Sunday, July 26, 2015

Unit 3: The Power of Addition

Exquisite Corpse

In our first two units, we looked at improvisations that prompted new perspectives by imposing constraints such as time and resources. There were no wrong answers, certainly, but the design of these activities can cause a particular type of anxiety for some students.

Another type of improvisation focuses on addition or expansion as opposed to constraint. These are often collaborative and/or flexible enough to allow participants to add new rules or modify the activity on the fly.

Addition improvs can be simple and brief, or focus and deeper levels of problem solving, like complex games.

Exquisite Corpse is good example of a simple addition improv. This improv was originally designed as a surrealist parlor game, and a common version asks a group of people to construct a story by having each person contribute a sentence (or sentences) without knowing what the person before or after has written.

My wife and I used to play Exquisite Corpse with our kids while waiting for our food at restaurants. We would take a napkin, and one of us would begin by writing the first line to a story. That person would fold the napkin so the others could not see what s/he had written and then the next person would write a line. Here are two actual samples we created in one of those activities.

Round 1

Player 1: It was a typical day in New York.

Player 2: And Batman was standing vigilantly against a wax paper moon with cutout stars of fluorescent glitter.

Player 3: He, as usual, pretended he knew what was happening when, as always, he didn’t have the slightest clue.

Player 1: She thought the toilet was a swimming pool and jumped in.

Player 2: But my mother blew her nose graciously and left.

Player 3: It was soft and squishy.

Player 1: KABOOM!

Player 2: His hands motioned soundlessly in the background while he belched.

Player 3: No one ever knew for certain, but they always suspected the mailman.

Round 2

Player 2: The dog howled at the lonely moon while three men sang badly around the fire.

Player 3: She always wondered why he did that.

Player 1: Blaaaaaahhh! He puked everywhere.

Player 2: The drink went down hard but came up with ease.

Player 3: Why oh why do these things always happen to me, she thought.

Player 1: Then I saw it, the huge marshmallow.

Player 2: I’m so in love I can’t stand it.

Player 3: What not? No one will ever know.

Player 1: And then I want to bed.

If you want to play this here, simply add a comment, put the the number in the story sequence in your title, and then write out your contribution. Stacy and I have already started the activity with our two contributions.

The Game of Life

As I mentioned, other addition improvs are more serious in nature. These are designed to be cerebral activities and are generally set up like thought experiments.

We can actually find the framework of such improvs or thought experiments in early thought simulations on self-replicating machines. John Von Neumann was an early pioneer in these experiments who, realizing that such machines could not be produced with the technologies available to him in the 1950s, turned to the computer pattern games created by the mathematician Stanislaw Ulam.

Ulam suggested that Von Neumann construct an abstract universe for his analysis of machine reproduction. It would be an imaginary world with self-consistent rules, as in Ulam’s computer games. It would be a world complex enough to embrace all the essentials of machine operation but otherwise as as simple as possible. The rules governing the world would be a simplified physics. A proof of machine reproduction ought to be easier to devise in such an imaginary world, as all the nonessential points of engineering would be stripped away.

With this inspiration, Von Neumann devised a thought experiment to show that it was indeed possible to provide machines with the necessary resources and sets instructions that would allow them to create copies of themselves or, new machines that were of equal or greater complexity. His experiment consisted of an infinite checkerboard as his universe. Each square on the checkerboard could be any of a number of states corresponding roughly to machine components. A "machine" in this model was a pattern of such cells.

As Poundstone points out, "Von Neumann’s cellular space can be thought of as an exotic, solitaire form of chess.The board is limitless, and each square can be empty or contain one of the 28 types of game pieces. The lone player arranges the game pieces in an initial pattern. From there on, strict rules determine all successive configurations of the board."

In other words, Von Neumann came up with an "open" model that allowed a "player" to establish the initial state or setup of the game pieces, and then watch to see if that setup would produce a self-replicating machine. What he discovered through this experiment was that yes, there are initial settings that can allow a machine to self-replicate. His experiment also provided a framework for modeling how a simple set of recursive rules can produce complex interactions and complexity in different environments.

The British mathematician John Conway revisited Von Neumann’s work in 1970, when he published his seminal Game of Life in Scientific American in 1970. Like Von Neumann’s experiment, Conway’s game was a zero-player game, meaning the evolution and result of the game is determined by its initial state, requiring no further input by the player.

Conway’s game was less complicated than Von Neumann’s, however, and it was more applicable. It was simple enough to be programmed into computers of the day and thus provide a simulated proof. Thankfully, Game of Life has retained its appeal and significance over the decades, and as a result there are a number of excellent online versions that allows us to play with the phenomenon of emergent systems first-hand (such as this javascript version).

Like von Neumann, Conway designed his game to be played on an infinite two-dimensional grid of square cells. Rather than having game pieces to place on the cells however, Game of Life allows us to set initial patterns simply by marking cells with one of two possible states, either "alive" or "dead." Once the game begins, at each step in time every cell interacts with its eight neighboring cells. Through these interactions, we can witness the following transitions:
  • Any live cell with fewer than two live neighbors dies, as if caused by under-population.
  • Any live cell with two or three live neighbors lives on to the next generation.
  • Any live cell with more than three live neighbors dies, as if by overcrowding.
  • Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.

As we play Conway’s game, we are indeed struck by the complexity that can be produced from simple, recursive rules. We see new patterns and behaviors develop. We find that patterns can actually recreate themselves along with their initial instruction set (just as von Neumann imagined). In fact, if we did not know how simple the game rules and components really were, we would swear that some of the resulting behaviors could not possibly be produced by anything so primitive.

Von Neumann’s self-replicating machines experiment, as well as Conway’s Game of Life, point to all kinds of fun addition and/or design improvs that we might practice across the curriculum. These improvs generally begin with a desired outcome or hypothesis, and then ask participants to come up with the simplest design or set of rules/components to achieve the outcome.

These improvs tend to be more advanced and require more thought. We’re going to try one out ourselves this week, in our discussion titled The Game of Education.

1 comment:

  1. Exqisite Corpse Line 1

    It was a dark and stormy night on the moor, and I could sense the weight of whatever what about to happen.