This week, we will set aside our discussion of the weekly portion. Instead, we continue last week’s lesson, “In and Within”, in which we presented our theory of “Halachic Interpolation”. We posited that the Torah contains a finite set of laws along with rules for interpolating between explicitly defined cases. The halachic ruling in any given case is determined by interpolating between the laws. This, we stated, enables a finite Torah to cope with an infinite world. This week, instead of looking inside, we will be looking outside.
Last week, we took a deep dive into the concept of interpolation by considering the calculations required to estimate the colour of a new pixel that lies in between a group of pixels in an image. This week, we ask a similar, and yet different, question: Is it possible to approximate or to guess the colour of a pixel that lies outside of an image? This is referred to as “extrapolation” – the estimation of what comes next. Extrapolation is considerably more tricky than interpolation. Consider a series of numbers: 1,2,3,4,x,6. It seems pretty clear that each member of the series is one greater than the previous member, such that “x”, the missing number between 4 and 6, is the number 5. Now consider a similar series of numbers: 1,2,3,4,x. What number comes next in the series after 4? Most people would guess that the next number would be 5. Their guess is based on the assumption that the series (1,2,3,4) is generated by the same rule used to generate the first series. Mathematically speaking, they are assuming that the rule used to generate both series is fn = n. However, it turns out that the series (1,2,3,4) can also be created using another rule: fn = 3.96n4-39.58n3+138.54n2-196.92n+95. Using this function, the next number in the series (1,2,3,4) would not be 5, but, rather, 100. This demonstrates the greatest problem with extrapolation, that it is based on an implicit assumption that observed trends will continue into the future. As trends change, extrapolation becomes less and less accurate.
Now let’s consider a real-life example of the pitfalls of extrapolation. Imagine you take a picture of a person standing on a sandy beach. The picture is so beautiful that you decide to take another picture but this time you want to get more of the background into the shot. So you zoom out and you hit the shutter button. It would be a good assumption that the second picture will look very much like the first picture except that it will include more of the beach. But what if on that very same sandy beach, just outside the first picture, lurks a great white shark? There would be no way of knowing about the existence of the shark merely by looking at the original picture. Our implicit assumption that observed trend – sandy beaches – continues does not entertain the possibility of a shark, great white or other.
With this background in hand, we can now present another hypothesis: While the Torah makes great use of interpolation, it absolutely scorns extrapolation, precisely because of its built-in inaccuracy. This can help explain the existence of certain “absurdities” in the halachic corpus. I am referring to cases that could never occur in a million lifetimes, cases that are all too often brandished to “demonstrate” the silliness of orthodox Judaism. Here is one example: The Talmud in Tractate Sukkah [23a] discusses the necessary structure of the walls of a sukkah in order for it to be considered fit for use (kosher). After discussing the use of standard materials like wood and trees, the Talmud segues to a more prosaic material, animals: “If he used an animal as a wall of the Sukkah, Rabbi Meir declares it invalid and Rabbi Judah declares it valid… What is the reason of Rabbi Meir? – Abaye replied, Lest it die. Rabbi Zera replied, Lest it escape. Concerning an elephant securely bound, all agree [that the Sukkah is valid], since even though it might die, there is still ten [handbreadths height] in its carcass. Regarding what do they dispute? Regarding an elephant which is not bound, all agree [that the Sukkah is invalid]; regarding what do they dispute? Regarding an[ordinary] animal which is bound: According to him who says, Lest it die, we fear [for that[ according to him who says, Lest it escape, we have no fear… But is there not an open space between [the animal’s legs? [It refers to] where he filled it in with branches of palms and bay-trees. But might it not lie down? – [It refers to] where it was tied with cords from above. And according to him who says, Lest it die, is it not tied with cords from above? – It may occur that it is made to stand within three [handbreadths] of the covering but when it dies, it shrinks, and this might not enter his mind.” Excuse me? Using an elephant? For the wall of a sukkah? An elephant that is tied up with rope in order to prevent it from running away? An elephant that is polite enough to allow a person to fill the space between its legs with “branches of palms”? An elephant that is hung from above to prevent it from lying down? I personally would be less concerned about the elephant lying down than the elephant leaving, how can I put this nicely, a malodorous offering that would make sukkah-dwelling impossible. And yet, this case features prominently in the Talmud. I suggest that the reason that the Talmud discusses such a case is precisely because it is completely detached from reality. The existence of such an extreme case in the halachic domain precludes the use of extrapolation. It stretches the set of well-defined halachic cases, such that the ruling for any real-life example of sukkah walls – say, carbon fibre curtains that automatically descend when a sensor detects that a person has entered the sukkah – can be calculated via interpolation using the elephant case and some other more down-to-earth cases.
The Torah’s aversion to extrapolation is not limited to halachic issues. I suggest that it lies at the very heart of Jewish Philosophy. The Mishnah in Tractate Chagigah [2:1] teaches “Whoever speculates upon four things, it would have been better had he not come into the world: what is above, what is beneath, what came before and what came after.” Our Sages in the Talmud explain that the term “what came before and what came after” is referring to “before” and “after” our universe. We are instructed not to ask questions like “What existed before G-d created our universe?” and “What will exist if our universe ever comes to an end?” These questions have piqued the minds of philosophers since time immemorial and Jews are warned to leave these questions to those philosophers. I suggest that the reason has to do with extrapolation: It is axiomatic that G-d is infinite. His vastness is incomprehensible. We discern G-d only through His actions. Recall the First Gulf War in 1991, where the Iraqis fired 39 Scud-B missiles at the heart of Israel and only two Israelis died as a direct result. We did not physically see the “Hand of G-d” reaching out to stop the Iraqi missiles from impacting their targets. We saw the “before”, we saw the “after”, and we interpolated the existence of G-d’s beneficence protecting us from our enemies. As a result, we can call G-d “kind”. And if G-d is kind, then it behoves us to be kind, as well. Look where interpolation has taken us: We can recognize G-d, we thank Him for His kindness, and we have become better people, to boot. On the other hand, in the “before” and “after” – outside the confines of our existence – we have no way of relating to G-d. We have no way of recognizing Him. We can draw no conclusions. We have nothing to imitate. Yes, we can make certain assumptions based on our experience from this world, but as we are extrapolating into completely uncharted territory, our estimates are potentially hugely inaccurate. We have nothing to gain from this exercise and everything to lose.
To paraphrase Dr Seuss’s “Inside, Outside, Upside Down”, the Torah adjures us to look on the inside, to stay away from the outside, and by doing so, to stay right side up.
Ari Sacher, Moreshet, 5780
Please daven for a Refu’a Shelema for Yechiel ben Shprintza, David ben Chaya, Shachar Yehuda ben Irit, and Tehila bat Adi.
 For the advanced reader: This hypothesis can help us understand the extensive use in the Talmud of the concept of “mechtza al mechtza”, literally “half and half”. “Mechtza al mechtza” is concerned with the halachic ruling if two distances, weights, volumes, or amounts are exactly the same. Practically speaking, this will never occur. Two measurements will never be exactly the same, especially when measurement error is taken into account. Why does the Talmud even mention these cases? Our answer would be that these cases, while physically impossible, expand the halachic domain so that real-world cases can be analysed and determined via interpolation and not extrapolation.
 One suffocated when he forgot to take the plug out of his gas mask and the other was killed by an errant Patriot anti-missile missile.
 See the Talmud in Tractate Sotah [14a] where it equates [Devarim 13:5] “walking after G-d” to imitating Him.