String theory and practice

Part I: Zoe

Zoe really liked her aquamarine pants with two strings.

She liked playing with the strings, and she liked counting them: one, two.  Then, one day, she pulled a little too hard on one of the strings, and it came out.

Zoe was a little upset by this turn of events, but she was most distressed by the disappearence of the second string.  Where could it have gone?  She began examining the pants, but string number two was nowhere to be seen.  So Zoe decided to call her mom over for help.

“Mom, where is the second string?” she asked.
“What second string?” Asked her mom, equally confused.
“My pants had two strings, now there is only one. Where did the second one go?” explained Zoe.

Now her mom understood Zoe’s confusion.  She took the string and put it back into the pants.

Zoe wasn’t paying attention to what her mom was doing, but when she saw the pants again she exclaimed, “You found the second string!”  Zoe’s mom tried to explain to her that there was only one string that had two ends, but Zoe was too busy playing with her pants and strings, and of course before long, two strings once again turned into one.

“It disappeared again,” cried Zoe.
So mom had to carefully put the string back one more time, showing Zoe how one string becomes what looks like two. To mom’s surprise, it worked. From then on, Zoe stopped asking where the second string went, and when asked how many strings her pants had, she replied “one”.

Part II: Katie

Once Zoe was convinced that no disappearing of strings was happening, Katie walked into the room.  Mom decided to see whether Katie knows how many strings are in the pants.

“One, of course,” replied Katie, as she pulled out the string.

The next day, mom decided to play a trick on Katie.  She found two identical strings and put one into each little hole on the front of the pants.  She then called over Katie.

“How many strings are here now?” mom asked.
Katie looked at the pants for a while, then she smiled and said, “Two.”
“How did you know?” was mom’s next question.
“You looked like you were trying to trick me.” (Busted!)

“Now let me do it for you and see whether you can guess!” exclaimed Katie. And so, Katie and mom took turns putting one or two strings into the pants and having the other one guess how many there were. Mom got her first two wrong, while Katie kept being correct.  Finally, mom was able to trick Katie into getting one wrong by tying two extra knots in the string so that it looked like this:

And then mom took a picture of Katie with the pants:

After which, Katie of course insisted on taking a picture of mom holding the pants:

It was a really fun game!