set koans II

by eidolon, 2018-10-14

IV

After playing Set for two years, the Student had grown greatly in wisdom, and approached the Master, asking:

“Master, to show my devotion I would tattoo a set onto my body. Have you any advice?”

The Master was solemn. "Your devotion is true. But tell me - what would this tattoo consist of?"

The Student said humbly, "Three cards, tattooed onto my arm. But which set?"

At once, the Master struck the Student across the face.

"How can you presume to show your devotion - when you do not even know how many cards make a set!" ​

V

A Student asked the Master, "How many sets are there in the whole deck?"

From a pocket in his robes, the Master produced his Set deck, containing 81 cards. He took a card and handed it to the Student.

"First, take this card, and do not come back until you can tell me how many sets you can make with this card. Then, I will give you another. In so doing you will be able to calculate the number of sets in the whole deck."

The Student bowed and left.

Three days later, the Master happened upon the Student in the faculty common room. The whiteboards on the walls were covered with frantic scribblings, and on the coffee tables, which themselves were also whiteboards, the Master could see the Student had devised a matrix representation of the card attributes.

The Master took another card from the deck of 80 in his pocket, and made to hand it to the Student.

The Student recoiled, saying, "Not another one! I have been enumerating for days, and I don't even have an upper bound for the number of sets this card could be a part of!" But being obedient to his Master, he took the card.

Now the Master reached into his pocket to select another of the 79 remaining cards in the deck.

Again the Student recoiled: "No! Now I have two cards, I cannot accept an arbitrary card, because only one of those cards could possibly make a set with these two!"

At once, the Student jumped up, erased everything he had written on the whiteboards, wrote "81 x 80", and turned to the Master with a great grin on his face.

The Master slapped him.

"You forgot to divide by 2!"

VI

Two Students were arguing over the nature of Meta-Set. They brought their disupte to the Master.

"A meta-set is when two sets are on the table, and they share a card, which we call the shadow card."

"No! The shadow card must not be on the table. That is why it is called the 'shadow card'."

When the Master heard this, he laughed and said, "Are you two not both my Students right now?"

"Yes," said both Students to the Master, "of course".

Then the Master turned and walked out of the room.

The two Students looked at each other. In that moment they both understood the nature of Meta-Set.