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Thursday, February 10, 2011

Dividing things equally, Part I

We have a saying in English "you can't add apples and oranges". In other languages it might be apples and pears, or yams and potatoes, but the point remains the same. Two dissimilar objects cannot be treated equally. (Read more)

Which brings me to the subject of today's blog. Dividing stuff equally. I have treated the subject of division before. And dividing equally before. Twice, in fact. So why treat it again? Because it comes up so frequently in life, and in death.

There's almost always something left behind when someone dies, and the deceased often says "share equally among my 4 children." Which turns into a nuisance when you have
  • an apartment building
  • a car
  • 4 pieces of jewelry
  • 3 gold coins
  • 2 apples
  • an orange
  • a cat
How do we divide those items evenly?

In math we can't easily some units or fractions. So we convert them.

If I want to divide .8751 by 3, and 11/16 by 3, I learn it is easiest to do so in decimal numbers. Why?

8751 ÷ 3
I can do the first one in my head - 3 goes into 8 just 2 times, leaving 2; then 3 goes into 27 exactly 9 times; then 3 goes into 5 just 1  time, leaving 2; then 3 goes into 21 exactly 7 times so the answer is .2917

11/16 ÷ 3
Akk! This is harder. 3 goes into 11 just 3 times, leaving 2; then 3 goes into 16 only 5 times, leaving 1. What now?

Let's convert this into a decimal number instead. I know 16 goes into 100 exactly 6.25 times. Multiply 11 by 6.25 and you get 62.5 + 6.25 which is (move the decimal 2 places) now .6875.

We can divide .6875 by 3 which goes into 6 exactly 2 times; 3 goes into 8 just 2 times, leaving 2; 3 goes into 27 exactly 9 times; leaving 3 to go into 5 only once with a remainder of 2 (out of 3). So the answer is .229166666 ... alas, it never comes out even.

This is similar to the level of difficulty in dividing 1 bracelet between 3 women that want it, not for its monetary value, but for its connection to their mother. It will never come out even.

We usually liquidate items from an estate, turning things into cash that can be divided evenly.

But that's not a solution for items with intangible or sentimental value. It's not a new problem, either, as this account from the reign of King Solomon indicates:

One day two women came to King Solomon. One of them said: 

"Your Majesty, this woman and I live in the same house. Not long ago my baby was born at home, and three days later her baby was born. Nobody else was there.

One night while we were all asleep, her baby died. While I was still asleep, she got up and took my son, put him in her bed, then put her dead baby next to me.

In the morning when I got up to feed my son, I saw that he was dead. But when I looked at him in the light, I knew he wasn't my son."

"No!" the other woman shouted. "He was your son. My baby is alive!"

"The dead baby is yours," the first woman yelled. "Mine is alive!"

They argued back and forth in front of Solomon, until finally he said, "Both of you say this baby is yours. Someone bring me a sword." 

Solomon ordered, "Cut the baby in half! That way each of you can have part of him."

"Please don't kill my son," the first woman pleaded. "Your Majesty, I love him, but give him to her. Just don't kill him." 

The other woman shouted, "Go ahead and cut him in half. Then neither of us will have a baby."

Solomon said, "Don't kill the baby." Then he pointed to the first woman, "She is his real mother. Give the baby to her."

Everyone in Israel was amazed when they heard how Solomon had made his decision. They realized that God had given him wisdom to judge fairly.