The Cake Problem
Jun 27: Tuesday of the Twelfth Week in Ordinary Time
Suppose you have a cupcake.1 You want your two kids to share it between them, but only one of them is old enough to handle the knife? Had do you make sure the bigger one shares fairly?
Easy—you tell the older one to cut it however they like, which means they’ll probably want to cut a huge piece for themselves and leave a tiny bit for the young sibling. Until you tell them the younger one gets to choose which piece they get.
Now they older, knife-wielding sibling has every incentive to cut the cupcake as fairly and evenly as possible. Now both kids are happy—the younger gets the piece they picked, and the older didn’t care which piece they got, since they chose the equal division.
In Game Theory, this is called the Cake Cutting Problem. It was first devised by mathematician Hugo Steinhaus during World War II, and is still a matter of intense research in several related fields.
But it turns out, the earliest example of the Cake Cutting Problem we know of is today’s first reading…
Reading 1
Gn 13:2, 5-18
Abram was very rich in livestock, silver, and gold.
Lot, who went with Abram, also had flocks and herds and tents, so that the land could not support them if they stayed together; their possessions were so great that they could not dwell together. There were quarrels between the herdsmen of Abram's livestock and those of Lot's. (At this time the Canaanites and the Perizzites were occupying the land.)
So Abram said to Lot: "Let there be no strife between you and me, or between your herdsmen and mine, for we are kinsmen. Is not the whole land at your disposal? Please separate from me. If you prefer the left, I will go to the right; if you prefer the right, I will go to the left."
Lot looked about and saw how well watered the whole Jordan Plain was as far as Zoar, like the LORD's own garden, or like Egypt. (This was before the LORD had destroyed Sodom and Gomorrah.) Lot, therefore, chose for himself the whole Jordan Plain and set out eastward. Thus they separated from each other; Abram stayed in the land of Canaan, while Lot settled among the cities of the Plain, pitching his tents near Sodom. Now the inhabitants of Sodom were very wicked in the sins they committed against the LORD.
After Lot had left, the LORD said to Abram: "Look about you, and from where you are, gaze to the north and south, east and west; all the land that you see I will give to you and your descendants forever. I will make your descendants like the dust of the earth; if anyone could count the dust of the earth, your descendants too might be counted. Set forth and walk about in the land, through its length and breadth, for to you I will give it." Abram moved his tents and went on to settle near the terebinth of Mamre, which is at Hebron. There he built an altar to the LORD.
There was squabbling between Abram’s family and Lot’s over grazing rights. Rather than letting things escalate, Abram decided to split things evenly, and keep the families separate but at peace. Just like in the cake cutting problem, Abram, the elder, divided the land, and Lot, the younger, chose his portion.
But Abram went a step further, and closed his eyes. He showed trust in God, that however things turned out, God would bless him. Lot looked about with his own eyes, rather than God’s, and chose to live right next to Sodom and Gomorrah. (You might have an idea how that turns out later.)
Responsorial Psalm
Ps 15:2-3a, 3bc-4ab, 5
R. He who does justice will live in the presence of the Lord.
He who walks blamelessly and does justice;
who thinks the truth in his heart
and slanders not with his tongue.
R. He who does justice will live in the presence of the Lord.
Who harms not his fellow man,
nor takes up a reproach against his neighbor;
By whom the reprobate is despised,
while he honors those who fear the LORD.
R. He who does justice will live in the presence of the Lord.
Who lends not his money at usury
and accepts no bribe against the innocent.
He who does these things
shall never be disturbed.
R. He who does justice will live in the presence of the Lord.
The reason lending money with interest (“usury”) was considered bad is that they didn’t really have a credit system like we do now. People didn’t borrow money to invest in large projects, or make big purchases that they were confident they’d be able to pay off over time.
No, in ancient times, when someone asked to borrow money, it was because something terrible had happened, they couldn’t earn money properly, and their kids were likely going to starve as a result.
When a bank charges you interest on a home loan or car loan, it’s just a business transaction. It’s a perfectly fair way to price time preferences. But when your brother is out of work and can’t pay for his kid’s medicine, “fair” isn’t really the question anymore.
God is asking us to look beyond what’s fair, and trust that the other person will, too.
Alleluia
Jn 8:12
R. Alleluia, alleluia.
I am the light of the world, says the Lord;
whoever follows me will have the light of life.
R. Alleluia, alleluia.
Notice that Jesus doesn’t claim to be “the light of Israel.” Prohibitions against usury and such usually only applied to fellow Israelites; Jesus wants to bring God’s light and justice to the whole world. Remember, Jesus didn’t come to abolish the law; he wants to make it universal.
Gospel
Mt 7:6, 12-14
Jesus said to his disciples: "Do not give what is holy to dogs, or throw your pearls before swine, lest they trample them underfoot, and turn and tear you to pieces.
"Do to others whatever you would have them do to you. This is the Law and the Prophets.
"Enter through the narrow gate; for the gate is wide and the road broad that leads to destruction, and those who enter through it are many. How narrow the gate and constricted the road that leads to life. And those who find it are few."
“Don’t cast pearls before swine” was originally a derogatory saying, meaning that Jewish revelation should not be shared with Gentiles. In the context following yesterday’s Gospel, Jesus flips that around. Don’t be a hypocrite, trying to remove the splinter from your brother’s eye, but also don’t waste time trying to preach to someone who won’t listen.
Ultimately, every law about how people treat each other, from cutting cakes to splitting grazing land to loaning money, comes down to the Golden Rule. And if you try to apply that, rather than pedantically split legal hairs, you really will be going through the narrow gate.
It’s much, much easier to find exceptions and loopholes to the law than to treat someone like you’d want to be treated. Most of us don’t, at least not without Jesus’ help. So pray for guidance to that narrow gate, instead.
Okay, okay, because this verse is the origin of the title, here’s a funny Pearls Before Swine comic strip—
In the original formulation of the problem, it’s a whole cake, which always seemed too big to me.