Play and Games

  • Demuth's Figure Five in Gold painting is in the New York City Metropolitan Museum of Art. But it started with a poem. For both please click Image and Poem. Visual interpretation of words is a form of play, a kind of game. We turn next to a checker game invented by Emanuel Lasker.

  • Lasker's form of checkers is a game example linked to other things. He studied mathematics and philosophy, was a student of Hilbert's, and received his doctorate in 1902. In another aspect, in 1894 Lasker became World Chess Champion, he is considered by many to be the greatest chess player ever, and he held the World Chess Championship until 1921. In this game pieces are stacked. Here side indicates red or black, i.e. the two players. The game has an interesting nature: side-change can result from captures. This is so because a jumped checker isn't removed from the board as in the ordinary game. Instead a jumped stack of checkers: this entity is a piece - its motion is under the control of the side with the same color as the top checker; has only the highest one carried off under the conqueror. The top checker of a stack is flipped over when a piece reaches the eighth rank, making a crown show. This piece acts like a king: it can move backwards as well as forwards. At least that is so until/unless it is jumped, causing the top checker to go with its conqueror. All jumps are forced. Ordinary-checker rules apply. A game ends when one side cannot move. Seeing the king/ordinary-distinction is easier if liquid white-out outlines each crown.

  • Numbers lead to power. Ideas like `odd' lead to problem-solving. Play and thought are connected: analysis of gambling games led to the part of modern mathematics known as probability.

  • Ideas behind the puzzle Apples & Baskets test understanding of odd and even. This idea in the form of on-off is the key one enabling digital computers.

  • Number-symbols are short for words that name concepts. The next puzzle is not the same as standard school questions about mathematical sequences. Even that may not be enough of a hint. People working with computers may want to try this item because it hinges on number-representations.

    Example 5. (Merwyn Sommer) Find the number that should follow 24 in:

    10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, __?

    For a detailed set of related information, please click Help Sequence? For more questions, please click Some Problems.

    ©2005 Allen Klinger
    2/1/05 Revision of Original 5/21/99 Version