‘Rabbits and Wolves’ Parashat Ekev 5778

I still remember learning about it. I was in Grade 7. The teacher was Mr. Tatel, who became Rabbi Tatel, who eventually became an aerospace engineer, a career trajectory with which I can identify. Mr. Tatel approached Torah from a scientific background and he was always showing us how the Torah was firmly rooted in science. For instance, he once taught us that when the Torah lists the four animals that either have a split hoof or chew their cud, it lists every known species in the world that shares this trait[1]. On this particular day, Mr. Tatel proudly told us that the Torah was very concerned about ecology. This was the mid-seventies and ecology was a popular topic. We were all duly excited and proud to learn that our Torah was eternally scientifically relevant, not to mention progressive. But what happens when we prove that the Torah reflects the latest scientific theory and then that theory is eclipsed by a newer and better theory?

Mr. Tatel’s source hails from Parashat Ekev. One week before his death, Moshe tells Am Yisrael that they will soon be waging war to capture the Land of Canaan and that they will be the beneficiaries of Divine assistance. He tells them that they should know that their conquest would take time and that Rome was not built in one day. He even tells them the reason for the delay [Devarim 7:22]: “Hashem will drive out those nations from before you, little by little. You will not be able to destroy them quickly, lest the beasts of the field outnumber you”. The Canaanites were the natural predators of the “beasts of the field”. If the Canaanites were to be defeated in one fell swoop, the population of the “beasts of the field” would quickly climb, making it very dangerous to walk the streets at night. Moshe tells Am Yisrael that their rout of the Canaanites would be Divinely monitored and controlled in order to prevent such a situation.

Prima facie, the Torah is indeed utilizing modern ecological concepts. Nevertheless, a number of questions require us to proceed with caution:

• Rashi comments, “But is it not so that if [Am Yisrael] obey the will of the Omnipresent, they need not fear the beasts? As it is said [Job 5:23], ‘The beasts of the field made peace with you’. [The answer is that] it was revealed before [Moshe] that they would sin in the future [and so would not merit Divine assistance].” Were Am Yisrael not to sin, the beasts of the field would not have become predators. But wait a minute – Moshe is describing a situation in which Am Yisrael, with Divine support, are successfully liberating the Land of Israel from the Canaanites. This does not sound like a description of a nation steeped in sin. Further, doesn’t the Talmud in Tractate Berachot [33b] teach us, “Everything is in the Hands of Heaven other than fear of Heaven”? Man alone decides when and when not to obey Hashem. How could Moshe predict that they would sin?[2]
• Moshe is actually reiterating a promise that Hashem made forty years earlier [Shemot 23:29-30]: “I will not drive [the Canaanites] away from before you in one year, lest the land become desolate and the beasts of the field outnumber you. I will drive them out from before you little by little, until you have increased and can occupy the land.” What information is Moshe adding in Parashat Ekev?
• Moshe describes the future defeat of the Canaanites with fuzzy terms like “quickly” and “little by little”. Hashem, on the other hand, tells them that the war will take at least one year. Why doesn’t Moshe use concrete terms to describe the timeline?

To address these questions we will dive into the waters of the “Predator-Prey Model” in which multiple species compete for limited resources[3]. Imagine a forest in which two species of animals live: rabbits and wolves. The rabbits eat the vegetation that grows in the forest while the wolves eat the rabbits. We refer to the wolves as “predators” and to the rabbits as “prey”.  Let’s look at the population of the wolves and the rabbits. In the absence of natural predators, the rabbit population will grow until the food resources are depleted and the rabbits begin to die of hunger. Eventually the number of rabbits drops to where the population can be sustained by the existing vegetation. We would expect the population of rabbits to rise and fall cyclically. Now we introduce wolves into the equation. The wolves prey on the rabbits, causing the wolf population to rise and the rabbit population to fall. These trends will continue until there are not enough rabbits to feed the growing wolf pack and the trends reverse: the population of wolves will begin to fall and the population of rabbits will begin to climb again. Again, we would expect to see some kind of cyclic behaviour.

Scientists have modelled the population dynamics described above in many ways. The most famous predator-prey model is the “Lotka-Volterra Model”, named after Alfred James Lotka and Vito Volterra, two scientists who independently came up with the same set of equations. The Lotka-Volterra model predicts three types of long-term behaviour: [1] the populations of both the predators and the prey oscillate cyclically, [2] both populations settle at constant numbers, or [3] both populations exhibit what is known as “chaotic behaviour”, fluctuating wildly and unpredictably. The long-term behaviour is determined by the values of four parameters built into the model. These parameters include the natural growth rate of the rabbits, the natural death rate of the wolves, and the efficiency of the rabbits in avoiding the wolves.  The Lotka-Volterra model is “non-linear”, meaning that the effect of even a small change in one of these parameters can often be counterintuitive. For example, imagine that the wolves and the rabbits have reached some kind of steady-state equilibrium in which the forest contains, say, 5012 rabbits and 146 wolves living together in peaceful harmony, other than the occasional rabbit dinner. If the rabbits become slightly better at avoiding the wolves, one (intuitive) result might be a slight increase in the number of rabbits while an equally possible (but far less intuitive) result could be the onset of chaotic fluctuations of both populations. Both results are mathematically possible.

Now here is the thing: nobody knows the precise value of the “Wolf Avoidance Efficiency Coefficient”. It could be 17, it could be 0.1234, it could even be e^iπ. We can estimate it but we can never know it with high precision. Only Hashem can know its value with perfect precision and because only He has access to the data, only He can make infinitesimal adjustments, if necessary, to ensure that the number of predators remains low and that Am Yisrael remain safe, unless they deserve otherwise.

Two weeks ago, we discussed the theory of the Netziv of Volozhn that the years Am Yisrael spent wandering in the desert were intended to wean them off overt miracles and to acclimatize them to the recognition of Hashem working through nature. Hence, Hashem’s vow of protection from wild animals is qualitatively different from Moshe’s vow. Hashem made His vow at a time when Am Yisrael still required shock and awe and Hashem would be overtly running the show. The words of the text show this clearly: “I will drive them out from before you…” Because Hashem is leading the charge, a clear and predefined timeline is possible. Things are different in Parashat Ekev, where Hashem is cloaking Himself in nature and in imprecision. Hence, Moshe tells Am Yisrael, “You will not be able to destroy them quickly…” You will be doing the fighting. It will take as long it takes. But don’t worry, Hashem will be keeping His eye on things, making sure that they don’t get out of hand.

It is critical that we internalize that Hashem’s control of our world is absolute, whether via twentieth century ecology or via twenty-first century chaos theory. Science progresses but the Torah remains eternally relevant.

ere’s

Shabbat Shalom,

Ari Sacher, Moreshet, 5778

Please daven for a Refu’a Shelema for Yechiel ben Shprintza, Tzvi ben Shoshana, and Dov ben Chana.

[1] This claim may not be fully accurate. See http://www.zootorah.com/assets/media/HyraxLayout.pdf and http://www.zootorah.com/books/the-camel-the-hare-and-the-hyrax at length.

[2] See Rambam Hilchot Teshuva [6:5] and the gloss of the Ra’avad.

[3] Hey, where did everybody go?