by only seven parshiot (less than two months of Torah readings), they are chronologically separated by thirty-eight years. Parashat Bemidbar takes place in the second year after the exodus and Parashat Pinchas occurs in the fortieth year after the exodus, just a few months before Am Yisrael enter the Land of Israel. Yet for some reason, the population difference between the two censuses is statistically insignificant. This is entirely unexpected. In the two hundred and ten years of the Egyptian exile, the population of Am Yisrael ballooned from seventy to 600,000. Had that growth rate continued over forty years in the Sinai Desert, we would have expected the population to nearly quadruple, but for some reason it hit a brick wall. Granted the Talmud in Tractate Sotah [11a] teaches that the exceptionally high birth rate in Egypt was miraculous, but even a natural birth rate over forty years should raise the population by a significant amount.

One way to deal with this paradox is by noting that during their forty years of wandering in the Sinai Desert, Am Yisrael suffer through a number of deadly plagues. While the Torah reveals the number of the dead in most of the plagues – and in no plague did more than 100,000 people die – two plagues do not divulge the number of dead: the Plague of the Mit’onenim [Bemidbar 11:1] and the Plague of the Venomous Snakes [Bemidbar 26:6]. One could hypothesize that hundreds of thousands or even millions of people died in these plagues, causing the population to plunge. Alternatively, the Abarbanel suggests that the adverse conditions in the desert helped keep the population stable.

We muddy the waters further if we note the populations of each of the individual twelve tribes in both of the censuses. While the sum total of the populations of the twelve tribes remained nearly constant, the populations of the individual tribes did not.  For instance, the population of the tribe of Shimon plummeted by more than half, from 59,300[2] to 22,000. Some of this depreciation can be attributed to the Midianite Plague, as Prince of the Tribe of Shimon was an active participant in the Midianite prostitution ring. On the other hand, the Tribe of Menashe experienced explosive population growth, growing from 32,200 to 52,700. This growth is more difficult to explain, as is the growth of the Tribes of Binyamin, Yissachar, and Asher. Conversely, the decreases in the populations of the Tribes of Ephraim, Naftali, and Gad are equally puzzling.

Not only do the populations of the tribes change, so do the names of the people who are being counted. The census in our parasha mentions a person from the Tribe of Yissachar by the name of “Yashuv” [Bemidbar 26:24]. Rashi comments that “Yashuv” is the same person as “Yov” [Bereishit 46:13], who went down to Egypt with Yaakov. Similarly, the names of two of Benjamin’s sons are changed (Mupim and Echi) while two of Benjamin’s children are listed as his grandchildren (Ard and Naaman). It seems that while everything was changing, everything somehow managed to remain the same.

An ordinary chemical process can shine some light on our paradox. Imagine a bowl of clear water. Imagine, now, that someone takes an eyedropper and adds two drops of green food colouring to the water. After a few minutes, the entire bowl of water acquires a uniform light-green colour. This process is called “diffusion”, in which particles move of from an area of high concentration to an area of low concentration. When all of the particles are equally dispersed and no further observable change occurs, the solution has reached “equilibrium”. While things in equilibrium seem to have slowed down to a standstill, this is far from the case. When seen under a microscope, molecules of food colouring are zipping along randomly at high speed[3]. After the solution has reached equilibrium, the concentration of food colouring in every location is uniform but the individual molecules of food colouring at any given location are constantly changing. At every location in the bowl, molecules come and molecules go but the sum-total of food colour molecules remains essentially unchanged[4]. This type of equilibrium is called “Dynamic Equilibrium”. In dynamic equilibrium, everything is changing but everything somehow manages to remain the same.

Looking back at the two censuses, it could be argued that the population of Am Yisrael reaches some sort of dynamic equilibrium at about 600,000. The Abarbanel quoted above suggests that the conditions in the Sinai Desert should have caused the population of Am Yisrael to decrease. Yet for some reason Hashem chose to keep the population at a cosy 600,000. While the Abarbanel chose to keep this concept vague, Rav Schneur Zalman of Liadi, writing in the 37th chapter of “Tanya”, is as clear as can be: “The community of Israel comprising 600,000 particular souls is the source of life for the world as a whole… Each of them contains and is related to the vitality of one part of 600,000 of the totality of the world”. The censuses in the Torah do not merely report numbers of people that lived 3500 years ago. The censuses contain an eternal message: the core, the essence, of Am Yisrael is somehow intricately connected with the number 600,000, and more importantly, this core contains the roots – the archetypes – for every single Jew who will ever live. Jews are born and Jews die, but Am Yisrael as a nation remains unchanged.

Last week, Rav Chaim Navon wrote a particularly poignant column in “Makor Rishon[5]. He voiced his concern over today’s modern Orthodox youth. While my generation took on a nuanced approach to merging this world with the next world, our children are living a life of what Rav Navon referred to as “Fusion” in that they want both worlds simultaneously: “Our children learn more Torah than we did but they consume more alcohol… Young women pray like our matriarch, Sarah, but dress in a way that would give her a heart-attack.” He was apprehensive that the next generation would not be up to the task of replacing the current one. And yet, Rav Navon concludes his column on a hopeful note: “I am uneasy and yet I believe in you. Because you are virtuous and you possess a good soul. For on the day when our time will come to pass the torch on to you, in the eternal relay race of our nation, you will see the hand reaching out to you and you will know that there is no one else to carry the torch. You will not let it drop.” Our children are not mirror images of ourselves just as we are not mirror images of our parents. They, like we, and like our parents before us, possess a “good soul”, one of the original 600,000. Am Yisrael is always in dynamic equilibrium. On a personal level, we learn, and we adapt, and we flourish, but on a national level, our core remains stable and unyielding, just as it has for the last 3500 years.


Shabbat Shalom,

Ari Sacher, Moreshet, 5778

Please daven for a Refu’a Shelema for Yechiel ben Shprintza and Tzvi ben Shoshana

[1] See Rashi on Bemidbar [26:2].

[2] See our shiur on Parashat Bemidbar 5761 that discusses the possible rounding of census numbers.

[3] This is known as “Brownian Motion”.

[4] In fact, it is statistically possible (though highly improbable) for all of the food colouring molecules to return to the original drops from whence they came.

[5]Makor Rishon” is an Israeli weekly newspaper read predominantly by the religiously orthodox and politically conservative.

About the Author
Ari Sacher is a Rocket Scientist, and has worked in the design and development of missiles for over thirty years. He has briefed hundreds of US Congressmen on Israeli Missile Defense, including three briefings on Capitol Hill at the invitation of House Majority Leader. Ari is a highly requested speaker, enabling even the layman to understand the "rocket science". Ari has also been a scholar in residence in numerous synagogues in the USA, Canada, UK, South Africa, and Australia. He is a riveting speaker, using his experience in the defense industry to explain the Torah in a way that is simultaneously enlightening and entertaining. Ari came on aliya from the USA in 1982. He studied at Yeshivat Kerem B’Yavneh, and then spent seven years studying at the Technion. Since 2000 he has published a weekly parasha shiur that is read around the world. Ari lives in Moreshet in the Western Galil along with his wife and eight children.
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