Articles

By Rabbi Dovid Cohen, Administrative Rabbinic Coordinator

Q. I teach high school math, and am looking for examples where math might be useful for halachic purposes.  Any ideas?

A. The first idea that comes to mind is that if a bit of non-kosher gets mixed into kosher (or some dairy into meat), the mixture is permitted if the non-kosher is batel b’shishim.  In other words, there must be 60 times as much kosher food as non-kosher.  In calculating that ratio, one must be careful to use the volume of the foods – meaning, how much space they take up – rather than their weight.  For example, flour is less dense than corn syrup, and therefore, a pound of flour has a larger volume than a pound of corn syrup.  If the information you have is in weight, you can convert from weight to volume using something called “specific gravity”, which compares the density of each item to that of water.  Water is assigned a density of 1, flour might have a density of 0.6 (i.e., it is less dense than water), and corn syrup might have a specific gravity of 1.4 (i.e., it is denser than water).

What if kosher food was cooked in a non-kosher pot?  There, we must calculate how much metal is in the pot and assume that that much non-kosher ta’am/flavor seeped into the kosher food.  To figure out the amount of metal there is, we will need to (a) calculate the volume of the interior and exterior of the pot, using mathematical formulas based on their measurements, and then (b) subtract the interior volume from the exterior, to figure out how much space the metal itself takes up.

A more complicated calculation is used when considering kosher whisky aged in wine barrels.  Wine is batel in six times its volume (rather than 60), but the barrel walls are thick.  Calculating the volume of the barrel’s wooden walls is complicated by the fact that the barrels have a bulge in middle, which means the typical formulas for volume of a cylinder will not work.

Another case where percentages must be calculated is when a gluten-free or low-carb bread or cake (or similar item) only has a small amount of one of the five primary grains (wheat, rye, spelt, oat, and barley), and one must determine what the bracha acharonah is for that food.  In many cases, one will only be required to recite birchas hamazon or al hamichyah when eating a kezayis of grain within a few minutes (k’dei achilas pras), and the only way to determine that is to measure the amount of grain and compute the possibilities.

One last case comes up for chalav Yisroel milk produced at factories that usually work with chalav stam (i.e., non-chalav Yisroel).  In many cases, it will be (close to) impossible to kasher the milk silos, and the chalav Yisroel must remain in those silos for more than 24 hours, which means that due to the rule of “kovush”, they will absorb chalav stam flavor/ta’am from the silo.  One way to avoid this issue is that before 24 hours elapse, the chalav Yisroel milk will slowly be pumped out of the silo into a small tank and pumped right back into the silo.  How long must that pump run in order to circulate/remove all the chalav Yisroel milk?  This calculation requires a complicated formula that bears in mind the fact that after a few minutes of pumping, some of the “new” milk being circulated will be milk that was already previously pumped out.

This article first appeared in the Let’s Talk Kashrus column, Yated Ne’eman, December 20, 2024.